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Whether Economic Freedom Is Significantly Related to Death of COVID-19
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abstract
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COVID-19 has caused a huge mayhem globally. Different economic freedom leads to different performances of a country's reaction to the pandemic. We study 164 countries and apply mathematical and statistical approaches to tackle the problem: whether economic freedom has a significant impact on the death of COVID-19. We devise a metric, some norms, and some orderings to construct an absolute reference and the actual relation via binary sequences. Then, we use the theoretical binary sequences to construct a probability distribution which linearises the strength of relation between economic freedom and death of COVID-19. Then, the actual relation from the data analysis provides an evidence to the hypothetical testing. Our analysis and model show that there is no significant relation between economic freedom and death of COVID-19.
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COVID-19 has caused a huge mayhem globally. Different economic freedom leads to different performances of a country's reaction to the pandemic. We study 164 countries and apply mathematical and statistical approaches to tackle the problem: whether economic freedom has a significant impact on the death of COVID-19. We devise a metric, some norms, and some orderings to construct an absolute reference and the actual relation via binary sequences. Then, we use the theoretical binary sequences to construct a probability distribution which linearises the strength of relation between economic freedom and death of COVID-19. Then, the actual relation from the data analysis provides an evidence to the hypothetical testing. Our analysis and model show that there is no significant relation between economic freedom and death of COVID-19.
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1. Introduction
Due to COVID-19 pandemic, there are many fatalities across the world. Many countries are baffled by whether to open the market or impose lockdown [1–3]. It creates a huge chaos in either economic or social stability [4, 5]. This motivates us to study the relation between economic freedom and the death rate or tolls of COVID-19. We locate 164 countries from some datasets [6, 7]—because some of the countries lack statistics of either the economic freedom or the death information regarding COVID-19. Then, we use a series of mathematical and statistical approaches to reach a conclusion. For the mathematical part, we define a new concept of metric d which could measure the difference between the scoring structures—this is hardly the case if one adopts the usual Euclidean metric. For reference purpose, one fixes the referential structure e⟶ (or scoring system) first. Then, one could compute the distances between all the (sampled) multivalued data N points v⟶i:1≤i≤N and I, i.e., de⟶,v⟶i:1≤i≤N. Based on these distances, we could then create an ordering for v⟶i:1≤i≤N with respect to the referential structure e⟶.
2. Modelling
2.1. Notations and Symbols
For a vector w⟶, we use w⟶ to denote its length; for any set H, we use |H| to denote its size (cardinality). Moreover, we use w⟶j to denote the j-th element in w⟶. Let b⟶ denote a binary vector, i.e., each element in b⟶ is either 0 or 1. Let 𝔹k denote the set of all the binary vectors with total length k. Let ℂ={C1, C2,…, Cm} be a set of countries. Let Aef={A1, A2,…, An} be a set of attributes of economic freedom (regarded as independent variables). Let Bj be a set of result (regarded as dependent variables). Each time we fix one Bj to study the relation between the attributes and Bj. In this article, we restrict our attribute values to be numerical numbers. The theoretical table is shown in Table 1, and for the actual forms, one could refer to Sections 3.2.1 and 3.2.2.
We use the notations Ci⟶=ai1,ai2,…,aim; Ai⟶=a1i,a2i,…,ami; and Bi⟶=b1i,b2i,…,bmi.
2.2. Binary Subvectors and Norm
Definition 1 .
(subvectors). Suppose b⟶ is a binary vector. We use Subb⟶ to denote all its truncated subvectors consisting of only 1.
Example 1 .
Suppose b⟶=1,0,1,0,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0. Then, Subb⟶=1,1,1,1,1,1,1,1,1,1,1,1,1.
We simply abbreviate it as Subb⟶=1111131211121211. Indeed Subb⟶ reveals the structure of an independent-dependent variable relation.
Definition 2 .
(binary norm). For any binary vector b⟶=b1,b2,…,bk with Subb⟶=1n11n2,…,1nt, define a binary norm b⟶=20+21+⋯+2n1−1+20+21+…+2n2−1+⋯+20+21+⋯+2nt−1.
One could, according to real situations, adopt other numbers (for example, replace 2 with other numbers) or other forms other than the one provided here.
Claim 1 .
b⟶=2n1+2n2+⋯+2nt−t.
Proof
It follows immediately from the definition.
Definition 3 .
(linear ordering on 𝔹k). b⟶1≥b⟶2 if and only if b⟶1≥b⟶2, for all b⟶1,b⟶2∈𝔹k.
Example 2 .
If b⟶1=1,0,1,1,1,0,0,1,1,0,1,0,1,b⟶2=1,0,0,0,0,1,1,0,0,1,1,1,1, then b⟶1=20·1+20·1+21·1+22·1+20·1+21·1+20·1+20·1=13 and b⟶2=20·1+20·1+21·1+20·1+21·1+22·1+23·1=19. Thus, b⟶2≤b⟶1.
Remark 1 .
A binary norm indeed serves an important technique in revealing the relation between dependent and independent variables. Given two pairs (x1, y1) and (x2, y2) of numerical data with x1 ≠ x2, if (x2 − x1) · (y2 − y1) > 0 (i.e., they act proportionally), we associate it with a value 1 to indicate such relation and 0, otherwise (i.e., they act inversely). Such mechanism gives a way to look into the fundamental relation between X and Y variables. This kind of analysis is in particular useful when the precision of the data is questionable or when the actual numbers are unknown or more suitable to be interpreted via ranks.
Example 3 .
(sign vector). Suppose D=((2,4), (3,2), (5,8), (7,9), (4,2), (3,8)), a set of ordered vectors. Then, we could associate D with a sign vector v⟶=0,1,1,1,0 via Remark 1.
Definition 4 .
(relational vector). Suppose that b⟶ is a sign vector; we associate it with a relational vector Relb⟶ whose i-th element is assigned 1 iff b⟶i=b⟶i+1 and 0, otherwise.
Example 4 .
Let us continue with Example 3. We could compute its relational vector Relv⟶=0,1,1,0, and thus SubRelv⟶=12 and SubRelv⟶=3. The higher the value of the norm is, the closer the relation between the dependent and independent variables is.
Definition 5 .
(equivalence relation ∼). For all b⟶1,b⟶2∈𝔹k, b⟶1∼b⟶2 iff b⟶1=b⟶2.
Let 𝔹k#=b⟶:b⟶∈𝔹k. One observes that ∼ partitions 𝔹k. If p ∈ 𝔹k#, we use [p] to denote the equivalence class whose elements' norms are all p.
2.3. Probability Distribution
Suppose 𝔹k={0,1}k is the sampling population. Define a statistic BN on 𝔹k by its binary norm. The range for BN is 𝔹k#. Define a counting ρ : 𝔹k#⟶ℕ by ρx=b⟶∈𝔹k:b⟶=x. Now, we could define the probability distribution for BN by prob : 𝔹k#⟶[0,1] by(1) probu=ρu∑h∈Ranρh.
One observes that(2) probu=u∑h∈Ranh.
This probability distribution reveals the relation between the independent variables and the dependent variables. This would serve our theoretical distribution for our statistical testing H0: the economic freedom and the death of COVID-19 has no significant relation, i.e., the economic freedom has no great impact on the death of COVID-19. For a concrete construction of such probability distribution, one could refer to Section 6.1.
2.4. Metric
A metric or a distance function is a non-negative function d on X × X satisfying identity, symmetry, and triangle properties. In this article, it suffices to define a metric on a closed interval of real number. Fix I=[a, b]⊆ℝ, where a, b ∈ ℝ and a < b. Let v⟶ be a finite vector whose first element is a, last element is b, and all the other elements are incrementally increased and lie between a and b. Let FIN[a, b] be the set of all such vectors. Let v⟶=a,v2,…,vm−1,b,w⟶=a,w2,w3,…,wn−1,b∈Fina,b be arbitrary. Let v⟶⊓w⟶ denote the vector q=(a, q1, q2,…, qh−1, b) whose elements are the projections from v⟶ and w⟶. One observes that FIN[a, b] is closed under ⊓.
Definition 6 .
(atomic norm)v⟶E=(3) v2−a2+v3−v22+v4−v32+⋯vm−2−vm−12+b−vm−12.
Definition 7 .
(metric). Define d : FIN[a, b] × FIN[a, b]⟶ℝ+ by(4) dv⟶,w⟶=v⟶E+w⟶E2−v⟶⊓w⟶E.
Example 5 .
Suppose the closed interval I=[0,20] and v⟶=0,2,4,8,19,20 and w⟶=0,1,4,6,12,14,15,20. Then, v⟶⊓w⟶=0,1,2,4,6,8,12,14,15,19,20. Hence, the norm v⟶E=22+22+42+112+12=146; the norm w⟶=12+32+22+62+22+12+52=80; and v⟶⊓w⟶E=52. Thus, dv⟶,w⟶=146+80/2−52=3.30.
Claim 2 .
d is a metric on FIN[a, b].
Proof
This can be shown by the definitions and some techniques.
This metric will be used in Section 3.3. This metric basically measures the differences between the structures of the attributes in the scoring system. The more similar the structures are, the lower the distances are. Unlike the static Euclidean distance, this metric takes the interval structures into consideration.
2.5. Procedures
Let us summarise the whole procedure of our modelling for the sake of data analysis. Let e⟶=100,100,100,100,…,100,100. Let Death(Ci) denote the death rate (or tolls, depending on the context) for the country i.Define a metric d on a real interval, in particular the transformed interval, an interval for attribute values which lie between 0 and 100, I=[0,1200]⊆ℝ for the range of attribute values of economic freedom, and calculate dI^,C⟶i:1≤i≤m (one could refer to Section 3.3).
Rank ℂ via the sorted distances with a rank function γ100 : ℂ⟶{1,2,…, m} in which γI(Ci) ≥ γI(Cj) iff dI⟶,C⟶i≥dI⟶,C⟶i.
Rank ℂ via the sorted distance with a rank function γ88 in which γ88(Ci) ≥ γ88(Cj) iff Death(Ci) ≥ Death(Cj).
Form the vector v⟶=γ100°γ88−1ll=1m.
Convert v⟶ into a sign vector sgv⟶:=χv⟶2−v⟶1,χv⟶3−v⟶2,…,χv⟶m−v⟶m−1, where χ(a)=1 if a > 0 and χ(a)=0 if a < 0.
Construct the probability distribution for the quotient space 𝔹k/∼.
Perform statistical testing by locating the position of v⟶ and significant level for the batch of country.
Apply the Monte Carlo approach on the sampled batches of countries repeatedly.
With the threshold probability 0.5, based on binary distribution for the whole spectrum of statistical testing, perform the overall statistical testing.
Draw a conclusion for the relation between γ100 and γ88.
3. Data Analysis
Following the procedures in Section 2.5, we start to collect, analyse, and produce a report via data analysis. Since the data are huge and hard to handle by the one-off approach, we resort to the sampling technique and reach a conclusion via statistical testing.
3.1. Sampling
The raw data consist of 164 countries (we use 1 to 164 to name the countries) up to 2020, June 27th. Since the size is too huge, we apply the Monte Carlo approach to sample the 164 countries. We do 20 times (or 20 batches: S1 to S20) sampling with 25 countries over the 164 countries per sampling. The sampled batches are listed in Tables 2 and 3.
3.2. Sampled Data
3.2.1. Economic Freedom
Corresponding to the form listed in Table 1, we associate ℂ with S1 and define Aef={A1, A2,…, A12}, where A1≡Property Rights, A2≡Judicial Effectiveness, A3≡Government Integrity, A4≡Tax Burden, A5≡Government Spending, A6≡Fiscal Health, A7≡Business Freedom, A8≡Labor Freedom, A9≡Monetary Freedom, A10≡Trade Freedom, A11≡Investment Freedom, and A12≡Financial Freedom. The attribute values are based on a 100-point scoring system [6]. Due to the limitation of space, we list only the first sampling (or S1) regarding its attributes of economic freedom in Table 4. We omit the other 19 similar tables of this form. Aef serves as the set of our independent variables.
3.2.2. COVID-19
Now we start to introduce the dependent variables. Indeed we tackle an individual dependent variable each time. Since the data are huge, we only extract the data [7] for sampling one (or S1) as shown in Table 5. Corresponding to the form listed in Table 1, we associate ℂ with S1 and define B1≡ Total Confirmed COVID-19 Cases, B2≡ Death Toll of COVID-19, B3≡ Total Recovered COVID-19 Cases, and B4≡ Population of the Countries. Due to the limitation of space, we list only the first sampling (or S1) regarding its dependent variables. We omit the other 19 similar tables of this form. Moreover, in the later analysis, we only take and fix B2 as our dependent variable. If the readers are interested in other dependent variables (or B1, B3, or other mixed forms), they could simply follow the same approach provided in this article.
3.3. Metric
Since we have defined an interval metric in Section 2.4, we could apply it over here. Here we measure the distance between every sampled data and the fixed reference vector e⟶=100,200,…,1100,1200. We construct the distances for the 164 countries based on economic freedom (for example, the data of sample one could be referred from Table 4) in Tables 6 and 7. Since all the data are presented in the form of 100-point score for the attribute values in Table 4, we need to transform the values in the table to the interval I=[0,1200]. For example, the reference vector e⟶ (we still use e⟶ to represent to newly transformed vector) will be e⟶=0,100,200,300,…,1100,1200. Each country C sampled in S1 will be transformed into C⟶, for example, C¯⟶11≡68⟶=0,64.8,145.7,247.5,379.9,…,1170,1200 are the converted data for the first country sampled in the first sampling or country 68. The economic freedom vector for each sampled country is converted by the same way. The converted data are not tabulated. Then, we apply d in Section 2.4 on the converted data and repeat the whole processes for other samplings. The complete results regarding the distance for the 20 sampled countries are presented in Tables 6 and 7. The (i, j) cell in the tables means the value de⟶,C¯⟶ij, where C¯ij denotes the i-th country sampled in j-th sampling and C¯⟶ij denotes the converted data for C¯ij.
4. Absolute Reference
By the derived distances presented in Tables 6 and 7, we could construct absolute references. The absolute references would server as the benchmarks for other internal structures. Let us use ℂs to denote the set of sampled countries in s-th sampling. Let C¯⟶si,C¯⟶sj∈ℂs be arbitrary.
Definition 8 .
(ordering of the sampled countries). C¯is≥C¯js iff de⟶,C¯⟶is≥de⟶,C¯⟶js.
Based on this ordering, we could generate the absolute references (Tables 8 and 9). Let us take S1 for example: C68 > C112 > C92 > ⋯>C41 > C85 > C14. From these absolute references (or ordering for the samplings), we could view the structure (or interval) difference between the ideal scoring (or e⟶) and real scoring results. Indeed, an absolute reference is a reference acting like ordering without specific scales. Such reference is useful when the precise values are unknown or when the precision of the data is questionable. In this article, we use relative distances between a country's economic freedom and others to create such ordering.
5. Ordering for COVID-19 Fatalities
Based on Table 5 and other omitted tables, we start to construct the ordering (or ranking) based on the fatalities of COVID-19.
Definition 9 .
(ordering on fatalities). C¯is≥C¯js iff DeathC¯is≥DeathC¯js, where DeathC¯is is the death toll for i-th country sampled in s-th sampling.
Based on this ordering, we have the results presented in Tables 10 and 11. Let us take the cells in S1 for example: C78 > C98 > C76 > ⋯>C14 > C99 > C21.
6. Norm and Probability
In this experiment, we only consider N=23 and construct its distribution accordingly. Hence, the domain is {0,1}23 and the range lies between 0 and 223 − 1=8388607 (indeed some of the values' probability is 0). This section generalises Example 3. The higher the value is, the higher the impact of independent variables on dependent variable is.
6.1. Probability Distribution
We have already constructed the theoretical setting of probability distribution for our testing in Section 2.3. Based on that framework and the data given, we could create the theoretical probability distribution prob in Figure 1.
The (one-tailed) critical values for 5 and 10 percentages are 138 and 78 (via numerical computation), respectively; that is, if the sampled value is larger than the critical values, we should reject Ho: there is no significant relation between the economic freedom and death of COVID-19.
6.2. Real Results
In comparison with the absolute reference, we could generate the binary sign vectors for the real data from each sampling Sj (or simply j) in Table 12—for the formula and explanation of sign vectors, one could refer to Section 2.2. However, in these 0 and 1 representations, it separates the proportional and inversely proportional relation between the economic freedom and death of COVID-19. To take all the factors into consideration, one further analyses the alternative behaviour of 0 and 1. If there are too many alternations between 0 and 1, it would indicate that there is a less relation between those two. On the other hand, if the alternative times are few, then it leads to the longer length of subvector consisting of pure 1. The alternative results are shown in Table 13.
Based on Table 13 and definitions in Section 2.2, we could compute the binary norm for each sampling batch Sj (or J) as shown in Table 14.
7. Conclusion and Future Work
The contribution of death in COVID-19 is very complicated. We use economic freedom to capture a potential factor in such contribution. To verify the truth of great impact from economic freedom, we devise a metric, two norms, absolute ordering, binary ordering, and probability distribution for the statistical testing population. Based on our research, we find out that the economic freedom has no significant relation to the death of COVID-19. This might provide some reference for the decision makers of the countries. In the future research, one could further study the relation between economic freedom and other ratios related to COVID-19. One could also use other nonparametric approaches to enrich the statistical testing. There is another related paper on the same topic [8]. In that paper, the authors use two-step estimators: negative binomial regression and nonlinear least squares, and find out there is a close relation between economic freedom and fatalities of COVID-19. In essence, their approach focuses more on statistical techniques, while ours focuses more on mathematical approaches. For the future researcher, he could compare or combine these methods to yield a comprehensive or generalised theory that could accommodate and single out the factors that cause the discrepancies.
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1. Introduction
Due to COVID-19 pandemic, there are many fatalities across the world. Many countries are baffled by whether to open the market or impose lockdown [1–3]. It creates a huge chaos in either economic or social stability [4, 5]. This motivates us to study the relation between economic freedom and the death rate or tolls of COVID-19. We locate 164 countries from some datasets [6, 7]—because some of the countries lack statistics of either the economic freedom or the death information regarding COVID-19. Then, we use a series of mathematical and statistical approaches to reach a conclusion. For the mathematical part, we define a new concept of metric d which could measure the difference between the scoring structures—this is hardly the case if one adopts the usual Euclidean metric. For reference purpose, one fixes the referential structure e⟶ (or scoring system) first. Then, one could compute the distances between all the (sampled) multivalued data N points v⟶i:1≤i≤N and I, i.e., de⟶,v⟶i:1≤i≤N. Based on these distances, we could then create an ordering for v⟶i:1≤i≤N with respect to the referential structure e⟶.
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title
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1. Introduction
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p
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Due to COVID-19 pandemic, there are many fatalities across the world. Many countries are baffled by whether to open the market or impose lockdown [1–3]. It creates a huge chaos in either economic or social stability [4, 5]. This motivates us to study the relation between economic freedom and the death rate or tolls of COVID-19. We locate 164 countries from some datasets [6, 7]—because some of the countries lack statistics of either the economic freedom or the death information regarding COVID-19. Then, we use a series of mathematical and statistical approaches to reach a conclusion. For the mathematical part, we define a new concept of metric d which could measure the difference between the scoring structures—this is hardly the case if one adopts the usual Euclidean metric. For reference purpose, one fixes the referential structure e⟶ (or scoring system) first. Then, one could compute the distances between all the (sampled) multivalued data N points v⟶i:1≤i≤N and I, i.e., de⟶,v⟶i:1≤i≤N. Based on these distances, we could then create an ordering for v⟶i:1≤i≤N with respect to the referential structure e⟶.
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2. Modelling
2.1. Notations and Symbols
For a vector w⟶, we use w⟶ to denote its length; for any set H, we use |H| to denote its size (cardinality). Moreover, we use w⟶j to denote the j-th element in w⟶. Let b⟶ denote a binary vector, i.e., each element in b⟶ is either 0 or 1. Let 𝔹k denote the set of all the binary vectors with total length k. Let ℂ={C1, C2,…, Cm} be a set of countries. Let Aef={A1, A2,…, An} be a set of attributes of economic freedom (regarded as independent variables). Let Bj be a set of result (regarded as dependent variables). Each time we fix one Bj to study the relation between the attributes and Bj. In this article, we restrict our attribute values to be numerical numbers. The theoretical table is shown in Table 1, and for the actual forms, one could refer to Sections 3.2.1 and 3.2.2.
We use the notations Ci⟶=ai1,ai2,…,aim; Ai⟶=a1i,a2i,…,ami; and Bi⟶=b1i,b2i,…,bmi.
2.2. Binary Subvectors and Norm
Definition 1 .
(subvectors). Suppose b⟶ is a binary vector. We use Subb⟶ to denote all its truncated subvectors consisting of only 1.
Example 1 .
Suppose b⟶=1,0,1,0,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0. Then, Subb⟶=1,1,1,1,1,1,1,1,1,1,1,1,1.
We simply abbreviate it as Subb⟶=1111131211121211. Indeed Subb⟶ reveals the structure of an independent-dependent variable relation.
Definition 2 .
(binary norm). For any binary vector b⟶=b1,b2,…,bk with Subb⟶=1n11n2,…,1nt, define a binary norm b⟶=20+21+⋯+2n1−1+20+21+…+2n2−1+⋯+20+21+⋯+2nt−1.
One could, according to real situations, adopt other numbers (for example, replace 2 with other numbers) or other forms other than the one provided here.
Claim 1 .
b⟶=2n1+2n2+⋯+2nt−t.
Proof
It follows immediately from the definition.
Definition 3 .
(linear ordering on 𝔹k). b⟶1≥b⟶2 if and only if b⟶1≥b⟶2, for all b⟶1,b⟶2∈𝔹k.
Example 2 .
If b⟶1=1,0,1,1,1,0,0,1,1,0,1,0,1,b⟶2=1,0,0,0,0,1,1,0,0,1,1,1,1, then b⟶1=20·1+20·1+21·1+22·1+20·1+21·1+20·1+20·1=13 and b⟶2=20·1+20·1+21·1+20·1+21·1+22·1+23·1=19. Thus, b⟶2≤b⟶1.
Remark 1 .
A binary norm indeed serves an important technique in revealing the relation between dependent and independent variables. Given two pairs (x1, y1) and (x2, y2) of numerical data with x1 ≠ x2, if (x2 − x1) · (y2 − y1) > 0 (i.e., they act proportionally), we associate it with a value 1 to indicate such relation and 0, otherwise (i.e., they act inversely). Such mechanism gives a way to look into the fundamental relation between X and Y variables. This kind of analysis is in particular useful when the precision of the data is questionable or when the actual numbers are unknown or more suitable to be interpreted via ranks.
Example 3 .
(sign vector). Suppose D=((2,4), (3,2), (5,8), (7,9), (4,2), (3,8)), a set of ordered vectors. Then, we could associate D with a sign vector v⟶=0,1,1,1,0 via Remark 1.
Definition 4 .
(relational vector). Suppose that b⟶ is a sign vector; we associate it with a relational vector Relb⟶ whose i-th element is assigned 1 iff b⟶i=b⟶i+1 and 0, otherwise.
Example 4 .
Let us continue with Example 3. We could compute its relational vector Relv⟶=0,1,1,0, and thus SubRelv⟶=12 and SubRelv⟶=3. The higher the value of the norm is, the closer the relation between the dependent and independent variables is.
Definition 5 .
(equivalence relation ∼). For all b⟶1,b⟶2∈𝔹k, b⟶1∼b⟶2 iff b⟶1=b⟶2.
Let 𝔹k#=b⟶:b⟶∈𝔹k. One observes that ∼ partitions 𝔹k. If p ∈ 𝔹k#, we use [p] to denote the equivalence class whose elements' norms are all p.
2.3. Probability Distribution
Suppose 𝔹k={0,1}k is the sampling population. Define a statistic BN on 𝔹k by its binary norm. The range for BN is 𝔹k#. Define a counting ρ : 𝔹k#⟶ℕ by ρx=b⟶∈𝔹k:b⟶=x. Now, we could define the probability distribution for BN by prob : 𝔹k#⟶[0,1] by(1) probu=ρu∑h∈Ranρh.
One observes that(2) probu=u∑h∈Ranh.
This probability distribution reveals the relation between the independent variables and the dependent variables. This would serve our theoretical distribution for our statistical testing H0: the economic freedom and the death of COVID-19 has no significant relation, i.e., the economic freedom has no great impact on the death of COVID-19. For a concrete construction of such probability distribution, one could refer to Section 6.1.
2.4. Metric
A metric or a distance function is a non-negative function d on X × X satisfying identity, symmetry, and triangle properties. In this article, it suffices to define a metric on a closed interval of real number. Fix I=[a, b]⊆ℝ, where a, b ∈ ℝ and a < b. Let v⟶ be a finite vector whose first element is a, last element is b, and all the other elements are incrementally increased and lie between a and b. Let FIN[a, b] be the set of all such vectors. Let v⟶=a,v2,…,vm−1,b,w⟶=a,w2,w3,…,wn−1,b∈Fina,b be arbitrary. Let v⟶⊓w⟶ denote the vector q=(a, q1, q2,…, qh−1, b) whose elements are the projections from v⟶ and w⟶. One observes that FIN[a, b] is closed under ⊓.
Definition 6 .
(atomic norm)v⟶E=(3) v2−a2+v3−v22+v4−v32+⋯vm−2−vm−12+b−vm−12.
Definition 7 .
(metric). Define d : FIN[a, b] × FIN[a, b]⟶ℝ+ by(4) dv⟶,w⟶=v⟶E+w⟶E2−v⟶⊓w⟶E.
Example 5 .
Suppose the closed interval I=[0,20] and v⟶=0,2,4,8,19,20 and w⟶=0,1,4,6,12,14,15,20. Then, v⟶⊓w⟶=0,1,2,4,6,8,12,14,15,19,20. Hence, the norm v⟶E=22+22+42+112+12=146; the norm w⟶=12+32+22+62+22+12+52=80; and v⟶⊓w⟶E=52. Thus, dv⟶,w⟶=146+80/2−52=3.30.
