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The cellular adaptive immune response plays a key role in resolving influenza infection. Experiments where individuals are successively infected with different strains within a short timeframe provide insight into the underlying viral dynamics and the role of a cross-reactive immune response in resolving an acute infection. We construct a mathematical model of within-host influenza viral dynamics including three possible factors which determine the strength of the cross-reactive cellular adaptive immune response: the initial naive T cell number, the avidity of the interaction between T cells and the epitopes presented by infected cells, and the epitope abundance per infected cell. Our model explains the experimentally observed shortening of a second infection when cross-reactivity is present, and shows that memory in the cellular adaptive immune response is necessary to protect against a second infection.
Studying the spatiotemporal distribution of SARS-CoV-2 infections among healthcare workers (HCWs) can aid in protecting them from exposure. Existing studies related to HCW infections have emphasized infection rates and protective measures. However, the spatiotemporal patterns and related external environmental factors of HCW infections remain unclear. To fill this gap, an open-source dataset of HCW diagnoses was provided, and the spatiotemporal distributions of SARS-CoV-2 infections among HCWs in Wuhan, China were explored. A geographical detector technique was then used to investigate the impacts of hospital level, type, distance from the infection source, and other external indicators of HCW infections. The results showed that the number of daily HCW infections over time in Wuhan followed a log-normal distribution, with and its mean observed on January 23, 2020 and a standard deviation of 10.8 days. The implementation of high-impact measures, such as the lockdown of the city, may have increased the probability of HCW infections in the short term, especially for HCWs in the outer ring of Wuhan. The infection of HCWs Wuhan exhibited clear spatial heterogeneity. The number of HCW in
Mathematical models are increasingly a part of microbiological research. Here, we share our perspective on how modeling advances the discipline by: (i) enforcing logical consistency, (ii) enabling quantitative prediction, (iii) extracting hidden parameters from data, and (iv) generating intuitive understanding. We map a spectrum of modeling frameworks, from whole-cell simulations to minimal logistic growth equations, and provide interactive examples for some common frameworks. Building on this overview, we outline pragmatic criteria for choosing an appropriate level of description to capture phenomena of interest. Finally, we present a case study in modeling of microbial ecosystems from our own work to illustrate how mechanistic modeling can yield generalizable intuition. This perspective aims to be an introductory roadmap for integrating mathematical modeling into experimental microbiology.
In this article, we have proposed an epidemic model by using probability cellular automata theory. The essential mathematical features are analyzed with the help of stability theory. We have given an alternative modelling approach for the spatiotemporal system which is more realistic and satisfactory from the practical point of view. A discrete and spatiotemporal approach are shown by using cellular automata theory. It is interesting to note that both size of the endemic equilibrium and density of the individual increase with the increasing of the neighborhood size and infection rate, but the infections decrease with the increasing of the recovery rate. The stability of the system around the positive interior equilibrium have been shown by using suitable Lyapunov function. Finally experimental data simulation for SARS disease in China and a brief discussion conclude the paper.
Motivated by recent theoretical and experimental advances, hyperbolic lattices have emerged as a paradigmatic setting in which geometry becomes an active organizing principle of quantum systems. Their negative curvature, exponential volume growth, and non-Abelian translation symmetry make them fundamentally distinct from Euclidean lattices and give rise to rich geometry-dependent physics, but also hinder the direct application of well-established analytical and computational approaches originally developed for physical systems defined on Euclidean lattices. To establish a unified framework for geometry-dependent physics on Euclidean and hyperbolic lattices, we develop \textit{higher-order non-uniform cellular automata} (NUCA) as a local-to-global construction for translationally invariant regular lattices. This construction derives geometry-dependent update rules through a lattice-deforming procedure that embeds hyperbolic lattices into a Euclidean square lattice, thereby encoding hyperbolic geometry while preserving physical locality. It thus provides a systematic route toward quantum and classical physics on hyperbolic lattices. We demonstrate the framework in three applications
Cellular vehicle-to-everything (V2X) communication is expected to herald the age of autonomous vehicles in the coming years. With the integration of blockchain in such networks, information of all granularity levels, from complete blocks to individual transactions, would be accessible to vehicles at any time. Specifically, the blockchain technology is expected to improve the security, immutability, and decentralization of cellular V2X communication through smart contract and distributed ledgers. Although blockchain-based cellular V2X networks hold promise, many challenges need to be addressed to enable the future interoperability and accessibility of such large-scale platforms. One such challenge is the offloading of mining tasks in cellular V2X networks. While transportation authorities may try to balance the network mining load, the vehicles may select the nearest mining clusters to offload a task. This may cause congestion and disproportionate use of vehicular network resources. To address this issue, we propose a game-theoretic approach for balancing the load at mining clusters while maintaining fairness among offloading vehicles. Keeping in mind the low-latency requirements of
