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Complex Systems, Volume 30, pp 375-390; https://doi.org/10.25088/complexsystems.30.3.375
A puzzle lies behind password authentication (PA) and blockchain proof of work (PoW). A cryptographic hash function is commonly used to implement them. The potential problem with secure hash functions is their complexity and rigidity. We explore the use of complex systems constructs such as a cellular automaton (CA) to provide puzzle functionality. The analysis shows that computational irreducibility and sensitivity to initial state phenomena are enough to create simple puzzle systems that can be used for PA and PoW. Moreover, we present puzzle schemata using CA and n-body problems.
Complex Systems, Volume 30, pp 323-346; https://doi.org/10.25088/complexsystems.30.3.323
The recent worldwide epidemic of COVID-19 disease, for which there are no medications to cure it and the vaccination is still at an early stage, led to the adoption of public health measures by governments and populations in most of the affected countries to avoid the contagion and its spread. These measures are known as nonpharmaceutical interventions (NPIs), and their implementation clearly produces social unrest as well as greatly affects the economy. Frequently, NPIs are implemented with an intensity quantified in an ad hoc manner. Control theory offers a worthwhile tool for determining the optimal intensity of the NPIs in order to avoid the collapse of the healthcare system while keeping them as low as possible, yielding concrete guidance to policymakers. A simple controller, which generates a control law that is easy to calculate and to implement is proposed. This controller is robust to large parametric uncertainties in the model used and to some level of noncompliance with the NPIs.
Complex Systems, Volume 30, pp 297-321; https://doi.org/10.25088/complexsystems.30.3.297
An agent-based model was developed to study outbreaks and outbreak control for COVID-19, mainly in urban communities. Rules for people’s interactions and virus infectiousness were derived based on previous sociology studies and recently published data-driven analyses of COVID-19 epidemics. The calculated basic reproduction number of epidemics from the developed model coincided with reported values. There were three control measures considered in this paper: social distancing, self-quarantine and community quarantine. Each control measure was assessed individually at first. Later on, an artificial neural network was used to study the effects of different combinations of control measures. To help quantify the impacts of self-quarantine and community quarantine on outbreak control, both were scaled respectively. The results showed that self-quarantine was more effective than the others, but any individual control measure was ineffective in controlling outbreaks in urban communities. The results also showed that a high level of self-quarantine and general community quarantine, assisted with social distancing, would be recommended for outbreak control.
Complex Systems, Volume 30, pp 239-272; https://doi.org/10.25088/complexsystems.30.3.239
One-dimensional cellular automata evolutions with both temporal and spatial periodicity are studied. The main objective is to investigate the longest temporal periods among all two-neighbor rules, with a fixed spatial period σ and number of states n. When σ = 2, 3, 4 or 6, and the rules are restricted to be additive, the longest period can be expressed as the exponent of the multiplicative group of an appropriate ring. Non-additive rules are also constructed with temporal period on the same order as the trivial upper bound n σ . Experimental results, open problems and possible extensions of the results are also discussed.
Complex Systems, Volume 30, pp 415-439; https://doi.org/10.25088/complexsystems.30.3.415
This paper proposes the synthesis of single length cycle, single attractor cellular automata (SACAs) for arbitrary length. The n-cell single length cycle, single attractor cellular automaton (SACA), synthesized in linear time O(n), generates a pattern and finally settles to a point state called the single length cycle attractor state. An analytical framework is developed around the graph-based tool referred to as the next state transition diagram to explore the properties of SACA rules for three-neighborhood, one-dimensional cellular automata. This enables synthesis of an (n+1)-cell SACA from the available configuration of an n-cell SACA in constant time and an (n+m)-cell SACA from the available configuration of n-cell and m-cell SACAs also in constant time.
Complex Systems, Volume 30, pp 273-296; https://doi.org/10.25088/complexsystems.30.3.273
We compare the statistical distributions of the geometrical properties of road networks for two representative datasets under different levels of planning: the cities comprising Metropolitan Manila show the conditions under bottom-up self-organized growth, while Brasilia and the Australian Capital Territory centered at Canberra represent the case of strict top-down planning. The distribution of segmented areas of the cities shows a dual power-law behavior, with the larger areas following the ∼1.9 scaling exponent observed in other cities, while the smaller areas show a lower exponent of ∼0.5, believed to be due to practical considerations. While all cities are found to favor the formation of straight road segments, the planned city roads have a preponderance of sinuous roads, with sinuosities approaching π. A simple model based on a nearest-neighbor directed branching coupled with sectional grid formations is proposed to capture the nontrivial statistical features observed.