Claim 2 .
d is a metric on FIN[a, b].
Proof
This can be shown by the definitions and some techniques.
This metric will be used in Section 3.3. This metric basically measures the differences between the structures of the attributes in the scoring system. The more similar the structures are, the lower the distances are. Unlike the static Euclidean distance, this metric takes the interval structures into consideration.
2.5. Procedures
Let us summarise the whole procedure of our modelling for the sake of data analysis. Let e⟶=100,100,100,100,…,100,100. Let Death(Ci) denote the death rate (or tolls, depending on the context) for the country i.Define a metric d on a real interval, in particular the transformed interval, an interval for attribute values which lie between 0 and 100, I=[0,1200]⊆ℝ for the range of attribute values of economic freedom, and calculate dI^,C⟶i:1≤i≤m (one could refer to Section 3.3).
Rank ℂ via the sorted distances with a rank function γ100 : ℂ⟶{1,2,…, m} in which γI(Ci) ≥ γI(Cj) iff dI⟶,C⟶i≥dI⟶,C⟶i.
Rank ℂ via the sorted distance with a rank function γ88 in which γ88(Ci) ≥ γ88(Cj) iff Death(Ci) ≥ Death(Cj).
Form the vector v⟶=γ100°γ88−1ll=1m.
Convert v⟶ into a sign vector sgv⟶:=χv⟶2−v⟶1,χv⟶3−v⟶2,…,χv⟶m−v⟶m−1, where χ(a)=1 if a > 0 and χ(a)=0 if a < 0.
Construct the probability distribution for the quotient space 𝔹k/∼.
Perform statistical testing by locating the position of v⟶ and significant level for the batch of country.
Apply the Monte Carlo approach on the sampled batches of countries repeatedly.
With the threshold probability 0.5, based on binary distribution for the whole spectrum of statistical testing, perform the overall statistical testing.
Draw a conclusion for the relation between γ100 and γ88.
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2. Modelling
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2.1. Notations and Symbols
For a vector w⟶, we use w⟶ to denote its length; for any set H, we use |H| to denote its size (cardinality). Moreover, we use w⟶j to denote the j-th element in w⟶. Let b⟶ denote a binary vector, i.e., each element in b⟶ is either 0 or 1. Let 𝔹k denote the set of all the binary vectors with total length k. Let ℂ={C1, C2,…, Cm} be a set of countries. Let Aef={A1, A2,…, An} be a set of attributes of economic freedom (regarded as independent variables). Let Bj be a set of result (regarded as dependent variables). Each time we fix one Bj to study the relation between the attributes and Bj. In this article, we restrict our attribute values to be numerical numbers. The theoretical table is shown in Table 1, and for the actual forms, one could refer to Sections 3.2.1 and 3.2.2.
We use the notations Ci⟶=ai1,ai2,…,aim; Ai⟶=a1i,a2i,…,ami; and Bi⟶=b1i,b2i,…,bmi.
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2.1. Notations and Symbols
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For a vector w⟶, we use w⟶ to denote its length; for any set H, we use |H| to denote its size (cardinality). Moreover, we use w⟶j to denote the j-th element in w⟶. Let b⟶ denote a binary vector, i.e., each element in b⟶ is either 0 or 1. Let 𝔹k denote the set of all the binary vectors with total length k. Let ℂ={C1, C2,…, Cm} be a set of countries. Let Aef={A1, A2,…, An} be a set of attributes of economic freedom (regarded as independent variables). Let Bj be a set of result (regarded as dependent variables). Each time we fix one Bj to study the relation between the attributes and Bj. In this article, we restrict our attribute values to be numerical numbers. The theoretical table is shown in Table 1, and for the actual forms, one could refer to Sections 3.2.1 and 3.2.2.
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We use the notations Ci⟶=ai1,ai2,…,aim; Ai⟶=a1i,a2i,…,ami; and Bi⟶=b1i,b2i,…,bmi.
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2.2. Binary Subvectors and Norm
Definition 1 .
(subvectors). Suppose b⟶ is a binary vector. We use Subb⟶ to denote all its truncated subvectors consisting of only 1.
Example 1 .
Suppose b⟶=1,0,1,0,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0. Then, Subb⟶=1,1,1,1,1,1,1,1,1,1,1,1,1.
We simply abbreviate it as Subb⟶=1111131211121211. Indeed Subb⟶ reveals the structure of an independent-dependent variable relation.
Definition 2 .
(binary norm). For any binary vector b⟶=b1,b2,…,bk with Subb⟶=1n11n2,…,1nt, define a binary norm b⟶=20+21+⋯+2n1−1+20+21+…+2n2−1+⋯+20+21+⋯+2nt−1.
One could, according to real situations, adopt other numbers (for example, replace 2 with other numbers) or other forms other than the one provided here.
Claim 1 .
b⟶=2n1+2n2+⋯+2nt−t.
Proof
It follows immediately from the definition.
Definition 3 .
(linear ordering on 𝔹k). b⟶1≥b⟶2 if and only if b⟶1≥b⟶2, for all b⟶1,b⟶2∈𝔹k.
Example 2 .
If b⟶1=1,0,1,1,1,0,0,1,1,0,1,0,1,b⟶2=1,0,0,0,0,1,1,0,0,1,1,1,1, then b⟶1=20·1+20·1+21·1+22·1+20·1+21·1+20·1+20·1=13 and b⟶2=20·1+20·1+21·1+20·1+21·1+22·1+23·1=19. Thus, b⟶2≤b⟶1.
Remark 1 .
A binary norm indeed serves an important technique in revealing the relation between dependent and independent variables. Given two pairs (x1, y1) and (x2, y2) of numerical data with x1 ≠ x2, if (x2 − x1) · (y2 − y1) > 0 (i.e., they act proportionally), we associate it with a value 1 to indicate such relation and 0, otherwise (i.e., they act inversely). Such mechanism gives a way to look into the fundamental relation between X and Y variables. This kind of analysis is in particular useful when the precision of the data is questionable or when the actual numbers are unknown or more suitable to be interpreted via ranks.
Example 3 .
(sign vector). Suppose D=((2,4), (3,2), (5,8), (7,9), (4,2), (3,8)), a set of ordered vectors. Then, we could associate D with a sign vector v⟶=0,1,1,1,0 via Remark 1.
Definition 4 .
(relational vector). Suppose that b⟶ is a sign vector; we associate it with a relational vector Relb⟶ whose i-th element is assigned 1 iff b⟶i=b⟶i+1 and 0, otherwise.
Example 4 .
Let us continue with Example 3. We could compute its relational vector Relv⟶=0,1,1,0, and thus SubRelv⟶=12 and SubRelv⟶=3. The higher the value of the norm is, the closer the relation between the dependent and independent variables is.
Definition 5 .
(equivalence relation ∼). For all b⟶1,b⟶2∈𝔹k, b⟶1∼b⟶2 iff b⟶1=b⟶2.
Let 𝔹k#=b⟶:b⟶∈𝔹k. One observes that ∼ partitions 𝔹k. If p ∈ 𝔹k#, we use [p] to denote the equivalence class whose elements' norms are all p.
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2.2. Binary Subvectors and Norm
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Definition 1 .
(subvectors). Suppose b⟶ is a binary vector. We use Subb⟶ to denote all its truncated subvectors consisting of only 1.
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Definition 1 .
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(subvectors). Suppose b⟶ is a binary vector. We use Subb⟶ to denote all its truncated subvectors consisting of only 1.
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Example 1 .
Suppose b⟶=1,0,1,0,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0. Then, Subb⟶=1,1,1,1,1,1,1,1,1,1,1,1,1.
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Example 1 .
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Suppose b⟶=1,0,1,0,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0. Then, Subb⟶=1,1,1,1,1,1,1,1,1,1,1,1,1.
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We simply abbreviate it as Subb⟶=1111131211121211. Indeed Subb⟶ reveals the structure of an independent-dependent variable relation.
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Definition 2 .
(binary norm). For any binary vector b⟶=b1,b2,…,bk with Subb⟶=1n11n2,…,1nt, define a binary norm b⟶=20+21+⋯+2n1−1+20+21+…+2n2−1+⋯+20+21+⋯+2nt−1.
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Definition 2 .
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(binary norm). For any binary vector b⟶=b1,b2,…,bk with Subb⟶=1n11n2,…,1nt, define a binary norm b⟶=20+21+⋯+2n1−1+20+21+…+2n2−1+⋯+20+21+⋯+2nt−1.
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One could, according to real situations, adopt other numbers (for example, replace 2 with other numbers) or other forms other than the one provided here.
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Claim 1 .
b⟶=2n1+2n2+⋯+2nt−t.
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Claim 1 .
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b⟶=2n1+2n2+⋯+2nt−t.
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Proof
It follows immediately from the definition.
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Proof
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It follows immediately from the definition.
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Definition 3 .
(linear ordering on 𝔹k). b⟶1≥b⟶2 if and only if b⟶1≥b⟶2, for all b⟶1,b⟶2∈𝔹k.
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Definition 3 .
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(linear ordering on 𝔹k). b⟶1≥b⟶2 if and only if b⟶1≥b⟶2, for all b⟶1,b⟶2∈𝔹k.
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Example 2 .
If b⟶1=1,0,1,1,1,0,0,1,1,0,1,0,1,b⟶2=1,0,0,0,0,1,1,0,0,1,1,1,1, then b⟶1=20·1+20·1+21·1+22·1+20·1+21·1+20·1+20·1=13 and b⟶2=20·1+20·1+21·1+20·1+21·1+22·1+23·1=19. Thus, b⟶2≤b⟶1.
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Example 2 .
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If b⟶1=1,0,1,1,1,0,0,1,1,0,1,0,1,b⟶2=1,0,0,0,0,1,1,0,0,1,1,1,1, then b⟶1=20·1+20·1+21·1+22·1+20·1+21·1+20·1+20·1=13 and b⟶2=20·1+20·1+21·1+20·1+21·1+22·1+23·1=19. Thus, b⟶2≤b⟶1.
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Remark 1 .
A binary norm indeed serves an important technique in revealing the relation between dependent and independent variables. Given two pairs (x1, y1) and (x2, y2) of numerical data with x1 ≠ x2, if (x2 − x1) · (y2 − y1) > 0 (i.e., they act proportionally), we associate it with a value 1 to indicate such relation and 0, otherwise (i.e., they act inversely). Such mechanism gives a way to look into the fundamental relation between X and Y variables. This kind of analysis is in particular useful when the precision of the data is questionable or when the actual numbers are unknown or more suitable to be interpreted via ranks.
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Remark 1 .
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p
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A binary norm indeed serves an important technique in revealing the relation between dependent and independent variables. Given two pairs (x1, y1) and (x2, y2) of numerical data with x1 ≠ x2, if (x2 − x1) · (y2 − y1) > 0 (i.e., they act proportionally), we associate it with a value 1 to indicate such relation and 0, otherwise (i.e., they act inversely). Such mechanism gives a way to look into the fundamental relation between X and Y variables. This kind of analysis is in particular useful when the precision of the data is questionable or when the actual numbers are unknown or more suitable to be interpreted via ranks.
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Example 3 .
(sign vector). Suppose D=((2,4), (3,2), (5,8), (7,9), (4,2), (3,8)), a set of ordered vectors. Then, we could associate D with a sign vector v⟶=0,1,1,1,0 via Remark 1.
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Example 3 .
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(sign vector). Suppose D=((2,4), (3,2), (5,8), (7,9), (4,2), (3,8)), a set of ordered vectors. Then, we could associate D with a sign vector v⟶=0,1,1,1,0 via Remark 1.
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Definition 4 .
(relational vector). Suppose that b⟶ is a sign vector; we associate it with a relational vector Relb⟶ whose i-th element is assigned 1 iff b⟶i=b⟶i+1 and 0, otherwise.
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Definition 4 .
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(relational vector). Suppose that b⟶ is a sign vector; we associate it with a relational vector Relb⟶ whose i-th element is assigned 1 iff b⟶i=b⟶i+1 and 0, otherwise.
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Example 4 .
Let us continue with Example 3. We could compute its relational vector Relv⟶=0,1,1,0, and thus SubRelv⟶=12 and SubRelv⟶=3. The higher the value of the norm is, the closer the relation between the dependent and independent variables is.
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Example 4 .
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Let us continue with Example 3. We could compute its relational vector Relv⟶=0,1,1,0, and thus SubRelv⟶=12 and SubRelv⟶=3. The higher the value of the norm is, the closer the relation between the dependent and independent variables is.
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Definition 5 .
(equivalence relation ∼). For all b⟶1,b⟶2∈𝔹k, b⟶1∼b⟶2 iff b⟶1=b⟶2.
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Definition 5 .
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(equivalence relation ∼). For all b⟶1,b⟶2∈𝔹k, b⟶1∼b⟶2 iff b⟶1=b⟶2.
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Let 𝔹k#=b⟶:b⟶∈𝔹k. One observes that ∼ partitions 𝔹k. If p ∈ 𝔹k#, we use [p] to denote the equivalence class whose elements' norms are all p.
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2.3. Probability Distribution
Suppose 𝔹k={0,1}k is the sampling population. Define a statistic BN on 𝔹k by its binary norm. The range for BN is 𝔹k#. Define a counting ρ : 𝔹k#⟶ℕ by ρx=b⟶∈𝔹k:b⟶=x. Now, we could define the probability distribution for BN by prob : 𝔹k#⟶[0,1] by(1) probu=ρu∑h∈Ranρh.
One observes that(2) probu=u∑h∈Ranh.
This probability distribution reveals the relation between the independent variables and the dependent variables. This would serve our theoretical distribution for our statistical testing H0: the economic freedom and the death of COVID-19 has no significant relation, i.e., the economic freedom has no great impact on the death of COVID-19. For a concrete construction of such probability distribution, one could refer to Section 6.1.
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2.3. Probability Distribution
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Suppose 𝔹k={0,1}k is the sampling population. Define a statistic BN on 𝔹k by its binary norm. The range for BN is 𝔹k#. Define a counting ρ : 𝔹k#⟶ℕ by ρx=b⟶∈𝔹k:b⟶=x. Now, we could define the probability distribution for BN by prob : 𝔹k#⟶[0,1] by(1) probu=ρu∑h∈Ranρh.
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(1)
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One observes that(2) probu=u∑h∈Ranh.
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(2)
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This probability distribution reveals the relation between the independent variables and the dependent variables. This would serve our theoretical distribution for our statistical testing H0: the economic freedom and the death of COVID-19 has no significant relation, i.e., the economic freedom has no great impact on the death of COVID-19. For a concrete construction of such probability distribution, one could refer to Section 6.1.
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2.4. Metric
A metric or a distance function is a non-negative function d on X × X satisfying identity, symmetry, and triangle properties. In this article, it suffices to define a metric on a closed interval of real number. Fix I=[a, b]⊆ℝ, where a, b ∈ ℝ and a < b. Let v⟶ be a finite vector whose first element is a, last element is b, and all the other elements are incrementally increased and lie between a and b. Let FIN[a, b] be the set of all such vectors. Let v⟶=a,v2,…,vm−1,b,w⟶=a,w2,w3,…,wn−1,b∈Fina,b be arbitrary. Let v⟶⊓w⟶ denote the vector q=(a, q1, q2,…, qh−1, b) whose elements are the projections from v⟶ and w⟶. One observes that FIN[a, b] is closed under ⊓.
Definition 6 .
(atomic norm)v⟶E=(3) v2−a2+v3−v22+v4−v32+⋯vm−2−vm−12+b−vm−12.
Definition 7 .
(metric). Define d : FIN[a, b] × FIN[a, b]⟶ℝ+ by(4) dv⟶,w⟶=v⟶E+w⟶E2−v⟶⊓w⟶E.
Example 5 .
Suppose the closed interval I=[0,20] and v⟶=0,2,4,8,19,20 and w⟶=0,1,4,6,12,14,15,20. Then, v⟶⊓w⟶=0,1,2,4,6,8,12,14,15,19,20. Hence, the norm v⟶E=22+22+42+112+12=146; the norm w⟶=12+32+22+62+22+12+52=80; and v⟶⊓w⟶E=52. Thus, dv⟶,w⟶=146+80/2−52=3.30.
Claim 2 .
d is a metric on FIN[a, b].
Proof
This can be shown by the definitions and some techniques.
This metric will be used in Section 3.3. This metric basically measures the differences between the structures of the attributes in the scoring system. The more similar the structures are, the lower the distances are. Unlike the static Euclidean distance, this metric takes the interval structures into consideration.
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2.4. Metric
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A metric or a distance function is a non-negative function d on X × X satisfying identity, symmetry, and triangle properties. In this article, it suffices to define a metric on a closed interval of real number. Fix I=[a, b]⊆ℝ, where a, b ∈ ℝ and a < b. Let v⟶ be a finite vector whose first element is a, last element is b, and all the other elements are incrementally increased and lie between a and b. Let FIN[a, b] be the set of all such vectors. Let v⟶=a,v2,…,vm−1,b,w⟶=a,w2,w3,…,wn−1,b∈Fina,b be arbitrary. Let v⟶⊓w⟶ denote the vector q=(a, q1, q2,…, qh−1, b) whose elements are the projections from v⟶ and w⟶. One observes that FIN[a, b] is closed under ⊓.
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Definition 6 .
(atomic norm)v⟶E=(3) v2−a2+v3−v22+v4−v32+⋯vm−2−vm−12+b−vm−12.
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Definition 6 .
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(atomic norm)v⟶E=(3) v2−a2+v3−v22+v4−v32+⋯vm−2−vm−12+b−vm−12.
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(3)
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Definition 7 .
(metric). Define d : FIN[a, b] × FIN[a, b]⟶ℝ+ by(4) dv⟶,w⟶=v⟶E+w⟶E2−v⟶⊓w⟶E.
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Definition 7 .
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(metric). Define d : FIN[a, b] × FIN[a, b]⟶ℝ+ by(4) dv⟶,w⟶=v⟶E+w⟶E2−v⟶⊓w⟶E.
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(4)
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Example 5 .
Suppose the closed interval I=[0,20] and v⟶=0,2,4,8,19,20 and w⟶=0,1,4,6,12,14,15,20. Then, v⟶⊓w⟶=0,1,2,4,6,8,12,14,15,19,20. Hence, the norm v⟶E=22+22+42+112+12=146; the norm w⟶=12+32+22+62+22+12+52=80; and v⟶⊓w⟶E=52. Thus, dv⟶,w⟶=146+80/2−52=3.30.
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Example 5 .
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Suppose the closed interval I=[0,20] and v⟶=0,2,4,8,19,20 and w⟶=0,1,4,6,12,14,15,20. Then, v⟶⊓w⟶=0,1,2,4,6,8,12,14,15,19,20. Hence, the norm v⟶E=22+22+42+112+12=146; the norm w⟶=12+32+22+62+22+12+52=80; and v⟶⊓w⟶E=52. Thus, dv⟶,w⟶=146+80/2−52=3.30.
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Claim 2 .
d is a metric on FIN[a, b].
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Claim 2 .
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d is a metric on FIN[a, b].
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Proof
This can be shown by the definitions and some techniques.
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Proof
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This can be shown by the definitions and some techniques.
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This metric will be used in Section 3.3. This metric basically measures the differences between the structures of the attributes in the scoring system. The more similar the structures are, the lower the distances are. Unlike the static Euclidean distance, this metric takes the interval structures into consideration.
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2.5. Procedures
Let us summarise the whole procedure of our modelling for the sake of data analysis. Let e⟶=100,100,100,100,…,100,100. Let Death(Ci) denote the death rate (or tolls, depending on the context) for the country i.Define a metric d on a real interval, in particular the transformed interval, an interval for attribute values which lie between 0 and 100, I=[0,1200]⊆ℝ for the range of attribute values of economic freedom, and calculate dI^,C⟶i:1≤i≤m (one could refer to Section 3.3).
Rank ℂ via the sorted distances with a rank function γ100 : ℂ⟶{1,2,…, m} in which γI(Ci) ≥ γI(Cj) iff dI⟶,C⟶i≥dI⟶,C⟶i.
Rank ℂ via the sorted distance with a rank function γ88 in which γ88(Ci) ≥ γ88(Cj) iff Death(Ci) ≥ Death(Cj).
Form the vector v⟶=γ100°γ88−1ll=1m.
Convert v⟶ into a sign vector sgv⟶:=χv⟶2−v⟶1,χv⟶3−v⟶2,…,χv⟶m−v⟶m−1, where χ(a)=1 if a > 0 and χ(a)=0 if a < 0.
Construct the probability distribution for the quotient space 𝔹k/∼.
Perform statistical testing by locating the position of v⟶ and significant level for the batch of country.
Apply the Monte Carlo approach on the sampled batches of countries repeatedly.
With the threshold probability 0.5, based on binary distribution for the whole spectrum of statistical testing, perform the overall statistical testing.
Draw a conclusion for the relation between γ100 and γ88.
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2.5. Procedures
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Let us summarise the whole procedure of our modelling for the sake of data analysis. Let e⟶=100,100,100,100,…,100,100. Let Death(Ci) denote the death rate (or tolls, depending on the context) for the country i.Define a metric d on a real interval, in particular the transformed interval, an interval for attribute values which lie between 0 and 100, I=[0,1200]⊆ℝ for the range of attribute values of economic freedom, and calculate dI^,C⟶i:1≤i≤m (one could refer to Section 3.3).
Rank ℂ via the sorted distances with a rank function γ100 : ℂ⟶{1,2,…, m} in which γI(Ci) ≥ γI(Cj) iff dI⟶,C⟶i≥dI⟶,C⟶i.
Rank ℂ via the sorted distance with a rank function γ88 in which γ88(Ci) ≥ γ88(Cj) iff Death(Ci) ≥ Death(Cj).
Form the vector v⟶=γ100°γ88−1ll=1m.
Convert v⟶ into a sign vector sgv⟶:=χv⟶2−v⟶1,χv⟶3−v⟶2,…,χv⟶m−v⟶m−1, where χ(a)=1 if a > 0 and χ(a)=0 if a < 0.
Construct the probability distribution for the quotient space 𝔹k/∼.
Perform statistical testing by locating the position of v⟶ and significant level for the batch of country.
Apply the Monte Carlo approach on the sampled batches of countries repeatedly.
With the threshold probability 0.5, based on binary distribution for the whole spectrum of statistical testing, perform the overall statistical testing.
Draw a conclusion for the relation between γ100 and γ88.
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p
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Define a metric d on a real interval, in particular the transformed interval, an interval for attribute values which lie between 0 and 100, I=[0,1200]⊆ℝ for the range of attribute values of economic freedom, and calculate dI^,C⟶i:1≤i≤m (one could refer to Section 3.3).
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p
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Rank ℂ via the sorted distances with a rank function γ100 : ℂ⟶{1,2,…, m} in which γI(Ci) ≥ γI(Cj) iff dI⟶,C⟶i≥dI⟶,C⟶i.
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p
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Rank ℂ via the sorted distance with a rank function γ88 in which γ88(Ci) ≥ γ88(Cj) iff Death(Ci) ≥ Death(Cj).
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p
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Form the vector v⟶=γ100°γ88−1ll=1m.
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p
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Convert v⟶ into a sign vector sgv⟶:=χv⟶2−v⟶1,χv⟶3−v⟶2,…,χv⟶m−v⟶m−1, where χ(a)=1 if a > 0 and χ(a)=0 if a < 0.
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p
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Construct the probability distribution for the quotient space 𝔹k/∼.
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p
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Perform statistical testing by locating the position of v⟶ and significant level for the batch of country.
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p
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Apply the Monte Carlo approach on the sampled batches of countries repeatedly.
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p
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With the threshold probability 0.5, based on binary distribution for the whole spectrum of statistical testing, perform the overall statistical testing.
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p
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Draw a conclusion for the relation between γ100 and γ88.
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sec
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3. Data Analysis
Following the procedures in Section 2.5, we start to collect, analyse, and produce a report via data analysis. Since the data are huge and hard to handle by the one-off approach, we resort to the sampling technique and reach a conclusion via statistical testing.
3.1. Sampling
The raw data consist of 164 countries (we use 1 to 164 to name the countries) up to 2020, June 27th. Since the size is too huge, we apply the Monte Carlo approach to sample the 164 countries. We do 20 times (or 20 batches: S1 to S20) sampling with 25 countries over the 164 countries per sampling. The sampled batches are listed in Tables 2 and 3.
3.2. Sampled Data
3.2.1. Economic Freedom
Corresponding to the form listed in Table 1, we associate ℂ with S1 and define Aef={A1, A2,…, A12}, where A1≡Property Rights, A2≡Judicial Effectiveness, A3≡Government Integrity, A4≡Tax Burden, A5≡Government Spending, A6≡Fiscal Health, A7≡Business Freedom, A8≡Labor Freedom, A9≡Monetary Freedom, A10≡Trade Freedom, A11≡Investment Freedom, and A12≡Financial Freedom. The attribute values are based on a 100-point scoring system [6]. Due to the limitation of space, we list only the first sampling (or S1) regarding its attributes of economic freedom in Table 4. We omit the other 19 similar tables of this form. Aef serves as the set of our independent variables.
3.2.2. COVID-19
Now we start to introduce the dependent variables. Indeed we tackle an individual dependent variable each time. Since the data are huge, we only extract the data [7] for sampling one (or S1) as shown in Table 5. Corresponding to the form listed in Table 1, we associate ℂ with S1 and define B1≡ Total Confirmed COVID-19 Cases, B2≡ Death Toll of COVID-19, B3≡ Total Recovered COVID-19 Cases, and B4≡ Population of the Countries. Due to the limitation of space, we list only the first sampling (or S1) regarding its dependent variables. We omit the other 19 similar tables of this form. Moreover, in the later analysis, we only take and fix B2 as our dependent variable. If the readers are interested in other dependent variables (or B1, B3, or other mixed forms), they could simply follow the same approach provided in this article.