Starting from the working hypothesis that both physics and the corresponding mathematics and in particular geometry have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face in this enterprise is to find the discrete protoforms of the building blocks of our ordinary continuum physics and mathematics living on a smooth background, and perhaps more importantly find a way how this continuum limit emerges from the mentioned discrete structure. We model this underlying substratum as a structurally dynamic cellular network (basically a generalisation of a cellular automaton). We regard these continuum concepts and continuum spacetime in particular as being emergent, coarse-grained and derived relative to this underlying erratic and disordered microscopic substratum, which we would like to call quantum geometry and which is expected to play by quite different rules, namely generalized cellular automaton rules. A central role in our analysis is played by a geometric renormalization group which creates (among other things) a kind of sparse translocal network of correlations between the points in classical continuous space-time and under
An investigation was conducted to study the robustness of the results obtained from the cellular automata model which describes the spread of the HIV infection within lymphoid tissues [R. M. Zorzenon dos Santos and S. Coutinho, Phys. Rev. Lett. 87, 168102 (2001)]. The analysis focussed on the dynamic behavior of the model when defined in lattices with different symmetries and dimensionalities. The results illustrated that the three-phase dynamics of the planar models suffered minor changes in relation to lattice symmetry variations and, while differences were observed regarding dimensionality changes, qualitative behavior was preserved. A further investigation was conducted into primary infection and sensitiveness of the latency period to variations of the model's stochastic parameters over wide ranging values. The variables characterizing primary infection and the latency period exhibited power-law behavior when the stochastic parameters varied over a few orders of magnitude. The power-law exponents were approximately the same when lattice symmetry varied, but there was a significant variation when dimensionality changed from two to three. The dynamics of the three-dimensional mod
We study the emergence of information integration in cellular automata (CA) with respect to states in the long run. Information integration is in this case quantified by applying the information-theoretic measure known as total correlation to the long-run distribution of CA states. Total correlation is the amount by which the total uncertainty associated with cell states surpasses the uncertainty of the CA state taken as a whole. It is an emergent property, in the sense that it can only be ascribed to how the cells interact with one another, and has been linked to the rise of consciousness in the brain. We investigate total correlation in the evolution of elementary CA for all update rules that are unique with respect to negation or reflection. For each rule we consider the usual, deterministic CA behavior, assuming that the initial state is chosen uniformly at random, and also the probabilistic variant in which every cell, at all time steps and independently of all others, disobeys the rule's prescription with a fixed probability. We have found rules that generate as much total correlation as possible, or nearly so, particularly in Wolfram classes 2 and 3. We conjecture that some
During the Coronavirus 2019 (the covid-19) pandemic, schools continuously strive to provide consistent education to their students. Teachers and education policymakers are seeking ways to re-open schools, as it is necessary for community and economic development. However, in light of the pandemic, schools require customized schedules that can address the health concerns and safety of the students considering classroom sizes, air conditioning equipment, classroom systems, e.g., self-contained or compartmentalized. To solve this issue, we developed the School-Virus-Infection-Simulator (SVIS) for teachers and education policymakers. SVIS simulates the spread of infection at a school considering the students' lesson schedules, classroom volume, air circulation rates in classrooms, and infectability of the students. Thus, teachers and education policymakers can simulate how their school schedules can impact current health concerns. We then demonstrate the impact of several school schedules in self-contained and departmentalized classrooms and evaluate them in terms of the maximum number of students infected simultaneously and the percentage of face-to-face lessons. The results show that
Viral kinetics have been extensively studied in the past through the use of spatially homogeneous ordinary differential equations describing the time evolution of the diseased state. However, spatial characteristics such as localized populations of dead cells might adversely affect the spread of infection, similar to the manner in which a counter-fire can stop a forest fire from spreading. In order to investigate the influence of spatial heterogeneities on viral spread, a simple 2-D cellular automaton (CA) model of a viral infection has been developed. In this initial phase of the investigation, the CA model is validated against clinical immunological data for uncomplicated influenza A infections. Our results will be shown and discussed.
