{"title":"Simulating the spread of COVID-19 with cellular automata: A new approach","authors":"Sourav Chowdhury, Suparna Roychowdhury, Indranath Chaudhuri","doi":"arxiv-2307.14576","DOIUrl":"https://doi.org/arxiv-2307.14576","url":null,"abstract":"Between the years 2020 to 2022, the world was hit by the pandemic of COVID-19\u0000giving rise to an extremely grave situation. The global economy was badly hurt\u0000due to the consequences of various intervention strategies (like social\u0000distancing, lockdown) which were applied by different countries to control this\u0000pandemic. There are multiple speculations that humanity will again face such\u0000pandemics in the future. Thus it is very important to learn and gain knowledge\u0000about the spread of such infectious diseases and the various factors which are\u0000responsible for it. In this study, we have extended our previous work\u0000(Chowdhury et.al., 2022) on the probabilistic cellular automata (CA) model to\u0000reproduce the spread of COVID-19 in several countries by modifying its earlier\u0000used neighbourhood criteria. This modification gives us the liberty to adopt\u0000the effect of different restrictions like lockdown and social distancing in our\u0000model. We have done some theoretical analysis for initial infection and\u0000simulations to gain insights into our model. We have also studied the data from\u0000eight countries for COVID-19 in a window of 876 days and compared it with our\u0000model. We have developed a proper framework to fit our model on the data for\u0000confirmed cases of COVID-19 and have also re-checked the goodness of the fit\u0000with the data of the deceased cases for this pandemic. This model fits well\u0000with different peaks of COVID-19 data for all the eight countries and can be\u0000possibly generalized for a global prediction.","PeriodicalId":501231,"journal":{"name":"arXiv - PHYS - Cellular Automata and Lattice Gases","volume":"64 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Layered Cellular Automata","authors":"Abhishek Dalai","doi":"arxiv-2308.06370","DOIUrl":"https://doi.org/arxiv-2308.06370","url":null,"abstract":"Layered Cellular Automata (LCA) extends the concept of traditional cellular\u0000automata (CA) to model complex systems and phenomena. In LCA, each cell's next\u0000state is determined by the interaction of two layers of computation, allowing\u0000for more dynamic and realistic simulations. This thesis explores the design,\u0000dynamics, and applications of LCA, with a focus on its potential in pattern\u0000recognition and classification. The research begins by introducing the\u0000limitations of traditional CA in capturing the complexity of real-world\u0000systems. It then presents the concept of LCA, where layer 0 corresponds to a\u0000predefined model, and layer 1 represents the proposed model with additional\u0000influence. The interlayer rules, denoted as f and g, enable interactions not\u0000only from adjacent neighboring cells but also from some far-away neighboring\u0000cells, capturing long-range dependencies. The thesis explores various LCA\u0000models, including those based on averaging, maximization, minimization, and\u0000modified ECA neighborhoods. Additionally, the implementation of LCA on the 2-D\u0000cellular automaton Game of Life is discussed, showcasing intriguing patterns\u0000and behaviors. Through extensive experiments, the dynamics of different LCA\u0000models are analyzed, revealing their sensitivity to rule changes and block size\u0000variations. Convergent LCAs, which converge to fixed points from any initial\u0000configuration, are identified and used to design a two-class pattern\u0000classifier. Comparative evaluations demonstrate the competitive performance of\u0000the LCA-based classifier against existing algorithms. Theoretical analysis of\u0000LCA properties contributes to a deeper understanding of its computational\u0000capabilities and behaviors. The research also suggests potential future\u0000directions, such as exploring advanced LCA models, higher-dimensional\u0000simulations, and hybrid approaches integrating LCA with other computational\u0000models.","PeriodicalId":501231,"journal":{"name":"arXiv - PHYS - Cellular Automata and Lattice Gases","volume":"74 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Supervised and unsupervised learning of (1+1)-dimensional even-offspring branching annihilating random walks","authors":"Yanyang Wang, Wei Li, Feiyi Liu, Jianmin Shen","doi":"arxiv-2307.05618","DOIUrl":"https://doi.org/arxiv-2307.05618","url":null,"abstract":"The machine learning (ML) of phase transitions (PTs) has gradually become an\u0000effective approach, which enables us to explore the nature of various PTs, more\u0000promptly, in both equilibrium and non-equilibrium systems. Unlike equilibrium\u0000systems, non-equilibrium systems display more complicated and diverse features,\u0000due to the extra dimension of time, which are not readily tractable, both\u0000theoretically and numerically. The combination of ML and the most renowned\u0000non-equilibrium model, the directed percolation (DP), has led to some\u0000significant findings. Here in this work, the ML technique will be applied to\u0000the (1+1)-d