3.3. Metric
Since we have defined an interval metric in Section 2.4, we could apply it over here. Here we measure the distance between every sampled data and the fixed reference vector e⟶=100,200,…,1100,1200. We construct the distances for the 164 countries based on economic freedom (for example, the data of sample one could be referred from Table 4) in Tables 6 and 7. Since all the data are presented in the form of 100-point score for the attribute values in Table 4, we need to transform the values in the table to the interval I=[0,1200]. For example, the reference vector e⟶ (we still use e⟶ to represent to newly transformed vector) will be e⟶=0,100,200,300,…,1100,1200. Each country C sampled in S1 will be transformed into C⟶, for example, C¯⟶11≡68⟶=0,64.8,145.7,247.5,379.9,…,1170,1200 are the converted data for the first country sampled in the first sampling or country 68. The economic freedom vector for each sampled country is converted by the same way. The converted data are not tabulated. Then, we apply d in Section 2.4 on the converted data and repeat the whole processes for other samplings. The complete results regarding the distance for the 20 sampled countries are presented in Tables 6 and 7. The (i, j) cell in the tables means the value de⟶,C¯⟶ij, where C¯ij denotes the i-th country sampled in j-th sampling and C¯⟶ij denotes the converted data for C¯ij.
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title
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3. Data Analysis
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p
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Following the procedures in Section 2.5, we start to collect, analyse, and produce a report via data analysis. Since the data are huge and hard to handle by the one-off approach, we resort to the sampling technique and reach a conclusion via statistical testing.
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sec
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3.1. Sampling
The raw data consist of 164 countries (we use 1 to 164 to name the countries) up to 2020, June 27th. Since the size is too huge, we apply the Monte Carlo approach to sample the 164 countries. We do 20 times (or 20 batches: S1 to S20) sampling with 25 countries over the 164 countries per sampling. The sampled batches are listed in Tables 2 and 3.
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title
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3.1. Sampling
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p
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The raw data consist of 164 countries (we use 1 to 164 to name the countries) up to 2020, June 27th. Since the size is too huge, we apply the Monte Carlo approach to sample the 164 countries. We do 20 times (or 20 batches: S1 to S20) sampling with 25 countries over the 164 countries per sampling. The sampled batches are listed in Tables 2 and 3.
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sec
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3.2. Sampled Data
3.2.1. Economic Freedom
Corresponding to the form listed in Table 1, we associate ℂ with S1 and define Aef={A1, A2,…, A12}, where A1≡Property Rights, A2≡Judicial Effectiveness, A3≡Government Integrity, A4≡Tax Burden, A5≡Government Spending, A6≡Fiscal Health, A7≡Business Freedom, A8≡Labor Freedom, A9≡Monetary Freedom, A10≡Trade Freedom, A11≡Investment Freedom, and A12≡Financial Freedom. The attribute values are based on a 100-point scoring system [6]. Due to the limitation of space, we list only the first sampling (or S1) regarding its attributes of economic freedom in Table 4. We omit the other 19 similar tables of this form. Aef serves as the set of our independent variables.
3.2.2. COVID-19
Now we start to introduce the dependent variables. Indeed we tackle an individual dependent variable each time. Since the data are huge, we only extract the data [7] for sampling one (or S1) as shown in Table 5. Corresponding to the form listed in Table 1, we associate ℂ with S1 and define B1≡ Total Confirmed COVID-19 Cases, B2≡ Death Toll of COVID-19, B3≡ Total Recovered COVID-19 Cases, and B4≡ Population of the Countries. Due to the limitation of space, we list only the first sampling (or S1) regarding its dependent variables. We omit the other 19 similar tables of this form. Moreover, in the later analysis, we only take and fix B2 as our dependent variable. If the readers are interested in other dependent variables (or B1, B3, or other mixed forms), they could simply follow the same approach provided in this article.
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title
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3.2. Sampled Data
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sec
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3.2.1. Economic Freedom
Corresponding to the form listed in Table 1, we associate ℂ with S1 and define Aef={A1, A2,…, A12}, where A1≡Property Rights, A2≡Judicial Effectiveness, A3≡Government Integrity, A4≡Tax Burden, A5≡Government Spending, A6≡Fiscal Health, A7≡Business Freedom, A8≡Labor Freedom, A9≡Monetary Freedom, A10≡Trade Freedom, A11≡Investment Freedom, and A12≡Financial Freedom. The attribute values are based on a 100-point scoring system [6]. Due to the limitation of space, we list only the first sampling (or S1) regarding its attributes of economic freedom in Table 4. We omit the other 19 similar tables of this form. Aef serves as the set of our independent variables.
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title
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3.2.1. Economic Freedom
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p
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Corresponding to the form listed in Table 1, we associate ℂ with S1 and define Aef={A1, A2,…, A12}, where A1≡Property Rights, A2≡Judicial Effectiveness, A3≡Government Integrity, A4≡Tax Burden, A5≡Government Spending, A6≡Fiscal Health, A7≡Business Freedom, A8≡Labor Freedom, A9≡Monetary Freedom, A10≡Trade Freedom, A11≡Investment Freedom, and A12≡Financial Freedom. The attribute values are based on a 100-point scoring system [6]. Due to the limitation of space, we list only the first sampling (or S1) regarding its attributes of economic freedom in Table 4. We omit the other 19 similar tables of this form. Aef serves as the set of our independent variables.
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sec
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3.2.2. COVID-19
Now we start to introduce the dependent variables. Indeed we tackle an individual dependent variable each time. Since the data are huge, we only extract the data [7] for sampling one (or S1) as shown in Table 5. Corresponding to the form listed in Table 1, we associate ℂ with S1 and define B1≡ Total Confirmed COVID-19 Cases, B2≡ Death Toll of COVID-19, B3≡ Total Recovered COVID-19 Cases, and B4≡ Population of the Countries. Due to the limitation of space, we list only the first sampling (or S1) regarding its dependent variables. We omit the other 19 similar tables of this form. Moreover, in the later analysis, we only take and fix B2 as our dependent variable. If the readers are interested in other dependent variables (or B1, B3, or other mixed forms), they could simply follow the same approach provided in this article.
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title
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3.2.2. COVID-19
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p
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Now we start to introduce the dependent variables. Indeed we tackle an individual dependent variable each time. Since the data are huge, we only extract the data [7] for sampling one (or S1) as shown in Table 5. Corresponding to the form listed in Table 1, we associate ℂ with S1 and define B1≡ Total Confirmed COVID-19 Cases, B2≡ Death Toll of COVID-19, B3≡ Total Recovered COVID-19 Cases, and B4≡ Population of the Countries. Due to the limitation of space, we list only the first sampling (or S1) regarding its dependent variables. We omit the other 19 similar tables of this form. Moreover, in the later analysis, we only take and fix B2 as our dependent variable. If the readers are interested in other dependent variables (or B1, B3, or other mixed forms), they could simply follow the same approach provided in this article.
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sec
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3.3. Metric
Since we have defined an interval metric in Section 2.4, we could apply it over here. Here we measure the distance between every sampled data and the fixed reference vector e⟶=100,200,…,1100,1200. We construct the distances for the 164 countries based on economic freedom (for example, the data of sample one could be referred from Table 4) in Tables 6 and 7. Since all the data are presented in the form of 100-point score for the attribute values in Table 4, we need to transform the values in the table to the interval I=[0,1200]. For example, the reference vector e⟶ (we still use e⟶ to represent to newly transformed vector) will be e⟶=0,100,200,300,…,1100,1200. Each country C sampled in S1 will be transformed into C⟶, for example, C¯⟶11≡68⟶=0,64.8,145.7,247.5,379.9,…,1170,1200 are the converted data for the first country sampled in the first sampling or country 68. The economic freedom vector for each sampled country is converted by the same way. The converted data are not tabulated. Then, we apply d in Section 2.4 on the converted data and repeat the whole processes for other samplings. The complete results regarding the distance for the 20 sampled countries are presented in Tables 6 and 7. The (i, j) cell in the tables means the value de⟶,C¯⟶ij, where C¯ij denotes the i-th country sampled in j-th sampling and C¯⟶ij denotes the converted data for C¯ij.
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title
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3.3. Metric
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p
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Since we have defined an interval metric in Section 2.4, we could apply it over here. Here we measure the distance between every sampled data and the fixed reference vector e⟶=100,200,…,1100,1200. We construct the distances for the 164 countries based on economic freedom (for example, the data of sample one could be referred from Table 4) in Tables 6 and 7. Since all the data are presented in the form of 100-point score for the attribute values in Table 4, we need to transform the values in the table to the interval I=[0,1200]. For example, the reference vector e⟶ (we still use e⟶ to represent to newly transformed vector) will be e⟶=0,100,200,300,…,1100,1200. Each country C sampled in S1 will be transformed into C⟶, for example, C¯⟶11≡68⟶=0,64.8,145.7,247.5,379.9,…,1170,1200 are the converted data for the first country sampled in the first sampling or country 68. The economic freedom vector for each sampled country is converted by the same way. The converted data are not tabulated. Then, we apply d in Section 2.4 on the converted data and repeat the whole processes for other samplings. The complete results regarding the distance for the 20 sampled countries are presented in Tables 6 and 7. The (i, j) cell in the tables means the value de⟶,C¯⟶ij, where C¯ij denotes the i-th country sampled in j-th sampling and C¯⟶ij denotes the converted data for C¯ij.
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sec
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4. Absolute Reference
By the derived distances presented in Tables 6 and 7, we could construct absolute references. The absolute references would server as the benchmarks for other internal structures. Let us use ℂs to denote the set of sampled countries in s-th sampling. Let C¯⟶si,C¯⟶sj∈ℂs be arbitrary.
Definition 8 .
(ordering of the sampled countries). C¯is≥C¯js iff de⟶,C¯⟶is≥de⟶,C¯⟶js.
Based on this ordering, we could generate the absolute references (Tables 8 and 9). Let us take S1 for example: C68 > C112 > C92 > ⋯>C41 > C85 > C14. From these absolute references (or ordering for the samplings), we could view the structure (or interval) difference between the ideal scoring (or e⟶) and real scoring results. Indeed, an absolute reference is a reference acting like ordering without specific scales. Such reference is useful when the precise values are unknown or when the precision of the data is questionable. In this article, we use relative distances between a country's economic freedom and others to create such ordering.
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title
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4. Absolute Reference
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p
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By the derived distances presented in Tables 6 and 7, we could construct absolute references. The absolute references would server as the benchmarks for other internal structures. Let us use ℂs to denote the set of sampled countries in s-th sampling. Let C¯⟶si,C¯⟶sj∈ℂs be arbitrary.
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p
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Definition 8 .
(ordering of the sampled countries). C¯is≥C¯js iff de⟶,C¯⟶is≥de⟶,C¯⟶js.
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title
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Definition 8 .
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p
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(ordering of the sampled countries). C¯is≥C¯js iff de⟶,C¯⟶is≥de⟶,C¯⟶js.
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p
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Based on this ordering, we could generate the absolute references (Tables 8 and 9). Let us take S1 for example: C68 > C112 > C92 > ⋯>C41 > C85 > C14. From these absolute references (or ordering for the samplings), we could view the structure (or interval) difference between the ideal scoring (or e⟶) and real scoring results. Indeed, an absolute reference is a reference acting like ordering without specific scales. Such reference is useful when the precise values are unknown or when the precision of the data is questionable. In this article, we use relative distances between a country's economic freedom and others to create such ordering.
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5. Ordering for COVID-19 Fatalities
Based on Table 5 and other omitted tables, we start to construct the ordering (or ranking) based on the fatalities of COVID-19.
Definition 9 .
(ordering on fatalities). C¯is≥C¯js iff DeathC¯is≥DeathC¯js, where DeathC¯is is the death toll for i-th country sampled in s-th sampling.
Based on this ordering, we have the results presented in Tables 10 and 11. Let us take the cells in S1 for example: C78 > C98 > C76 > ⋯>C14 > C99 > C21.
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title
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5. Ordering for COVID-19 Fatalities
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p
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Based on Table 5 and other omitted tables, we start to construct the ordering (or ranking) based on the fatalities of COVID-19.
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p
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Definition 9 .
(ordering on fatalities). C¯is≥C¯js iff DeathC¯is≥DeathC¯js, where DeathC¯is is the death toll for i-th country sampled in s-th sampling.
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title
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Definition 9 .
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p
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(ordering on fatalities). C¯is≥C¯js iff DeathC¯is≥DeathC¯js, where DeathC¯is is the death toll for i-th country sampled in s-th sampling.
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p
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Based on this ordering, we have the results presented in Tables 10 and 11. Let us take the cells in S1 for example: C78 > C98 > C76 > ⋯>C14 > C99 > C21.
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6. Norm and Probability
In this experiment, we only consider N=23 and construct its distribution accordingly. Hence, the domain is {0,1}23 and the range lies between 0 and 223 − 1=8388607 (indeed some of the values' probability is 0). This section generalises Example 3. The higher the value is, the higher the impact of independent variables on dependent variable is.
6.1. Probability Distribution
We have already constructed the theoretical setting of probability distribution for our testing in Section 2.3. Based on that framework and the data given, we could create the theoretical probability distribution prob in Figure 1.
The (one-tailed) critical values for 5 and 10 percentages are 138 and 78 (via numerical computation), respectively; that is, if the sampled value is larger than the critical values, we should reject Ho: there is no significant relation between the economic freedom and death of COVID-19.
6.2. Real Results
In comparison with the absolute reference, we could generate the binary sign vectors for the real data from each sampling Sj (or simply j) in Table 12—for the formula and explanation of sign vectors, one could refer to Section 2.2. However, in these 0 and 1 representations, it separates the proportional and inversely proportional relation between the economic freedom and death of COVID-19. To take all the factors into consideration, one further analyses the alternative behaviour of 0 and 1. If there are too many alternations between 0 and 1, it would indicate that there is a less relation between those two. On the other hand, if the alternative times are few, then it leads to the longer length of subvector consisting of pure 1. The alternative results are shown in Table 13.
Based on Table 13 and definitions in Section 2.2, we could compute the binary norm for each sampling batch Sj (or J) as shown in Table 14.
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title
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6. Norm and Probability
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p
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In this experiment, we only consider N=23 and construct its distribution accordingly. Hence, the domain is {0,1}23 and the range lies between 0 and 223 − 1=8388607 (indeed some of the values' probability is 0). This section generalises Example 3. The higher the value is, the higher the impact of independent variables on dependent variable is.
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sec
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6.1. Probability Distribution
We have already constructed the theoretical setting of probability distribution for our testing in Section 2.3. Based on that framework and the data given, we could create the theoretical probability distribution prob in Figure 1.
The (one-tailed) critical values for 5 and 10 percentages are 138 and 78 (via numerical computation), respectively; that is, if the sampled value is larger than the critical values, we should reject Ho: there is no significant relation between the economic freedom and death of COVID-19.
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title
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6.1. Probability Distribution
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p
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We have already constructed the theoretical setting of probability distribution for our testing in Section 2.3. Based on that framework and the data given, we could create the theoretical probability distribution prob in Figure 1.
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p
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The (one-tailed) critical values for 5 and 10 percentages are 138 and 78 (via numerical computation), respectively; that is, if the sampled value is larger than the critical values, we should reject Ho: there is no significant relation between the economic freedom and death of COVID-19.
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sec
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6.2. Real Results
In comparison with the absolute reference, we could generate the binary sign vectors for the real data from each sampling Sj (or simply j) in Table 12—for the formula and explanation of sign vectors, one could refer to Section 2.2. However, in these 0 and 1 representations, it separates the proportional and inversely proportional relation between the economic freedom and death of COVID-19. To take all the factors into consideration, one further analyses the alternative behaviour of 0 and 1. If there are too many alternations between 0 and 1, it would indicate that there is a less relation between those two. On the other hand, if the alternative times are few, then it leads to the longer length of subvector consisting of pure 1. The alternative results are shown in Table 13.
Based on Table 13 and definitions in Section 2.2, we could compute the binary norm for each sampling batch Sj (or J) as shown in Table 14.
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title
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6.2. Real Results
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p
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In comparison with the absolute reference, we could generate the binary sign vectors for the real data from each sampling Sj (or simply j) in Table 12—for the formula and explanation of sign vectors, one could refer to Section 2.2. However, in these 0 and 1 representations, it separates the proportional and inversely proportional relation between the economic freedom and death of COVID-19. To take all the factors into consideration, one further analyses the alternative behaviour of 0 and 1. If there are too many alternations between 0 and 1, it would indicate that there is a less relation between those two. On the other hand, if the alternative times are few, then it leads to the longer length of subvector consisting of pure 1. The alternative results are shown in Table 13.
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p
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Based on Table 13 and definitions in Section 2.2, we could compute the binary norm for each sampling batch Sj (or J) as shown in Table 14.
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7. Conclusion and Future Work
The contribution of death in COVID-19 is very complicated. We use economic freedom to capture a potential factor in such contribution. To verify the truth of great impact from economic freedom, we devise a metric, two norms, absolute ordering, binary ordering, and probability distribution for the statistical testing population. Based on our research, we find out that the economic freedom has no significant relation to the death of COVID-19. This might provide some reference for the decision makers of the countries. In the future research, one could further study the relation between economic freedom and other ratios related to COVID-19. One could also use other nonparametric approaches to enrich the statistical testing. There is another related paper on the same topic [8]. In that paper, the authors use two-step estimators: negative binomial regression and nonlinear least squares, and find out there is a close relation between economic freedom and fatalities of COVID-19. In essence, their approach focuses more on statistical techniques, while ours focuses more on mathematical approaches. For the future researcher, he could compare or combine these methods to yield a comprehensive or generalised theory that could accommodate and single out the factors that cause the discrepancies.
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7. Conclusion and Future Work
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p
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The contribution of death in COVID-19 is very complicated. We use economic freedom to capture a potential factor in such contribution. To verify the truth of great impact from economic freedom, we devise a metric, two norms, absolute ordering, binary ordering, and probability distribution for the statistical testing population. Based on our research, we find out that the economic freedom has no significant relation to the death of COVID-19. This might provide some reference for the decision makers of the countries. In the future research, one could further study the relation between economic freedom and other ratios related to COVID-19. One could also use other nonparametric approaches to enrich the statistical testing. There is another related paper on the same topic [8]. In that paper, the authors use two-step estimators: negative binomial regression and nonlinear least squares, and find out there is a close relation between economic freedom and fatalities of COVID-19. In essence, their approach focuses more on statistical techniques, while ours focuses more on mathematical approaches. For the future researcher, he could compare or combine these methods to yield a comprehensive or generalised theory that could accommodate and single out the factors that cause the discrepancies.
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Acknowledgments
This study was supported by the Humanities and Social Science Research Planning Fund Project under the Ministry of Education of China (grant no. 20XJAGAT001).
Data Availability
The data supporting the findings of this study are included within the article.
Conflicts of Interest
The author declares that there are no conflicts of interest.
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Acknowledgments
This study was supported by the Humanities and Social Science Research Planning Fund Project under the Ministry of Education of China (grant no. 20XJAGAT001).
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Acknowledgments
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This study was supported by the Humanities and Social Science Research Planning Fund Project under the Ministry of Education of China (grant no. 20XJAGAT001).
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Data Availability
The data supporting the findings of this study are included within the article.
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Data Availability
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The data supporting the findings of this study are included within the article.
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Conflicts of Interest
The author declares that there are no conflicts of interest.
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Conflicts of Interest
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The author declares that there are no conflicts of interest.
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figure
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Figure 1 Theoretical distribution of binary norm.
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label
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Figure 1
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caption
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Theoretical distribution of binary norm.
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Theoretical distribution of binary norm.
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table-wrap
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Table 1 Independent-dependent analysis.
Countries A 1 A 2 … A p B 1 B 2 … B q
C 1 a 11 a 12 … a 1p b 11 b 12 … B 1q
C 2 a 21 a 22 … a 2p b 21 b 22 … b 2q
…
C m a m1 a m2 … a mp b m1 b m2 … b mq
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label
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Table 1
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caption
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Independent-dependent analysis.
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p
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Independent-dependent analysis.
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table
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Countries A 1 A 2 … A p B 1 B 2 … B q
C 1 a 11 a 12 … a 1p b 11 b 12 … B 1q
C 2 a 21 a 22 … a 2p b 21 b 22 … b 2q
…
C m a m1 a m2 … a mp b m1 b m2 … b mq
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tr
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Countries A 1 A 2 … A p B 1 B 2 … B q
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th
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Countries
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th
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A 1
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th
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A 2
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th
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…
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th
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A p
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th
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B 1
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th
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B 2
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th
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…
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th
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B q
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tr
|
C 1 a 11 a 12 … a 1p b 11 b 12 … B 1q
|
|
td
|
C 1
|
|
td
|
a 11
|
|
td
|
a 12
|
|
td
|
…
|
|
td
|
a 1p
|
|
td
|
b 11
|
|
td
|
b 12
|
|
td
|
…
|
|
td
|
B 1q
|
|
tr
|
C 2 a 21 a 22 … a 2p b 21 b 22 … b 2q
|
|
td
|
C 2
|
|
td
|
a 21
|
|
td
|
a 22
|
|
td
|
…
|
|
td
|
a 2p
|
|
td
|
b 21
|
|
td
|
b 22
|
|
td
|
…
|
|
td
|
b 2q
|
|
tr
|
…
|
|
td
|
…
|
|
td
|
|
|
td
|
|
|
td
|
|
|
td
|
|
|
td
|
|
|
td
|
|
|
td
|
|
|
td
|
|
|
tr
|
C m a m1 a m2 … a mp b m1 b m2 … b mq
|
|
td
|
C m
|
|
td
|
a m1
|
|
td
|
a m2
|
|
td
|
…
|
|
td
|
a mp
|
|
td
|
b m1
|
|
td
|
b m2
|
|
td
|
…
|
|
td
|
b mq
|
|
table-wrap
|
Table 2 20 sampled batches—S1 to S10.
Order S1 S2 S3 S4 S5 S6 S7 S8 S9 S10
1 68 25 69 10 27 65 72 56 64 163
2 141 127 93 98 55 85 75 151 150 19
3 21 95 5 56 14 115 159 112 65 10
4 129 41 30 45 7 35 130 136 9 117
5 127 17 151 74 119 57 128 139 69 52
6 99 151 33 89 20 160 147 100 27 18
7 89 14 156 26 124 95 19 27 113 88
8 2 43 132 73 35 118 122 83 53 65
9 128 76 44 84 153 29 129 16 84 105
10 108 28 48 70 150 15 9 47 110 150
11 112 62 126 67 151 71 118 134 156 26
12 92 131 6 121 90 86 91 87 89 161
13 98 10 46 69 80 89 39 107 52 82
14 18 119 84 50 37 50 71 52 21 27
15 148 128 39 97 84 13 81 111 132 57
16 124 121 34 3 45 56 15 48 15 29
17 1 18 95 92 75 91 158 101 66 20
18 32 16 98 18 113 41 125 46 127 116
19 76 92 26 87 59 7 144 113 56 38
20 14 42 85 142 85 32 46 70 97 41
21 41 60 1 37 48 61 21 76 140 92
22 137 103 144 137 38 75 86 84 102 128
23 85 120 53 2 132 124 132 119 31 7
24 78 163 117 122 111 122 99 74 163 22
25 52 118 62 77 66 19 35 123 88 103
|
|
label
|
Table 2
|
|
caption
|
20 sampled batches—S1 to S10.
|
|
p
|
20 sampled batches—S1 to S10.
