Charles Darwin's Origin of Species, published in 1859, was a revolutionary attempt “to overthrow the dogma of separate creations,” a declaration that provoked different reactions among the religious, ranging from mild enthusiasm to anger. Christians sympathetic to Darwin's effort sought to make Darwinism appear compatible with their religious beliefs. Two of Darwin's most prominent defenders in the United States were the Calvinists Asa Gray, a Harvard botanist, and George Frederick Wright, a cleric-geologist. Gray, who long favored a “special origination” in (...) connection with the evolution of humans and questioned whether natural selection can account for the formation of organs, the making of eyes, etc., embraced natural selection as the primary mechanism underlying the production of most species. He also went so far as to invoke divine providence, rather than randomness, to explain the variations on which natural selection acted. This chapter discusses creationism, intelligent design, and modern biology. (shrink)

many symbols. We define o, as the probability that an arbitrary machine be circular and we prove that o, is a random number that goes beyond..

The Random Number Generation task has a long history in neuropsychology as an assessment procedure for executive functioning. In recent years, understanding of human behavior has gradually changed from reflecting a static to a dynamic process and this shift in thinking about behavior gives a new angle to interpret test results. However, this shift also asks for different methods to process random number sequences. The RNG task is suited for applying non-linear methods needed to uncover the underlying dynamics (...) of random number generation. In the current article we present RandseqR: an R-package that combines the calculation of classic randomization measures and Recurrence Quantification Analysis. RandseqR is an easy to use, flexible and fast way to process random number sequences and readies the RNG task for current scientific and clinical use. (shrink)

Many experiments have been conducted over the past eight decades to explore whether the ostensible psychic ability of psychokinesis (PK, or "mind over matter") might be a genuine human potential, and the most extensive of these have involved attempts to mentally influence the output of electronic, binary-bit random number generators (RNGs). Research of this type can generally be divided into two lines: proof-oriented (concerned with the accumulation and statistical evaluation of data from controlled experiments designed specifically to test for (...) the presence of PK effects on the microscopic scale) and process-oriented (concerned with conducting exploratory experiments designed to systematically vary certain test conditions in order to search for and identify any physical, biological, and psychological factors which might have a role in improving or moderating PK effects). To help orient novice investigators and cross-disciplinary researchers who may be considering work along these lines (as well as offer some initial guiding insight on possible directions for future research), this paper provides a general review of some of the notable proof- and process-oriented findings that have been obtained to date in experimental microscopic PK research using RNGs. The review generally indicates that although a considerable amount of proof-oriented data for micro-PK has accumulated over the years, the relatively sparse amount of process-oriented data available at present leaves a lot of open questions regarding the underlying factors involved, providing ample opportunity for novice investigators and cross-disciplinary researchers to make valuable research contributions in the future. (shrink)

A real is computable if it is the limit of a computable, increasing, computably converging sequence of rational...

The risk priority number calculation method is one of the critical subjects of failure mode and effects analysis research. Recently, RPN research under a fuzzy uncertainty environment has become a hot topic. Accordingly, increasing studies have ignored the important impact of the random sampling uncertainty in the FMEA assessment. In this study, a fuzzy beta-binomial RPN evaluation method is proposed by integrating fuzzy theory, Bayesian statistical inference, and the beta-binomial distribution. This model can effectively realize real-time, dynamic, and long-term (...) evaluation of RPN under the condition of continuous knowledge accumulation. The major contribution of the proposed model is to use the random uncertainty and fuzzy uncertainty in an integrated model and provide a Markov Chain Monte Carlo method to solve the complex integrated model. The study presented a case study, which presented how to apply this model in practice and indicated the significant influence on the measurement error caused by ignoring the random uncertainty caused by expert evaluation in RPN calculations. (shrink)

“Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.”1 John von Neumann’s famous dictum points an accusing finger at all who set their ordered minds to engender disorder. Much as in times past thieves, pimps, and actors carried on their profession with an uneasy conscience, so in this day scientists who devise random number generators suffer pangs of guilt. George Marsaglia, perhaps the preeminent worker in the field, quips when he (...) asks his colleagues, “Who among us has not sinned?” Marsaglia’s work at the Supercomputer Computations Research Institute at Florida State University is well-known. Inasmuch as Marsaglia’s design and testing of random number generators depends on computation, and inasmuch as computation is fundamentally arithmetical, Marsaglia is by von Neumann’s own account a sinner. Working as he does on a supercomputer, Marsaglia is in fact a gross sinner. This he freely admits. Writing of the best random number generators he is aware of, Marsaglia states, “they are the result of arithmetic methods and those using them must, as all sinners must, face Redemption [sic] Day. But perhaps with better understanding we can postpone it.”. (shrink)

