Article
Engineering, Multidisciplinary
Jian Tang, Siddhant Kumar, Laura De Lorenzis, Ehsan Hosseini
Summary: We propose Neural Cellular Automata (NCA) for simulating microstructure development in the solidification process of metals. NCA, based on convolutional neural networks, can learn essential features of solidification and are much faster than conventional Cellular Automata (CA). Notably, NCA can make reliable predictions beyond their training range, indicating their understanding of the physics of solidification. While CA data is used for training in this study, NCA can be trained on any microstructural simulation data, such as phase-field models.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Physics, Fluids & Plasmas
Edward Gillman, Federico Carollo, Igor Lesanovsky
Summary: The design of quantum perceptrons and neural network architectures is central to the field of quantum machine learning. This study establishes a connection between (1 + 1)D quantum cellular automata and quantum neural networks (QNNs), allowing for the construction of structured QNNs that can be connected to continuous-time Lindblad dynamics. An example case analysis reveals a change in critical behavior when quantum effects are varied, demonstrating the potential impact on information processing in large-scale QNNs.
Article
Mathematics, Applied
Sidney Pontes-Filho, Pedro G. Lind, Stefano Nichele
Summary: This study investigates the robustness of critical systems to noise by examining the robustness of stochastic cellular automata (CAs) at criticality. The findings indicate that a specific CA can remain in a critical regime even under certain levels of noise, as demonstrated by error metrics of power-law fitting. The implications of these results for future brain-inspired artificial intelligence systems are discussed.
PHYSICA D-NONLINEAR PHENOMENA
(2022)
Article
Computer Science, Information Systems
Wenxiang Fang, Tao Xie, Biwen LI
Summary: This paper discusses the robustness analysis of fuzzy cellular neural networks with deviating arguments and stochastic disturbances. The main focus is on determining the upper bounds of disturbances and deviating intervals that the network can withstand without losing stability. By using the Gronwall-Bellman lemma and inequality techniques, these problems are solved. The theoretical results indicate that for an exponentially stable fuzzy cellular neural network, the perturbed network can maintain its globally exponential stability if the upper bound of deviating intervals or the intensity of stochastic disturbances is less than the bound derived in this paper. Several numerical cases are provided to support the conjectural values.
Article
Physics, Multidisciplinary
Enrique C. Gabrick, Paulo R. Protachevicz, Antonio M. Batista, Kelly C. Iarosz, Silvio L. T. de Souza, Alexandre C. L. Almeida, Jose D. Szezech Jr, Michele Mugnaine, Ibere L. Caldas
Summary: In this study, we propose the inclusion of two vaccination doses in the SEIR model using a stochastic cellular automaton to support decision making of immunisation strategies. Our results suggest that the number of vaccinations and time to start the vaccination have more impact than vaccine efficacy and delays between doses.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2022)
Article
Computer Science, Theory & Methods
Wenxia Cui, Zhenjie Wang, Wenbin Jin
Summary: This paper investigates the fixed-time synchronization of Markovian jump fuzzy cellular neural networks with stochastic perturbations and time-varying delays. By designing delay-dependent controllers, constructing a suitable stochastic Lyapunov functional, and utilizing matrix analysis techniques, novel and useful sufficient conditions are derived to guarantee the synchronization in fixed time. The results are delay-dependent and less conservative, with finite time being independent of initial states.
FUZZY SETS AND SYSTEMS
(2021)
Article
Mathematics, Interdisciplinary Applications
Souvik Roy, Subrata Paul, Sukanta Das
Summary: This article introduces temporally stochastic cellular automata and studies its dynamics using qualitative and quantitative simulations. The article classifies and observes phase transitions and class transitions in the temporally stochastic cellular automata.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Environmental Sciences
Yasir Abdulameer Nayyef Aldabbagh, Helmi Zulhaidi Mohd Shafri, Shattri Mansor, Mohd Hasmadi Ismail
Summary: This study employs remote sensing and geospatial solutions to investigate desertification in Al-Khidhir district. By constructing prediction models and analyzing historical land cover maps and desertification indicators, the study predicts the future trend of desertification in Al-Khidhir district. The results indicate that without control strategies, the extent of bare land will expand.
ENVIRONMENTAL MONITORING AND ASSESSMENT
(2022)
Article
Environmental Sciences
Antonio-Juan Collados-Lara, Eulogio Pardo-Iguzquiza, David Pulido-Velazquez
Summary: This study introduces a novel methodology to assess the impact of climate change on snow cover areas in alpine systems, focusing on the Sierra Nevada in southern Spain. The findings suggest significant reductions in snow cover area over the next few decades, with potential implications equivalent to a 400-meter elevation shift in snow distribution.