|
|
table
|
Order S1 S2 S3 S4 S5 S6 S7 S8 S9 S10
1 68 25 69 10 27 65 72 56 64 163
2 141 127 93 98 55 85 75 151 150 19
3 21 95 5 56 14 115 159 112 65 10
4 129 41 30 45 7 35 130 136 9 117
5 127 17 151 74 119 57 128 139 69 52
6 99 151 33 89 20 160 147 100 27 18
7 89 14 156 26 124 95 19 27 113 88
8 2 43 132 73 35 118 122 83 53 65
9 128 76 44 84 153 29 129 16 84 105
10 108 28 48 70 150 15 9 47 110 150
11 112 62 126 67 151 71 118 134 156 26
12 92 131 6 121 90 86 91 87 89 161
13 98 10 46 69 80 89 39 107 52 82
14 18 119 84 50 37 50 71 52 21 27
15 148 128 39 97 84 13 81 111 132 57
16 124 121 34 3 45 56 15 48 15 29
17 1 18 95 92 75 91 158 101 66 20
18 32 16 98 18 113 41 125 46 127 116
19 76 92 26 87 59 7 144 113 56 38
20 14 42 85 142 85 32 46 70 97 41
21 41 60 1 37 48 61 21 76 140 92
22 137 103 144 137 38 75 86 84 102 128
23 85 120 53 2 132 124 132 119 31 7
24 78 163 117 122 111 122 99 74 163 22
25 52 118 62 77 66 19 35 123 88 103
|
|
tr
|
Order S1 S2 S3 S4 S5 S6 S7 S8 S9 S10
|
|
th
|
Order
|
|
th
|
S1
|
|
th
|
S2
|
|
th
|
S3
|
|
th
|
S4
|
|
th
|
S5
|
|
th
|
S6
|
|
th
|
S7
|
|
th
|
S8
|
|
th
|
S9
|
|
th
|
S10
|
|
tr
|
1 68 25 69 10 27 65 72 56 64 163
|
|
td
|
1
|
|
td
|
68
|
|
td
|
25
|
|
td
|
69
|
|
td
|
10
|
|
td
|
27
|
|
td
|
65
|
|
td
|
72
|
|
td
|
56
|
|
td
|
64
|
|
td
|
163
|
|
tr
|
2 141 127 93 98 55 85 75 151 150 19
|
|
td
|
2
|
|
td
|
141
|
|
td
|
127
|
|
td
|
93
|
|
td
|
98
|
|
td
|
55
|
|
td
|
85
|
|
td
|
75
|
|
td
|
151
|
|
td
|
150
|
|
td
|
19
|
|
tr
|
3 21 95 5 56 14 115 159 112 65 10
|
|
td
|
3
|
|
td
|
21
|
|
td
|
95
|
|
td
|
5
|
|
td
|
56
|
|
td
|
14
|
|
td
|
115
|
|
td
|
159
|
|
td
|
112
|
|
td
|
65
|
|
td
|
10
|
|
tr
|
4 129 41 30 45 7 35 130 136 9 117
|
|
td
|
4
|
|
td
|
129
|
|
td
|
41
|
|
td
|
30
|
|
td
|
45
|
|
td
|
7
|
|
td
|
35
|
|
td
|
130
|
|
td
|
136
|
|
td
|
9
|
|
td
|
117
|
|
tr
|
5 127 17 151 74 119 57 128 139 69 52
|
|
td
|
5
|
|
td
|
127
|
|
td
|
17
|
|
td
|
151
|
|
td
|
74
|
|
td
|
119
|
|
td
|
57
|
|
td
|
128
|
|
td
|
139
|
|
td
|
69
|
|
td
|
52
|
|
tr
|
6 99 151 33 89 20 160 147 100 27 18
|
|
td
|
6
|
|
td
|
99
|
|
td
|
151
|
|
td
|
33
|
|
td
|
89
|
|
td
|
20
|
|
td
|
160
|
|
td
|
147
|
|
td
|
100
|
|
td
|
27
|
|
td
|
18
|
|
tr
|
7 89 14 156 26 124 95 19 27 113 88
|
|
td
|
7
|
|
td
|
89
|
|
td
|
14
|
|
td
|
156
|
|
td
|
26
|
|
td
|
124
|
|
td
|
95
|
|
td
|
19
|
|
td
|
27
|
|
td
|
113
|
|
td
|
88
|
|
tr
|
8 2 43 132 73 35 118 122 83 53 65
|
|
td
|
8
|
|
td
|
2
|
|
td
|
43
|
|
td
|
132
|
|
td
|
73
|
|
td
|
35
|
|
td
|
118
|
|
td
|
122
|
|
td
|
83
|
|
td
|
53
|
|
td
|
65
|
|
tr
|
9 128 76 44 84 153 29 129 16 84 105
|
|
td
|
9
|
|
td
|
128
|
|
td
|
76
|
|
td
|
44
|
|
td
|
84
|
|
td
|
153
|
|
td
|
29
|
|
td
|
129
|
|
td
|
16
|
|
td
|
84
|
|
td
|
105
|
|
tr
|
10 108 28 48 70 150 15 9 47 110 150
|
|
td
|
10
|
|
td
|
108
|
|
td
|
28
|
|
td
|
48
|
|
td
|
70
|
|
td
|
150
|
|
td
|
15
|
|
td
|
9
|
|
td
|
47
|
|
td
|
110
|
|
td
|
150
|
|
tr
|
11 112 62 126 67 151 71 118 134 156 26
|
|
td
|
11
|
|
td
|
112
|
|
td
|
62
|
|
td
|
126
|
|
td
|
67
|
|
td
|
151
|
|
td
|
71
|
|
td
|
118
|
|
td
|
134
|
|
td
|
156
|
|
td
|
26
|
|
tr
|
12 92 131 6 121 90 86 91 87 89 161
|
|
td
|
12
|
|
td
|
92
|
|
td
|
131
|
|
td
|
6
|
|
td
|
121
|
|
td
|
90
|
|
td
|
86
|
|
td
|
91
|
|
td
|
87
|
|
td
|
89
|
|
td
|
161
|
|
tr
|
13 98 10 46 69 80 89 39 107 52 82
|
|
td
|
13
|
|
td
|
98
|
|
td
|
10
|
|
td
|
46
|
|
td
|
69
|
|
td
|
80
|
|
td
|
89
|
|
td
|
39
|
|
td
|
107
|
|
td
|
52
|
|
td
|
82
|
|
tr
|
14 18 119 84 50 37 50 71 52 21 27
|
|
td
|
14
|
|
td
|
18
|
|
td
|
119
|
|
td
|
84
|
|
td
|
50
|
|
td
|
37
|
|
td
|
50
|
|
td
|
71
|
|
td
|
52
|
|
td
|
21
|
|
td
|
27
|
|
tr
|
15 148 128 39 97 84 13 81 111 132 57
|
|
td
|
15
|
|
td
|
148
|
|
td
|
128
|
|
td
|
39
|
|
td
|
97
|
|
td
|
84
|
|
td
|
13
|
|
td
|
81
|
|
td
|
111
|
|
td
|
132
|
|
td
|
57
|
|
tr
|
16 124 121 34 3 45 56 15 48 15 29
|
|
td
|
16
|
|
td
|
124
|
|
td
|
121
|
|
td
|
34
|
|
td
|
3
|
|
td
|
45
|
|
td
|
56
|
|
td
|
15
|
|
td
|
48
|
|
td
|
15
|
|
td
|
29
|
|
tr
|
17 1 18 95 92 75 91 158 101 66 20
|
|
td
|
17
|
|
td
|
1
|
|
td
|
18
|
|
td
|
95
|
|
td
|
92
|
|
td
|
75
|
|
td
|
91
|
|
td
|
158
|
|
td
|
101
|
|
td
|
66
|
|
td
|
20
|
|
tr
|
18 32 16 98 18 113 41 125 46 127 116
|
|
td
|
18
|
|
td
|
32
|
|
td
|
16
|
|
td
|
98
|
|
td
|
18
|
|
td
|
113
|
|
td
|
41
|
|
td
|
125
|
|
td
|
46
|
|
td
|
127
|
|
td
|
116
|
|
tr
|
19 76 92 26 87 59 7 144 113 56 38
|
|
td
|
19
|
|
td
|
76
|
|
td
|
92
|
|
td
|
26
|
|
td
|
87
|
|
td
|
59
|
|
td
|
7
|
|
td
|
144
|
|
td
|
113
|
|
td
|
56
|
|
td
|
38
|
|
tr
|
20 14 42 85 142 85 32 46 70 97 41
|
|
td
|
20
|
|
td
|
14
|
|
td
|
42
|
|
td
|
85
|
|
td
|
142
|
|
td
|
85
|
|
td
|
32
|
|
td
|
46
|
|
td
|
70
|
|
td
|
97
|
|
td
|
41
|
|
tr
|
21 41 60 1 37 48 61 21 76 140 92
|
|
td
|
21
|
|
td
|
41
|
|
td
|
60
|
|
td
|
1
|
|
td
|
37
|
|
td
|
48
|
|
td
|
61
|
|
td
|
21
|
|
td
|
76
|
|
td
|
140
|
|
td
|
92
|
|
tr
|
22 137 103 144 137 38 75 86 84 102 128
|
|
td
|
22
|
|
td
|
137
|
|
td
|
103
|
|
td
|
144
|
|
td
|
137
|
|
td
|
38
|
|
td
|
75
|
|
td
|
86
|
|
td
|
84
|
|
td
|
102
|
|
td
|
128
|
|
tr
|
23 85 120 53 2 132 124 132 119 31 7
|
|
td
|
23
|
|
td
|
85
|
|
td
|
120
|
|
td
|
53
|
|
td
|
2
|
|
td
|
132
|
|
td
|
124
|
|
td
|
132
|
|
td
|
119
|
|
td
|
31
|
|
td
|
7
|
|
tr
|
24 78 163 117 122 111 122 99 74 163 22
|
|
td
|
24
|
|
td
|
78
|
|
td
|
163
|
|
td
|
117
|
|
td
|
122
|
|
td
|
111
|
|
td
|
122
|
|
td
|
99
|
|
td
|
74
|
|
td
|
163
|
|
td
|
22
|
|
tr
|
25 52 118 62 77 66 19 35 123 88 103
|
|
td
|
25
|
|
td
|
52
|
|
td
|
118
|
|
td
|
62
|
|
td
|
77
|
|
td
|
66
|
|
td
|
19
|
|
td
|
35
|
|
td
|
123
|
|
td
|
88
|
|
td
|
103
|
|
table-wrap
|
Table 3 20 sampled batches—S11 to S20.
Order S11 S12 S13 S14 S15 S16 S17 S18 S19 S20
1 76 91 83 59 64 119 129 154 15 37
2 23 124 53 63 46 123 8 82 30 55
3 29 151 126 24 143 137 6 35 43 119
4 12 126 129 55 53 108 122 4 148 163
5 73 65 9 143 86 54 152 40 76 155
6 157 86 18 100 59 76 7 69 133 18
7 49 54 102 50 40 6 120 19 8 6
8 68 119 50 85 52 156 93 89 146 99
9 15 87 104 74 32 152 70 146 145 122
10 48 8 74 40 68 111 27 143 57 162
11 104 11 87 115 36 101 25 134 26 25
12 99 67 125 79 135 85 136 70 101 156
13 142 59 158 52 156 3 66 38 131 147
14 136 139 20 159 39 37 110 61 31 10
15 41 43 57 69 96 30 67 20 20 134
16 115 148 151 108 50 66 50 142 6 79
17 151 56 54 49 27 51 53 54 63 44
18 77 15 27 36 47 162 26 98 25 157
19 126 16 90 136 154 124 132 56 70 4
20 108 82 93 87 132 95 89 151 85 20
21 95 39 161 98 138 138 44 111 71 67
22 60 37 44 21 62 120 76 113 118 153
23 36 6 16 54 120 69 141 108 84 97
24 1 42 86 109 12 134 84 7 41 148
25 74 10 103 119 157 136 73 52 58 136
|
|
label
|
Table 3
|
|
caption
|
20 sampled batches—S11 to S20.
|
|
p
|
20 sampled batches—S11 to S20.
|
|
table
|
Order S11 S12 S13 S14 S15 S16 S17 S18 S19 S20
1 76 91 83 59 64 119 129 154 15 37
2 23 124 53 63 46 123 8 82 30 55
3 29 151 126 24 143 137 6 35 43 119
4 12 126 129 55 53 108 122 4 148 163
5 73 65 9 143 86 54 152 40 76 155
6 157 86 18 100 59 76 7 69 133 18
7 49 54 102 50 40 6 120 19 8 6
8 68 119 50 85 52 156 93 89 146 99
9 15 87 104 74 32 152 70 146 145 122
10 48 8 74 40 68 111 27 143 57 162
11 104 11 87 115 36 101 25 134 26 25
12 99 67 125 79 135 85 136 70 101 156
13 142 59 158 52 156 3 66 38 131 147
14 136 139 20 159 39 37 110 61 31 10
15 41 43 57 69 96 30 67 20 20 134
16 115 148 151 108 50 66 50 142 6 79
17 151 56 54 49 27 51 53 54 63 44
18 77 15 27 36 47 162 26 98 25 157
19 126 16 90 136 154 124 132 56 70 4
20 108 82 93 87 132 95 89 151 85 20
21 95 39 161 98 138 138 44 111 71 67
22 60 37 44 21 62 120 76 113 118 153
23 36 6 16 54 120 69 141 108 84 97
24 1 42 86 109 12 134 84 7 41 148
25 74 10 103 119 157 136 73 52 58 136
|
|
tr
|
Order S11 S12 S13 S14 S15 S16 S17 S18 S19 S20
|
|
th
|
Order
|
|
th
|
S11
|
|
th
|
S12
|
|
th
|
S13
|
|
th
|
S14
|
|
th
|
S15
|
|
th
|
S16
|
|
th
|
S17
|
|
th
|
S18
|
|
th
|
S19
|
|
th
|
S20
|
|
tr
|
1 76 91 83 59 64 119 129 154 15 37
|
|
td
|
1
|
|
td
|
76
|
|
td
|
91
|
|
td
|
83
|
|
td
|
59
|
|
td
|
64
|
|
td
|
119
|
|
td
|
129
|
|
td
|
154
|
|
td
|
15
|
|
td
|
37
|
|
tr
|
2 23 124 53 63 46 123 8 82 30 55
|
|
td
|
2
|
|
td
|
23
|
|
td
|
124
|
|
td
|
53
|
|
td
|
63
|
|
td
|
46
|
|
td
|
123
|
|
td
|
8
|
|
td
|
82
|
|
td
|
30
|
|
td
|
55
|
|
tr
|
3 29 151 126 24 143 137 6 35 43 119
|
|
td
|
3
|
|
td
|
29
|
|
td
|
151
|
|
td
|
126
|
|
td
|
24
|
|
td
|
143
|
|
td
|
137
|
|
td
|
6
|
|
td
|
35
|
|
td
|
43
|
|
td
|
119
|
|
tr
|
4 12 126 129 55 53 108 122 4 148 163
|
|
td
|
4
|
|
td
|
12
|
|
td
|
126
|
|
td
|
129
|
|
td
|
55
|
|
td
|
53
|
|
td
|
108
|
|
td
|
122
|
|
td
|
4
|
|
td
|
148
|
|
td
|
163
|
|
tr
|
5 73 65 9 143 86 54 152 40 76 155
|
|
td
|
5
|
|
td
|
73
|
|
td
|
65
|
|
td
|
9
|
|
td
|
143
|
|
td
|
86
|
|
td
|
54
|
|
td
|
152
|
|
td
|
40
|
|
td
|
76
|
|
td
|
155
|
|
tr
|
6 157 86 18 100 59 76 7 69 133 18
|
|
td
|
6
|
|
td
|
157
|
|
td
|
86
|
|
td
|
18
|
|
td
|
100
|
|
td
|
59
|
|
td
|
76
|
|
td
|
7
|
|
td
|
69
|
|
td
|
133
|
|
td
|
18
|
|
tr
|
7 49 54 102 50 40 6 120 19 8 6
|
|
td
|
7
|
|
td
|
49
|
|
td
|
54
|
|
td
|
102
|
|
td
|
50
|
|
td
|
40
|
|
td
|
6
|
|
td
|
120
|
|
td
|
19
|
|
td
|
8
|
|
td
|
6
|
|
tr
|
8 68 119 50 85 52 156 93 89 146 99
|
|
td
|
8
|
|
td
|
68
|
|
td
|
119
|
|
td
|
50
|
|
td
|
85
|
|
td
|
52
|
|
td
|
156
|
|
td
|
93
|
|
td
|
89
|
|
td
|
146
|
|
td
|
99
|
|
tr
|
9 15 87 104 74 32 152 70 146 145 122
|
|
td
|
9
|
|
td
|
15
|
|
td
|
87
|
|
td
|
104
|
|
td
|
74
|
|
td
|
32
|
|
td
|
152
|
|
td
|
70
|
|
td
|
146
|
|
td
|
145
|
|
td
|
122
|
|
tr
|
10 48 8 74 40 68 111 27 143 57 162
|
|
td
|
10
|
|
td
|
48
|
|
td
|
8
|
|
td
|
74
|
|
td
|
40
|
|
td
|
68
|
|
td
|
111
|
|
td
|
27
|
|
td
|
143
|
|
td
|
57
|
|
td
|
162
|
|
tr
|
11 104 11 87 115 36 101 25 134 26 25
|
|
td
|
11
|
|
td
|
104
|
|
td
|
11
|
|
td
|
87
|
|
td
|
115
|
|
td
|
36
|
|
td
|
101
|
|
td
|
25
|
|
td
|
134
|
|
td
|
26
|
|
td
|
25
|
|
tr
|
12 99 67 125 79 135 85 136 70 101 156
|
|
td
|
12
|
|
td
|
99
|
|
td
|
67
|
|
td
|
125
|
|
td
|
79
|
|
td
|
135
|
|
td
|
85
|
|
td
|
136
|
|
td
|
70
|
|
td
|
101
|
|
td
|
156
|
|
tr
|
13 142 59 158 52 156 3 66 38 131 147
|
|
td
|
13
|
|
td
|
142
|
|
td
|
59
|
|
td
|
158
|
|
td
|
52
|
|
td
|
156
|
|
td
|
3
|
|
td
|
66
|
|
td
|
38
|
|
td
|
131
|
|
td
|
147
|
|
tr
|
14 136 139 20 159 39 37 110 61 31 10
|
|
td
|
14
|
|
td
|
136
|
|
td
|
139
|
|
td
|
20
|
|
td
|
159
|
|
td
|
39
|
|
td
|
37
|
|
td
|
110
|
|
td
|
61
|
|
td
|
31
|
|
td
|
10
|
|
tr
|
15 41 43 57 69 96 30 67 20 20 134
|
|
td
|
15
|
|
td
|
41
|
|
td
|
43
|
|
td
|
57
|
|
td
|
69
|
|
td
|
96
|
|
td
|
30
|
|
td
|
67
|
|
td
|
20
|
|
td
|
20
|
|
td
|
134
|
|
tr
|
16 115 148 151 108 50 66 50 142 6 79
|
|
td
|
16
|
|
td
|
115
|
|
td
|
148
|
|
td
|
151
|
|
td
|
108
|
|
td
|
50
|
|
td
|
66
|
|
td
|
50
|
|
td
|
142
|
|
td
|
6
|
|
td
|
79
|
|
tr
|
17 151 56 54 49 27 51 53 54 63 44
|
|
td
|
17
|
|
td
|
151
|
|
td
|
56
|
|
td
|
54
|
|
td
|
49
|
|
td
|
27
|
|
td
|
51
|
|
td
|
53
|
|
td
|
54
|
|
td
|
63
|
|
td
|
44
|
|
tr
|
18 77 15 27 36 47 162 26 98 25 157
|
|
td
|
18
|
|
td
|
77
|
|
td
|
15
|
|
td
|
27
|
|
td
|
36
|
|
td
|
47
|
|
td
|
162
|
|
td
|
26
|
|
td
|
98
|
|
td
|
25
|
|
td
|
157
|
|
tr
|
19 126 16 90 136 154 124 132 56 70 4
|
|
td
|
19
|
|
td
|
126
|
|
td
|
16
|
|
td
|
90
|
|
td
|
136
|
|
td
|
154
|
|
td
|
124
|
|
td
|
132
|
|
td
|
56
|
|
td
|
70
|
|
td
|
4
|
|
tr
|
20 108 82 93 87 132 95 89 151 85 20
|
|
td
|
20
|
|
td
|
108
|
|
td
|
82
|
|
td
|
93
|
|
td
|
87
|
|
td
|
132
|
|
td
|
95
|
|
td
|
89
|
|
td
|
151
|
|
td
|
85
|
|
td
|
20
|
|
tr
|
21 95 39 161 98 138 138 44 111 71 67
|
|
td
|
21
|
|
td
|
95
|
|
td
|
39
|
|
td
|
161
|
|
td
|
98
|
|
td
|
138
|
|
td
|
138
|
|
td
|
44
|
|
td
|
111
|
|
td
|
71
|
|
td
|
67
|
|
tr
|
22 60 37 44 21 62 120 76 113 118 153
|
|
td
|
22
|
|
td
|
60
|
|
td
|
37
|
|
td
|
44
|
|
td
|
21
|
|
td
|
62
|
|
td
|
120
|
|
td
|
76
|
|
td
|
113
|
|
td
|
118
|
|
td
|
153
|
|
tr
|
23 36 6 16 54 120 69 141 108 84 97
|
|
td
|
23
|
|
td
|
36
|
|
td
|
6
|
|
td
|
16
|
|
td
|
54
|
|
td
|
120
|
|
td
|
69
|
|
td
|
141
|
|
td
|
108
|
|
td
|
84
|
|
td
|
97
|
|
tr
|
24 1 42 86 109 12 134 84 7 41 148
|
|
td
|
24
|
|
td
|
1
|
|
td
|
42
|
|
td
|
86
|
|
td
|
109
|
|
td
|
12
|
|
td
|
134
|
|
td
|
84
|
|
td
|
7
|
|
td
|
41
|
|
td
|
148
|
|
tr
|
25 74 10 103 119 157 136 73 52 58 136
|
|
td
|
25
|
|
td
|
74
|
|
td
|
10
|
|
td
|
103
|
|
td
|
119
|
|
td
|
157
|
|
td
|
136
|
|
td
|
73
|
|
td
|
52
|
|
td
|
58
|
|
td
|
136
|
|
table-wrap
|
Table 4 Sample one for economic freedom.
S1 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12
68 64.8 45.7 47.5 79.9 34.5 83.6 60.2 64.6 79.9 86.4 80 70
141 33.7 20.8 25.5 86.1 94.5 12.4 53.5 60 77 52 5 20
21 57.3 46.7 45.6 70.4 54.6 4.6 60.5 49.5 77.2 67.8 60 50
129 64.6 72.3 49.6 99.8 61.8 19.3 66.6 63.3 81 75.4 45 50
127 69.8 62.6 41.8 76.9 80.6 83.8 76.7 66.4 82 73.2 65 40
99 58.3 34.7 36.7 76.1 79.3 87.5 67 58.4 70.9 87.6 75 60
89 86.4 74.4 90.3 64.1 45.4 99 66.8 45.3 76.4 86.4 95 80
2 57.1 33 38.8 85.9 74.6 86.3 65.7 52.1 81.2 88.4 70 70
128 41 26.5 37.4 88.3 77.1 73 64.8 43.4 68.1 64.2 60 30
108 93.3 79.1 93.9 71 57.8 98.3 90.4 86.7 87 92.2 80 80
112 62.5 42.7 42.2 91.5 71 87.7 80.6 67 77.7 86.2 65 60
92 43.1 42.1 24.8 79 71.7 23.6 41.9 62.8 69.1 75.4 50 50
8 75.8 62.6 53.3 91.5 82.1 79.3 82.5 60.2 73.8 88.2 80 70
18 20.1 11.2 23.1 86.3 54.2 14.2 58.3 52.9 69.9 67.8 15 40
148 59.5 48 43.4 80.7 85.9 96.4 83 63.7 74 83 55 60
124 72.5 56.1 55.1 90.3 70.4 85.6 58.6 63 78.1 86.4 70 50
1 48.3 30 24.8 91.4 79.2 99.9 54.7 61.6 81 66 10 10
32 69.9 61.1 73.4 76.4 80.8 90.5 75 64.7 85.2 89 85 70
76 62.1 50.5 46.8 80 74.8 80.2 77.7 74 77.7 68.4 80 50
14 84.5 62.5 80.2 46.7 17.2 77 75.2 61.1 80.5 86.4 85 70
41 86.3 84.6 93 42 19.7 97.7 88.7 86.2 84.6 86.4 90 80
137 58.4 38 46.6 63.7 67.4 64 62 58.8 75.9 75.8 45 50
85 44.6 30.8 25 90.8 72.5 0 45.6 47.8 75.6 77.4 60 50
78 64.8 54.6 49.6 91.8 73.5 55.9 60.1 52.5 77.6 81.2 70 60
52 36.5 45.1 29.4 77.4 90.8 79.2 48.6 57.6 62.7 60.8 35 20
|
|
label
|
Table 4
|
|
caption
|
Sample one for economic freedom.
|
|
p
|
Sample one for economic freedom.
