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The rock–paper–scissors game, commonly played in East Asia, gives a simple model to understand physical, biological, psychological, and other problems. The interacting rock–paper–scissors particle system connects two models: the collision model (Maxwell and Boltzmann's kinetic theory of gas) and the coalescence model (Smoluchowski's coagulation theory). A 2 s + 1 type rock–paper–scissors collision model naturally introduces a nonlinear integrable Lotka–Volterra system. The time evolution of the coalescence model is obtained from the logarithmic time change of the collision model. We also discuss the behavior of a discrete rock–paper–scissors coalescence model. • The interacting rock–paper–scissors particle system connects two models, the collision model (Maxwell and Boltzmann's kinetic theory of gas) and the coalescence model (Smoluchowski's coagulation theory). • The time evolution of the coalescence model is obtained from the logarithmic time change of the collision model. • We discuss which type of particle finally survives out of three types: rock, paper, and scissors. It seems the three types coexist until the very final stage. [ABSTRACT FROM AUTHOR]

Spatial and temporal behaviors of the rock–paper–scissors (RPS) game is key to understanding not only biodiversity but also a variety of cyclic systems. It has been demonstrated that, in the stochastic cellular automaton of RPS game, three species cannot survive on one-dimensional (1-d) lattice; only a single species survives. Previous studies have shown that three species are able to coexist if the migration of species is considered. However, their definitions of migration are the swapping of two species or the random walk of species, which rarely occurs in nature. Here, we investigate the effect of migration by using the 1-d lattice traffic model in which species can move rightward if the site ahead is empty. Computer simulations reveal that three species can survive at the same time within the wide range of parameter values. At low densities, all species can coexist. In contrast, the extinction of two species occurs if the density exceeds the critical limit of the jamming transition. This dynamical phase transition between the coexistence and single (non-coexistence) phase clearly separates due to the self-organized pattern: condensation and rarefaction in the stripe-pattern of three species. [ABSTRACT FROM AUTHOR]

Abstract: The Rock–Paper–Scissors (RPS) game is a widely used model system in game theory. Evolutionary game theory predicts the existence of persistent cycles in the evolutionary trajectories of the RPS game, but experimental evidence has remained to be rather weak. In this work, we performed laboratory experiments on the RPS game and analyzed the social-state evolutionary trajectories of twelve populations of players. We found strong evidence supporting the existence of persistent cycles. The mean cycling frequency was measured to be period per experimental round. Our experimental observations can be quantitatively explained by a simple non-equilibrium model, namely the discrete-time logit dynamical process with a noise parameter. Our work therefore favors the evolutionary game theory over the classical game theory for describing the dynamical behavior of the RPS game. [Copyright &y& Elsevier]

This paper aims at providing a statistical model for the preferred behavior of authors submitting a paper to a scientific journal. The electronic submission of (about 600) papers to the Journal of the Serbian Chemical Society has been recorded for every day from Jan. 01, 2013 till Dec. 31, 2014, together with the acceptance or rejection paper fate. Seasonal effects and editor roles (through desk rejection and subfield editors) are examined. An ARCH-like econometric model is derived stressing the main determinants of the favorite day-of-week process. [ABSTRACT FROM AUTHOR]

Abstract: We investigate a population of individuals who play the Rock–Paper–Scissors (RPS) game. The players choose strategies not only by optimizing their payoffs, but also taking into account the popularity of the strategies. For the standard RPS game, we find an asymptotically stable polymorphism with coexistence of all strategies. For the general RPS game we find the limit cycles. Their stability depends exclusively on two model parameters: the sum of the entries of the RPS payoff matrix, and a sensitivity parameter which characterizes the personality of the players. Apart from the supercritical Hopf bifurcation, we found the subcritical bifurcation numerically for some intervals of the parameters of the model. [Copyright &y& Elsevier]

This paper aims at providing an introduction to the behavior of authors submitting a paper to a scientific journal. Dates of electronic submission of papers to the Journal of the Serbian Chemical Society have been recorded from the 1st January 2013 till the 31st December 2014, thus over 2 years. There is no Monday or Friday effect like in financial markets, but rather a Tuesday–Wednesday effect occurs: papers are more often submitted on Wednesday; however, the relative number of going to be accepted papers is larger if these are submitted on Tuesday. On the other hand, weekend days (Saturday and Sunday) are not the best days to finalize and submit manuscripts. An interpretation based on the type of submitted work (“experimental chemistry”) and on the influence of (senior) coauthors is presented. A thermodynamic connection is proposed within an entropy context. A (new) entropic distance is defined in order to measure the “opaqueness” = disorder) of the submission process. [ABSTRACT FROM AUTHOR]

