arXiv subjects

Long Wang

Publications and source records attributed to Long Wang.

At least 271 records · Page 15Linked to original sources

arXiv2013

The signature of line graphs and power trees

Let $G$ be a graph and let $A(G)$ be the adjacency matrix of $G$. The signature $s(G)$ of $G$ is the difference between the positive inertia index and the negative inertia index of $A(G)$. Ma et al. [Positive and negative inertia index of a graph, Linear Algebra and its Applications 438(2013)331-341] conjectured that $-c_3(G)\leq s(G)\leq c_5(G),$ where $c_3(G)$ and $c_5(G)$ respectively denote the number of cycles in $G$ which have length $4k+3$ and $4k+5$ for some integers $k \ge 0$, and proved the conjecture holds for trees, unicyclic or bicyclic graphs. It is known that $s(G)=0$ if $G$ is bipartite, and the signature is closely related to the odd cycles or nonbipartiteness of a graph from the existed results. In this paper we show that the conjecture holds for the line graph and power trees.

math.CO↗

arXiv2013

Projections and Idempotents in star-reducing Rings Involving the Moore-Penrose Inverse

In [Comput. Math. Appl. 59 (2010) 764-778], Baksalary and Trenkler characterized some complex idempotent matrices of the form $(I-PQ)^†P(I-Q)$, $(I-QP)^†(I-Q)$ and $P(P+Q-QP)^†$ in terms of the column spaces and null spaces of $P$ and $Q$, where $P, Q\in \mathbb{C}^{\textsf{OP}}_n = \{L\in \mathbb{C}_{n,n}\ |\ L^2 = L = L^*\}$. We generalize these results from $\mathbb{C}_{n,n}$ to any *-reducing rings.

math.RA↗

arXiv2013

Moore-Penrose Invertibility of Differences and Products of Projections in Rings with Involution

This article concerns the MP inverse of the differences and the products of projections in a ring $R$ with involution. Some equivalent conditions are obtained. As applications, the MP invertibility of the commutator $pq-qp$ and the anti-commutator $pq+qp$ are characterized, where $p$ and $q$ are projections in $R$. Some related known results in $C^*$-algebra are generalized.

math.RA↗

arXiv2013

Additive Property of Drazin Invertibility of Elements

In this article, we investigate additive properties of the Drazin inverse of elements in rings and algebras over an arbitrary field. Under the weakly commutative condition of $ab = λba$, we show that $a-b$ is Drazin invertible if and only if $aa^{D}(a-b)bb^{D}$ is Drazin invertible. Next, we give explicit representations of $(a+b)^{D}$, as a function of $a, b, a^{D}$ and $b^{D}$, under the conditions $a^{3}b = ba$ and $b^{3}a = ab$.

math.RA↗

arXiv2013

The triangle-free graphs with rank 6

The rank of a graph G is defined to be the rank of its adjacency matrix A(G). In this paper we characterize all connected triangle-free graphs with rank 6.

math.CO↗

arXiv2012

Bulk flow of halos in ΛCDM simulation

Analysis of the Pangu N-body simulation validates that the bulk flow of halos follows a Maxwellian distribution which variance is consistent with the prediction of the linear theory of structure formation. We propose that the consistency between the observed bulk velocity and theories should be examined at the effective scale of the radius of a spherical top-hat window function yielding the same smoothed velocity variance in linear theory as the sample window function does. We compared some recently estimated bulk flows from observational samples with the prediction of the ΛCDM model we used; some results deviate from expectation at a level of ~ 3σbut the discrepancy is not as severe as previously claimed. We show that bulk flow is only weakly correlated with the dipole of the internal mass distribution, the alignment angle between the mass dipole and the bulk flow has a broad distribution peaked at ~ 30-50 deg., and also that the bulk flow shows little dependence on the mass of the halos used in the estimation. In a simulation of box size 1Gpc/h, for a cell of radius 100 Mpc/h the maximal bulk velocity is >500 km/s, dipoles of the environmental mass outside the cell are not tightly aligned with the bulk flow, but are rather located randomly around it with separation angles ~ 20-40 deg. In the fastest cell there is a slightly smaller number of low-mass halos; however halos inside are clustered more strongly at scales > ~ 20 Mpc/h, which might be a significant feature since the correlation between bulk flow and halo clustering actually increases in significance beyond such scales.

astro-ph.CO↗

arXiv2012

Probabilistic interconnection between interdependent networks promotes cooperation in the public goods game

Most previous works study the evolution of cooperation in a structured population by commonly employing an isolated single network. However, realistic systems are composed of many interdependent networks coupled with each other, rather than the isolated single one. In this paper, we consider a system including two interacting networks with the same size, entangled with each other by the introduction of probabilistic interconnections. We introduce the public goods game into such system, and study how the probabilistic interconnection influences the evolution of cooperation of the whole system and the coupling effect between two layers of interdependent networks. Simulation results show that there exists an intermediate region of interconnection probability leading to the maximum cooperation level in the whole system. Interestingly, we find that at the optimal interconnection probability the fraction of internal links between cooperators in two layers is maximal. Also, even if initially there are no cooperators in one layer of interdependent networks, cooperation can still be promoted by probabilistic interconnection, and the cooperation levels in both layers can more easily reach an agreement at the intermediate interconnection probability. Our results may be helpful in understanding the cooperative behavior in some realistic interdependent networks and thus highlight the importance of probabilistic interconnection on the evolution of cooperation.