|
|
table
|
S1 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12
68 64.8 45.7 47.5 79.9 34.5 83.6 60.2 64.6 79.9 86.4 80 70
141 33.7 20.8 25.5 86.1 94.5 12.4 53.5 60 77 52 5 20
21 57.3 46.7 45.6 70.4 54.6 4.6 60.5 49.5 77.2 67.8 60 50
129 64.6 72.3 49.6 99.8 61.8 19.3 66.6 63.3 81 75.4 45 50
127 69.8 62.6 41.8 76.9 80.6 83.8 76.7 66.4 82 73.2 65 40
99 58.3 34.7 36.7 76.1 79.3 87.5 67 58.4 70.9 87.6 75 60
89 86.4 74.4 90.3 64.1 45.4 99 66.8 45.3 76.4 86.4 95 80
2 57.1 33 38.8 85.9 74.6 86.3 65.7 52.1 81.2 88.4 70 70
128 41 26.5 37.4 88.3 77.1 73 64.8 43.4 68.1 64.2 60 30
108 93.3 79.1 93.9 71 57.8 98.3 90.4 86.7 87 92.2 80 80
112 62.5 42.7 42.2 91.5 71 87.7 80.6 67 77.7 86.2 65 60
92 43.1 42.1 24.8 79 71.7 23.6 41.9 62.8 69.1 75.4 50 50
8 75.8 62.6 53.3 91.5 82.1 79.3 82.5 60.2 73.8 88.2 80 70
18 20.1 11.2 23.1 86.3 54.2 14.2 58.3 52.9 69.9 67.8 15 40
148 59.5 48 43.4 80.7 85.9 96.4 83 63.7 74 83 55 60
124 72.5 56.1 55.1 90.3 70.4 85.6 58.6 63 78.1 86.4 70 50
1 48.3 30 24.8 91.4 79.2 99.9 54.7 61.6 81 66 10 10
32 69.9 61.1 73.4 76.4 80.8 90.5 75 64.7 85.2 89 85 70
76 62.1 50.5 46.8 80 74.8 80.2 77.7 74 77.7 68.4 80 50
14 84.5 62.5 80.2 46.7 17.2 77 75.2 61.1 80.5 86.4 85 70
41 86.3 84.6 93 42 19.7 97.7 88.7 86.2 84.6 86.4 90 80
137 58.4 38 46.6 63.7 67.4 64 62 58.8 75.9 75.8 45 50
85 44.6 30.8 25 90.8 72.5 0 45.6 47.8 75.6 77.4 60 50
78 64.8 54.6 49.6 91.8 73.5 55.9 60.1 52.5 77.6 81.2 70 60
52 36.5 45.1 29.4 77.4 90.8 79.2 48.6 57.6 62.7 60.8 35 20
|
|
tr
|
S1 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12
|
|
th
|
S1
|
|
th
|
A1
|
|
th
|
A2
|
|
th
|
A3
|
|
th
|
A4
|
|
th
|
A5
|
|
th
|
A6
|
|
th
|
A7
|
|
th
|
A8
|
|
th
|
A9
|
|
th
|
A10
|
|
th
|
A11
|
|
th
|
A12
|
|
tr
|
68 64.8 45.7 47.5 79.9 34.5 83.6 60.2 64.6 79.9 86.4 80 70
|
|
td
|
68
|
|
td
|
64.8
|
|
td
|
45.7
|
|
td
|
47.5
|
|
td
|
79.9
|
|
td
|
34.5
|
|
td
|
83.6
|
|
td
|
60.2
|
|
td
|
64.6
|
|
td
|
79.9
|
|
td
|
86.4
|
|
td
|
80
|
|
td
|
70
|
|
tr
|
141 33.7 20.8 25.5 86.1 94.5 12.4 53.5 60 77 52 5 20
|
|
td
|
141
|
|
td
|
33.7
|
|
td
|
20.8
|
|
td
|
25.5
|
|
td
|
86.1
|
|
td
|
94.5
|
|
td
|
12.4
|
|
td
|
53.5
|
|
td
|
60
|
|
td
|
77
|
|
td
|
52
|
|
td
|
5
|
|
td
|
20
|
|
tr
|
21 57.3 46.7 45.6 70.4 54.6 4.6 60.5 49.5 77.2 67.8 60 50
|
|
td
|
21
|
|
td
|
57.3
|
|
td
|
46.7
|
|
td
|
45.6
|
|
td
|
70.4
|
|
td
|
54.6
|
|
td
|
4.6
|
|
td
|
60.5
|
|
td
|
49.5
|
|
td
|
77.2
|
|
td
|
67.8
|
|
td
|
60
|
|
td
|
50
|
|
tr
|
129 64.6 72.3 49.6 99.8 61.8 19.3 66.6 63.3 81 75.4 45 50
|
|
td
|
129
|
|
td
|
64.6
|
|
td
|
72.3
|
|
td
|
49.6
|
|
td
|
99.8
|
|
td
|
61.8
|
|
td
|
19.3
|
|
td
|
66.6
|
|
td
|
63.3
|
|
td
|
81
|
|
td
|
75.4
|
|
td
|
45
|
|
td
|
50
|
|
tr
|
127 69.8 62.6 41.8 76.9 80.6 83.8 76.7 66.4 82 73.2 65 40
|
|
td
|
127
|
|
td
|
69.8
|
|
td
|
62.6
|
|
td
|
41.8
|
|
td
|
76.9
|
|
td
|
80.6
|
|
td
|
83.8
|
|
td
|
76.7
|
|
td
|
66.4
|
|
td
|
82
|
|
td
|
73.2
|
|
td
|
65
|
|
td
|
40
|
|
tr
|
99 58.3 34.7 36.7 76.1 79.3 87.5 67 58.4 70.9 87.6 75 60
|
|
td
|
99
|
|
td
|
58.3
|
|
td
|
34.7
|
|
td
|
36.7
|
|
td
|
76.1
|
|
td
|
79.3
|
|
td
|
87.5
|
|
td
|
67
|
|
td
|
58.4
|
|
td
|
70.9
|
|
td
|
87.6
|
|
td
|
75
|
|
td
|
60
|
|
tr
|
89 86.4 74.4 90.3 64.1 45.4 99 66.8 45.3 76.4 86.4 95 80
|
|
td
|
89
|
|
td
|
86.4
|
|
td
|
74.4
|
|
td
|
90.3
|
|
td
|
64.1
|
|
td
|
45.4
|
|
td
|
99
|
|
td
|
66.8
|
|
td
|
45.3
|
|
td
|
76.4
|
|
td
|
86.4
|
|
td
|
95
|
|
td
|
80
|
|
tr
|
2 57.1 33 38.8 85.9 74.6 86.3 65.7 52.1 81.2 88.4 70 70
|
|
td
|
2
|
|
td
|
57.1
|
|
td
|
33
|
|
td
|
38.8
|
|
td
|
85.9
|
|
td
|
74.6
|
|
td
|
86.3
|
|
td
|
65.7
|
|
td
|
52.1
|
|
td
|
81.2
|
|
td
|
88.4
|
|
td
|
70
|
|
td
|
70
|
|
tr
|
128 41 26.5 37.4 88.3 77.1 73 64.8 43.4 68.1 64.2 60 30
|
|
td
|
128
|
|
td
|
41
|
|
td
|
26.5
|
|
td
|
37.4
|
|
td
|
88.3
|
|
td
|
77.1
|
|
td
|
73
|
|
td
|
64.8
|
|
td
|
43.4
|
|
td
|
68.1
|
|
td
|
64.2
|
|
td
|
60
|
|
td
|
30
|
|
tr
|
108 93.3 79.1 93.9 71 57.8 98.3 90.4 86.7 87 92.2 80 80
|
|
td
|
108
|
|
td
|
93.3
|
|
td
|
79.1
|
|
td
|
93.9
|
|
td
|
71
|
|
td
|
57.8
|
|
td
|
98.3
|
|
td
|
90.4
|
|
td
|
86.7
|
|
td
|
87
|
|
td
|
92.2
|
|
td
|
80
|
|
td
|
80
|
|
tr
|
112 62.5 42.7 42.2 91.5 71 87.7 80.6 67 77.7 86.2 65 60
|
|
td
|
112
|
|
td
|
62.5
|
|
td
|
42.7
|
|
td
|
42.2
|
|
td
|
91.5
|
|
td
|
71
|
|
td
|
87.7
|
|
td
|
80.6
|
|
td
|
67
|
|
td
|
77.7
|
|
td
|
86.2
|
|
td
|
65
|
|
td
|
60
|
|
tr
|
92 43.1 42.1 24.8 79 71.7 23.6 41.9 62.8 69.1 75.4 50 50
|
|
td
|
92
|
|
td
|
43.1
|
|
td
|
42.1
|
|
td
|
24.8
|
|
td
|
79
|
|
td
|
71.7
|
|
td
|
23.6
|
|
td
|
41.9
|
|
td
|
62.8
|
|
td
|
69.1
|
|
td
|
75.4
|
|
td
|
50
|
|
td
|
50
|
|
tr
|
8 75.8 62.6 53.3 91.5 82.1 79.3 82.5 60.2 73.8 88.2 80 70
|
|
td
|
8
|
|
td
|
75.8
|
|
td
|
62.6
|
|
td
|
53.3
|
|
td
|
91.5
|
|
td
|
82.1
|
|
td
|
79.3
|
|
td
|
82.5
|
|
td
|
60.2
|
|
td
|
73.8
|
|
td
|
88.2
|
|
td
|
80
|
|
td
|
70
|
|
tr
|
18 20.1 11.2 23.1 86.3 54.2 14.2 58.3 52.9 69.9 67.8 15 40
|
|
td
|
18
|
|
td
|
20.1
|
|
td
|
11.2
|
|
td
|
23.1
|
|
td
|
86.3
|
|
td
|
54.2
|
|
td
|
14.2
|
|
td
|
58.3
|
|
td
|
52.9
|
|
td
|
69.9
|
|
td
|
67.8
|
|
td
|
15
|
|
td
|
40
|
|
tr
|
148 59.5 48 43.4 80.7 85.9 96.4 83 63.7 74 83 55 60
|
|
td
|
148
|
|
td
|
59.5
|
|
td
|
48
|
|
td
|
43.4
|
|
td
|
80.7
|
|
td
|
85.9
|
|
td
|
96.4
|
|
td
|
83
|
|
td
|
63.7
|
|
td
|
74
|
|
td
|
83
|
|
td
|
55
|
|
td
|
60
|
|
tr
|
124 72.5 56.1 55.1 90.3 70.4 85.6 58.6 63 78.1 86.4 70 50
|
|
td
|
124
|
|
td
|
72.5
|
|
td
|
56.1
|
|
td
|
55.1
|
|
td
|
90.3
|
|
td
|
70.4
|
|
td
|
85.6
|
|
td
|
58.6
|
|
td
|
63
|
|
td
|
78.1
|
|
td
|
86.4
|
|
td
|
70
|
|
td
|
50
|
|
tr
|
1 48.3 30 24.8 91.4 79.2 99.9 54.7 61.6 81 66 10 10
|
|
td
|
1
|
|
td
|
48.3
|
|
td
|
30
|
|
td
|
24.8
|
|
td
|
91.4
|
|
td
|
79.2
|
|
td
|
99.9
|
|
td
|
54.7
|
|
td
|
61.6
|
|
td
|
81
|
|
td
|
66
|
|
td
|
10
|
|
td
|
10
|
|
tr
|
32 69.9 61.1 73.4 76.4 80.8 90.5 75 64.7 85.2 89 85 70
|
|
td
|
32
|
|
td
|
69.9
|
|
td
|
61.1
|
|
td
|
73.4
|
|
td
|
76.4
|
|
td
|
80.8
|
|
td
|
90.5
|
|
td
|
75
|
|
td
|
64.7
|
|
td
|
85.2
|
|
td
|
89
|
|
td
|
85
|
|
td
|
70
|
|
tr
|
76 62.1 50.5 46.8 80 74.8 80.2 77.7 74 77.7 68.4 80 50
|
|
td
|
76
|
|
td
|
62.1
|
|
td
|
50.5
|
|
td
|
46.8
|
|
td
|
80
|
|
td
|
74.8
|
|
td
|
80.2
|
|
td
|
77.7
|
|
td
|
74
|
|
td
|
77.7
|
|
td
|
68.4
|
|
td
|
80
|
|
td
|
50
|
|
tr
|
14 84.5 62.5 80.2 46.7 17.2 77 75.2 61.1 80.5 86.4 85 70
|
|
td
|
14
|
|
td
|
84.5
|
|
td
|
62.5
|
|
td
|
80.2
|
|
td
|
46.7
|
|
td
|
17.2
|
|
td
|
77
|
|
td
|
75.2
|
|
td
|
61.1
|
|
td
|
80.5
|
|
td
|
86.4
|
|
td
|
85
|
|
td
|
70
|
|
tr
|
41 86.3 84.6 93 42 19.7 97.7 88.7 86.2 84.6 86.4 90 80
|
|
td
|
41
|
|
td
|
86.3
|
|
td
|
84.6
|
|
td
|
93
|
|
td
|
42
|
|
td
|
19.7
|
|
td
|
97.7
|
|
td
|
88.7
|
|
td
|
86.2
|
|
td
|
84.6
|
|
td
|
86.4
|
|
td
|
90
|
|
td
|
80
|
|
tr
|
137 58.4 38 46.6 63.7 67.4 64 62 58.8 75.9 75.8 45 50
|
|
td
|
137
|
|
td
|
58.4
|
|
td
|
38
|
|
td
|
46.6
|
|
td
|
63.7
|
|
td
|
67.4
|
|
td
|
64
|
|
td
|
62
|
|
td
|
58.8
|
|
td
|
75.9
|
|
td
|
75.8
|
|
td
|
45
|
|
td
|
50
|
|
tr
|
85 44.6 30.8 25 90.8 72.5 0 45.6 47.8 75.6 77.4 60 50
|
|
td
|
85
|
|
td
|
44.6
|
|
td
|
30.8
|
|
td
|
25
|
|
td
|
90.8
|
|
td
|
72.5
|
|
td
|
0
|
|
td
|
45.6
|
|
td
|
47.8
|
|
td
|
75.6
|
|
td
|
77.4
|
|
td
|
60
|
|
td
|
50
|
|
tr
|
78 64.8 54.6 49.6 91.8 73.5 55.9 60.1 52.5 77.6 81.2 70 60
|
|
td
|
78
|
|
td
|
64.8
|
|
td
|
54.6
|
|
td
|
49.6
|
|
td
|
91.8
|
|
td
|
73.5
|
|
td
|
55.9
|
|
td
|
60.1
|
|
td
|
52.5
|
|
td
|
77.6
|
|
td
|
81.2
|
|
td
|
70
|
|
td
|
60
|
|
tr
|
52 36.5 45.1 29.4 77.4 90.8 79.2 48.6 57.6 62.7 60.8 35 20
|
|
td
|
52
|
|
td
|
36.5
|
|
td
|
45.1
|
|
td
|
29.4
|
|
td
|
77.4
|
|
td
|
90.8
|
|
td
|
79.2
|
|
td
|
48.6
|
|
td
|
57.6
|
|
td
|
62.7
|
|
td
|
60.8
|
|
td
|
35
|
|
td
|
20
|
|
table-wrap
|
Table 5 Sample one for COVID-19.
S1 ℂ B 1 B 2 B 3 B 4
68 Hungary 4127 578 2663 9660521
141 Sudan 9257 572 4014 43828543
21 Brazil 1280054 56109 697526 212541690
129 Senegal 6354 98 4193 16734279
127 Sao Tome and Principe 712 13 219 219087
99 Mexico 208392 25779 120562 128914507
89 Luxembourg 4173 110 3968 625810
2 Albania 2269 51 1298 2877821
128 Saudi Arabia 174577 1474 120471 34805142
108 New Zealand 1520 22 1484 5002100
112 North Macedonia 5758 268 2206 2083375
92 Malawi 1005 13 260 19119281
98 Mauritius 341 10 326 1271749
18 Bolivia 28503 913 7338 11670618
148 Thailand 3162 58 3040 69798329
124 Romania 25697 1579 18181 19238321
1 Afghanistan 30451 683 10306 38910996
32 Chile 263360 5068 223431 19114153
76 Jamaica 686 10 539 2961033
14 Belgium 61106 9731 16918 11589102
41 Denmark 12675 604 11508 5792000
137 South Africa 124590 2340 64111 59297807
85 Lebanon 1697 33 1144 6825627
78 Jordan 1104 9 830 10201800
52 Ethiopia 5425 89 1688 114903773
|
|
label
|
Table 5
|
|
caption
|
Sample one for COVID-19.
|
|
p
|
Sample one for COVID-19.
|
|
table
|
S1 ℂ B 1 B 2 B 3 B 4
68 Hungary 4127 578 2663 9660521
141 Sudan 9257 572 4014 43828543
21 Brazil 1280054 56109 697526 212541690
129 Senegal 6354 98 4193 16734279
127 Sao Tome and Principe 712 13 219 219087
99 Mexico 208392 25779 120562 128914507
89 Luxembourg 4173 110 3968 625810
2 Albania 2269 51 1298 2877821
128 Saudi Arabia 174577 1474 120471 34805142
108 New Zealand 1520 22 1484 5002100
112 North Macedonia 5758 268 2206 2083375
92 Malawi 1005 13 260 19119281
98 Mauritius 341 10 326 1271749
18 Bolivia 28503 913 7338 11670618
148 Thailand 3162 58 3040 69798329
124 Romania 25697 1579 18181 19238321
1 Afghanistan 30451 683 10306 38910996
32 Chile 263360 5068 223431 19114153
76 Jamaica 686 10 539 2961033
14 Belgium 61106 9731 16918 11589102
41 Denmark 12675 604 11508 5792000
137 South Africa 124590 2340 64111 59297807
85 Lebanon 1697 33 1144 6825627
78 Jordan 1104 9 830 10201800
52 Ethiopia 5425 89 1688 114903773
|
|
tr
|
S1 ℂ B 1 B 2 B 3 B 4
|
|
th
|
S1
|
|
th
|
ℂ
|
|
th
|
B 1
|
|
th
|
B 2
|
|
th
|
B 3
|
|
th
|
B 4
|
|
tr
|
68 Hungary 4127 578 2663 9660521
|
|
td
|
68
|
|
td
|
Hungary
|
|
td
|
4127
|
|
td
|
578
|
|
td
|
2663
|
|
td
|
9660521
|
|
tr
|
141 Sudan 9257 572 4014 43828543
|
|
td
|
141
|
|
td
|
Sudan
|
|
td
|
9257
|
|
td
|
572
|
|
td
|
4014
|
|
td
|
43828543
|
|
tr
|
21 Brazil 1280054 56109 697526 212541690
|
|
td
|
21
|
|
td
|
Brazil
|
|
td
|
1280054
|
|
td
|
56109
|
|
td
|
697526
|
|
td
|
212541690
|
|
tr
|
129 Senegal 6354 98 4193 16734279
|
|
td
|
129
|
|
td
|
Senegal
|
|
td
|
6354
|
|
td
|
98
|
|
td
|
4193
|
|
td
|
16734279
|
|
tr
|
127 Sao Tome and Principe 712 13 219 219087
|
|
td
|
127
|
|
td
|
Sao Tome and Principe
|
|
td
|
712
|
|
td
|
13
|
|
td
|
219
|
|
td
|
219087
|
|
tr
|
99 Mexico 208392 25779 120562 128914507
|
|
td
|
99
|
|
td
|
Mexico
|
|
td
|
208392
|
|
td
|
25779
|
|
td
|
120562
|
|
td
|
128914507
|
|
tr
|
89 Luxembourg 4173 110 3968 625810
|
|
td
|
89
|
|
td
|
Luxembourg
|
|
td
|
4173
|
|
td
|
110
|
|
td
|
3968
|
|
td
|
625810
|
|
tr
|
2 Albania 2269 51 1298 2877821
|
|
td
|
2
|
|
td
|
Albania
|
|
td
|
2269
|
|
td
|
51
|
|
td
|
1298
|
|
td
|
2877821
|
|
tr
|
128 Saudi Arabia 174577 1474 120471 34805142
|
|
td
|
128
|
|
td
|
Saudi Arabia
|
|
td
|
174577
|
|
td
|
1474
|
|
td
|
120471
|
|
td
|
34805142
|
|
tr
|
108 New Zealand 1520 22 1484 5002100
|
|
td
|
108
|
|
td
|
New Zealand
|
|
td
|
1520
|
|
td
|
22
|
|
td
|
1484
|
|
td
|
5002100
|
|
tr
|
112 North Macedonia 5758 268 2206 2083375
|
|
td
|
112
|
|
td
|
North Macedonia
|
|
td
|
5758
|
|
td
|
268
|
|
td
|
2206
|
|
td
|
2083375
|
|
tr
|
92 Malawi 1005 13 260 19119281
|
|
td
|
92
|
|
td
|
Malawi
|
|
td
|
1005
|
|
td
|
13
|
|
td
|
260
|
|
td
|
19119281
|
|
tr
|
98 Mauritius 341 10 326 1271749
|
|
td
|
98
|
|
td
|
Mauritius
|
|
td
|
341
|
|
td
|
10
|
|
td
|
326
|
|
td
|
1271749
|
|
tr
|
18 Bolivia 28503 913 7338 11670618
|
|
td
|
18
|
|
td
|
Bolivia
|
|
td
|
28503
|
|
td
|
913
|
|
td
|
7338
|
|
td
|
11670618
|
|
tr
|
148 Thailand 3162 58 3040 69798329
|
|
td
|
148
|
|
td
|
Thailand
|
|
td
|
3162
|
|
td
|
58
|
|
td
|
3040
|
|
td
|
69798329
|
|
tr
|
124 Romania 25697 1579 18181 19238321
|
|
td
|
124
|
|
td
|
Romania
|
|
td
|
25697
|
|
td
|
1579
|
|
td
|
18181
|
|
td
|
19238321
|
|
tr
|
1 Afghanistan 30451 683 10306 38910996
|
|
td
|
1
|
|
td
|
Afghanistan
|
|
td
|
30451
|
|
td
|
683
|
|
td
|
10306
|
|
td
|
38910996
|
|
tr
|
32 Chile 263360 5068 223431 19114153
|
|
td
|
32
|
|
td
|
Chile
|
|
td
|
263360
|
|
td
|
5068
|
|
td
|
223431
|
|
td
|
19114153
|
|
tr
|
76 Jamaica 686 10 539 2961033
|
|
td
|
76
|
|
td
|
Jamaica
|
|
td
|
686
|
|
td
|
10
|
|
td
|
539
|
|
td
|
2961033
|
|
tr
|
14 Belgium 61106 9731 16918 11589102
|
|
td
|
14
|
|
td
|
Belgium
|
|
td
|
61106
|
|
td
|
9731
|
|
td
|
16918
|
|
td
|
11589102
|
|
tr
|
41 Denmark 12675 604 11508 5792000
|
|
td
|
41
|
|
td
|
Denmark
|
|
td
|
12675
|
|
td
|
604
|
|
td
|
11508
|
|
td
|
5792000
|
|
tr
|
137 South Africa 124590 2340 64111 59297807
|
|
td
|
137
|
|
td
|
South Africa
|
|
td
|
124590
|
|
td
|
2340
|
|
td
|
64111
|
|
td
|
59297807
|
|
tr
|
85 Lebanon 1697 33 1144 6825627
|
|
td
|
85
|
|
td
|
Lebanon
|
|
td
|
1697
|
|
td
|
33
|
|
td
|
1144
|
|
td
|
6825627
|
|
tr
|
78 Jordan 1104 9 830 10201800
|
|
td
|
78
|
|
td
|
Jordan
|
|
td
|
1104
|
|
td
|
9
|
|
td
|
830
|
|
td
|
10201800
|
|
tr
|
52 Ethiopia 5425 89 1688 114903773
|
|
td
|
52
|
|
td
|
Ethiopia
|
|
td
|
5425
|
|
td
|
89
|
|
td
|
1688
|
|
td
|
114903773
|
|
table-wrap
|
Table 6 Distance function for 20 samplings—S1 to S10.
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10
61.0 80.1 82.2 74.2 78.3 73.2 53.9 59.2 66.8 72.2
76.2 76.8 75.4 72.4 73.6 84.0 72.8 83.4 80.4 71.3
70.7 72.4 71.1 59.2 85.1 68.6 66.5 62.3 73.2 74.2
80.8 82.1 71.4 82.3 64.9 77.2 74.3 85.7 70.2 65.0
76.8 71.8 83.4 78.5 72.8 67.1 76.9 78.9 82.2 80.7
75.0 83.4 69.7 65.5 84.4 49.2 67.7 77.4 78.3 75.8
65.5 85.1 57.3 71.3 71.1 72.4 71.3 78.3 74.4 61.8
80.4 70.4 74.8 68.7 77.2 65.0 67.8 67.3 57.5 73.2
76.9 69.5 81.5 74.8 73.1 71.8 80.8 73.1 74.8 68.1
73.3 61.3 60.1 71.4 80.4 83.2 70.2 72.3 72.7 80.4
62.3 73.8 71.9 76.5 83.4 64.2 65.0 77.6 57.3 71.3
63.0 74.9 49.9 77.8 71.9 80.1 82.6 62.7 65.5 82.3
72.4 74.2 74.0 82.2 78.4 65.5 66.0 45.7 80.7 72.5
75.8 72.8 74.8 79.9 54.1 79.9 64.2 80.7 70.7 78.3
68.8 76.9 66.0 65.1 74.8 70.4 74.4 69.2 74.8 67.1
71.1 77.8 77.3 71.4 82.3 59.2 83.2 60.1 83.2 71.8
71.3 75.8 72.4 63.0 72.8 82.6 71.6 75.4 33.6 84.4
74.3 73.1 72.4 75.8 74.4 82.1 68.8 74.0 76.8 74.5
69.5 63.0 71.3 62.7 82.6 64.9 59.4 74.4 59.2 74.0
85.1 77.7 84.0 59.7 84.0 74.3 74.0 71.4 65.1 82.1
82.1 66.0 71.3 54.1 60.1 72.0 70.7 69.5 64.2 63.0
67.7 82.7 59.4 67.7 74.0 72.8 80.1 74.8 82.3 76.9
84.0 73.3 57.5 80.4 74.8 71.1 74.8 72.8 60.9 64.9
67.7 72.2 65.0 67.8 69.2 67.8 75.0 78.5 72.2 68.2
80.7 65.0 73.8 78.6 33.6 71.3 77.2 72.3 61.8 82.7
|
|
label
|
Table 6
|
|
caption
|
Distance function for 20 samplings—S1 to S10.
|
|
p
|
Distance function for 20 samplings—S1 to S10.