One recursively enumerable real α dominates another one β if there are nondecreasing recursive sequences of rational numbers (a[n] : n ∈ ω) approximating α and (b[n] : n ∈ ω) approximating β and a positive constant C such that for all n, C(α − a[n]) ≥ (β − b[n]). See [R. M. Solovay, Draft of a Paper (or Series of Papers) on Chaitin’s Work, manuscript, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, 1974, p. 215] and [G. (...) J. Chaitin, IBM J. Res. Develop., 21 (1977), pp. 350–359]. We show that every recursively enumerable random real dominates all other recursively enumerable reals. We conclude that the recursively enumerable random reals are exactly the Ω-numbers [G. J. Chaitin, IBM J. Res. Develop., 21 (1977), pp. 350–359]. Second, we show that the sets in a universal Martin-Lof test for randomness have random measure, and every recursively enumerable random number is the sum of the measures represented in a universal Martin-Lof test. (shrink)

We prove optimal lower bounds on the computation time for several well-known test problems on a quite realistic computational model: the random access machine. These lower bound arguments may be of special interest for logicians because they rely on finitary analogues of two important concepts from mathematical logic: inaccessible numbers and order indiscernibles.

We say that A ≤LR B if every B-random number is A-random. Intuitively this means that if oracle A can identify some patterns on some real γ. In other words. B is at least as good as A for this purpose. We study the structure of the LR degrees globally and locally (i.e., restricted to the computably enumberable degrees) and their relationship with the Turing degrees. Among other results we show that whenever α in not GL₂ the LR (...) degree of α bounds $2^{\aleph _{0}}$ degrees (so that, in particular, there exist LR degrees with uncountably many predecessors) and we give sample results which demonstrate how various techniques from the theory of the c.e. degrees can be used to prove results about the c.e. LR degrees. (shrink)

The Art of Randomness teaches readers to harness the power of randomness (and Python code) to solve real-world problems in programming, science, and art through hands-on experiments-from simulating evolution to encrypting messages to making machine-learning algorithms. Each chapter describes how randomness plays into the given topic area, then proceeds to demonstrate its problem-solving role with hands-on experiments to work through using Python code.

Almost everyone has an intuitive notion of what a random number is. For example, consider these two series of binary digits: 01010101010101010101 01101100110111100010 The first is obviously constructed according to a simple rule; it consists of the number 01 repeated ten times. If one were asked to speculate on how the series might continue, one could predict with considerable confidence that the next two digits would be 0 and 1. Inspection of the second series of digits yields no such (...) comprehensive pattern. There is no obvious rule governing the formation of the number, and there is no rational way to guess the succeeding digits. The arrangement seems haphazard; in other words, the sequence appears to be a random assortment of 0's and 1's. (shrink)

It is time for a new paper about open questions in the currently very active area of randomness and computability. Ambos-Spies and Kučera presented such a paper in 1999 [1]. All the question in it have been solved, except for one: is KL-randomness different from Martin-Löf randomness? This question is discussed in Section 6.Not all the questions are necessarily hard—some simply have not been tried seriously. When we think a question is a major one, and therefore likely to be hard, (...) we indicate this by the symbol ▶, the criterion being that it is of considerable interest and has been tried by a number of researchers. Some questions are close contenders here; these are marked by ▷. With few exceptions, the questions are precise. They mostly have a yes/no answer. However, there are often more general questions of an intuitive or even philosophical nature behind. We give an outline, indicating the more general questions.All sets will be sets of natural numbers, unless otherwise stated. These sets are identified with infinite strings over {0, 1}. Other terms used in the literature are sequence and real. (shrink)