physics.soc-ph↗

arXiv2012

Beyond pairwise strategy updating in the prisoner's dilemma game

In spatial games players typically alter their strategy by imitating the most successful or one randomly selected neighbor. Since a single neighbor is taken as reference, the information stemming from other neighbors is neglected, which begets the consideration of alternative, possibly more realistic approaches. Here we show that strategy changes inspired not only by the performance of individual neighbors but rather by entire neighborhoods introduce a qualitatively different evolutionary dynamics that is able to support the stable existence of very small cooperative clusters. This leads to phase diagrams that differ significantly from those obtained by means of pairwise strategy updating. In particular, the survivability of cooperators is possible even by high temptations to defect and over a much wider uncertainty range. We support the simulation results by means of pair approximations and analysis of spatial patterns, which jointly highlight the importance of local information for the resolution of social dilemmas.

physics.soc-ph↗

arXiv2012

Adaptive and bounded investment returns promote cooperation in spatial public goods games

The public goods game is one of the most famous models for studying the evolution of cooperation in sizable groups. The multiplication factor in this game can characterize the investment return from the public good, which may be variable depending on the interactive environment in realistic situations. Instead of using the same universal value, here we consider that the multiplication factor in each group is updated based on the differences between the local and global interactive environments in the spatial public goods game, but meanwhile limited to within a certain range. We find that the adaptive and bounded investment returns can significantly promote cooperation. In particular, full cooperation can be achieved for high feedback strength when appropriate limitation is set for the investment return. Also, we show that the fraction of cooperators in the whole population can become larger if the lower and upper limits of the multiplication factor are increased. Furthermore, in comparison to the traditionally spatial public goods game where the multiplication factor in each group is identical and fixed, we find that cooperation can be better promoted if the multiplication factor is constrained to adjust between one and the group size in our model. Our results highlight the importance of the locally adaptive and bounded investment returns for the emergence and dominance of cooperative behavior in structured populations.

physics.soc-ph↗

arXiv2012

Impact of generalized benefit functions on the evolution of cooperation in spatial public goods games with continuous strategies

Cooperation and defection may be considered as two extreme responses to a social dilemma. Yet the reality is much less clear-cut. Between the two extremes lies an interval of ambivalent choices, which may be captured theoretically by means of continuous strategies defining the extent of the contributions of each individual player to the common pool. If strategies are chosen from the unit interval, where 0 corresponds to pure defection and 1 corresponds to the maximal contribution, the question is what is the characteristic level of individual investments to the common pool that emerges if the evolution is guided by different benefit functions. Here we consider the steepness and the threshold as two parameters defining an array of generalized benefit functions, and we show that in a structured population there exist intermediate values of both at which the collective contributions are maximal. However, as the cost-to-benefit ratio of cooperation increases the characteristic threshold decreases, while the corresponding steepness increases. Our observations remain valid if more complex sigmoid functions are used, thus reenforcing the importance of carefully adjusted benefits for high levels of public cooperation.

physics.soc-ph↗

arXiv2012

Different reactions to adverse neighborhoods in games of cooperation

In social dilemmas, cooperation among randomly interacting individuals is often difficult to achieve. The situation changes if interactions take place in a network where the network structure jointly evolves with the behavioral strategies of the interacting individuals. In particular, cooperation can be stabilized if individuals tend to cut interaction links when facing adverse neighborhoods. Here we consider two different types of reaction to adverse neighborhoods, and all possible mixtures between these reactions. When faced with a gloomy outlook, players can either choose to cut and rewire some of their links to other individuals, or they can migrate to another location and establish new links in the new local neighborhood. We find that in general local rewiring is more favorable for the evolution of cooperation than emigration from adverse neighborhoods. Rewiring helps to maintain the diversity in the degree distribution of players and favors the spontaneous emergence of cooperative clusters. Both properties are known to favor the evolution of cooperation on networks. Interestingly, a mixture of migration and rewiring is even more favorable for the evolution of cooperation than rewiring on its own. While most models only consider a single type of reaction to adverse neighborhoods, the coexistence of several such reactions may actually be an optimal setting for the evolution of cooperation.