|
|
table
|
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10
61.0 80.1 82.2 74.2 78.3 73.2 53.9 59.2 66.8 72.2
76.2 76.8 75.4 72.4 73.6 84.0 72.8 83.4 80.4 71.3
70.7 72.4 71.1 59.2 85.1 68.6 66.5 62.3 73.2 74.2
80.8 82.1 71.4 82.3 64.9 77.2 74.3 85.7 70.2 65.0
76.8 71.8 83.4 78.5 72.8 67.1 76.9 78.9 82.2 80.7
75.0 83.4 69.7 65.5 84.4 49.2 67.7 77.4 78.3 75.8
65.5 85.1 57.3 71.3 71.1 72.4 71.3 78.3 74.4 61.8
80.4 70.4 74.8 68.7 77.2 65.0 67.8 67.3 57.5 73.2
76.9 69.5 81.5 74.8 73.1 71.8 80.8 73.1 74.8 68.1
73.3 61.3 60.1 71.4 80.4 83.2 70.2 72.3 72.7 80.4
62.3 73.8 71.9 76.5 83.4 64.2 65.0 77.6 57.3 71.3
63.0 74.9 49.9 77.8 71.9 80.1 82.6 62.7 65.5 82.3
72.4 74.2 74.0 82.2 78.4 65.5 66.0 45.7 80.7 72.5
75.8 72.8 74.8 79.9 54.1 79.9 64.2 80.7 70.7 78.3
68.8 76.9 66.0 65.1 74.8 70.4 74.4 69.2 74.8 67.1
71.1 77.8 77.3 71.4 82.3 59.2 83.2 60.1 83.2 71.8
71.3 75.8 72.4 63.0 72.8 82.6 71.6 75.4 33.6 84.4
74.3 73.1 72.4 75.8 74.4 82.1 68.8 74.0 76.8 74.5
69.5 63.0 71.3 62.7 82.6 64.9 59.4 74.4 59.2 74.0
85.1 77.7 84.0 59.7 84.0 74.3 74.0 71.4 65.1 82.1
82.1 66.0 71.3 54.1 60.1 72.0 70.7 69.5 64.2 63.0
67.7 82.7 59.4 67.7 74.0 72.8 80.1 74.8 82.3 76.9
84.0 73.3 57.5 80.4 74.8 71.1 74.8 72.8 60.9 64.9
67.7 72.2 65.0 67.8 69.2 67.8 75.0 78.5 72.2 68.2
80.7 65.0 73.8 78.6 33.6 71.3 77.2 72.3 61.8 82.7
|
|
tr
|
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10
|
|
th
|
S1
|
|
th
|
S2
|
|
th
|
S3
|
|
th
|
S4
|
|
th
|
S5
|
|
th
|
S6
|
|
th
|
S7
|
|
th
|
S8
|
|
th
|
S9
|
|
th
|
S10
|
|
tr
|
61.0 80.1 82.2 74.2 78.3 73.2 53.9 59.2 66.8 72.2
|
|
td
|
61.0
|
|
td
|
80.1
|
|
td
|
82.2
|
|
td
|
74.2
|
|
td
|
78.3
|
|
td
|
73.2
|
|
td
|
53.9
|
|
td
|
59.2
|
|
td
|
66.8
|
|
td
|
72.2
|
|
tr
|
76.2 76.8 75.4 72.4 73.6 84.0 72.8 83.4 80.4 71.3
|
|
td
|
76.2
|
|
td
|
76.8
|
|
td
|
75.4
|
|
td
|
72.4
|
|
td
|
73.6
|
|
td
|
84.0
|
|
td
|
72.8
|
|
td
|
83.4
|
|
td
|
80.4
|
|
td
|
71.3
|
|
tr
|
70.7 72.4 71.1 59.2 85.1 68.6 66.5 62.3 73.2 74.2
|
|
td
|
70.7
|
|
td
|
72.4
|
|
td
|
71.1
|
|
td
|
59.2
|
|
td
|
85.1
|
|
td
|
68.6
|
|
td
|
66.5
|
|
td
|
62.3
|
|
td
|
73.2
|
|
td
|
74.2
|
|
tr
|
80.8 82.1 71.4 82.3 64.9 77.2 74.3 85.7 70.2 65.0
|
|
td
|
80.8
|
|
td
|
82.1
|
|
td
|
71.4
|
|
td
|
82.3
|
|
td
|
64.9
|
|
td
|
77.2
|
|
td
|
74.3
|
|
td
|
85.7
|
|
td
|
70.2
|
|
td
|
65.0
|
|
tr
|
76.8 71.8 83.4 78.5 72.8 67.1 76.9 78.9 82.2 80.7
|
|
td
|
76.8
|
|
td
|
71.8
|
|
td
|
83.4
|
|
td
|
78.5
|
|
td
|
72.8
|
|
td
|
67.1
|
|
td
|
76.9
|
|
td
|
78.9
|
|
td
|
82.2
|
|
td
|
80.7
|
|
tr
|
75.0 83.4 69.7 65.5 84.4 49.2 67.7 77.4 78.3 75.8
|
|
td
|
75.0
|
|
td
|
83.4
|
|
td
|
69.7
|
|
td
|
65.5
|
|
td
|
84.4
|
|
td
|
49.2
|
|
td
|
67.7
|
|
td
|
77.4
|
|
td
|
78.3
|
|
td
|
75.8
|
|
tr
|
65.5 85.1 57.3 71.3 71.1 72.4 71.3 78.3 74.4 61.8
|
|
td
|
65.5
|
|
td
|
85.1
|
|
td
|
57.3
|
|
td
|
71.3
|
|
td
|
71.1
|
|
td
|
72.4
|
|
td
|
71.3
|
|
td
|
78.3
|
|
td
|
74.4
|
|
td
|
61.8
|
|
tr
|
80.4 70.4 74.8 68.7 77.2 65.0 67.8 67.3 57.5 73.2
|
|
td
|
80.4
|
|
td
|
70.4
|
|
td
|
74.8
|
|
td
|
68.7
|
|
td
|
77.2
|
|
td
|
65.0
|
|
td
|
67.8
|
|
td
|
67.3
|
|
td
|
57.5
|
|
td
|
73.2
|
|
tr
|
76.9 69.5 81.5 74.8 73.1 71.8 80.8 73.1 74.8 68.1
|
|
td
|
76.9
|
|
td
|
69.5
|
|
td
|
81.5
|
|
td
|
74.8
|
|
td
|
73.1
|
|
td
|
71.8
|
|
td
|
80.8
|
|
td
|
73.1
|
|
td
|
74.8
|
|
td
|
68.1
|
|
tr
|
73.3 61.3 60.1 71.4 80.4 83.2 70.2 72.3 72.7 80.4
|
|
td
|
73.3
|
|
td
|
61.3
|
|
td
|
60.1
|
|
td
|
71.4
|
|
td
|
80.4
|
|
td
|
83.2
|
|
td
|
70.2
|
|
td
|
72.3
|
|
td
|
72.7
|
|
td
|
80.4
|
|
tr
|
62.3 73.8 71.9 76.5 83.4 64.2 65.0 77.6 57.3 71.3
|
|
td
|
62.3
|
|
td
|
73.8
|
|
td
|
71.9
|
|
td
|
76.5
|
|
td
|
83.4
|
|
td
|
64.2
|
|
td
|
65.0
|
|
td
|
77.6
|
|
td
|
57.3
|
|
td
|
71.3
|
|
tr
|
63.0 74.9 49.9 77.8 71.9 80.1 82.6 62.7 65.5 82.3
|
|
td
|
63.0
|
|
td
|
74.9
|
|
td
|
49.9
|
|
td
|
77.8
|
|
td
|
71.9
|
|
td
|
80.1
|
|
td
|
82.6
|
|
td
|
62.7
|
|
td
|
65.5
|
|
td
|
82.3
|
|
tr
|
72.4 74.2 74.0 82.2 78.4 65.5 66.0 45.7 80.7 72.5
|
|
td
|
72.4
|
|
td
|
74.2
|
|
td
|
74.0
|
|
td
|
82.2
|
|
td
|
78.4
|
|
td
|
65.5
|
|
td
|
66.0
|
|
td
|
45.7
|
|
td
|
80.7
|
|
td
|
72.5
|
|
tr
|
75.8 72.8 74.8 79.9 54.1 79.9 64.2 80.7 70.7 78.3
|
|
td
|
75.8
|
|
td
|
72.8
|
|
td
|
74.8
|
|
td
|
79.9
|
|
td
|
54.1
|
|
td
|
79.9
|
|
td
|
64.2
|
|
td
|
80.7
|
|
td
|
70.7
|
|
td
|
78.3
|
|
tr
|
68.8 76.9 66.0 65.1 74.8 70.4 74.4 69.2 74.8 67.1
|
|
td
|
68.8
|
|
td
|
76.9
|
|
td
|
66.0
|
|
td
|
65.1
|
|
td
|
74.8
|
|
td
|
70.4
|
|
td
|
74.4
|
|
td
|
69.2
|
|
td
|
74.8
|
|
td
|
67.1
|
|
tr
|
71.1 77.8 77.3 71.4 82.3 59.2 83.2 60.1 83.2 71.8
|
|
td
|
71.1
|
|
td
|
77.8
|
|
td
|
77.3
|
|
td
|
71.4
|
|
td
|
82.3
|
|
td
|
59.2
|
|
td
|
83.2
|
|
td
|
60.1
|
|
td
|
83.2
|
|
td
|
71.8
|
|
tr
|
71.3 75.8 72.4 63.0 72.8 82.6 71.6 75.4 33.6 84.4
|
|
td
|
71.3
|
|
td
|
75.8
|
|
td
|
72.4
|
|
td
|
63.0
|
|
td
|
72.8
|
|
td
|
82.6
|
|
td
|
71.6
|
|
td
|
75.4
|
|
td
|
33.6
|
|
td
|
84.4
|
|
tr
|
74.3 73.1 72.4 75.8 74.4 82.1 68.8 74.0 76.8 74.5
|
|
td
|
74.3
|
|
td
|
73.1
|
|
td
|
72.4
|
|
td
|
75.8
|
|
td
|
74.4
|
|
td
|
82.1
|
|
td
|
68.8
|
|
td
|
74.0
|
|
td
|
76.8
|
|
td
|
74.5
|
|
tr
|
69.5 63.0 71.3 62.7 82.6 64.9 59.4 74.4 59.2 74.0
|
|
td
|
69.5
|
|
td
|
63.0
|
|
td
|
71.3
|
|
td
|
62.7
|
|
td
|
82.6
|
|
td
|
64.9
|
|
td
|
59.4
|
|
td
|
74.4
|
|
td
|
59.2
|
|
td
|
74.0
|
|
tr
|
85.1 77.7 84.0 59.7 84.0 74.3 74.0 71.4 65.1 82.1
|
|
td
|
85.1
|
|
td
|
77.7
|
|
td
|
84.0
|
|
td
|
59.7
|
|
td
|
84.0
|
|
td
|
74.3
|
|
td
|
74.0
|
|
td
|
71.4
|
|
td
|
65.1
|
|
td
|
82.1
|
|
tr
|
82.1 66.0 71.3 54.1 60.1 72.0 70.7 69.5 64.2 63.0
|
|
td
|
82.1
|
|
td
|
66.0
|
|
td
|
71.3
|
|
td
|
54.1
|
|
td
|
60.1
|
|
td
|
72.0
|
|
td
|
70.7
|
|
td
|
69.5
|
|
td
|
64.2
|
|
td
|
63.0
|
|
tr
|
67.7 82.7 59.4 67.7 74.0 72.8 80.1 74.8 82.3 76.9
|
|
td
|
67.7
|
|
td
|
82.7
|
|
td
|
59.4
|
|
td
|
67.7
|
|
td
|
74.0
|
|
td
|
72.8
|
|
td
|
80.1
|
|
td
|
74.8
|
|
td
|
82.3
|
|
td
|
76.9
|
|
tr
|
84.0 73.3 57.5 80.4 74.8 71.1 74.8 72.8 60.9 64.9
|
|
td
|
84.0
|
|
td
|
73.3
|
|
td
|
57.5
|
|
td
|
80.4
|
|
td
|
74.8
|
|
td
|
71.1
|
|
td
|
74.8
|
|
td
|
72.8
|
|
td
|
60.9
|
|
td
|
64.9
|
|
tr
|
67.7 72.2 65.0 67.8 69.2 67.8 75.0 78.5 72.2 68.2
|
|
td
|
67.7
|
|
td
|
72.2
|
|
td
|
65.0
|
|
td
|
67.8
|
|
td
|
69.2
|
|
td
|
67.8
|
|
td
|
75.0
|
|
td
|
78.5
|
|
td
|
72.2
|
|
td
|
68.2
|
|
tr
|
80.7 65.0 73.8 78.6 33.6 71.3 77.2 72.3 61.8 82.7
|
|
td
|
80.7
|
|
td
|
65.0
|
|
td
|
73.8
|
|
td
|
78.6
|
|
td
|
33.6
|
|
td
|
71.3
|
|
td
|
77.2
|
|
td
|
72.3
|
|
td
|
61.8
|
|
td
|
82.7
|
|
table-wrap
|
Table 7 Distance function for 20 samplings—S11 to S20.
S11 S12 S13 S14 S15 S16 S17 S18 S19 S20
69.5 82.6 67.3 82.6 66.8 72.8 80.8 81.1 83.2 54.1
82.3 71.1 57.5 83.2 74.0 72.3 71.6 72.5 71.4 73.6
71.8 83.4 71.9 74.4 52.9 67.7 49.9 77.2 70.4 72.8
68.7 71.9 80.8 73.6 57.5 73.3 67.8 90.3 68.8 72.2
68.7 73.2 70.2 52.9 80.1 71.6 80.6 49.1 69.5 58.9
62.9 80.1 75.8 77.4 82.6 69.5 64.9 82.2 32.3 75.8
59.6 71.6 82.3 79.9 49.1 49.9 73.3 71.3 71.6 49.9
61.0 72.8 79.9 84.0 80.7 57.3 75.4 65.5 73.5 75.0
83.2 62.7 78.8 78.5 74.3 80.6 71.4 73.5 80.1 67.8
60.1 71.6 78.5 49.1 61.0 69.2 78.3 52.9 67.1 82.0
78.8 84.0 62.7 68.6 80.7 75.4 80.1 77.6 71.3 80.1
75.0 76.5 68.8 83.9 74.5 84.0 85.7 71.4 75.4 57.3
59.7 82.6 71.6 80.7 57.3 71.4 33.6 74.0 74.9 67.7
85.7 78.9 84.4 66.5 66.0 54.1 72.7 72.0 60.9 74.2
82.1 70.4 67.1 82.2 72.7 71.4 76.5 84.4 84.4 77.6
68.6 68.8 83.4 73.3 79.9 33.6 79.9 59.7 49.9 83.9
83.4 59.2 71.6 59.6 78.3 74.1 57.5 71.6 83.2 81.5
78.6 83.2 78.3 80.7 72.3 82.0 71.3 72.4 80.1 62.9
71.9 73.1 71.9 85.7 81.1 71.1 74.8 59.2 71.4 90.3
73.3 72.5 75.4 62.7 74.8 72.4 65.5 83.4 84.0 84.4
72.4 66.0 82.3 72.4 78.2 78.2 81.5 69.2 64.2 76.5
66.0 54.1 81.5 70.7 73.8 73.3 69.5 74.4 65.0 73.1
80.7 49.9 73.1 71.6 73.3 82.2 76.2 73.3 74.8 65.1
71.3 77.7 80.1 84.7 68.7 77.6 74.8 64.9 82.1 68.8
78.5 74.2 82.7 72.8 62.9 85.7 68.7 80.7 82.9 85.7
|
|
label
|
Table 7
|
|
caption
|
Distance function for 20 samplings—S11 to S20.
|
|
p
|
Distance function for 20 samplings—S11 to S20.
|
|
table
|
S11 S12 S13 S14 S15 S16 S17 S18 S19 S20
69.5 82.6 67.3 82.6 66.8 72.8 80.8 81.1 83.2 54.1
82.3 71.1 57.5 83.2 74.0 72.3 71.6 72.5 71.4 73.6
71.8 83.4 71.9 74.4 52.9 67.7 49.9 77.2 70.4 72.8
68.7 71.9 80.8 73.6 57.5 73.3 67.8 90.3 68.8 72.2
68.7 73.2 70.2 52.9 80.1 71.6 80.6 49.1 69.5 58.9
62.9 80.1 75.8 77.4 82.6 69.5 64.9 82.2 32.3 75.8
59.6 71.6 82.3 79.9 49.1 49.9 73.3 71.3 71.6 49.9
61.0 72.8 79.9 84.0 80.7 57.3 75.4 65.5 73.5 75.0
83.2 62.7 78.8 78.5 74.3 80.6 71.4 73.5 80.1 67.8
60.1 71.6 78.5 49.1 61.0 69.2 78.3 52.9 67.1 82.0
78.8 84.0 62.7 68.6 80.7 75.4 80.1 77.6 71.3 80.1
75.0 76.5 68.8 83.9 74.5 84.0 85.7 71.4 75.4 57.3
59.7 82.6 71.6 80.7 57.3 71.4 33.6 74.0 74.9 67.7
85.7 78.9 84.4 66.5 66.0 54.1 72.7 72.0 60.9 74.2
82.1 70.4 67.1 82.2 72.7 71.4 76.5 84.4 84.4 77.6
68.6 68.8 83.4 73.3 79.9 33.6 79.9 59.7 49.9 83.9
83.4 59.2 71.6 59.6 78.3 74.1 57.5 71.6 83.2 81.5
78.6 83.2 78.3 80.7 72.3 82.0 71.3 72.4 80.1 62.9
71.9 73.1 71.9 85.7 81.1 71.1 74.8 59.2 71.4 90.3
73.3 72.5 75.4 62.7 74.8 72.4 65.5 83.4 84.0 84.4
72.4 66.0 82.3 72.4 78.2 78.2 81.5 69.2 64.2 76.5
66.0 54.1 81.5 70.7 73.8 73.3 69.5 74.4 65.0 73.1
80.7 49.9 73.1 71.6 73.3 82.2 76.2 73.3 74.8 65.1
71.3 77.7 80.1 84.7 68.7 77.6 74.8 64.9 82.1 68.8
78.5 74.2 82.7 72.8 62.9 85.7 68.7 80.7 82.9 85.7
|
|
tr
|
S11 S12 S13 S14 S15 S16 S17 S18 S19 S20
|
|
th
|
S11
|
|
th
|
S12
|
|
th
|
S13
|
|
th
|
S14
|
|
th
|
S15
|
|
th
|
S16
|
|
th
|
S17
|
|
th
|
S18
|
|
th
|
S19
|
|
th
|
S20
|
|
tr
|
69.5 82.6 67.3 82.6 66.8 72.8 80.8 81.1 83.2 54.1
|
|
td
|
69.5
|
|
td
|
82.6
|
|
td
|
67.3
|
|
td
|
82.6
|
|
td
|
66.8
|
|
td
|
72.8
|
|
td
|
80.8
|
|
td
|
81.1
|
|
td
|
83.2
|
|
td
|
54.1
|
|
tr
|
82.3 71.1 57.5 83.2 74.0 72.3 71.6 72.5 71.4 73.6
|
|
td
|
82.3
|
|
td
|
71.1
|
|
td
|
57.5
|
|
td
|
83.2
|
|
td
|
74.0
|
|
td
|
72.3
|
|
td
|
71.6
|
|
td
|
72.5
|
|
td
|
71.4
|
|
td
|
73.6
|
|
tr
|
71.8 83.4 71.9 74.4 52.9 67.7 49.9 77.2 70.4 72.8
|
|
td
|
71.8
|
|
td
|
83.4
|
|
td
|
71.9
|
|
td
|
74.4
|
|
td
|
52.9
|
|
td
|
67.7
|
|
td
|
49.9
|
|
td
|
77.2
|
|
td
|
70.4
|
|
td
|
72.8
|
|
tr
|
68.7 71.9 80.8 73.6 57.5 73.3 67.8 90.3 68.8 72.2
|
|
td
|
68.7
|
|
td
|
71.9
|
|
td
|
80.8
|
|
td
|
73.6
|
|
td
|
57.5
|
|
td
|
73.3
|
|
td
|
67.8
|
|
td
|
90.3
|
|
td
|
68.8
|
|
td
|
72.2
|
|
tr
|
68.7 73.2 70.2 52.9 80.1 71.6 80.6 49.1 69.5 58.9
|
|
td
|
68.7
|
|
td
|
73.2
|
|
td
|
70.2
|
|
td
|
52.9
|
|
td
|
80.1
|
|
td
|
71.6
|
|
td
|
80.6
|
|
td
|
49.1
|
|
td
|
69.5
|
|
td
|
58.9
|
|
tr
|
62.9 80.1 75.8 77.4 82.6 69.5 64.9 82.2 32.3 75.8
|
|
td
|
62.9
|
|
td
|
80.1
|
|
td
|
75.8
|
|
td
|
77.4
|
|
td
|
82.6
|
|
td
|
69.5
|
|
td
|
64.9
|
|
td
|
82.2
|
|
td
|
32.3
|
|
td
|
75.8
|
|
tr
|
59.6 71.6 82.3 79.9 49.1 49.9 73.3 71.3 71.6 49.9
|
|
td
|
59.6
|
|
td
|
71.6
|
|
td
|
82.3
|
|
td
|
79.9
|
|
td
|
49.1
|
|
td
|
49.9
|
|
td
|
73.3
|
|
td
|
71.3
|
|
td
|
71.6
|
|
td
|
49.9
|
|
tr
|
61.0 72.8 79.9 84.0 80.7 57.3 75.4 65.5 73.5 75.0
|
|
td
|
61.0
|
|
td
|
72.8
|
|
td
|
79.9
|
|
td
|
84.0
|
|
td
|
80.7
|
|
td
|
57.3
|
|
td
|
75.4
|
|
td
|
65.5
|
|
td
|
73.5
|
|
td
|
75.0
|
|
tr
|
83.2 62.7 78.8 78.5 74.3 80.6 71.4 73.5 80.1 67.8
|
|
td
|
83.2
|
|
td
|
62.7
|
|
td
|
78.8
|
|
td
|
78.5
|
|
td
|
74.3
|
|
td
|
80.6
|
|
td
|
71.4
|
|
td
|
73.5
|
|
td
|
80.1
|
|
td
|
67.8
|
|
tr
|
60.1 71.6 78.5 49.1 61.0 69.2 78.3 52.9 67.1 82.0
|
|
td
|
60.1
|
|
td
|
71.6
|
|
td
|
78.5
|
|
td
|
49.1
|
|
td
|
61.0
|
|
td
|
69.2
|
|
td
|
78.3
|
|
td
|
52.9
|
|
td
|
67.1
|
|
td
|
82.0
|
|
tr
|
78.8 84.0 62.7 68.6 80.7 75.4 80.1 77.6 71.3 80.1
|
|
td
|
78.8
|
|
td
|
84.0
|
|
td
|
62.7
|
|
td
|
68.6
|
|
td
|
80.7
|
|
td
|
75.4
|
|
td
|
80.1
|
|
td
|
77.6
|
|
td
|
71.3
|
|
td
|
80.1
|
|
tr
|
75.0 76.5 68.8 83.9 74.5 84.0 85.7 71.4 75.4 57.3
|
|
td
|
75.0
|
|
td
|
76.5
|
|
td
|
68.8
|
|
td
|
83.9
|
|
td
|
74.5
|
|
td
|
84.0
|
|
td
|
85.7
|
|
td
|
71.4
|
|
td
|
75.4
|
|
td
|
57.3
|
|
tr
|
59.7 82.6 71.6 80.7 57.3 71.4 33.6 74.0 74.9 67.7
|
|
td
|
59.7
|
|
td
|
82.6
|
|
td
|
71.6
|
|
td
|
80.7
|
|
td
|
57.3
|
|
td
|
71.4
|
|
td
|
33.6
|
|
td
|
74.0
|
|
td
|
74.9
|
|
td
|
67.7
|
|
tr
|
85.7 78.9 84.4 66.5 66.0 54.1 72.7 72.0 60.9 74.2
|
|
td
|
85.7
|
|
td
|
78.9
|
|
td
|
84.4
|
|
td
|
66.5
|
|
td
|
66.0
|
|
td
|
54.1
|
|
td
|
72.7
|
|
td
|
72.0
|
|
td
|
60.9
|
|
td
|
74.2
|
|
tr
|
82.1 70.4 67.1 82.2 72.7 71.4 76.5 84.4 84.4 77.6
|
|
td
|
82.1
|
|
td
|
70.4
|
|
td
|
67.1
|
|
td
|
82.2
|
|
td
|
72.7
|
|
td
|
71.4
|
|
td
|
76.5
|
|
td
|
84.4
|
|
td
|
84.4
|
|
td
|
77.6
|
|
tr
|
68.6 68.8 83.4 73.3 79.9 33.6 79.9 59.7 49.9 83.9
|
|
td
|
68.6
|
|
td
|
68.8
|
|
td
|
83.4
|
|
td
|
73.3
|
|
td
|
79.9
|
|
td
|
33.6
|
|
td
|
79.9
|
|
td
|
59.7
|
|
td
|
49.9
|
|
td
|
83.9
|
|
tr
|
83.4 59.2 71.6 59.6 78.3 74.1 57.5 71.6 83.2 81.5
|
|
td
|
83.4
|
|
td
|
59.2
|
|
td
|
71.6
|
|
td
|
59.6
|
|
td
|
78.3
|
|
td
|
74.1
|
|
td
|
57.5
|
|
td
|
71.6
|
|
td
|
83.2
|
|
td
|
81.5
|
|
tr
|
78.6 83.2 78.3 80.7 72.3 82.0 71.3 72.4 80.1 62.9
|
|
td
|
78.6
|
|
td
|
83.2
|
|
td
|
78.3
|
|
td
|
80.7
|
|
td
|
72.3
|
|
td
|
82.0
|
|
td
|
71.3
|
|
td
|
72.4
|
|
td
|
80.1
|
|
td
|
62.9
|
|
tr
|
71.9 73.1 71.9 85.7 81.1 71.1 74.8 59.2 71.4 90.3
|
|
td
|
71.9
|
|
td
|
73.1
|
|
td
|
71.9
|
|
td
|
85.7
|
|
td
|
81.1
|
|
td
|
71.1
|
|
td
|
74.8
|
|
td
|
59.2
|
|
td
|
71.4
|
|
td
|
90.3
|
|
tr
|
73.3 72.5 75.4 62.7 74.8 72.4 65.5 83.4 84.0 84.4
|
|
td
|
73.3
|
|
td
|
72.5
|
|
td
|
75.4
|
|
td
|
62.7
|
|
td
|
74.8
|
|
td
|
72.4
|
|
td
|
65.5
|
|
td
|
83.4
|
|
td
|
84.0
|
|
td
|
84.4
|
|
tr
|
72.4 66.0 82.3 72.4 78.2 78.2 81.5 69.2 64.2 76.5
|
|
td
|
72.4
|
|
td
|
66.0
|
|
td
|
82.3
|
|
td
|
72.4
|
|
td
|
78.2
|
|
td
|
78.2
|
|
td
|
81.5
|
|
td
|
69.2
|
|
td
|
64.2
|
|
td
|
76.5
|
|
tr
|
66.0 54.1 81.5 70.7 73.8 73.3 69.5 74.4 65.0 73.1
|
|
td
|
66.0
|
|
td
|
54.1
|
|
td
|
81.5
|
|
td
|
70.7
|
|
td
|
73.8
|
|
td
|
73.3
|
|
td
|
69.5
|
|
td
|
74.4
|
|
td
|
65.0
|
|
td
|
73.1
|
|
tr
|
80.7 49.9 73.1 71.6 73.3 82.2 76.2 73.3 74.8 65.1
|
|
td
|
80.7
|
|
td
|
49.9
|
|
td
|
73.1
|
|
td
|
71.6
|
|
td
|
73.3
|
|
td
|
82.2
|
|
td
|
76.2
|
|
td
|
73.3
|
|
td
|
74.8
|
|
td
|
65.1
|
|
tr
|
71.3 77.7 80.1 84.7 68.7 77.6 74.8 64.9 82.1 68.8
|
|
td
|
71.3
|
|
td
|
77.7
|
|
td
|
80.1
|
|
td
|
84.7
|
|
td
|
68.7
|
|
td
|
77.6
|
|
td
|
74.8
|
|
td
|
64.9
|
|
td
|
82.1
|
|
td
|
68.8
|
|
tr
|
78.5 74.2 82.7 72.8 62.9 85.7 68.7 80.7 82.9 85.7
|
|
td
|
78.5
|
|
td
|
74.2
|
|
td
|
82.7
|
|
td
|
72.8
|
|
td
|
62.9
|
|
td
|
85.7
|
|
td
|
68.7
|
|
td
|
80.7
|
|
td
|
82.9
|
|
td
|
85.7
|
|
table-wrap
|
Table 8 Absolute references for 20 samplings—S1 to S10.