Complex Systems, Volume 30, pp 347-373; https://doi.org/10.25088/complexsystems.30.3.347
Managing diversity is a challenging problem for organizations and governments. Diversity in a population may be of two kinds—acquired and innate. The former refers to diversity acquired by pre-existing social or organizational environments, attracting employees or immigrants because of their wealth and opportunities. Innate diversity, on the other hand, refers to a collection of pre-existing communities having to interact with one another and to build an overarching social or organizational identity. While acquired diversity has a prior element of common identity, innate diversity needs to build a common identity from a number of disparate regional or local identities. Diversity in any large population may have different extents of acquired and innate elements. In this paper, innate and acquired diversity are modeled in terms of two factors, namely: insularity and homophily, respectively. Insularity is the tendency of agents to act cooperatively only with others from the same community, which is often the primary challenge of innate diversity; while homophily is the tendency of agents to prefer members from their own community to start new social or business connections, which is often the primary challenge in acquired diversity. The emergence of network structure is studied when insularity and homophily are varied. In order to promote cooperation in a diverse population, the role played by a subset of agents called “global” agents who are not affected by homophily and insularity considerations is also studied. Simulation results show several interesting emergent properties. While the global agents are shown to acquire high betweenness, they are by no means the wealthiest or the most powerful in the network. However, the presence of global agents is important for the regional agents whose own wealth prospects increase because of their interaction with global agents.
Complex Systems, Volume 30, pp 391-413; https://doi.org/10.25088/complexsystems.30.3.391
This review article focuses on studying problems of observability and controllability of cellular automata (CAs) considered in the context of control theory, an important feature of which is the adoption of a state-space model. Our work first consists in generalizing the obtained results to systems described by CAs considered as the discrete counterpart of partial differential equations, and in exploring possible approaches to prove controllability and observability. After having introduced the notion of control and observation in cellular automata models, in a similar way to the case of discrete-time distributed parameter systems, we investigate these key concepts of control theory in the case of complex systems. For the controllability issue, the Boolean class is particularly studied and applied to the regional case, while the observability is approached in the general case and related to the reconstructibility problem for linear or nonlinear CAs.
Complex Systems, Volume 30, pp 133-158; https://doi.org/10.25088/complexsystems.30.2.133
The Besicovitch pseudodistance defined in  for biinfinite sequences is invariant by translations. We generalize the definition to arbitrary locally compact second-countable groups and study how properties of the pseudodistance, including invariance by translations, are determined by those of the sequence of sets of finite positive measure used to define it. In particular, we restate from  that if the Besicovitch pseudodistance comes from an exhaustive Følner sequence, then every shift is an isometry. For non-Følner sequences, it is proved that some shifts are not isometries, and the Besicovitch pseudodistance with respect to some subsequences even makes them discontinuous.
Complex Systems, Volume 30, pp 111-132; https://doi.org/10.25088/complexsystems.30.2.111
In contrast to many investigations of cellular automata with regard to their ability to accept inputs under certain time constraints, in this paper we are studying cellular automata with regard to their ability to generate strings in real time. Structural properties such as speedup results and closure properties are investigated. On the one hand, constructions for the closure under intersection, reversal and length-preserving homomorphism are presented, whereas on the other hand the nonclosure under union, complementation and arbitrary homomorphism are obtained. Finally, decidability questions such as emptiness, finiteness, equivalence, inclusion, regularity and context-freeness are addressed.
Complex Systems, Volume 30, pp 187-203; https://doi.org/10.25088/complexsystems.30.2.187
This paper develops a formal logic, named L CA , targeting modeling of one-dimensional binary cellular automata. We first develop the syntax of L CA , then give semantics to L CA in the domain of all binary strings. Then the elementary cellular automata and four-neighborhood binary cellular automata are shown as models of the logic. These instances point out that there are other models of L CA . Finally it is proved that any one-dimensional binary cellular automaton is a model of the proposed logic.