This paper aims to map and identify topics of interest within the field of Microbiology and identify the main sources driving such attention. We combine data from Web of Science and Altmetric.com, a platform which retrieves mentions to scientific literature from social media and other non-academic communication outlets. We focus on the dissemination of microbial publications in Twitter, news media and policy briefs. A two-mode network of social accounts shows distinctive areas of activity. We identify a cluster of papers mentioned solely by regional news media. A central area of the network is formed by papers discussed by the three outlets. A large portion of the network is driven by Twitter activity. When analyzing top actors contributing to such network, we observe that more than half of the Twitter accounts are bots, mentioning 32% of the documents in our dataset. Within news media outlets, there is a predominance of popular science outlets. With regard to policy briefs, both international and national bodies are represented. Finally, our topic analysis shows that the thematic focus of papers mentioned varies by outlet. While news media cover the wider range of topics, policy b
With the increasing demand for vehicular data transmission, limited dedicated cellular spectrum becomes a bottleneck to satisfy the requirements of all cellular vehicle-to-everything (V2X) users. To address this issue, unlicensed spectrum is considered to serve as the complement to support cellular V2X users. In this paper, we study the coexistence problem of cellular V2X users and vehicular ad-hoc network~(VANET) users over the unlicensed spectrum. To facilitate the coexistence, we design an energy sensing based spectrum sharing scheme, where cellular V2X users are able to access the unlicensed channels fairly while reducing the data transmission collisions between cellular V2X and VANET users. In order to maximize the number of active cellular V2X users, we formulate the scheduling and resource allocation problem as a two-sided many-to-many matching with peer effects. We then propose a dynamic vehicle-resource matching algorithm (DV-RMA) and present the analytical results on the convergence time and computational complexity. Simulation results show that the proposed algorithm outperforms existing approaches in terms of the performance of cellular V2X system when the unlicensed sp
Partitioned cellular automata are known to be an useful tool to simulate linear and nonlinear problems in physics, specially because they allow for a straightforward way to define conserved quantities and reversible dynamics. Here we show how to construct a local coarse graining description of partitioned cellular automata. By making use of this tool we investigate the effective dynamics in this model of computation. All examples explored are in the scenario of lattice gases, so that the information lost after the coarse graining is related to the number of particles. It becomes apparent how difficult it is to remain with a deterministic dynamics after coarse graining. Several examples are shown where an effective stochastic dynamics is obtained after a deterministic dynamics is coarse grained. These results suggest why random processes are so common in nature.
Many decision problems concerning cellular automata are known to be decidable in the case of algebraic cellular automata, that is, when the state set has an algebraic structure and the automaton acts as a morphism. The most studied cases include finite fields, finite commutative rings and finite commutative groups. In this paper, we provide methods to generalize these results to the broader case of group cellular automata, that is, the case where the state set is a finite (possibly non-commutative) finite group. The configuration space is not even necessarily the full shift but a subshift -- called a group shift -- that is a subgroup of the full shift on Z^d, for any number d of dimensions. We show, in particular, that injectivity, surjectivity, equicontinuity, sensitivity and nilpotency are decidable for group cellular automata, and non-transitivity is semi-decidable. Injectivity always implies surjectivity, and jointly periodic points are dense in the limit set. The Moore direction of the Garden-of-Eden theorem holds for all group cellular automata, while the Myhill direction fails in some cases. The proofs are based on effective projection operations on group shifts that are, in
The minimal number of inputs in the local function of a non-trivial cellular automaton is two. Such a function can be viewed as as a kind of binary operation. If this operation is associative, it forms, together with the set of states, a semigroup. There are 18 semigroups of order 3 up to equivalence, and they define 18 cellular automata rules with three states. We investigate these rules with respect to solvability and show that all of them are solvable, meaning that the state of a given cell after $n$ iterations can be expressed by an explicit formula. We derive the relevant formulae for all 18 rules using some additional properties possessed by particular semigroups of order 3, such as commutativity and idempotence.
For many cellular automata, it is possible to express the state of a given cell after $n$ iterations as an explicit function of the initial configuration. We say that for such rules the solution of the initial value problem can be obtained. In some cases, one can construct the solution formula for the initial value problem by analyzing the spatiotemporal pattern generated by the rule and decomposing it into simpler segments which one can then describe algebraically. We show an example of a rule when such approach is successful, namely elementary rule 156. Solution of the initial value problem for this rule is constructed and then used to compute the density of ones after $n$ iterations, starting from a random initial condition. We also show how to obtain probabilities of occurrence of longer blocks of symbols.
We investigate elementary cellular automata (ECA) from the point of view of (discrete) dynamical systems. By studying small lattice sizes, we obtain the complete phase space of all minimal ECA, and, starting from a maximal entropy distribution (all configurations equiprobable), we show how the dynamics affects this distribution. We then investigate how a vanishing noise alters this phase space, connecting attractors and modifying the asymptotic probability distribution. What is interesting is that this modification not always goes in the sense of decreasing the entropy.
We conduct a brief survey on Wolfram's classification, in particular related to the computing capabilities of Cellular Automata (CA) in Wolfram's classes III and IV. We formulate and shed light on the question of whether Class III systems are capable of Turing universality or may turn out to be "too hot" in practice to be controlled and programmed. We show that systems in Class III are indeed capable of computation and that there is no reason to believe that they are unable, in principle, to reach Turing-completness.
To respect physics and nature, cellular automata (CA) models of self-organisation, emergence, computation and logical universality should be isotropic, having equivalent dynamics in all directions. We present a novel paradigm, the iso-rule, a concise expression for isotropic CA by the output table for each isotropic neighborhood group, allowing an efficient method of navigating and exploring iso-rule-space. We describe new functions and tools in DDLab to generate iso-groups and iso-rules, for multi-value as well as binary, in one, two and three dimensions. These methods include filing, filtering, mutating, analysing dynamics by input-frequency and entropy, identifying the critical iso-groups for glider-gun/eater dynamics, and automatically classifying iso-rule-space. We illustrate these ideas and methods for two dimensional CA on square and hexagonal lattices.