Schnorr randomness is a notion of algorithmic randomness for real numbers closely related to Martin-Löf randomness. After its initial development in the 1970s the notion received considerably less attention than Martin-Löf randomness, but recently interest has increased in a range of randomness concepts. In this article, we explore the properties of Schnorr random reals, and in particular the c.e. Schnorr random reals. We show that there are c.e. reals that are Schnorr random but not Martin-Löf (...) class='Hi'>random, and provide a new characterization of Schnorr random real numbers in terms of prefix-free machines. We prove that unlike Martin-Löf random c.e. reals, not all Schnorr random c.e. reals are Turing complete, though all are in high Turing degrees. We use the machine characterization to define a notion of "Schnorr reducibility" which allows us to calibrate the Schnorr complexity of reals. We define the class of "Schnorr trivial" reals, which are ones whose initial segment complexity is identical with the computable reals, and demonstrate that this class has non-computable members. (shrink)

The book is intended to explain the larger and intuitive concept of randomness by means of computation, particularly through algorithmic complexity and recursion theory. It also includes the transcriptions (by A. German) of two panel discussion on the topics: Is The Universe Random?, held at the University of Vermont in 2007; and What is Computation? (How) Does Nature Compute?, held at the University of Indiana Bloomington in 2008. The book is intended to the general public, undergraduate and graduate students (...) in math, computer science, physics and other sciences, but also to philosophers of science and researchers. (shrink)

Demuth tests generalize Martin-Löf tests in that one can exchange the m-th component a computably bounded number of times. A set fails a Demuth test if Z is in infinitely many final versions of the Gm. If we only allow Demuth tests such that GmGm+1 for each m, we have weak Demuth randomness.We show that a weakly Demuth random set can be high and , yet not superhigh. Next, any c.e. set Turing below a Demuth random set is (...) strongly jump-traceable.We also prove a basis theorem for non-empty classes P. It extends the Jockusch–Soare basis theorem that some member of P is computably dominated. We use the result to show that some weakly 2-random set does not compute a 2-fixed point free function. (shrink)

We investigate the question “To what extent can random reals be used as a tool to establish number theoretic facts?” Let $\text{2-\textit{RAN\/}}$ be the principle that for every real $X$ there is a real $R$ which is 2-random relative to $X$. In Section 2, we observe that the arguments of Csima and Mileti [3] can be implemented in the base theory $\text{\textit{RCA}}_0$ and so $\text{\textit{RCA}}_0+\text{2-\textit{RAN\/}}$ implies the Rainbow Ramsey Theorem. In Section 3, we show that the Rainbow Ramsey (...) Theorem is not conservative over $\text{\textit{RCA}}_0$ for arithmetic sentences. Thus, from the Csima—Mileti fact that the existence of random reals has infinitary-combinatorial consequences we can conclude that $\text{2-\textit{RAN\/}}$ has non-trivial arithmetic consequences. In Section 4, we show that $\text{2-\textit{RAN\/}}$ is conservative over $\text{\textit{RCA}}_0+\text{\textit{B\/}$\,\Sigma$}_2$ for $\Pi^1_1$-sentences. Thus, the set of first-order consequences of $\text{2-\textit{RAN\/}}$ is strictly stronger than $P^-+I\Sigma_1$ and no stronger than $P^-+\text{\textit{B\/}$\,\Sigma$}_2$. (shrink)

The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in the classical mechanics there is fundamental and irreducible randomness. The classical Newtonian trajectory does not have a direct physical meaning since arbitrary real numbers are not observable. There are classical uncertainty relations: Δq>0 and Δp>0, i.e. the uncertainty (errors of observation) in the determination of coordinate and momentum is (...) always positive (non zero).A “functional” formulation of classical mechanics was suggested. The fundamental equation of the microscopic dynamics in the functional approach is not the Newton equation but the Liouville equation for the distribution function of the single particle. Solutions of the Liouville equation have the property of delocalization which accounts for irreversibility. The Newton equation in this approach appears as an approximate equation describing the dynamics of the average values of the position and momenta for not too long time intervals. Corrections to the Newton trajectories are computed. An interpretation of quantum mechanics is attempted in which both classical and quantum mechanics contain fundamental randomness. Instead of an ensemble of events one introduces an ensemble of observers. (shrink)

This paper argues, first, that biological evolution can be both random and divinely guided at the same time. Next it discusses the idea that the claim that evolution is unguided is not part of the science of evolution, and defends it against a number of objections.

