arXiv subjects

Norihito Toyota

Publications and source records attributed to Norihito Toyota.

At least 19 recordsLinked to original sources

arXiv2019

Promotion of Cooperation in Coevolutionary Public Goods Game on Complex Networks with and without Topology Change

The evolution of cooperation among unrelated individuals in human and animal societies remains a challenging issue across disciplines. It is an important subject also in the evolutionary game theory to understand how cooperation arises. The subject has been extensively studied especially in Prisoners' dilemma game(PD) but the emergence of cooperation is also an important subject in public goods game(PGG). In this article, we consider coevolutionary PGG on complex networks where both the topology of the networks and strategies that players adopt under the influence of game dynamics varies. Though cooperators can contribute a fixed amount per game in PGG on networks in the previous studies, the cooperators contribute a fixed amount per member of the group in PGG of this article. The latter is seemed to be more natural than the former model. These models lead to great differences in both PGGs. We study what effects on the evolution of player's strategies, defection and cooperation and the average payoff does the interaction between the game dynamics and the network topology bring. Moreover by comparing the models that do not depend on game dynamics to the models without topology changing, we intend to uncover the effect of the topology chnage and the game dynamics on the promotion of the cooperation. As result we intend to clear in what situations cooperation strategy is promoted or preserved by investigating them by making computer simulations. We also investigate the relation between the ratio of the cooperator and the average payoff over all players. Furthermore we study how do the topology of initial networks have an influence on the cooperation and the average payoff.

physics.soc-ph↗

arXiv2018

Cooperation in Evolutionary Public Goods Game on Complex Networks with Topology Change

physics.soc-ph↗

arXiv2018

A study of Inverse Ultra-discretization of cellular automata

In this article, I propose a systematic method for the inverse ultra-discretization of cell automata using a functionally complete operation. We derive difference equations for the 256 kinds of elementary cellular automata(ECA) introduced Wolfram\cite{wolfram} by the proposed means of the inverse ultra-discretization. We show that the behaviors of ECAs can be completely reproduced by numerically solving the obtained difference equations.

nlin.CG↗

arXiv2016

Remark on Structure of Expectation Values of Flavor-Lepton Numbers with respect to Neutrino-Source Hadron States: Deviation from Fermi's Golden Relatio

In our preceeding reports, we have pointed out that a unified description of weak decays accompanying neutrinos and the oscillation process is obtained on the basis of the expectation values of flavor-neutrino numbers with respect to the neutrino-source hadron state. In the present report, we investigate the effect on the expectation values due to the deviation from Fermi's golden relation, and give concrete features of these deviations in the case of $π^+$ and $K^+$-decays under the simple situation with the $3$-momentum $\vec{p_A}=0$ for $A=π^+$, $K^+$. %numerical results under simple situations.

hep-ph↗

arXiv2015

Braess like Paradox on Ladder Network

Braess \cite{1} has been studied about a traffic flow on a diamond type network and found that introducing new edges to the networks always does not achieve the efficiency. Some researchers studied the Braess' paradox in similar type networks by introducing various types of cost functions. But whether such paradox occurs or not is not scarcely studied in complex networks except for Dorogovtsev-Mendes network\cite{2}. In this article, we study the paradox on Ladder type networks, as the first step to the research about Braess' paradox on Watts and Strogatz type small world network\cite{Watt1}\cite{Watt2}. %We theoretically and numerically studied Braess' paradox on Ladder networks. For the purpose, we construct $4 \times 3$ models as extensions of the original Braess' models. We analyze theoretically and numerically studied the models on Ladder networks. Last we give a phase diagram for (a) model, where the cost functions of bypasses are constant =0 or flow, base on two parameters $r$ and $p$ by numerical simulations. Simulation experiments also show some conditions that paradox can not occur. These facts give some sugestions for designing effective transportation networks.

physics.soc-ph↗

arXiv2014

The Effect of Network-Topology to Propagation on Networks

We study the effect of the network topology to propagation phenomena on networks in this article. We do not assume any propagation model such as the contact process or SIR model\cite{Ker} because the study is only the consideratons of the purely topological effect, especially the effect of cycles of a network. To uncover universal properties independent of explicit propagation models is expected due to it. First of all, we introduce some indeces for propagation phenomena of a network. Second we introduce a concept of cycles with a little differences to usal cycles, which is called "STOC" in the body of this article. We find some analytic relations between thesm, STOC and some indeces. Moreover we can find the total number of STOCs in a network, analytically. This consideration leads to an extension of the celebrated "Euler's polyhedron formula", which is only applicable to planar graphs. This extended formula is applicable to any graphs. Last we estimate numerically the indeces and the number of STOCs based on the theoretical considerations for some complex networks and make some discussion on the effects of cycles in networks to propagation.

math-ph↗

arXiv2014

Expectation values of flavor-neutrino numbers with respect to neutrino-source hadron states --Neutrino oscillations and decay probabilities--