In citation networks, the content relativity of papers is a precondition of engendering citations, which is hard to model by a topological graph. A geometric graph is proposed to predict some features of the citation networks with exponentially growing papers, which addresses the precondition by using coordinates of nodes to model the research contents of papers, and geometric distances between nodes to diversities of research contents between papers. Citations between modeled papers are drawn according to a geometric rule, which addresses the precondition as well as some other factors engendering citations, namely academic influences of papers, aging of those influences, and incomplete copying of references. Instead of cumulative advantage of degree, the model illustrates that the scale-free property of modeled networks arises from the inhomogeneous academic influences of modeled papers. The model can also reproduce some other statistical features of citation networks, e.g. in- and out-assortativities, which show the model provides a suitable tool to understand some aspects of citation networks by geometry. [ABSTRACT FROM AUTHOR]

Identification of the mechanisms which permit ecological communities to maintain high levels of biodiversity is of both theoretical interest and practical importance. Intransitive competition, in which there is no single superior competitor, is known to play an important role in this problem. In this study, we undertake a systematic comparative analysis of how different competition modes and ranges affect community stability in paper–rock–scissors games. We confirm that short-ranged interactions, in combination with cyclic competition, permits relatively stable coexistence. However, in contrast to previous studies, we show that long-range interactions can also produce stable communities. This stability emerges when competition interactions create asymmetries in the opportunities for population growth depending on the abundance of the species. Our findings demonstrate that small differences in the way species compete can qualitatively change dynamic behaviours of the system, and therefore emphasize the importance of correctly identifying these competition modes when designing conservation actions. • We compare system stability among four interaction modes in cyclic competition. • We find that long-ranged competition can also produce stable coexistence. • Small differences in interaction modes qualitatively change dynamic behaviours. • We emphasize the importance of correctly identifying species competition modes. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we investigated the influences of the age of papers on the preferential attachment on the basis of three actual citation networks. We found that the time dependence of the attachment rate follows a uniform exponentially decreasing function, , in different citation networks. Younger papers are more likely to be cited by new ones than older papers. On the basis of the aging influences, we modified the expression for the preferential attachment, to . Our results show that the modified preferential attachment works well for citation networks. [Copyright &y& Elsevier]

In the framework of a 1D cyclic competition model, the Rock-Paper-Scissors model, where three kinds of generic agents are allowed to mutate, to interact and to move in space, we study the formation of stochastic patterns, where all the agents do coexist. We modelled the problem using an individual-based setting and we used the system size van Kampen expansion to deal with the Master Equation. We have hence been able to characterise the spatio-temporal patterns using the power spectrum of the fluctuations. We proved that such patterns are robust against the intrinsic noise and they can be found for parameter values beyond the ones fixed by the deterministic approach (mean field approximation). We complement such analytical results with numerical simulations based on the Gillespie algorithm. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we study the topological structure of semantic networks based on titles of papers published in scientific journals. It discusses its properties and presents some reflections on how the use of social and complex network models can contribute to the diffusion of knowledge. The proposed method presented here is applied to scientific journals where the titles of papers are in English or in Portuguese. We show that the topology of studied semantic networks are small-world and scale-free. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of this comment is to correct mistaken assumptions and claims made in the paper “Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker–Planck equations” by T. D. Frank [T.D. Frank, Stochastic feedback, non-linear families of Markov processes, and nonlinear Fokker–Planck equations, Physica A 331 (2004) 391]. Our comment centers on the claims of a “non-linear Markov process” and a “non-linear Fokker–Planck equation.” First, memory in transition densities is misidentified as a Markov process. Second, the paper assumes that one can derive a Fokker–Planck equation from a Chapman–Kolmogorov equation, but no proof was offered that a Chapman–Kolmogorov equation exists for the memory-dependent processes considered. A “non-linear Markov process” is claimed on the basis of a non-linear diffusion pde for a 1-point probability density. We show that, regardless of which initial value problem one may solve for the 1-point density, the resulting stochastic process, defined necessarily by the conditional probabilities (the transition probabilities), is either an ordinary linearly generated Markovian one, or else is a linearly generated non-Markovian process with memory. We provide explicit examples of diffusion coefficients that reflect both the Markovian and the memory-dependent cases. So there is neither a “non-linear Markov process”, nor a “non-linear Fokker–Planck equation” for a conditional probability density. The confusion rampant in the literature arises in part from labeling a non-linear diffusion equation for a 1-point probability density as “non-linear Fokker–Planck,” whereas neither a 1-point density nor an equation of motion for a 1-point density can define a stochastic process. In a closely related context, we point out that Borland misidentified a translation invariant 1-point probability density derived from a non-linear diffusion equation as a conditional probability density. Finally, in the we present the theory of Fokker–Planck pdes and Chapman–Kolmogorov equations for stochastic processes with finite memory. [Copyright &y& Elsevier]