Complex Systems, Volume 30, pp 205-237; https://doi.org/10.25088/complexsystems.30.2.205
This paper introduces a cycle-based clustering technique using the cyclic spaces of reversible cellular automata (CAs). Traditionally, a cluster consists of close objects, which in the case of CAs necessarily means that the objects belong to the same cycle; that is, they are reachable from each other. Each of the cyclic spaces of a cellular automaton (CA) forms a unique cluster. This paper identifies CA properties based on “reachability” that make the clustering effective. To do that, we first figure out which CA rules contribute to maintaining the minimum intracluster distance. Our CA is then designed with such rules to ensure that a limited number of cycles exist in the configuration space. An iterative strategy is also introduced that can generate a desired number of clusters by merging objects of closely reachable clusters from a previous level in the present level using a unique auxiliary CA. Finally, the performance of our algorithm is measured using some standard benchmark validation indices and compared with existing well-known clustering techniques. It is found that our algorithm is at least on a par with the best algorithms existing today on the metric of these standard validation indices.
Complex Systems, Volume 30, pp 159-185; https://doi.org/10.25088/complexsystems.30.2.159
Gellular automata are cellular automata with the properties of asynchrony, Boolean totality and noncamouflage. In distributed computing, it is essential to determine whether problems can be solved by self-stable gellular automata. From any initial configuration, self-stable gellular automata converge to desired configurations, as self-stability implies the ability to recover from temporary malfunctions in transitions or states. This paper shows that three typical problems in distributed computing, namely, solving a maze, distance-2 coloring and spanning tree construction, can be solved with self-stable gellular automata.
Complex Systems, Volume 30, pp 93-110; https://doi.org/10.25088/complexsystems.30.1.93
Differential equations are widely used to model systems that change over time, some of which exhibit chaotic behaviors. This paper proposes two new methods to classify these behaviors that are utilized by a supervised machine learning algorithm. Dissipative chaotic systems, in contrast to conservative chaotic systems, seem to follow a certain visual pattern. Also, the machine learning program written in the Wolfram Language is utilized to classify chaotic behavior with an accuracy around 99.1±1.1%.
Complex Systems, Volume 30, pp 1-32; https://doi.org/10.25088/complexsystems.30.1.1
Synchronization, which occurs for both chaotic and nonchaotic systems, is a striking phenomenon with many practical implications for natural phenomena and technological applications. However, even before synchronization, strong correlations and complex patterns occur in the collective dynamics of natural systems. To characterize their nature is essential for understanding many phenomena in physical and social sciences as well as the perspectives to control their behavior. Because simple correlation measures are unable to characterize these collective patterns, we have developed more general methods for their detection and parametrization. The emergence of patterns of strong correlations before synchronization is illustrated in a few models. They are shown to be associated with the behavior of ergodic parameters. The models are then used as a testing ground of the new pattern characterization tools.
Complex Systems, Volume 30, pp 33-46; https://doi.org/10.25088/complexsystems.30.1.33
In a temporal network, causal paths are characterized by the fact that links from a source to a target must respect the chronological order. In this paper we study the causal paths structure in temporal networks of face-to-face human interactions in different social contexts. In a static network, paths are transitive; that is, the existence of a link from a to b and from b to c implies the existence of a path from a to c via b. In a temporal network, the chronological constraint introduces time correlations that affect transitivity. A probabilistic model based on higher-order Markov chains shows that correlations that can invalidate transitivity are present only when the time gap between consecutive events is larger than the average value and are negligible below such a value. The comparison between the densities of the temporal and static accessibility matrices shows that the static representation can be used with good approximation. Moreover, we quantify the extent of the causally connected region of the networks over time.
Complex Systems, Volume 30, pp 75-92; https://doi.org/10.25088/complexsystems.30.1.75
Evolution patterns of a one-dimensional homogeneous cellular automaton (CA) are investigated for some standard transition functions. The different possible evolution patterns for an elementary CA starting with at most one active cell or ON state cell are discussed. Also, with respect to some initial configurations, evolution-wise equivalent Wolfram codes are investigated. It is shown that these equivalent codes are automorphic.