On the basis of quantum field theory, we consider a unified description of various processes accompanied by neutrinos, namely weak decays and oscillation processes. The structures of the expectation values of flavor-neutrino numbers with respect to neutrino-source hadron state are investigated. Due to the smallness of neutrino masses, we naturally obtain the old (i.e. pre-mixing) formulas of decay probabilities. Together, it is shown that the oscillation formulas, similar to the usual ones, are applied irrespectively of the details of neutrino-producing processes. The derived oscillation formulas are the same in form as the usually used ones except for the oscillation length.

hep-ph↗

arXiv2013

Braess like Paradox in a Small World Network

Braess \cite{1} has been studied about a traffic flow on a diamond type network and found that introducing new edges to the networks always does not achieve the efficiency. Some researchers studied the Braess' paradox in similar type networks by introducing various types of cost functions. But whether such paradox occurs or not is not scarcely studied in complex networks. In this article, I analytically and numerically study whether Braess like paradox occurs or not on Dorogovtsev-Mendes network\cite{2}, which is a sort of small world networks. The cost function needed to go along an edge is postulated to be equally identified with the length between two nodes, independently of an amount of traffic on the edge. It is also assumed the it takes a certain cost $c$ to pass through the center node in Dorogovtsev-Mendes network. If $c$ is small, then bypasses have the function to provide short cuts. As result of numerical and theoretical analyses, while I find that any Braess' like paradox will not occur when the network size becomes infinite, I can show that a paradoxical phenomenon appears at finite size of network.

physics.soc-ph↗

arXiv2012

Second Parrondo's Paradox in Scale Free Networks

Parrondo's paradox occurs in sequences of games in which a winning expectation value of a payoff may be obtained by playing two games in a random order, even though each game in the sequence may be lost when played individually.Several variations of Parrondo's games apparently with the same paradoxical property have been introduced by G.P. Harmer and D. Abbott; history dependence, one dimensional line, two dimensional lattice and so on. I have shown that Parrondo's paradox does not occur in scale free networks in the simplest case with the same number of parameters as the original Parrondo's paradox. It suggests that some technical complexities are needed to present Parrondo's paradox in scale free networks. In this article, I show that a simple modification with the same number of parameters as the original Parrondo's paradox creates Parrondo's paradox in scale free. This paradox is, however, created by a quite different mechanism from the original Parrondo's paradox and a considerably rare phenomenon, where the discrete property of degree of nodes is crucial. I call it the second Parrondo's paradox.

physics.soc-ph↗

arXiv2012

Effect of Closed Paths in Complex networks on Six Degrees of Separation and Disorder

Milgram Condition proposed by Aoyama et al. plays an important role on the analysis of "six degrees of separation". We have shown that the relations between Milgram condition and the generalized clustering coefficient, which was introduced as an index for measuring the number of closed paths by us, are absolutely different in scale free networks (Barabasi and Albert) and small world networks (Watts and Strogatz, Watts). This fact implies that the effect of closed paths on information propagation is different in both networks. In this article, we first investigate the difference and pursuit what is a crucial mathematical quantity for information propagation. As a result we find that a sort of "disorder" plays more important role for information propagation than partially closed paths included in a network. Next we inquired into it in more detail by introducing two types of intermediate networks. Then we find that the average of the local clustering coefficient and the generalized clustering coefficients $C_{(q)}$ have some different functions and important meanings, respectively. We also find that $C_{(q)}$ is close to the propagation of information on networks. Lastly, we show that realizability of six degrees of separation in networks can be understood in a unified way by disorder.

physics.soc-ph↗

arXiv2012

Parrondo Paradox in Scale Free Networks

physics.soc-ph↗

arXiv2012

Does Parrondo Paradox occur in Scale Free Networks? -A simple Consideration-

Parrondo's paradox occurs in sequences of games in which a winning expectation may be obtained by playing the games in a random order, even though each game in the sequence may be lost when played individually. Several variations of Parrondo's games apparently with paradoxical property have been introduced; history dependence, one dimensional line, two dimensional lattice and so on. In this article, we examine whether Parrondo's paradox occurs or not in scale free networks. This is interesting as an empirical study, since scale free networks are ubiquitous in our real world. First some simulation results are given and after that theoretical studies are made. As a result, we mostly confirm that Parrondo's paradox can not occur in the naive case, where the game has the same number of parameters as the original Parrondo's game.