even-offspring branching annihilating random walks (BAW), whose\u0000universality class is not DP-like. The supervised learning of (1+1)-d BAW, via\u0000convolutional neural networks (CNN), results in a more accurate prediction of\u0000the critical point than the Monte Carlo (MC) simulation at the same system\u0000sizes. The dynamic exponent ;$z$; and the spatial correlation length\u0000correlation exponent ;$nu_{perp}$ are also measured and found to be\u0000consistent with the respective theoretical values. The unsupervised learning of\u0000(1+1)-d BAW, via autoencoder (AE), also gives rise to a transition point which\u0000is the same as the critical point. The output of AE, through a single neuron,\u0000can be regarded as the order parameter of the system, being re-scaled properly.\u0000We therefore have the reason to believe that ML has an exciting application\u0000prospect in such reaction-diffusion systems as the BAW and DP.","PeriodicalId":501231,"journal":{"name":"arXiv - PHYS - Cellular Automata and Lattice Gases","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Words fixing the kernel network and maximum independent sets in graphs","authors":"Maximilien Gadouleau, David C. Kutner","doi":"arxiv-2307.05216","DOIUrl":"https://doi.org/arxiv-2307.05216","url":null,"abstract":"The simple greedy algorithm to find a maximal independent set of a graph can\u0000be viewed as a sequential update of a Boolean network, where the update\u0000function at each vertex is the conjunction of all the negated variables in its\u0000neighbourhood. In general, the convergence of the so-called kernel network is\u0000complex. A word (sequence of vertices) fixes the kernel network if applying the\u0000updates sequentially according to that word. We prove that determining whether\u0000a word fixes the kernel network is coNP-complete. We also consider the\u0000so-called permis, which are permutation words that fix the kernel network. We\u0000exhibit large classes of graphs that have a permis, but we also construct many\u0000graphs without a permis.","PeriodicalId":501231,"journal":{"name":"arXiv - PHYS - Cellular Automata and Lattice Gases","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"When greediness and self-confidence meet in a social dilemma","authors":"Chaoqian Wang, Wenqiang Zhu, Attila Szolnoki","doi":"arxiv-2307.04044","DOIUrl":"https://doi.org/arxiv-2307.04044","url":null,"abstract":"A greedy personality is usually accompanied by arrogance and confidence. This\u0000work investigates the cooperation success condition in the context of biased\u0000payoff allocation and self-confidence. The first component allows the organizer\u0000in a spatial public goods game to receive a different proportion of goods than\u0000other participants. The second aspect influences the micro-level dynamics of\u0000strategy updates, wherein players can maintain their strategy with a certain\u0000weight. Analytical results are obtained on square lattices under the weak\u0000selection limit. If the organizer attempts to monopolize the public goods,\u0000cooperation becomes more attainable. If the confidence increases, cooperation\u0000is inhibited. Consequently, these elements have conflicting effects on\u0000cooperation, and their simultaneous presence can result in a heterogeneous\u0000change of the critical synergy factor. Our theoretical findings underscore the\u0000subtle implications of a mutual trait that may manifest as greediness or\u0000self-confidence under different circumstances, which are validated through\u0000Monte Carlo simulations.","PeriodicalId":501231,"journal":{"name":"arXiv - PHYS - Cellular Automata and Lattice Gases","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
David Auger, Pierre Coucheney, Loric Duhazé, Kossi Roland Etse
{"title":"Generalized ARRIVAL Problem for Rotor Walks in Path Multigraphs","authors":"David Auger, Pierre Coucheney, Loric Duhazé, Kossi Roland Etse","doi":"arxiv-2307.01897","DOIUrl":"https://doi.org/arxiv-2307.01897","url":null,"abstract":"Rotor walks are cellular automata that determine deterministic traversals of\u0000particles in a directed multigraph using simple local rules, yet they can\u0000generate complex behaviors. Furthermore, these trajectories exhibit statistical\u0000properties similar to random walks. In this study, we investigate a generalized version of the reachability\u0000problem known as ARRIVAL in Path Multigraphs, which involves predicting the\u0000number of particles that will reach designated target vertices. We show that\u0000this problem is in NP and co-NP in the general case. However, we exhibit\u0000algebraic invariants for Path Multigraphs that allow us to solve the problem\u0000efficiently, even for an exponential configuration of particles. These\u0000invariants are based on harmonic functions and are connected to the\u0000decomposition of integers in rational bases.","PeriodicalId":501231,"journal":{"name":"arXiv - PHYS - Cellular Automata and Lattice Gases","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On lattice Boltzmann scheme, finite volumes and boundary conditions","authors":"François DuboisLMO, LMSSC, Pierre LallemandCSRC","doi":"arxiv-2306.15291","DOIUrl":"https://doi.org/arxiv-2306.15291","url":null,"abstract":"We