SCIENCE OF THE TOTAL ENVIRONMENT
(2021)
Article
Meteorology & Atmospheric Sciences
Lisa Bengtsson, Juliana Dias, Stefan Tulich, Maria Gehne, Jian-Wen Bao
Summary: In this study, the impact of using cellular automata in atmospheric convection models for subgrid organization parameterization is explored. Results indicate that with the cellular automata scheme, precipitation becomes more organized spatially and temporally, and there is a noticeable shift in equatorial wave phase speed.
JOURNAL OF ADVANCES IN MODELING EARTH SYSTEMS
(2021)
Article
Computer Science, Information Systems
Pedro Paulo Balbi, Eurico Ruivo, Fernando Faria
Summary: The parity problem is a classical benchmark for studying the computational ability of cellular automata. This article presents a synchronous solution to the problem using elementary cellular automaton rule 150 and a connection pattern defined by a family of directed, non-circulant, regular graphs. This solution represents the simplest synchronous solution known for cyclic configurations and demonstrates solving a non-trivial global problem with a local counterpart.
INFORMATION SCIENCES
(2022)
Article
Computer Science, Artificial Intelligence
Pacome Perrotin
Summary: This paper proves the exact correspondence between the limit dynamics of a finite automata network under the parallel update schedule and the fixed points of a strictly one-way cellular automaton. The transformation from a strictly one-way cellular automaton to a corresponding automata network is accomplished using output functions developed in the author's previous works.
Article
Computer Science, Artificial Intelligence
Gail Weiss, Yoav Goldberg, Eran Yahav
Summary: The paper introduces a new algorithm for extracting DFA from trained RNNs, avoiding state explosion even in cases of large state vectors and fine differentiation. The authors discuss the relevance of applying this technique to language models and experimentally demonstrate limitations of RNN learning in certain cases.
Article
Physics, Mathematical
Bruno Hideki Fukushima-Kimura, Satoshi Handa, Katsuhiro Kamakura, Yoshinori Kamijima, Kazushi Kawamura, Akira Sakai
Summary: In this paper, we investigate a type of stochastic cellular automata where all spins are updated independently and simultaneously. We prove that if the temperature is sufficiently high, the mixing time is at most logarithmic in the size of the graph, and that if the temperature decreases as 1/logn, the limiting measure is uniformly distributed over the ground states. We also provide simulations showing the superior performance of the algorithms studied in this paper compared to conventional simulated annealing.
JOURNAL OF STATISTICAL PHYSICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Jaume Ojer, Alvaro G. Lopez, Javier Used, Miguel A. F. Sanjuan
Summary: We reproduce the phenomenon of chemotaxis using a hybrid random walk model on a two-dimensional lattice. The dynamics of the chemoattractant is modelled using a partial differential equation, while the cell is treated discretely and influenced by concentration gradients. The bias towards higher chemical concentrations is determined by a stochastic process, which is controlled by a single parameter related to the attractiveness of the source and its efficiency in cellular capture. The model has been thoroughly analyzed in terms of parameter space and the efficiency of cellular capture is illustrated using stochastic basins of attraction.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
E. A. P. Wright, S. Yoon, J. F. F. Mendes, A. Goltsev
Summary: A complete bifurcation analysis of the periodically forced Kuramoto model identified all bifurcations within the model, but it was found that the predicted phase diagram was incomplete. Numerical analysis showed that the model can undergo a phase transition from oscillations to wobbly rotations, not revealed by bifurcation analysis, due to a singular point in the order-parameter space.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics
Ricardo J. Jesus, Mario L. Antunes, Rui A. da Costa, Sergey N. Dorogovtsev, Jose F. F. Mendes, Rui L. Aguiar
Summary: The study statistically characterized the deviation of weights of two-hidden-layer feedforward ReLU networks trained via Stochastic Gradient Descent (SGD), finding that successful training leaves the network in the vicinity of the initial configuration of weights. However, there is a sudden increase in deviation observed within the overfitting region.
Article
Physics, Multidisciplinary
Xin-Jian Xu, Cheng Chen, J. F. F. Mendes
Summary: Quantifying dissimilarities between networks is a challenging problem. Current metrics may assume homogeneous distribution of nodal degrees or ignore network community structure. The proposed measure efficiently compares heterogeneous networks with communities, considering probability distribution functions, and returns non-zero values only for non-isomorphic networks.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2022)
Article
Biology
Alexander V. Goltsev, Edgar A. P. Wright, Jose F. F. Mendes, Sooyeon Yoon
Summary: This study focuses on how the core-shell organization controls the behavior of the suprachiasmatic nucleus (SCN), synchronization of the core and shell with the environment, and the impact on SCN behavior under different lighting conditions. The reduced Kuramoto model is used to analyze free-running and entrained SCN activity, as well as the phenomena of anticipation and dissociation. The results show that the core-shell organization enables anticipation of future events and predicts the emergence of a second rhythm for large and small lighting periods.