physics.soc-ph↗

arXiv2012

Key Distribution based on Three Player Quantum Games

We study a new QKD that is different from the scheme proposed by \cite{Ramz2}, though it essentially takes our ground on three-player quantum games and Greenberg-Horne-Zeilinger triplet entangled state (GHZ state) \cite{Gree} is used. In the scheme proposed in this paper, players in the game, Bob and Charlie (and Alice also) can get some common key or information (applied strategies and their payoffs in the game), when Alice informs Bob and Charlie about some results of the measurement made by her. Even if somebody else knows the public information, he/she can not get any key information. There is not any arbiter in our scheme, since existence of an arbiter increases the risk of wiretapping. Lastly we discuss robustness of the proposed QKD method for eavesdrop. We show that though maximally entangled case and non-entangled case essentially provide an equivalent way as QKD, the latter is not available in the case where there are some eavesdroppers. At the same time, we point put that the entanglement of the initial state is crucial when a partially entangled state is used.

quant-ph↗

arXiv2011

Separation Number and Generalized Clustering Coefficient in Small World Networks based on String Formalism

We reformulated the string formalism given by Aoyama, using an adjacent matrix of a network and introduced a series of generalized clustering coefficients based on it. Furthermore we numerically evaluated Milgram condition proposed by their article in order to explore $q$-$th$ degrees of separation in scale free networks. In this article, we apply the reformulation to small world networks and numerically evaluate Milgram condition, especially the separation number of small world networks and its relation to cycle structures are discussed. Considering the number of non-zero elements of an adjacent matrix, the average path length and Milgram condition, we show that the formalism proposed by us is effective to analyze the six degrees of separation, especially effective for analyzing the relation between the separation number and cycle structures in a network. By this analysis of small world networks, it proves that a sort of power low holds between $M_n$, which is a key quantity in Milgram condition, and the generalized clustering coefficients. This property in small world networks stands in contrast to that of scale free networks.

physics.soc-ph↗

arXiv2010

Generalized Clustering Coefficients and Milgram Condition for q-th Degrees of Separation

We introduce a series of generalized clustering coefficients based on String formalism given by Aoyama, using adjacent matrix in networks. We numerically evaluate Milgram condition proposed in order to explore q-th degrees of separation in scale free networks and small world networks. We find that scale free network with exponent 3 just shows 6-degrees of separation. Moreover we find some relations between separation numbers and generalized clustering coefficient in both networks.

cs.SI↗

arXiv2010

$p$-th Clustering coefficients and $q$-$th$ degrees of separation based on String-Adjacent Formulation

The phenomenon of six degrees of separation is an old but attractive subject. The deep understanding has been uncovered yet, especially how closed paths included in a network affect six degrees of separation are an important subject left yet. For it, some researches have been made\cite{Newm21}, \cite{Aoyama}. Recently we have develop a formalism \cite{Toyota3},\cite{Toyota4} to explore the subject based on the string formalism developed by Aoyama\cite{Aoyama}. The formalism can systematically investigate the effect of closed paths, especially generalized clustering coefficient $C_{(p)}$ introduced in \cite{Toyota4}, on six degrees of separation. In this article, we analyze general $q$-th degrees of separation by using the formalism developed by us. So we find that the scale free network with exponent $γ=3$ just display six degrees of separation. Furthermore we drive a phenomenological relation between the separation number $q$ and $C_{(p)}$ that has crucial information on circle structures in networks.

physics.soc-ph↗

arXiv2009

$p$-th Clustering coefficients $C_{p}$ and Adjacent Matrix for Networks: Formulation based on String

The phenomenon of six degrees of separation is an old but interesting problem. The considerations of the clustering coefficient reflecting triangular structures and its extension to square one to six degrees of separation have been made\cite{Newm21}. Recently, Aoyama\cite{Aoyama} has given some considerations to this problem in networks without loops, using a sort of general formalism, "string formalism". In this article, we describe relations between the string formulation proposed by Aoyama and an adjacent matrix. Thus we provided a reformulation of the string formulation proposed by \cite{Aoyama} to analyze networks. According to it, we introduced a series of generalized $q$-$th$ clustering coefficients. The available rules between diagrams of graphs and formulae are also given based on the formulation. Next we apply the formulation to some subjects in order to mainly check consistency with former studies. By evaluating the clustering coefficient for typical networks studied well earlier, we confirm a validity of our formulation. Lastly we applied it to the subject of two degrees of separation.

physics.soc-ph↗

arXiv2009

Comments on Six Degrees of Separation based on the le Pool and Kochen Models

In this article we discuss six degrees of separation, which has been suggested by Milgram's famous experiment\cite{Milg},\cite{Milg2}, from a theoretical point of view again. Though Milgram's experiment was partly inspired to Pool and Kochen's study \cite{Pool} that was made from a theoretical point of view. At the time numerically detailed study could not be made because computers and important concepts, such as the clustering coefficient, needed for a network analysis nowadays, have not yet developed. In this article we devote deep study to the six degrees of separation based on some models proposed by Pool and Kochen by using a computer, numerically. Moreover we estimate the clustering coefficient along the method developed by us \cite{Toyota1} and extend our analysis of the subject through marrying Pool and Kochen's models to our method.

physics.soc-ph↗