In this response to the comments made by A. Vezzani on our paper [Random walk model for coordinate-dependent diffusion in a force field, Physica A 584 (2021) 126348] we explain our stand in relation to the comments made. [ABSTRACT FROM AUTHOR]

Paper (Maniar and Bhattacharyay, 2021) introduces a discrete random-walk (RW) model with a site dependent waiting time and an external force i.e. a site dependent drift. The RW is compared with a Smoluchowski equation in continuous space and time with space dependent diffusivity and space dependent damping. Using numerical simulations in Maniar and Bhattacharyay (2021) it is shown that the equilibrium distribution satisfies locally the Stokes–Einstein relation i.e. there is a constant temperature in the whole system. Here we show that the result can be recovered analytically with a continuous limit in the RW master equation. Moreover, we evidence that the RW model should be carefully defined in order to satisfy locally Stokes–Einstein relation, indeed a different definition of the discrete RW process describes a system that satisfies the Smoluchowski equation with constant damping, where the temperature is not uniform. [ABSTRACT FROM AUTHOR]

Some errors exist in the above paper. [ABSTRACT FROM AUTHOR]

Abstract: We study a novel five-species system on two-dimensional lattices when each species have two superior and two inferior partners. Here we simplify the huge parameter space of predation probability to only two parameters. Both of Monte Carlo simulation and Mean Field Theory reveal that two of strategies may die out when the ratio of the two parameters is close to the golden point 0.618, and the remaining three strategies are provided a cyclic dominance system. [Copyright &y& Elsevier]

Some errors exist in the above paper. [ABSTRACT FROM AUTHOR]

A fair assignment of credit for multi-authored publications is a long-standing issue in scientometrics. In the calculation of the h -index, for instance, all co-authors receive equal credit for a given publication, independent of a given author's contribution to the work or of the total number of co-authors. Several attempts have been made to distribute the credit in a more appropriate manner. In a recent paper, Hirsch has suggested a new way of credit assignment that is fundamentally different from the previous ones: All credit for a multi-author paper goes to a single author, the called " α -author", defined as the person with the highest current h -index (not the highest h -index at the time of the paper's publication) (Hirsch, 2019). The collection of papers this author has received credit for as α -author is then used to calculate a new index, h α , following the same recipe as for the usual h index. The objective of this new assignment is not a fairer distribution of credit, but rather the determination of an altogether different property, the degree of a person's scientific leadership. We show that given the complex time dependence of h for individual scientists, the approach of using the current h value instead of the historic one is problematic, and we argue that it would be feasible to determine the α -author at the time of the paper's publication instead. On the other hand, there are other practical considerations that make the calculation of the proposed h α very difficult. As an alternative, we explore other ways of crediting papers to a single author in order to test early career achievement or scientific leadership. • The time-dependent evolution of the h-index in a large set of individual scientists is investigated. • The presented data allows to identify the α -author at the time of publication rather than at the present time. • We suggest h-index variants emphasizing early career success and later achievements appropriately. [ABSTRACT FROM AUTHOR]

We combine the rock–paper–scissors (RPS) game with SIS epidemic model. We study the effect of infection on population dynamics of RPS games with epidemic by using the metapopulation dynamic model on graphs. Via infection, an individual R changes to I with infection rate β. An infected individual I returns to R with recovery rate γ. All agents move by random walk between patches (subpopulations) and the RPS game with epidemic is performed in each patch. The dynamics are represented by the reaction–diffusion equations in diffusively coupled reactors. We obtain the solutions of the reaction–diffusion equations for the mean-field dynamics in a single patch analytically. The numerical solutions are obtained for metapopulation dynamics on graphs with three nodes. The analytical solutions are also obtained for metapopulation dynamics on complete graph. When the recovery rate is lower than the critical value, infected individuals survive, the dynamics exhibit stable focuses, and all species coexist. Infection promotes the coexistence of species. • We studied the effect of infection on the population dynamics in the diffusively coupled rock–paper–scissors RPS game with epidemic. • We presented the reaction–diffusion equations for RPS game with epidemic on graphs. • We showed that the infection has the important effect on the coexistence of R, S, and P species. [ABSTRACT FROM AUTHOR]

In the commented paper, the authors study a gas of noninteracting fermions confined in a one-dimensional harmonic trap, and calculate the Boltzmann temperature and the Gibbs temperature of this system. They find that the Gibbs temperature is closer to the corresponding temperature given by the grand-canonical approach than the Boltzmann temperature. In this comment we point out their conclusion is not always true. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, two examples are given where the cluster labeling algorithm of Al-Futaisi and Patzek for arbitrary networks produces incorrect results. The reason for this is pointed out, and an improvement to the algorithm is proposed so that such errors can be avoided in future. [Copyright &y& Elsevier]

In the above paper five equations are wrong. [ABSTRACT FROM AUTHOR]