We show that for any real number, the class of real numbers less random than it, in the sense of rK-reducibility, forms a countable real closed subfield of the real ordered field. This generalizes the well-known fact that the computable reals form a real closed field. With the same technique we show that the class of differences of computably enumerable reals (d.c.e. reals) and the class of computably approximable reals (c.a. reals) form real closed fields. The d.c.e. result (...) was also proved nearly simultaneously and independently by Ng (Keng Meng Ng. Master's Thesis. National University of Singapore, in preparation). Lastly, we show that the class of d.c.e. reals is properly contained in the class or reals less random than Ω (the halting probability), which in turn is properly contained in the class of c.a. reals, and that neither the first nor last class is a randomness class (as captured by rK-reducibility). (shrink)

This paper argues, first, that biological evolution can be both random and divinely guided at the same time. Next it discusses the idea that the claim that evolution is unguided is not part of the science of evolution, and defends it against a number of objections.

A number of formal models, including a highly influential model from Hong and Page, purport to show that functionally diverse groups often beat groups of individually high-performing agents in solving problems. Thompson argues that in Hong and Page’s model, that the diverse groups are created by a random process explains their success, not the diversity. Here, I defend the diversity interpretation of the Hong and Page result. The failure of Thompson’s argument shows that to understand the value of functional (...) diversity, we should be clearer about how we conceive of and measure that diversity. (shrink)

The way research is, and should be, funded by the public sphere is the subject of renewed interest for sociology, economics, management sciences, and more recently, for the philosophy of science. In this contribution, I propose a qualitative, epistemological criticism of the funding by lottery model, which is advocated by a growing number of scholars as an alternative to peer-review. This lottery scheme draws on the lack of efficiency and of robustness of the peer-review based evaluation to argue that the (...) majority of public resources for basic science should be allocated randomly. I first differentiate between two distinct arguments used to defend this alternative funding scheme based on considerations about the logic of scientific research. To assess their epistemological limits, I then present and develop a conceptual frame, grounded on the notion of “system of practice”, which can be used to understand what precisely it means, for a research project, to be interesting or significant. I use this epistemological analysis to show that the lottery model is not theoretically optimal, since it underestimates the integration of all scientific projects in densely interconnected systems of conceptual, experimental, or technical practices which confer their proper interest to them. I also apply these arguments in order to criticize the classical peer-review process. I finally suggest, as a discussion, that some recently proposed models that bring to the fore a principle of decentralization of the evaluation and selection process may constitute a better alternative, if the practical conditions of their implementation are adequately settled. (shrink)

When does it make sense to act randomly? A persuasive argument from Bayesian decision theory legitimizes randomization essentially only in tie-breaking situations. Rational behaviour in humans, non-human animals, and artificial agents, however, often seems indeterminate, even random. Moreover, rationales for randomized acts have been offered in a number of disciplines, including game theory, experimental design, and machine learning. A common way of accommodating some of these observations is by appeal to a decision-maker’s bounded computational resources. Making this suggestion both (...) precise and compelling is surprisingly difficult. Toward this end, I propose two fundamental rationales for randomization, drawing upon diverse ideas and results from the wider theory of computation. The first unifies common intuitions in favour of randomization from the aforementioned disciplines. The second introduces a deep connection between randomization and memory: access to a randomizing device is provably helpful for an agent burdened with a finite memory. Aside from fit with ordinary intuitions about rational action, the two rationales also make sense of empirical observations in the biological world. Indeed, random behaviour emerges more or less where it should, according to the proposal. (shrink)

Examinations form part of the assessment processes that constitute the basis for benchmarking individual educational progress, and must consequently fulfill credibility, reliability, and transparency standards in order to promote learning outcomes and ensure academic integrity. A randomly selected question examination is considered to be an effective solution to mitigate sharing of questions between students by addressing replicated inter-examination questions that compromise examination integrity and sequential intra- examination questions that compromise examination comprehensivity. In this study, a Monte Carlo approach was used (...) to design six examination schemes for the purpose of generating and evaluating 600 RSQEs in order to investigate the effects of RSQE design on replicated inter-examination and sequential and intra-examination questions. Results revealed that the number of randomly selected questions from the pool and the number of sub-pools inversely affected the replication and sequencing of the examination questions. Thus, by designing the RSQE in many sub-pools, in equivalence to the number of examination questions and selecting only one question from each sub-pool, and updating the sub-pools after each examination, the passing of information can be prevented, ensuring the integrity of the examinations. (shrink)