develop the idea that a natural link between Boltzmann schemes and finite\u0000volumes exists naturally: the conserved mass and momentum during the collision\u0000phase of the Boltzmann scheme induces general expressions for mass and momentum\u0000fluxes. We treat a unidimensional case and focus our development in two\u0000dimensions on possible flux boundary conditions. Several test cases show that a\u0000high level of accuracy can be achieved with this scheme.","PeriodicalId":501231,"journal":{"name":"arXiv - PHYS - Cellular Automata and Lattice Gases","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Towards quantization Conway Game of Life","authors":"Krzysztof Pomorski, Dariusz Kotula","doi":"arxiv-2306.15151","DOIUrl":"https://doi.org/arxiv-2306.15151","url":null,"abstract":"Classical stochastic Conway Game of Life is expressed by the dissipative\u0000Schr\"odinger equation and dissipative tight-binding model. This is conducted\u0000at the prize of usage of time dependent anomalous non-Hermitian Hamiltonians as\u0000with occurrence of complex value potential that do not preserve the\u0000normalization of wave-function and thus allows for mimicking creationism or\u0000annihilationism of cellular automaton. Simply saying time-dependent complex\u0000value eigenenergies are similar to complex values of resonant frequencies in\u0000electromagnetic resonant cavities reflecting presence of dissipation that\u0000reflects energy leaving the system or being pumped into the system. At the same\u0000time various aspects of thermodynamics were observed in cellular automata that\u0000can be later reformulated by quantum mechanical pictures. The usage of Shannon\u0000entropy and mass equivalence to energy points definition of cellular automata\u0000temperature. Contrary to intuitive statement the system dynamical equilibrium\u0000is always reflected by negative temperatures. Diffusion of mass, energy and\u0000temperature as well as phase of proposed wave function is reported and can be\u0000directly linked with second thermodynamics law approximately valid for the\u0000system, where neither mass nor energy is conserved. The concept of\u0000complex-valued mass mimics wave-function behavior. Equivalence an anomalous\u0000second Fick law and dissipative Schr\"odinger equation is given. Dissipative\u0000Conway Game of Life tight-binding Hamiltonian is given using phenomenological\u0000justification.","PeriodicalId":501231,"journal":{"name":"arXiv - PHYS - Cellular Automata and Lattice Gases","volume":"72 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Probabilistic cellular automata with Andrei Toom","authors":"Peter Gacs","doi":"arxiv-2306.13226","DOIUrl":"https://doi.org/arxiv-2306.13226","url":null,"abstract":"Andrei Toom, who died in September 2022, contributed some of the most\u0000fundamental results on probabilistic cellular automata. We want to acquaint the\u0000reader with these and will also try to give the reader a look at the\u0000environment in which they were born. Toom was an original and strong\u0000personality, and other aspects of his life (education, literature) will also\u0000deserve mention.","PeriodicalId":501231,"journal":{"name":"arXiv - PHYS - Cellular Automata and Lattice Gases","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sina Khajehabdollahi, Emmanouil Giannakakis, Victor Buendia, Georg Martius, Anna Levina
{"title":"Locally adaptive cellular automata for goal-oriented self-organization","authors":"Sina Khajehabdollahi, Emmanouil Giannakakis, Victor Buendia, Georg Martius, Anna Levina","doi":"arxiv-2306.07067","DOIUrl":"https://doi.org/arxiv-2306.07067","url":null,"abstract":"The essential ingredient for studying the phenomena of emergence is the\u0000ability to generate and manipulate emergent systems that span large scales.\u0000Cellular automata are the model class particularly known for their effective\u0000scalability but are also typically constrained by fixed local rules. In this\u0000paper, we propose a new model class of adaptive cellular automata that allows\u0000for the generation of scalable and expressive models. We show how to implement\u0000computation-effective adaptation by coupling the update rule of the cellular\u0000automaton with itself and the system state in a localized way. To demonstrate\u0000the applications of this approach, we implement two different emergent models:\u0000a self-organizing Ising model and two types of plastic neural networks, a rate\u0000and spiking model. With the Ising model, we show how coupling local/global\u0000temperatures to local/global measurements can tune the model to stay in the\u0000vicinity of the critical temperature. With the neural models, we reproduce a\u0000classical balanced state in large recurrent neuronal networks with excitatory\u0000and inhibitory neurons and various plasticity mechanisms. Our study opens\u0000multiple directions for studying collective behavior and emergence.","PeriodicalId":501231,"journal":{"name":"arXiv - PHYS - Cellular Automata and Lattice Gases","volume":"61 32","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138510835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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