Complex Systems, Volume 30, pp 47-73; https://doi.org/10.25088/complexsystems.30.1.47
This paper presents a mathematical model for a piston flow reactor based on the material balance law using partial differential equations. A more general, nondimensional variant of the model is also derived. The finite difference method and coupled map lattice are used to create numerical algorithms to simulate spatio-temporal behavior in the studied system. The paper also includes a stability analysis of the proposed algorithms and results of numerous numerical simulations, done in order to compare both methods and to visualize the spatio-temporal behavior of the reactor and the effects of different model parameters. Discussion of the obtained results and comparison of both algorithms is also provided.
The Mathematica Journal; https://doi.org/10.3888/tmj.23-3
We present a straightforward implementation of contour integration by setting options for Integrate and NIntegrate, taking advantage of powerful results in complex analysis. As such, this article can be viewed as documentation to perform numerical contour integration with the existing built-in tools. We provide examples of how this method can be used when integrating analytically and numerically some commonly used distributions, such as Wightman functions in quantum field theory. We also provide an approximating technique when time-ordering is involved, a commonly encountered scenario in quantum field theory for computing second-order terms in Dyson series expansion and Feynman propagators. We believe our implementation will be useful for more general calculations involving advanced or retarded Green’s functions, propagators, kernels and so on.
The Mathematica Journal, Volume 23; https://doi.org/10.3888/tmj.23-1
This article is intended to help students understand the concept of a coverage probability involving confidence intervals. Mathematica is used as a language for describing an algorithm to compute the coverage probability for a simple confidence interval based on the binomial distribution. Then, higher-level functions are used to compute probabilities of expressions in order to obtain coverage probabilities. Several examples are presented: two confidence intervals for a population proportion based on the binomial distribution, an asymptotic confidence interval for the mean of the Poisson distribution, and an asymptotic confidence interval for a population proportion based on the negative binomial distribution.
The Mathematica Journal, Volume 23; https://doi.org/10.3888/tmj.23-2
Lehmer defined a measure depending on numbers beta_i used in a Machin-like formula for pi. When the beta_i are integers, Lehmer's measure can be used to determine the computational efficiency of the given Machin-like formula for pi. However, because the computations are complicated, it is unclear if Lehmer's measure applies when one or more of the beta_i are rational. In this article, we develop a new algorithm for a two-term Machin-like formula for pi as an example of the unconditional applicability of Lehmer's measure. This approach does not involve any irrational numbers and may allow calculating pi rapidly by the Newton-Raphson iteration method for the tangent function.
The Mathematica Journal, Volume 23; https://doi.org/10.3888/tmj.23-4
Complex Systems, Volume 29, pp 759-778; https://doi.org/10.25088/complexsystems.29.4.759
We study a cellular automaton (CA) model of information dynamics on a single hypha of a fungal mycelium. Such a filament is divided in compartments (here also called cells) by septa. These septa are invaginations of the cell wall and their pores allow for the flow of cytoplasm between compartments and hyphae. The septal pores of the fungal phylum of the Ascomycota can be closed by organelles called Woronin bodies. Septal closure is increased when the septa become older and when exposed to stress conditions. Thus, Woronin bodies act as informational flow valves. The one-dimensional fungal automaton is a binary-state ternary neighborhood CA, where every compartment follows one of the elementary cellular automaton (ECA) rules if its pores are open and either remains in state 0 (first species of fungal automata) or its previous state (second species of fungal automata) if its pores are closed. The Woronin bodies closing the pores are also governed by ECA rules. We analyze a structure of the composition space of cell-state transition and pore-state transition rules and the complexity of fungal automata with just a few Woronin bodies, and exemplify several important local events in the automaton dynamics.
Complex Systems, Volume 29, pp 837-860; https://doi.org/10.25088/complexsystems.29.4.837
The enumeration of all sequential substitution system rulesets is modified to include generalized substitution system rulesets. Unlike its predecessor, the new enumeration is one-to-one: each ruleset is guaranteed to appear exactly once in the new enumeration, which moreover possesses an elegant simplicity that allows jumps over increasingly longer undesired subsequences of many types. This process effectively results in an increased acceleration and greatly improved performance.