We consider tautologies formed form a pseudo-random number generator, defined in Krajicek [11] and in Alekhnovich et al. [2]. We explain a strategy of proving their hardness for Extended Frege systems via a conjecture about bounded arithmetic formulated in Krajicek [11]. Further we give a purely finitary statement, in the form of a hardness condition imposed on a function, equivalent to the conjecture. This is accompanied by a brief explanation, aimed at non-specialists, of the relation between prepositional proof complexity (...) and bounded arithmetic. (shrink)

In article <[email protected]> [email protected] writes: Reminds me of a friend of mine who claims that the number 17 is "the most random" number. His proof ran as follows: pick a number. It's not really as good a random number as 17, is it? (Invariable Answer: "Umm, well, no...") This reminds me of a little experiment I did a couple of years ago. I stood on a busy street corner in Oxford, and asked passers by to "name a (...) class='Hi'>random number between zero and infinity." I was wondering what this "random" distribution would look like. (shrink)

The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows that, conversely, (...) concepts and methods originating from randomness enrich computability theory.The book covers topics such as lowness and highness properties, Kolmogorov complexity, betting strategies and higher computability. Both the basics and recent research results are desribed, providing a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory. (shrink)

Why don't we see large macroscopic objects in entangled states? Even if the particles composing the object were all entangled and insulated from the environment, we shall still find it almost always impossible to observe the superposition. The reason is that as the number of particles n grows, we need an ever more careful preparation, and an ever more carefully designed experiment, in order to recognize the entangled character of the state of the object. An observable W that distinguishes all (...) the unentangled states from some entangled states is called a witness. We consider witnesses on n quantum bits (qbits), and use the following normalization: A witness W satisfies |tr(Wr)|<= 1 for all separable states r, while ||W|| >1, with the norm being the maximum among the absolute values of the eigenvalues of W. Although there are n-qbit witnesses whose norm is exponential in n, we conjecture that for a large majority of such witnesses ||W||<=O[(nlogn)^1/2]. We prove this conjecture for the family of extremal witnesses introduced by Werner and Wolf (Phys. Rev. A 64, 032112 (2001)). Assuming the conjecture is valid we argue that multiparticle entanglement can be detected only if a system has been carefully prepared in a very special state. Otherwise, multiparticle entanglement lies below the threshold of detection, even if it exists, and even if decoherence has been ``turned off''. (shrink)

Gödel's Incompleteness Theorems have the same scientific status as Einstein's principle of relativity, Heisenberg's uncertainty principle, and Watson and Crick's double helix model of DNA. Our aim is to discuss some new faces of the incompleteness phenomenon unveiled by an information-theoretic approach to randomness and recent developments in quantum computing.

We study the sets that are computable from both halves of some (Martin–Löf) random sequence, which we call 1/2-bases. We show that the collection of such sets forms an ideal in the Turing degrees that is generated by its c.e. elements. It is a proper subideal of the K-trivial sets. We characterize 1/2-bases as the sets computable from both halves of Chaitin’s Ω, and as the sets that obey the cost function c(x,s)=Ωs−Ωx−−−−−−−√. Generalizing these results yields a dense hierarchy (...) of subideals in the K-trivial degrees: For k<n, let Bk/n be the collection of sets that are below any k out of n columns of some random sequence. As before, this is an ideal generated by its c.e. elements and the random sequence in the definition can always be taken to be Ω. Furthermore, the corresponding cost function characterization reveals that Bk/n is independent of the particular representation of the rational k/n, and that Bp is properly contained in Bq for rational numbers p<q. These results are proved using a generalization of the Loomis–Whitney inequality, which bounds the measure of an open set in terms of the measures of its projections. The generality allows us to analyze arbitrary families of orthogonal projections. As it turns out, these do not give us new subideals of the K-trivial sets; we can calculate from the family which Bp it characterizes. We finish by studying the union of Bp for p<1; we prove that this ideal consists of the sets that are robustly computable from some random sequence. This class was previously studied by Hirschfeldt [D. R. Hirschfeldt, C. G. Jockusch, R. Kuyper and P. E. Schupp, Coarse reducibility and algorithmic randomness, J. Symbolic Logic81(3) (2016) 1028–1046], who showed that it is a proper subclass of the K-trivial sets. We prove that all such sets are robustly computable from Ω, and that they form a proper subideal of the sets computable from every (weakly) LR-hard random sequence. We also show that the ideal cannot be characterized by a cost function, giving the first such example of a Σ03 subideal of the K-trivial sets. (shrink)