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10
68 28 6 37 66 160 72 107 66 88
112 92 156 56 37 56 144 56 156 92
92 118 53 142 48 71 71 48 53 7
89 60 144 87 7 7 118 112 56 117
78 76 48 92 111 118 39 87 31 57
137 43 117 97 124 89 159 83 88 105
148 17 39 89 90 57 147 111 140 22
76 163 33 137 75 122 122 76 97 26
21 95 5 122 119 115 125 70 89 19
124 119 1 73 153 13 9 123 64 29
1 16 26 26 55 124 21 47 9 163
98 120 30 70 38 19 19 119 21 82
108 62 126 3 113 29 158 16 163 65
32 10 98 98 132 61 75 46 110 38
99 131 95 10 84 95 46 113 65 10
18 18 62 84 35 75 130 84 113 116
141 127 46 18 27 65 81 101 132 18
127 128 132 67 80 32 132 100 84 128
128 42 84 121 150 35 99 134 127 27
2 121 93 74 45 50 128 27 27 150
52 25 34 77 59 86 35 74 150 52
129 41 44 50 151 41 86 139 52 41
41 103 69 2 85 91 129 52 69 161
85 151 151 69 20 15 91 151 102 103
14 14 85 45 14 85 15 136 15 20
|
|
label
|
Table 8
|
|
caption
|
Absolute references for 20 samplings—S1 to S10.
|
|
p
|
Absolute references for 20 samplings—S1 to S10.
|
|
table
|
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10
68 28 6 37 66 160 72 107 66 88
112 92 156 56 37 56 144 56 156 92
92 118 53 142 48 71 71 48 53 7
89 60 144 87 7 7 118 112 56 117
78 76 48 92 111 118 39 87 31 57
137 43 117 97 124 89 159 83 88 105
148 17 39 89 90 57 147 111 140 22
76 163 33 137 75 122 122 76 97 26
21 95 5 122 119 115 125 70 89 19
124 119 1 73 153 13 9 123 64 29
1 16 26 26 55 124 21 47 9 163
98 120 30 70 38 19 19 119 21 82
108 62 126 3 113 29 158 16 163 65
32 10 98 98 132 61 75 46 110 38
99 131 95 10 84 95 46 113 65 10
18 18 62 84 35 75 130 84 113 116
141 127 46 18 27 65 81 101 132 18
127 128 132 67 80 32 132 100 84 128
128 42 84 121 150 35 99 134 127 27
2 121 93 74 45 50 128 27 27 150
52 25 34 77 59 86 35 74 150 52
129 41 44 50 151 41 86 139 52 41
41 103 69 2 85 91 129 52 69 161
85 151 151 69 20 15 91 151 102 103
14 14 85 45 14 85 15 136 15 20
|
|
tr
|
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10
|
|
th
|
S1
|
|
th
|
S2
|
|
th
|
S3
|
|
th
|
S4
|
|
th
|
S5
|
|
th
|
S6
|
|
th
|
S7
|
|
th
|
S8
|
|
th
|
S9
|
|
th
|
S10
|
|
tr
|
68 28 6 37 66 160 72 107 66 88
|
|
td
|
68
|
|
td
|
28
|
|
td
|
6
|
|
td
|
37
|
|
td
|
66
|
|
td
|
160
|
|
td
|
72
|
|
td
|
107
|
|
td
|
66
|
|
td
|
88
|
|
tr
|
112 92 156 56 37 56 144 56 156 92
|
|
td
|
112
|
|
td
|
92
|
|
td
|
156
|
|
td
|
56
|
|
td
|
37
|
|
td
|
56
|
|
td
|
144
|
|
td
|
56
|
|
td
|
156
|
|
td
|
92
|
|
tr
|
92 118 53 142 48 71 71 48 53 7
|
|
td
|
92
|
|
td
|
118
|
|
td
|
53
|
|
td
|
142
|
|
td
|
48
|
|
td
|
71
|
|
td
|
71
|
|
td
|
48
|
|
td
|
53
|
|
td
|
7
|
|
tr
|
89 60 144 87 7 7 118 112 56 117
|
|
td
|
89
|
|
td
|
60
|
|
td
|
144
|
|
td
|
87
|
|
td
|
7
|
|
td
|
7
|
|
td
|
118
|
|
td
|
112
|
|
td
|
56
|
|
td
|
117
|
|
tr
|
78 76 48 92 111 118 39 87 31 57
|
|
td
|
78
|
|
td
|
76
|
|
td
|
48
|
|
td
|
92
|
|
td
|
111
|
|
td
|
118
|
|
td
|
39
|
|
td
|
87
|
|
td
|
31
|
|
td
|
57
|
|
tr
|
137 43 117 97 124 89 159 83 88 105
|
|
td
|
137
|
|
td
|
43
|
|
td
|
117
|
|
td
|
97
|
|
td
|
124
|
|
td
|
89
|
|
td
|
159
|
|
td
|
83
|
|
td
|
88
|
|
td
|
105
|
|
tr
|
148 17 39 89 90 57 147 111 140 22
|
|
td
|
148
|
|
td
|
17
|
|
td
|
39
|
|
td
|
89
|
|
td
|
90
|
|
td
|
57
|
|
td
|
147
|
|
td
|
111
|
|
td
|
140
|
|
td
|
22
|
|
tr
|
76 163 33 137 75 122 122 76 97 26
|
|
td
|
76
|
|
td
|
163
|
|
td
|
33
|
|
td
|
137
|
|
td
|
75
|
|
td
|
122
|
|
td
|
122
|
|
td
|
76
|
|
td
|
97
|
|
td
|
26
|
|
tr
|
21 95 5 122 119 115 125 70 89 19
|
|
td
|
21
|
|
td
|
95
|
|
td
|
5
|
|
td
|
122
|
|
td
|
119
|
|
td
|
115
|
|
td
|
125
|
|
td
|
70
|
|
td
|
89
|
|
td
|
19
|
|
tr
|
124 119 1 73 153 13 9 123 64 29
|
|
td
|
124
|
|
td
|
119
|
|
td
|
1
|
|
td
|
73
|
|
td
|
153
|
|
td
|
13
|
|
td
|
9
|
|
td
|
123
|
|
td
|
64
|
|
td
|
29
|
|
tr
|
1 16 26 26 55 124 21 47 9 163
|
|
td
|
1
|
|
td
|
16
|
|
td
|
26
|
|
td
|
26
|
|
td
|
55
|
|
td
|
124
|
|
td
|
21
|
|
td
|
47
|
|
td
|
9
|
|
td
|
163
|
|
tr
|
98 120 30 70 38 19 19 119 21 82
|
|
td
|
98
|
|
td
|
120
|
|
td
|
30
|
|
td
|
70
|
|
td
|
38
|
|
td
|
19
|
|
td
|
19
|
|
td
|
119
|
|
td
|
21
|
|
td
|
82
|
|
tr
|
108 62 126 3 113 29 158 16 163 65
|
|
td
|
108
|
|
td
|
62
|
|
td
|
126
|
|
td
|
3
|
|
td
|
113
|
|
td
|
29
|
|
td
|
158
|
|
td
|
16
|
|
td
|
163
|
|
td
|
65
|
|
tr
|
32 10 98 98 132 61 75 46 110 38
|
|
td
|
32
|
|
td
|
10
|
|
td
|
98
|
|
td
|
98
|
|
td
|
132
|
|
td
|
61
|
|
td
|
75
|
|
td
|
46
|
|
td
|
110
|
|
td
|
38
|
|
tr
|
99 131 95 10 84 95 46 113 65 10
|
|
td
|
99
|
|
td
|
131
|
|
td
|
95
|
|
td
|
10
|
|
td
|
84
|
|
td
|
95
|
|
td
|
46
|
|
td
|
113
|
|
td
|
65
|
|
td
|
10
|
|
tr
|
18 18 62 84 35 75 130 84 113 116
|
|
td
|
18
|
|
td
|
18
|
|
td
|
62
|
|
td
|
84
|
|
td
|
35
|
|
td
|
75
|
|
td
|
130
|
|
td
|
84
|
|
td
|
113
|
|
td
|
116
|
|
tr
|
141 127 46 18 27 65 81 101 132 18
|
|
td
|
141
|
|
td
|
127
|
|
td
|
46
|
|
td
|
18
|
|
td
|
27
|
|
td
|
65
|
|
td
|
81
|
|
td
|
101
|
|
td
|
132
|
|
td
|
18
|
|
tr
|
127 128 132 67 80 32 132 100 84 128
|
|
td
|
127
|
|
td
|
128
|
|
td
|
132
|
|
td
|
67
|
|
td
|
80
|
|
td
|
32
|
|
td
|
132
|
|
td
|
100
|
|
td
|
84
|
|
td
|
128
|
|
tr
|
128 42 84 121 150 35 99 134 127 27
|
|
td
|
128
|
|
td
|
42
|
|
td
|
84
|
|
td
|
121
|
|
td
|
150
|
|
td
|
35
|
|
td
|
99
|
|
td
|
134
|
|
td
|
127
|
|
td
|
27
|
|
tr
|
2 121 93 74 45 50 128 27 27 150
|
|
td
|
2
|
|
td
|
121
|
|
td
|
93
|
|
td
|
74
|
|
td
|
45
|
|
td
|
50
|
|
td
|
128
|
|
td
|
27
|
|
td
|
27
|
|
td
|
150
|
|
tr
|
52 25 34 77 59 86 35 74 150 52
|
|
td
|
52
|
|
td
|
25
|
|
td
|
34
|
|
td
|
77
|
|
td
|
59
|
|
td
|
86
|
|
td
|
35
|
|
td
|
74
|
|
td
|
150
|
|
td
|
52
|
|
tr
|
129 41 44 50 151 41 86 139 52 41
|
|
td
|
129
|
|
td
|
41
|
|
td
|
44
|
|
td
|
50
|
|
td
|
151
|
|
td
|
41
|
|
td
|
86
|
|
td
|
139
|
|
td
|
52
|
|
td
|
41
|
|
tr
|
41 103 69 2 85 91 129 52 69 161
|
|
td
|
41
|
|
td
|
103
|
|
td
|
69
|
|
td
|
2
|
|
td
|
85
|
|
td
|
91
|
|
td
|
129
|
|
td
|
52
|
|
td
|
69
|
|
td
|
161
|
|
tr
|
85 151 151 69 20 15 91 151 102 103
|
|
td
|
85
|
|
td
|
151
|
|
td
|
151
|
|
td
|
69
|
|
td
|
20
|
|
td
|
15
|
|
td
|
91
|
|
td
|
151
|
|
td
|
102
|
|
td
|
103
|
|
tr
|
14 14 85 45 14 85 15 136 15 20
|
|
td
|
14
|
|
td
|
14
|
|
td
|
85
|
|
td
|
45
|
|
td
|
14
|
|
td
|
85
|
|
td
|
15
|
|
td
|
136
|
|
td
|
15
|
|
td
|
20
|
|
table-wrap
|
Table 9 Absolute references for 20 samplings—S11 to S20.
S11 S12 S13 S14 S15 S16 S17 S18 S19 S20
49 6 53 40 40 66 66 40 133 6
142 37 87 143 143 6 6 143 6 37
48 56 57 49 156 37 53 56 31 156
68 87 83 87 53 156 7 142 71 155
157 39 125 159 68 137 89 7 118 157
60 148 9 115 157 111 122 89 57 97
115 43 158 21 39 76 73 111 148 147
73 124 54 54 64 124 76 19 76 122
12 8 126 98 12 30 26 70 43 148
76 54 90 119 47 3 70 54 26 163
1 126 16 108 96 54 8 61 70 119
29 82 93 55 120 123 110 98 30 153
126 119 18 24 62 95 120 82 8 55
95 16 27 100 46 119 132 108 146 10
108 65 74 74 32 120 84 146 84 99
99 10 104 50 135 108 93 38 131 18
74 67 50 52 132 51 141 113 101 67
77 42 86 36 138 101 67 35 145 134
104 139 129 69 27 134 27 134 25 25
36 86 44 59 50 138 50 52 41 44
41 91 102 63 86 152 25 154 58 162
23 59 161 79 52 162 152 69 63 79
15 15 103 85 36 69 129 151 15 20
151 151 151 109 154 85 44 20 85 136
136 11 20 136 59 136 136 4 20 4
|
|
label
|
Table 9
|
|
caption
|
Absolute references for 20 samplings—S11 to S20.
|
|
p
|
Absolute references for 20 samplings—S11 to S20.
|
|
table
|
S11 S12 S13 S14 S15 S16 S17 S18 S19 S20
49 6 53 40 40 66 66 40 133 6
142 37 87 143 143 6 6 143 6 37
48 56 57 49 156 37 53 56 31 156
68 87 83 87 53 156 7 142 71 155
157 39 125 159 68 137 89 7 118 157
60 148 9 115 157 111 122 89 57 97
115 43 158 21 39 76 73 111 148 147
73 124 54 54 64 124 76 19 76 122
12 8 126 98 12 30 26 70 43 148
76 54 90 119 47 3 70 54 26 163
1 126 16 108 96 54 8 61 70 119
29 82 93 55 120 123 110 98 30 153
126 119 18 24 62 95 120 82 8 55
95 16 27 100 46 119 132 108 146 10
108 65 74 74 32 120 84 146 84 99
99 10 104 50 135 108 93 38 131 18
74 67 50 52 132 51 141 113 101 67
77 42 86 36 138 101 67 35 145 134
104 139 129 69 27 134 27 134 25 25
36 86 44 59 50 138 50 52 41 44
41 91 102 63 86 152 25 154 58 162
23 59 161 79 52 162 152 69 63 79
15 15 103 85 36 69 129 151 15 20
151 151 151 109 154 85 44 20 85 136
136 11 20 136 59 136 136 4 20 4
|
|
tr
|
S11 S12 S13 S14 S15 S16 S17 S18 S19 S20
|
|
th
|
S11
|
|
th
|
S12
|
|
th
|
S13
|
|
th
|
S14
|
|
th
|
S15
|
|
th
|
S16
|
|
th
|
S17
|
|
th
|
S18
|
|
th
|
S19
|
|
th
|
S20
|
|
tr
|
49 6 53 40 40 66 66 40 133 6
|
|
td
|
49
|
|
td
|
6
|
|
td
|
53
|
|
td
|
40
|
|
td
|
40
|
|
td
|
66
|
|
td
|
66
|
|
td
|
40
|
|
td
|
133
|
|
td
|
6
|
|
tr
|
142 37 87 143 143 6 6 143 6 37
|
|
td
|
142
|
|
td
|
37
|
|
td
|
87
|
|
td
|
143
|
|
td
|
143
|
|
td
|
6
|
|
td
|
6
|
|
td
|
143
|
|
td
|
6
|
|
td
|
37
|
|
tr
|
48 56 57 49 156 37 53 56 31 156
|
|
td
|
48
|
|
td
|
56
|
|
td
|
57
|
|
td
|
49
|
|
td
|
156
|
|
td
|
37
|
|
td
|
53
|
|
td
|
56
|
|
td
|
31
|
|
td
|
156
|
|
tr
|
68 87 83 87 53 156 7 142 71 155
|
|
td
|
68
|
|
td
|
87
|
|
td
|
83
|
|
td
|
87
|
|
td
|
53
|
|
td
|
156
|
|
td
|
7
|
|
td
|
142
|
|
td
|
71
|
|
td
|
155
|
|
tr
|
157 39 125 159 68 137 89 7 118 157
|
|
td
|
157
|
|
td
|
39
|
|
td
|
125
|
|
td
|
159
|
|
td
|
68
|
|
td
|
137
|
|
td
|
89
|
|
td
|
7
|
|
td
|
118
|
|
td
|
157
|
|
tr
|
60 148 9 115 157 111 122 89 57 97
|
|
td
|
60
|
|
td
|
148
|
|
td
|
9
|
|
td
|
115
|
|
td
|
157
|
|
td
|
111
|
|
td
|
122
|
|
td
|
89
|
|
td
|
57
|
|
td
|
97
|
|
tr
|
115 43 158 21 39 76 73 111 148 147
|
|
td
|
115
|
|
td
|
43
|
|
td
|
158
|
|
td
|
21
|
|
td
|
39
|
|
td
|
76
|
|
td
|
73
|
|
td
|
111
|
|
td
|
148
|
|
td
|
147
|
|
tr
|
73 124 54 54 64 124 76 19 76 122
|
|
td
|
73
|
|
td
|
124
|
|
td
|
54
|
|
td
|
54
|
|
td
|
64
|
|
td
|
124
|
|
td
|
76
|
|
td
|
19
|
|
td
|
76
|
|
td
|
122
|
|
tr
|
12 8 126 98 12 30 26 70 43 148
|
|
td
|
12
|
|
td
|
8
|
|
td
|
126
|
|
td
|
98
|
|
td
|
12
|
|
td
|
30
|
|
td
|
26
|
|
td
|
70
|
|
td
|
43
|
|
td
|
148
|
|
tr
|
76 54 90 119 47 3 70 54 26 163
|
|
td
|
76
|
|
td
|
54
|
|
td
|
90
|
|
td
|
119
|
|
td
|
47
|
|
td
|
3
|
|
td
|
70
|
|
td
|
54
|
|
td
|
26
|
|
td
|
163
|
|
tr
|
1 126 16 108 96 54 8 61 70 119
|
|
td
|
1
|
|
td
|
126
|
|
td
|
16
|
|
td
|
108
|
|
td
|
96
|
|
td
|
54
|
|
td
|
8
|
|
td
|
61
|
|
td
|
70
|
|
td
|
119
|
|
tr
|
29 82 93 55 120 123 110 98 30 153
|
|
td
|
29
|
|
td
|
82
|
|
td
|
93
|
|
td
|
55
|
|
td
|
120
|
|
td
|
123
|
|
td
|
110
|
|
td
|
98
|
|
td
|
30
|
|
td
|
153
|
|
tr
|
126 119 18 24 62 95 120 82 8 55
|
|
td
|
126
|
|
td
|
119
|
|
td
|
18
|
|
td
|
24
|
|
td
|
62
|
|
td
|
95
|
|
td
|
120
|
|
td
|
82
|
|
td
|
8
|
|
td
|
55
|
|
tr
|
95 16 27 100 46 119 132 108 146 10
|
|
td
|
95
|
|
td
|
16
|
|
td
|
27
|
|
td
|
100
|
|
td
|
46
|
|
td
|
119
|
|
td
|
132
|
|
td
|
108
|
|
td
|
146
|
|
td
|
10
|
|
tr
|
108 65 74 74 32 120 84 146 84 99
|
|
td
|
108
|
|
td
|
65
|
|
td
|
74
|
|
td
|
74
|
|
td
|
32
|
|
td
|
120
|
|
td
|
84
|
|
td
|
146
|
|
td
|
84
|
|
td
|
99
|
|
tr
|
99 10 104 50 135 108 93 38 131 18
|
|
td
|
99
|
|
td
|
10
|
|
td
|
104
|
|
td
|
50
|
|
td
|
135
|
|
td
|
108
|
|
td
|
93
|
|
td
|
38
|
|
td
|
131
|
|
td
|
18
|
|
tr
|
74 67 50 52 132 51 141 113 101 67
|
|
td
|
74
|
|
td
|
67
|
|
td
|
50
|
|
td
|
52
|
|
td
|
132
|
|
td
|
51
|
|
td
|
141
|
|
td
|
113
|
|
td
|
101
|
|
td
|
67
|
|
tr
|
77 42 86 36 138 101 67 35 145 134
|
|
td
|
77
|
|
td
|
42
|
|
td
|
86
|
|
td
|
36
|
|
td
|
138
|
|
td
|
101
|
|
td
|
67
|
|
td
|
35
|
|
td
|
145
|
|
td
|
134
|
|
tr
|
104 139 129 69 27 134 27 134 25 25
|
|
td
|
104
|
|
td
|
139
|
|
td
|
129
|
|
td
|
69
|
|
td
|
27
|
|
td
|
134
|
|
td
|
27
|
|
td
|
134
|
|
td
|
25
|
|
td
|
25
|
|
tr
|
36 86 44 59 50 138 50 52 41 44
|
|
td
|
36
|
|
td
|
86
|
|
td
|
44
|
|
td
|
59
|
|
td
|
50
|
|
td
|
138
|
|
td
|
50
|
|
td
|
52
|
|
td
|
41
|
|
td
|
44
|
|
tr
|
41 91 102 63 86 152 25 154 58 162
|
|
td
|
41
|
|
td
|
91
|
|
td
|
102
|
|
td
|
63
|
|
td
|
86
|
|
td
|
152
|
|
td
|
25
|
|
td
|
154
|
|
td
|
58
|
|
td
|
162
|
|
tr
|
23 59 161 79 52 162 152 69 63 79
|
|
td
|
23
|
|
td
|
59
|
|
td
|
161
|
|
td
|
79
|
|
td
|
52
|
|
td
|
162
|
|
td
|
152
|
|
td
|
69
|
|
td
|
63
|
|
td
|
79
|
|
tr
|
15 15 103 85 36 69 129 151 15 20
|
|
td
|
15
|
|
td
|
15
|
|
td
|
103
|
|
td
|
85
|
|
td
|
36
|
|
td
|
69
|
|
td
|
129
|
|
td
|
151
|
|
td
|
15
|
|
td
|
20
|
|
tr
|
151 151 151 109 154 85 44 20 85 136
|
|
td
|
151
|
|
td
|
151
|
|
td
|
151
|
|
td
|
109
|
|
td
|
154
|
|
td
|
85
|
|
td
|
44
|
|
td
|
20
|
|
td
|
85
|
|
td
|
136
|
|
tr
|
136 11 20 136 59 136 136 4 20 4
|
|
td
|
136
|
|
td
|
11
|
|
td
|
20
|
|
td
|
136
|
|
td
|
59
|
|
td
|
136
|
|
td
|
136
|
|
td
|
4
|
|
td
|
20
|
|
td
|
4
|
|
table-wrap
|
Table 10 Ordering for each batch based on death toll of COVID-19—S1 to S10.