Complex Systems, Volume 29, pp 779-835; https://doi.org/10.25088/complexsystems.29.4.779
Cancers remain the leading cause of disease-related pediatric death in North America. The emerging field of complex systems has redefined cancer networks as a computational system. Herein, a tumor and its heterogeneous phenotypes are discussed as dynamical systems having multiple strange attractors. Machine learning, network science and algorithmic information dynamics are discussed as current tools for cancer network reconstruction. Deep learning architectures and computational fluid models are proposed for better forecasting gene expression patterns in cancer ecosystems. Cancer cell decision-making is investigated within the framework of complex systems and complexity theory.
Complex Systems, Volume 29, pp 861-875; https://doi.org/10.25088/complexsystems.29.4.861
The wisdom of crowds is the idea that the combination of independent estimates of the magnitude of some quantity yields a remarkably accurate prediction, which is always more accurate than the average individual estimate. In addition, it is largely believed that the accuracy of the crowd can be improved by increasing the diversity of the estimates. Here we report the results of three experiments to probe the current understanding of the wisdom of crowds, namely, the estimates of the number of candies in a jar, the length of a paper strip and the number of pages of a book. We find that the collective estimate is better than the majority of the individual estimates in all three experiments. In disagreement with the prediction diversity theorem, we find no significant correlation between the prediction diversity and the collective error. The poor accuracy of the crowd on some experiments leads us to conjecture that its alleged accuracy is most likely an artifact of selective attention.
Complex Systems, Volume 29, pp 741-757; https://doi.org/10.25088/complexsystems.29.4.741
This paper deals with the issue of model construction of the self-regeneration and self-replication processes using movable cellular automata (MCAs). The rules of cellular automaton (CA) interactions are found according to the concept of equilibrium neighborhood. The method is implemented by establishing these rules between different types of cellular automata (CAs). Several models for two- and three-dimensional cases are described, which depict both stable and unstable structures. As a result, computer models imitating such natural phenomena as self-replication and self-regeneration are obtained and graphically presented.
Complex Systems, Volume 29, pp 655-667; https://doi.org/10.25088/complexsystems.29.3.655
Complex Systems, Volume 29; https://doi.org/10.25088/complexsystems.29.3.i
Complex Systems, Volume 29, pp 729-739; https://doi.org/10.25088/complexsystems.29.3.729
Complex Systems, Volume 29, pp 669-688; https://doi.org/10.25088/complexsystems.29.3.669
Complex Systems, Volume 29, pp 689-709; https://doi.org/10.25088/complexsystems.29.3.689
Complex Systems, Volume 29, pp 711-728; https://doi.org/10.25088/complexsystems.29.3.711
Complex Systems, Volume 29, pp 107-536; https://doi.org/10.25088/complexsystems.29.1.2
Complex Systems, Volume 29, pp 599-654; https://doi.org/10.25088/complexsystems.29.2.599
Complex Systems, Volume 29, pp 537-598; https://doi.org/10.25088/complexsystems.29.2.537
Complex Systems, Volume 29, pp 107-536; https://doi.org/10.25088/complexsystems.29.2.107
Complex Systems, Volume 29, pp 45-61; https://doi.org/10.25088/complexsystems.29.1.45
Complex Systems, Volume 29, pp 63-76; https://doi.org/10.25088/complexsystems.29.1.63
Complex Systems, Volume 29, pp 1-44; https://doi.org/10.25088/complexsystems.29.1.1
Complex Systems, Volume 29, pp 87-105; https://doi.org/10.25088/complexsystems.29.1.87
Complex Systems, Volume 29, pp 77-86; https://doi.org/10.25088/complexsystems.29.1.77
Wolfram Research Data Repository; https://doi.org/10.24097/wolfram.04123.data
Wolfram Research Data Repository; https://doi.org/10.24097/wolfram.11224.data
Medical records of patients infected with novel coronavirus
Wolfram Research Data Repository; https://doi.org/10.24097/wolfram.03304.data
Wolfram Research Data Repository; https://doi.org/10.24097/wolfram.11224.data/
The Mathematica Journal, Volume 22; https://doi.org/10.3888/tmj.22-1
The Mathematica Journal, Volume 22; https://doi.org/10.3888/tmj.22-5
The Mathematica Journal, Volume 22; https://doi.org/10.3888/tmj.22-4
The Mathematica Journal, Volume 22; https://doi.org/10.3888/tmj.22-3