We study the cardinal invariants of measure and category after adding one random real. In particular, we show that the number of measure zero subsets of the plane which are necessary to cover graphs of all continuous functions may be large while the covering for measure is small.

We review briefly the attempts to define random sequences. These attempts suggest two theorems: one concerning the number of subsequence selection procedures that transform a random sequence into a random sequence; the other concerning the relationship between definitions of randomness based on subsequence selection and those based on statistical tests.

Let f be a computable function from finite sequences of 0ʼs and 1ʼs to real numbers. We prove that strong f-randomness implies strong f-randomness relative to a PA-degree. We also prove: if X is strongly f-random and Turing reducible to Y where Y is Martin-Löf random relative to Z, then X is strongly f-random relative to Z. In addition, we prove analogous propagation results for other notions of partial randomness, including non-K-triviality and autocomplexity. We prove that (...) f-randomness relative to a PA-degree implies strong f-randomness, hence f-randomness does not imply f-randomness relative to a PA-degree. (shrink)

We prove a number of results in effective randomness, using methods in which Π⁰₁ classes play an essential role. The results proved include the fact that every PA Turing degree is the join of two random Turing degrees, and the existence of a minimal pair of LR degrees below the LR degree of the halting problem.

Many psychological studies have shown that human‐generated sequences are hardly ever random in the strict mathematical sense. However, what remains an open question is the degree to which this (in)ability varies between people and is affected by contextual factors. Herein, we investigated this problem. In two studies, we used a modern, robust measure of randomness based on algorithmic information theory to assess human‐generated series. In Study 1 (), in a factorial design with task description as a between‐subjects variable, we (...) tested the effects of context and mental fatigue on human‐generated randomness. In Study 2 (), in online research, in experimental design, we further investigated the effect of mental fatigue on the randomness of human‐generated series and the relationship between the need for cognition (NFC) and the ability to produce random‐like series. Results of Study 1 show that the activation of the ability to produce random‐like series depends on the relevance of the contextual cues (), whether they activate known representations of a random series generator and consequently help to avoid the production of trivial sequences. Our findings from both studies on the effect of mental fatigue (Study 1 – ; Study 2 – ) and cognitive motivation () demonstrate that regardless of the context or task's novelty people quickly lose interest in the random series generation. Therefore, their performance decreases over time. However, people high in the NFC can maintain the cognitive motivation for a longer period and consequently on average generate more random series. In general, our results suggest that when contextual cues and intrinsic constraints are in optimal interaction people can temporarily escape the structured and trivial patterns and produce more random‐like sequences. (shrink)

Since the outbreak of the novel coronavirus disease at the beginning of December 2019, there have been more than 28.69 million cumulative confirmed cases worldwide as of 12th September 2020, affecting over 200 countries and regions with more than 920,463 deaths. The COVID-19 pandemic has been sweeping worldwide with unexpected rapidity. In this paper, a hybrid modelling strategy based on tessellation structure- configured SEIR model is adopted to estimate the scale of the pandemic spread. Building on the data pertaining to (...) the global pandemic transmission over the last six months around the world, key impact factors in the transmission and control procedure have been analysed, including isolation rate, number of the infected cases before taking prevention measures, degree of contact scope, and medical level, so as to capture the fundamental factor influencing the pandemic. The quantitative evaluation allowed us to illustrate the magnitude of risks of pandemic and to recommend appropriate national health policy of prevention measures for effectively controlling both intra- and interregional pandemic spread. Our modelling results clearly indicate that the early-stage preventive measures are the most effective action to be taken to contain the pandemic spread of the highly contagious nature of the COVID-19. (shrink)