JOURNAL OF BIOLOGICAL RHYTHMS
(2022)
Article
Mathematics, Interdisciplinary Applications
G. J. Baxter, R. A. da Costa, S. N. Dorogovtsev, J. F. F. Mendes
Summary: We solve the weak percolation problem for multiplex networks with overlapping edges. Our theory shows that in two layers, any (nonzero) concentration of overlaps drives the weak percolation transition to the ordinary percolation universality class. In three layers, the phase diagram of the problem contains two lines - of a continuous phase transition and of a discontinuous one - connected in various ways depending on how the layers overlap.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Immunology
Thiago B. Murari, Larissa Moraes Dos Santos Fonseca, Hernane B. de B. Pereira, Aloisio S. Nascimento Filho, Hugo Saba, Fulvio A. Scorza, Antonio-Carlos G. de Almeida, Ethel L. N. Maciel, Jose F. F. Mendes, Tarcisio M. Rocha Filho, John R. David, Roberto Badaro, Bruna Aparecida Souza Machado, Marcelo A. Moret
Summary: Hospitlization due to the Omicron variant is associated with lower mortality and shorter hospitalization time compared to the Delta variant, which may lead to a misinterpretation of the results.
Article
Astronomy & Astrophysics
Natalia Gorobey, Alexander Lukyanenko, Alexander V. Goltsev
Summary: This paper proposes a theory of the initial state of the universe within the framework of the Euclidean quantum theory of gravity. It investigates the eigenvalue of the action operator in the area of the origin of the universe and presents the wave function of the initial state.
Article
Mathematics, Interdisciplinary Applications
D. S. R. Ferreira, J. Ribeiro, P. S. L. Oliveira Jr, A. R. Pimenta, R. P. Freitas, R. S. Dutra, A. R. R. Papa, J. F. F. Mendes
Summary: This study analyzes the spatiotemporal distributions of earthquakes and finds that there is no differentiation in the statistical features of earthquakes. The results reveal the critical behavior and long-range spatiotemporal correlations in earthquakes.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Physics, Multidisciplinary
S. Yoon, K. P. O'Keeffe, J. F. F. Mendes, A. Goltsev
Summary: This article studies a model of nonidentical swarmalators, which are generalizations of phase oscillators that sync in time and swarm in space. The article introduces four collective states produced by the model and their applications, and proposes a generalized hypothesis that provides the first analytic description and conditions for the existence of these states.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Fluids & Plasmas
G. Timar, S. N. Dorogovtsev, J. F. F. Mendes
Summary: The nonbacktracking matrix and its centrality measure play a significant role in percolation-type processes on networks. This study investigates the localization of nonbacktracking centrality in infinite sparse networks containing a finite subgraph. The results show that the largest eigenvalue of the nonbacktracking matrix of the composite network is determined by the larger of the two largest eigenvalues of the subgraph and the enclosing network. In the localized state, the nonbacktracking centrality is concentrated on the subgraph and its immediate neighborhood in the enclosing network.
Article
Physics, Fluids & Plasmas
G. Timar, R. A. da Costa, S. N. Dorogovtsev, J. F. F. Mendes
Summary: Message-passing theories are useful in studying dynamical processes on real-world networks. This study proposes a degree-class-based method to approximate key quantities related to the nonbacktracking matrix. The findings suggest that degree-degree correlations in most networks are not strong, and accurate estimates can be obtained using the proposed method.
Article
Physics, Fluids & Plasmas
S. Yoon, E. A. P. Wright, J. F. F. Mendes, A. V. Goltsev
Summary: The impact of field heterogeneity on entrainment was studied in a system of uniformly interacting phase oscillators. Field heterogeneity induces dynamical heterogeneity in the system, disrupting synchronization between groups of oscillators and causing them to enter a new disrupted state. It is found that disrupted dynamics can vary between different groups.
Article
Physics, Fluids & Plasmas
G. Timar, Gy Kovacs, J. F. F. Mendes
Summary: Dependence links in single-layer networks provide a way to model nonlocal percolation effects, with nodes being able to function if at least one dependency neighbor is active. This relaxation of the dependency rule leads to more robust structures and a variety of critical phenomena. Special points are identified where systems are stable and different percolation transitions are observed for Erdos-Renyi and scale-free networks with dependency links.