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10
78 43 53 67 90 15 15 83 53 117
98 131 117 98 20 35 35 101 15 20
76 25 126 26 35 118 118 151 102 22
127 151 151 69 151 57 91 76 69 26
92 17 69 142 150 91 39 16 140 92
108 76 98 92 84 160 147 134 64 150
85 127 26 84 48 85 159 84 127 57
2 92 39 87 85 56 132 48 150 163
148 118 62 56 132 50 129 87 163 161
52 16 84 2 38 65 19 56 84 82
129 163 48 50 59 7 9 52 56 10
89 62 85 10 7 89 130 136 132 88
112 42 30 37 37 95 81 123 110 38
141 10 132 89 80 19 128 47 31 52
68 95 95 97 113 13 122 113 88 65
41 60 93 74 66 41 144 112 52 7
1 103 156 3 111 61 46 74 65 19
18 28 6 18 124 122 71 100 89 103
128 41 1 77 45 124 125 111 97 116
124 18 44 121 153 71 72 46 9 41
137 120 5 122 119 115 99 107 113 18
32 121 144 73 14 32 75 119 156 128
14 128 46 137 55 29 21 70 66 29
99 119 34 45 75 75 158 139 21 105
21 14 33 70 27 86 86 27 27 27
|
|
label
|
Table 10
|
|
caption
|
Ordering for each batch based on death toll of COVID-19—S1 to S10.
|
|
p
|
Ordering for each batch based on death toll of COVID-19—S1 to S10.
|
|
table
|
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10
78 43 53 67 90 15 15 83 53 117
98 131 117 98 20 35 35 101 15 20
76 25 126 26 35 118 118 151 102 22
127 151 151 69 151 57 91 76 69 26
92 17 69 142 150 91 39 16 140 92
108 76 98 92 84 160 147 134 64 150
85 127 26 84 48 85 159 84 127 57
2 92 39 87 85 56 132 48 150 163
148 118 62 56 132 50 129 87 163 161
52 16 84 2 38 65 19 56 84 82
129 163 48 50 59 7 9 52 56 10
89 62 85 10 7 89 130 136 132 88
112 42 30 37 37 95 81 123 110 38
141 10 132 89 80 19 128 47 31 52
68 95 95 97 113 13 122 113 88 65
41 60 93 74 66 41 144 112 52 7
1 103 156 3 111 61 46 74 65 19
18 28 6 18 124 122 71 100 89 103
128 41 1 77 45 124 125 111 97 116
124 18 44 121 153 71 72 46 9 41
137 120 5 122 119 115 99 107 113 18
32 121 144 73 14 32 75 119 156 128
14 128 46 137 55 29 21 70 66 29
99 119 34 45 75 75 158 139 21 105
21 14 33 70 27 86 86 27 27 27
|
|
tr
|
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10
|
|
th
|
S1
|
|
th
|
S2
|
|
th
|
S3
|
|
th
|
S4
|
|
th
|
S5
|
|
th
|
S6
|
|
th
|
S7
|
|
th
|
S8
|
|
th
|
S9
|
|
th
|
S10
|
|
tr
|
78 43 53 67 90 15 15 83 53 117
|
|
td
|
78
|
|
td
|
43
|
|
td
|
53
|
|
td
|
67
|
|
td
|
90
|
|
td
|
15
|
|
td
|
15
|
|
td
|
83
|
|
td
|
53
|
|
td
|
117
|
|
tr
|
98 131 117 98 20 35 35 101 15 20
|
|
td
|
98
|
|
td
|
131
|
|
td
|
117
|
|
td
|
98
|
|
td
|
20
|
|
td
|
35
|
|
td
|
35
|
|
td
|
101
|
|
td
|
15
|
|
td
|
20
|
|
tr
|
76 25 126 26 35 118 118 151 102 22
|
|
td
|
76
|
|
td
|
25
|
|
td
|
126
|
|
td
|
26
|
|
td
|
35
|
|
td
|
118
|
|
td
|
118
|
|
td
|
151
|
|
td
|
102
|
|
td
|
22
|
|
tr
|
127 151 151 69 151 57 91 76 69 26
|
|
td
|
127
|
|
td
|
151
|
|
td
|
151
|
|
td
|
69
|
|
td
|
151
|
|
td
|
57
|
|
td
|
91
|
|
td
|
76
|
|
td
|
69
|
|
td
|
26
|
|
tr
|
92 17 69 142 150 91 39 16 140 92
|
|
td
|
92
|
|
td
|
17
|
|
td
|
69
|
|
td
|
142
|
|
td
|
150
|
|
td
|
91
|
|
td
|
39
|
|
td
|
16
|
|
td
|
140
|
|
td
|
92
|
|
tr
|
108 76 98 92 84 160 147 134 64 150
|
|
td
|
108
|
|
td
|
76
|
|
td
|
98
|
|
td
|
92
|
|
td
|
84
|
|
td
|
160
|
|
td
|
147
|
|
td
|
134
|
|
td
|
64
|
|
td
|
150
|
|
tr
|
85 127 26 84 48 85 159 84 127 57
|
|
td
|
85
|
|
td
|
127
|
|
td
|
26
|
|
td
|
84
|
|
td
|
48
|
|
td
|
85
|
|
td
|
159
|
|
td
|
84
|
|
td
|
127
|
|
td
|
57
|
|
tr
|
2 92 39 87 85 56 132 48 150 163
|
|
td
|
2
|
|
td
|
92
|
|
td
|
39
|
|
td
|
87
|
|
td
|
85
|
|
td
|
56
|
|
td
|
132
|
|
td
|
48
|
|
td
|
150
|
|
td
|
163
|
|
tr
|
148 118 62 56 132 50 129 87 163 161
|
|
td
|
148
|
|
td
|
118
|
|
td
|
62
|
|
td
|
56
|
|
td
|
132
|
|
td
|
50
|
|
td
|
129
|
|
td
|
87
|
|
td
|
163
|
|
td
|
161
|
|
tr
|
52 16 84 2 38 65 19 56 84 82
|
|
td
|
52
|
|
td
|
16
|
|
td
|
84
|
|
td
|
2
|
|
td
|
38
|
|
td
|
65
|
|
td
|
19
|
|
td
|
56
|
|
td
|
84
|
|
td
|
82
|
|
tr
|
129 163 48 50 59 7 9 52 56 10
|
|
td
|
129
|
|
td
|
163
|
|
td
|
48
|
|
td
|
50
|
|
td
|
59
|
|
td
|
7
|
|
td
|
9
|
|
td
|
52
|
|
td
|
56
|
|
td
|
10
|
|
tr
|
89 62 85 10 7 89 130 136 132 88
|
|
td
|
89
|
|
td
|
62
|
|
td
|
85
|
|
td
|
10
|
|
td
|
7
|
|
td
|
89
|
|
td
|
130
|
|
td
|
136
|
|
td
|
132
|
|
td
|
88
|
|
tr
|
112 42 30 37 37 95 81 123 110 38
|
|
td
|
112
|
|
td
|
42
|
|
td
|
30
|
|
td
|
37
|
|
td
|
37
|
|
td
|
95
|
|
td
|
81
|
|
td
|
123
|
|
td
|
110
|
|
td
|
38
|
|
tr
|
141 10 132 89 80 19 128 47 31 52
|
|
td
|
141
|
|
td
|
10
|
|
td
|
132
|
|
td
|
89
|
|
td
|
80
|
|
td
|
19
|
|
td
|
128
|
|
td
|
47
|
|
td
|
31
|
|
td
|
52
|
|
tr
|
68 95 95 97 113 13 122 113 88 65
|
|
td
|
68
|
|
td
|
95
|
|
td
|
95
|
|
td
|
97
|
|
td
|
113
|
|
td
|
13
|
|
td
|
122
|
|
td
|
113
|
|
td
|
88
|
|
td
|
65
|
|
tr
|
41 60 93 74 66 41 144 112 52 7
|
|
td
|
41
|
|
td
|
60
|
|
td
|
93
|
|
td
|
74
|
|
td
|
66
|
|
td
|
41
|
|
td
|
144
|
|
td
|
112
|
|
td
|
52
|
|
td
|
7
|
|
tr
|
1 103 156 3 111 61 46 74 65 19
|
|
td
|
1
|
|
td
|
103
|
|
td
|
156
|
|
td
|
3
|
|
td
|
111
|
|
td
|
61
|
|
td
|
46
|
|
td
|
74
|
|
td
|
65
|
|
td
|
19
|
|
tr
|
18 28 6 18 124 122 71 100 89 103
|
|
td
|
18
|
|
td
|
28
|
|
td
|
6
|
|
td
|
18
|
|
td
|
124
|
|
td
|
122
|
|
td
|
71
|
|
td
|
100
|
|
td
|
89
|
|
td
|
103
|
|
tr
|
128 41 1 77 45 124 125 111 97 116
|
|
td
|
128
|
|
td
|
41
|
|
td
|
1
|
|
td
|
77
|
|
td
|
45
|
|
td
|
124
|
|
td
|
125
|
|
td
|
111
|
|
td
|
97
|
|
td
|
116
|
|
tr
|
124 18 44 121 153 71 72 46 9 41
|
|
td
|
124
|
|
td
|
18
|
|
td
|
44
|
|
td
|
121
|
|
td
|
153
|
|
td
|
71
|
|
td
|
72
|
|
td
|
46
|
|
td
|
9
|
|
td
|
41
|
|
tr
|
137 120 5 122 119 115 99 107 113 18
|
|
td
|
137
|
|
td
|
120
|
|
td
|
5
|
|
td
|
122
|
|
td
|
119
|
|
td
|
115
|
|
td
|
99
|
|
td
|
107
|
|
td
|
113
|
|
td
|
18
|
|
tr
|
32 121 144 73 14 32 75 119 156 128
|
|
td
|
32
|
|
td
|
121
|
|
td
|
144
|
|
td
|
73
|
|
td
|
14
|
|
td
|
32
|
|
td
|
75
|
|
td
|
119
|
|
td
|
156
|
|
td
|
128
|
|
tr
|
14 128 46 137 55 29 21 70 66 29
|
|
td
|
14
|
|
td
|
128
|
|
td
|
46
|
|
td
|
137
|
|
td
|
55
|
|
td
|
29
|
|
td
|
21
|
|
td
|
70
|
|
td
|
66
|
|
td
|
29
|
|
tr
|
99 119 34 45 75 75 158 139 21 105
|
|
td
|
99
|
|
td
|
119
|
|
td
|
34
|
|
td
|
45
|
|
td
|
75
|
|
td
|
75
|
|
td
|
158
|
|
td
|
139
|
|
td
|
21
|
|
td
|
105
|
|
tr
|
21 14 33 70 27 86 86 27 27 27
|
|
td
|
21
|
|
td
|
14
|
|
td
|
33
|
|
td
|
70
|
|
td
|
27
|
|
td
|
86
|
|
td
|
86
|
|
td
|
27
|
|
td
|
27
|
|
td
|
27
|
|
table-wrap
|
Table 11 Ordering for each batch based on death toll of COVID-19—S11 to S20.
S11 S12 S13 S14 S15 S16 S17 S18 S19 S20
49 43 83 49 53 101 53 20 43 162
15 126 53 69 12 162 25 35 101 25
126 15 90 98 96 51 67 151 131 20
104 67 20 36 64 76 26 4 20 67
12 151 126 63 36 69 76 69 25 4
151 16 104 108 39 134 84 142 15 134
76 91 151 159 135 108 152 98 145 163
142 39 102 85 62 85 132 134 76 147
36 87 57 87 132 30 110 108 26 148
108 56 16 24 50 152 50 56 118 10
48 82 87 50 52 37 129 82 57 37
136 42 161 109 59 123 7 146 63 136
95 148 50 52 47 136 136 38 133 97
60 10 129 59 138 95 89 52 84 79
23 65 93 136 156 138 93 7 85 156
74 59 9 79 40 156 6 89 30 6
68 37 103 74 68 54 66 19 146 44
41 54 74 54 120 6 141 113 148 18
1 6 54 40 46 66 8 54 31 155
77 8 44 100 32 111 44 40 6 122
73 124 18 115 143 3 120 111 41 153
115 11 125 143 157 120 122 61 8 119
29 119 158 119 86 124 73 143 71 99
99 139 27 55 27 137 70 70 58 55
157 86 86 21 154 119 27 154 70 157
|
|
label
|
Table 11
|
|
caption
|
Ordering for each batch based on death toll of COVID-19—S11 to S20.
|
|
p
|
Ordering for each batch based on death toll of COVID-19—S11 to S20.
|
|
table
|
S11 S12 S13 S14 S15 S16 S17 S18 S19 S20
49 43 83 49 53 101 53 20 43 162
15 126 53 69 12 162 25 35 101 25
126 15 90 98 96 51 67 151 131 20
104 67 20 36 64 76 26 4 20 67
12 151 126 63 36 69 76 69 25 4
151 16 104 108 39 134 84 142 15 134
76 91 151 159 135 108 152 98 145 163
142 39 102 85 62 85 132 134 76 147
36 87 57 87 132 30 110 108 26 148
108 56 16 24 50 152 50 56 118 10
48 82 87 50 52 37 129 82 57 37
136 42 161 109 59 123 7 146 63 136
95 148 50 52 47 136 136 38 133 97
60 10 129 59 138 95 89 52 84 79
23 65 93 136 156 138 93 7 85 156
74 59 9 79 40 156 6 89 30 6
68 37 103 74 68 54 66 19 146 44
41 54 74 54 120 6 141 113 148 18
1 6 54 40 46 66 8 54 31 155
77 8 44 100 32 111 44 40 6 122
73 124 18 115 143 3 120 111 41 153
115 11 125 143 157 120 122 61 8 119
29 119 158 119 86 124 73 143 71 99
99 139 27 55 27 137 70 70 58 55
157 86 86 21 154 119 27 154 70 157
|
|
tr
|
S11 S12 S13 S14 S15 S16 S17 S18 S19 S20
|
|
th
|
S11
|
|
th
|
S12
|
|
th
|
S13
|
|
th
|
S14
|
|
th
|
S15
|
|
th
|
S16
|
|
th
|
S17
|
|
th
|
S18
|
|
th
|
S19
|
|
th
|
S20
|
|
tr
|
49 43 83 49 53 101 53 20 43 162
|
|
td
|
49
|
|
td
|
43
|
|
td
|
83
|
|
td
|
49
|
|
td
|
53
|
|
td
|
101
|
|
td
|
53
|
|
td
|
20
|
|
td
|
43
|
|
td
|
162
|
|
tr
|
15 126 53 69 12 162 25 35 101 25
|
|
td
|
15
|
|
td
|
126
|
|
td
|
53
|
|
td
|
69
|
|
td
|
12
|
|
td
|
162
|
|
td
|
25
|
|
td
|
35
|
|
td
|
101
|
|
td
|
25
|
|
tr
|
126 15 90 98 96 51 67 151 131 20
|
|
td
|
126
|
|
td
|
15
|
|
td
|
90
|
|
td
|
98
|
|
td
|
96
|
|
td
|
51
|
|
td
|
67
|
|
td
|
151
|
|
td
|
131
|
|
td
|
20
|
|
tr
|
104 67 20 36 64 76 26 4 20 67
|
|
td
|
104
|
|
td
|
67
|
|
td
|
20
|
|
td
|
36
|
|
td
|
64
|
|
td
|
76
|
|
td
|
26
|
|
td
|
4
|
|
td
|
20
|
|
td
|
67
|
|
tr
|
12 151 126 63 36 69 76 69 25 4
|
|
td
|
12
|
|
td
|
151
|
|
td
|
126
|
|
td
|
63
|
|
td
|
36
|
|
td
|
69
|
|
td
|
76
|
|
td
|
69
|
|
td
|
25
|
|
td
|
4
|
|
tr
|
151 16 104 108 39 134 84 142 15 134
|
|
td
|
151
|
|
td
|
16
|
|
td
|
104
|
|
td
|
108
|
|
td
|
39
|
|
td
|
134
|
|
td
|
84
|
|
td
|
142
|
|
td
|
15
|
|
td
|
134
|
|
tr
|
76 91 151 159 135 108 152 98 145 163
|
|
td
|
76
|
|
td
|
91
|
|
td
|
151
|
|
td
|
159
|
|
td
|
135
|
|
td
|
108
|
|
td
|
152
|
|
td
|
98
|
|
td
|
145
|
|
td
|
163
|
|
tr
|
142 39 102 85 62 85 132 134 76 147
|
|
td
|
142
|
|
td
|
39
|
|
td
|
102
|
|
td
|
85
|
|
td
|
62
|
|
td
|
85
|
|
td
|
132
|
|
td
|
134
|
|
td
|
76
|
|
td
|
147
|
|
tr
|
36 87 57 87 132 30 110 108 26 148
|
|
td
|
36
|
|
td
|
87
|
|
td
|
57
|
|
td
|
87
|
|
td
|
132
|
|
td
|
30
|
|
td
|
110
|
|
td
|
108
|
|
td
|
26
|
|
td
|
148
|
|
tr
|
108 56 16 24 50 152 50 56 118 10
|
|
td
|
108
|
|
td
|
56
|
|
td
|
16
|
|
td
|
24
|
|
td
|
50
|
|
td
|
152
|
|
td
|
50
|
|
td
|
56
|
|
td
|
118
|
|
td
|
10
|
|
tr
|
48 82 87 50 52 37 129 82 57 37
|
|
td
|
48
|
|
td
|
82
|
|
td
|
87
|
|
td
|
50
|
|
td
|
52
|
|
td
|
37
|
|
td
|
129
|
|
td
|
82
|
|
td
|
57
|
|
td
|
37
|
|
tr
|
136 42 161 109 59 123 7 146 63 136
|
|
td
|
136
|
|
td
|
42
|
|
td
|
161
|
|
td
|
109
|
|
td
|
59
|
|
td
|
123
|
|
td
|
7
|
|
td
|
146
|
|
td
|
63
|
|
td
|
136
|
|
tr
|
95 148 50 52 47 136 136 38 133 97
|
|
td
|
95
|
|
td
|
148
|
|
td
|
50
|
|
td
|
52
|
|
td
|
47
|
|
td
|
136
|
|
td
|
136
|
|
td
|
38
|
|
td
|
133
|
|
td
|
97
|
|
tr
|
60 10 129 59 138 95 89 52 84 79
|
|
td
|
60
|
|
td
|
10
|
|
td
|
129
|
|
td
|
59
|
|
td
|
138
|
|
td
|
95
|
|
td
|
89
|
|
td
|
52
|
|
td
|
84
|
|
td
|
79
|
|
tr
|
23 65 93 136 156 138 93 7 85 156
|
|
td
|
23
|
|
td
|
65
|
|
td
|
93
|
|
td
|
136
|
|
td
|
156
|
|
td
|
138
|
|
td
|
93
|
|
td
|
7
|
|
td
|
85
|
|
td
|
156
|
|
tr
|
74 59 9 79 40 156 6 89 30 6
|
|
td
|
74
|
|
td
|
59
|
|
td
|
9
|
|
td
|
79
|
|
td
|
40
|
|
td
|
156
|
|
td
|
6
|
|
td
|
89
|
|
td
|
30
|
|
td
|
6
|
|
tr
|
68 37 103 74 68 54 66 19 146 44
|
|
td
|
68
|
|
td
|
37
|
|
td
|
103
|
|
td
|
74
|
|
td
|
68
|
|
td
|
54
|
|
td
|
66
|
|
td
|
19
|
|
td
|
146
|
|
td
|
44
|
|
tr
|
41 54 74 54 120 6 141 113 148 18
|
|
td
|
41
|
|
td
|
54
|
|
td
|
74
|
|
td
|
54
|
|
td
|
120
|
|
td
|
6
|
|
td
|
141
|
|
td
|
113
|
|
td
|
148
|
|
td
|
18
|
|
tr
|
1 6 54 40 46 66 8 54 31 155
|
|
td
|
1
|
|
td
|
6
|
|
td
|
54
|
|
td
|
40
|
|
td
|
46
|
|
td
|
66
|
|
td
|
8
|
|
td
|
54
|
|
td
|
31
|
|
td
|
155
|
|
tr
|
77 8 44 100 32 111 44 40 6 122
|
|
td
|
77
|
|
td
|
8
|
|
td
|
44
|
|
td
|
100
|
|
td
|
32
|
|
td
|
111
|
|
td
|
44
|
|
td
|
40
|
|
td
|
6
|
|
td
|
122
|
|
tr
|
73 124 18 115 143 3 120 111 41 153
|
|
td
|
73
|
|
td
|
124
|
|
td
|
18
|
|
td
|
115
|
|
td
|
143
|
|
td
|
3
|
|
td
|
120
|
|
td
|
111
|
|
td
|
41
|
|
td
|
153
|
|
tr
|
115 11 125 143 157 120 122 61 8 119
|
|
td
|
115
|
|
td
|
11
|
|
td
|
125
|
|
td
|
143
|
|
td
|
157
|
|
td
|
120
|
|
td
|
122
|
|
td
|
61
|
|
td
|
8
|
|
td
|
119
|
|
tr
|
29 119 158 119 86 124 73 143 71 99
|
|
td
|
29
|
|
td
|
119
|
|
td
|
158
|
|
td
|
119
|
|
td
|
86
|
|
td
|
124
|
|
td
|
73
|
|
td
|
143
|
|
td
|
71
|
|
td
|
99
|
|
tr
|
99 139 27 55 27 137 70 70 58 55
|
|
td
|
99
|
|
td
|
139
|
|
td
|
27
|
|
td
|
55
|
|
td
|
27
|
|
td
|
137
|
|
td
|
70
|
|
td
|
70
|
|
td
|
58
|
|
td
|
55
|
|
tr
|
157 86 86 21 154 119 27 154 70 157
|
|
td
|
157
|
|
td
|
86
|
|
td
|
86
|
|
td
|
21
|
|
td
|
154
|
|
td
|
119
|
|
td
|
27
|
|
td
|
154
|
|
td
|
70
|
|
td
|
157
|
|
table-wrap
|
Table 12 Sign vectors.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 1 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0
0 1 1 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 1
1 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 1 1 0
0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 1 0 0 0 1
1 0 0 1 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 0
1 1 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 0 0
0 0 0 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1 0 0
0 1 1 0 0 1 1 1 0 1 1 0 0 0 1 0 0 0 1 1
1 1 1 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1
1 0 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 1 1 0
0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1
0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 1 1 1 0 0
1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 1
0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0
1 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0
0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 1 1
1 0 0 1 1 0 0 0 0 1 1 1 0 0 1 0 1 1 0 0
1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1
0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1
1 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 0 0
1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 1
0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 0
0 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 0
|
|
label
|
Table 12
|
|
caption
|
Sign vectors.
|
|
p
|
Sign vectors.
|
|
table
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 1 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0
0 1 1 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 1
1 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 1 1 0
0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 1 0 0 0 1
1 0 0 1 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 0
1 1 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 0 0
0 0 0 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1 0 0
0 1 1 0 0 1 1 1 0 1 1 0 0 0 1 0 0 0 1 1
1 1 1 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1
1 0 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 1 1 0
0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1
0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 1 1 1 0 0
1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 1
0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0
1 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0
0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 1 1
1 0 0 1 1 0 0 0 0 1 1 1 0 0 1 0 1 1 0 0
1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1
0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1
1 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 0 0
1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 1
0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 0
0 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 0
|
|
tr
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
|
|
th
|
1
|
|
th
|
2
|
|
th
|
3
|
|
th
|
4
|
|
th
|
5
|
|
th
|
6
|
|
th
|
7
|
|
th
|
8
|
|
th
|
9
|
|
th
|
10
|
|
th
|
11
|
|
th
|
12
|
|
th
|
13
|
|
th
|
14
|
|
th
|
15
|
|
th
|
16
|
|
th
|
17
|
|
th
|
18
|
|
th
|
19
|
|
th
|
20
|
|
tr
|
1 1 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
tr
|
0 1 1 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
tr
|
1 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 1 1 0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
tr
|
0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 1 0 0 0 1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
tr
|
1 0 0 1 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
tr
|
1 1 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 0 0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
tr
|
0 0 0 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1 0 0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
tr
|
0 1 1 0 0 1 1 1 0 1 1 0 0 0 1 0 0 0 1 1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
tr
|
1 1 1 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
tr
|
1 0 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 1 1 0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
tr
|
0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
tr
|
0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 1 1 1 0 0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
tr
|
1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
tr
|
0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
tr
|
1 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
tr
|
0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 1 1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
tr
|
1 0 0 1 1 0 0 0 0 1 1 1 0 0 1 0 1 1 0 0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
tr
|
1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
tr
|
0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
tr
|
0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
tr
|
1 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 0 0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
tr
|
1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
tr
|
0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
tr
|
0 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
table-wrap
|
Table 13 Relational vectors.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0
0 1 1 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 0 0
0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0
0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0
1 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 1 0 0 1
0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 1 1
1 0 0 1 0 0 1 0 0 1 0 1 1 0 0 0 1 0 0 0
0 1 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1
1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0
0 0 0 1 0 0 0 1 0 0 0 1 0 1 1 0 0 1 1 0
1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0
0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 1 0 0
0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0
0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0
0 0 1 0 1 1 0 0 1 1 0 0 0 1 1 0 0 1 0 0
1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0 1 1
0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0
1 1 0 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1
0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0
1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0
0 1 1 0 1 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0
1 0 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 1 0 1
|
|
label
|
Table 13
|
|
caption
|
Relational vectors.
|
|
p
|
Relational vectors.
|
|
table
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0
0 1 1 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 0 0
0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0
0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0
1 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 1 0 0 1
0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 1 1
1 0 0 1 0 0 1 0 0 1 0 1 1 0 0 0 1 0 0 0
0 1 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1
1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0
0 0 0 1 0 0 0 1 0 0 0 1 0 1 1 0 0 1 1 0
1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0
0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 1 0 0
0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0
0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0
0 0 1 0 1 1 0 0 1 1 0 0 0 1 1 0 0 1 0 0
1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0 1 1
0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0
1 1 0 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1
0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0
1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0
0 1 1 0 1 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0
1 0 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 1 0 1
|
|
tr
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
|
|
th
|
1
|
|
th
|
2
|
|
th
|
3
|
|
th
|
4
|
|
th
|
5
|
|
th
|
6
|
|
th
|
7
|
|
th
|
8
|
|
th
|
9
|
|
th
|
10
|
|
th
|
11
|
|
th
|
12
|
|
th
|
13
|
|
th
|
14
|
|
th
|
15
|
|
th
|
16
|
|
th
|
17
|
|
th
|
18
|
|
th
|
19
|
|
th
|
20
|
|
tr
|
0 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
tr
|
0 1 1 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 0 0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
tr
|
0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
tr
|
0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
tr
|
1 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 1 0 0 1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
tr
|
0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 1 1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
tr
|
1 0 0 1 0 0 1 0 0 1 0 1 1 0 0 0 1 0 0 0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
tr
|
0 1 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
tr
|
1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
tr
|
0 0 0 1 0 0 0 1 0 0 0 1 0 1 1 0 0 1 1 0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
tr
|
1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
tr
|
0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 1 0 0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
tr
|
0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
tr
|
0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 0 0 0 0 1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
tr
|
0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
tr
|
0 0 1 0 1 1 0 0 1 1 0 0 0 1 1 0 0 1 0 0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
tr
|
1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0 1 1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
tr
|
0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
tr
|
1 1 0 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
tr
|
0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
tr
|
1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
tr
|
0 1 1 0 1 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
tr
|
1 0 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 1 0 1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
0
|
|
td
|
0
|
|
td
|
1
|
|
td
|
1
|
|
td
|
0
|
|
td
|
1
|
|
table-wrap
|
Table 14 Binary norm for the 20 samplings: S1 to S20.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
8 11 15 8 11 8 9 6 14 5 6 6 9 15 17 8 11 17 7 8
|
|
label
|
Table 14
|
|
caption
|
Binary norm for the 20 samplings: S1 to S20.
|
|
p
|
Binary norm for the 20 samplings: S1 to S20.
|
|
table
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
8 11 15 8 11 8 9 6 14 5 6 6 9 15 17 8 11 17 7 8
|
|
tr
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
|
|
th
|
1
|
|
th
|
2
|
|
th
|
3
|
|
th
|
4
|
|
th
|
5
|
|
th
|
6
|
|
th
|
7
|
|
th
|
8
|
|
th
|
9
|
|
th
|
10
|
|
th
|
11
|
|
th
|
12
|
|
th
|
13
|
|
th
|
14
|
|
th
|
15
|
|
th
|
16
|
|
th
|
17
|
|
th
|
18
|
|
th
|
19
|
|
th
|
20
|
|
tr
|
8 11 15 8 11 8 9 6 14 5 6 6 9 15 17 8 11 17 7 8
|
|
td
|
8
|
|
td
|
11
|
|
td
|
15
|
|
td
|
8
|
|
td
|
11
|
|
td
|
8
|
|
td
|
9
|
|
td
|
6
|
|
td
|
14
|
|
td
|
5
|
|
td
|
6
|
|
td
|
6
|
|
td
|
9
|
|
td
|
15
|
|
td
|
17
|
|
td
|
8
|
|
td
|
11
|
|
td
|
17
|
|
td
|
7
|
|
td
|
8
|