physics.soc-ph↗

arXiv2012

Win-stay-lose-learn promotes cooperation in the spatial prisoner's dilemma game

Holding on to one's strategy is natural and common if the later warrants success and satisfaction. This goes against widespread simulation practices of evolutionary games, where players frequently consider changing their strategy even though their payoffs may be marginally different than those of the other players. Inspired by this observation, we introduce an aspiration-based win-stay-lose-learn strategy updating rule into the spatial prisoner's dilemma game. The rule is simple and intuitive, foreseeing strategy changes only by dissatisfied players, who then attempt to adopt the strategy of one of their nearest neighbors, while the strategies of satisfied players are not subject to change. We find that the proposed win-stay-lose-learn rule promotes the evolution of cooperation, and it does so very robustly and independently of the initial conditions. In fact, we show that even a minute initial fraction of cooperators may be sufficient to eventually secure a highly cooperative final state. In addition to extensive simulation results that support our conclusions, we also present results obtained by means of the pair approximation of the studied game. Our findings continue the success story of related win-stay strategy updating rules, and by doing so reveal new ways of resolving the prisoner's dilemma.

q-bio.PE↗

arXiv2012

Maximum Estrada Index of Bicyclic Graphs

Let $G$ be a simple graph of order $n$, let $λ_1(G),λ_2(G),...,λ_n(G)$ be the eigenvalues of the adjacency matrix of $G$. The Esrada index of $G$ is defined as $EE(G)=\sum_{i=1}^{n}e^{λ_i(G)}$. In this paper we determine the unique graph with maximum Estrada index among bicyclic graphs with fixed order.

math.CO↗

arXiv2011

Evolution of interactions and cooperation in the spatial prisoner's dilemma game

We study the evolution of cooperation in the spatial prisoner's dilemma game where players are allowed to establish new interactions with others. By employing a simple coevolutionary rule entailing only two crucial parameters, we find that different selection criteria for the new interaction partners as well as their number vitally affect the outcome of the game. The resolution of the social dilemma is most probable if the selection favors more successful players and if their maximally attainable number is restricted. While the preferential selection of the best players promotes cooperation irrespective of game parametrization, the optimal number of new interactions depends somewhat on the temptation to defect. Our findings reveal that the "making of new friends" may be an important activity for the successful evolution of cooperation, but also that partners must be selected carefully and their number limited.

physics.soc-ph↗

arXiv2011

Evolution of cooperation in multilevel public goods games with community structures

In a community-structured population, public goods games (PGG) occur both within and between communities. Such type of PGG is referred as multilevel public goods games (MPGG). We propose a minimalist evolutionary model of the MPGG and analytically study the evolution of cooperation. We demonstrate that in the case of sufficiently large community size and community number, if the imitation strength within community is weak, i.e., an individual imitates another one in the same community almost randomly, cooperation as well as punishment are more abundant than defection in the long run; if the imitation strength between communities is strong, i.e., the more successful strategy in two individuals from distinct communities is always imitated, cooperation and punishment are also more abundant. However, when both of the two imitation intensities are strong, defection becomes the most abundant strategy in the population. Our model provides insight into the investigation of the large-scale cooperation in public social dilemma among contemporary communities.

q-bio.PE↗

arXiv2010

Universality of weak selection

Weak selection, which means a phenotype is slightly advantageous over another, is an important limiting case in evolutionary biology. Recently it has been introduced into evolutionary game theory. In evolutionary game dynamics, the probability to be imitated or to reproduce depends on the performance in a game. The influence of the game on the stochastic dynamics in finite populations is governed by the intensity of selection. In many models of both unstructured and structured populations, a key assumption allowing analytical calculations is weak selection, which means that all individuals perform approximately equally well. In the weak selection limit many different microscopic evolutionary models have the same or similar properties. How universal is weak selection for those microscopic evolutionary processes? We answer this question by investigating the fixation probability and the average fixation time not only up to linear, but also up to higher orders in selection intensity. We find universal higher order expansions, which allow a rescaling of the selection intensity. With this, we can identify specific models which violate (linear) weak selection results, such as the one--third rule of coordination games in finite but large populations.

q-bio.PE↗

arXiv2009

Partner selections in public goods games with constant group size

Most of previous studies concerning the Public Goods Game assume either participation is unconditional or the number of actual participants in a competitive group changes over time. How the fixed group size, prescribed by social institutions, affects the evolution of cooperation is still unclear. We propose a model where individuals with heterogeneous social ties might well engage in differing numbers of Public Goods Games, yet with each Public Goods Game being constant size during the course of evolution. To do this, we assume that each focal individual unidirectionally selects a constant number of interaction partners from his immediate neighbors with probabilities proportional to the degrees or the reputations of these neighbors, corresponding to degree-based partner selection or reputation-based partner selection, respectively. Because of the stochasticity the group formation is dynamical. In both selection regimes, monotonical dependence of the stationary density of cooperators on the group size was found, the former over the whole range but the latter over a restricted range of the renormalized enhancement factor. Moreover, the reputation-based regime can substantially improve cooperation. To interpret these differences, the microscopic characteristics of individuals are probed. We later extend the degree-based partner selection to general cases where focal individuals have preferences towards their neighbors of varying social ties to form groups. As a comparison, we as well investigate the situation where individuals locating on the degree regular graphs choose their co-players at random. Our results may give some insights into better understanding the widespread teamwork and cooperation in the real world.

physics.soc-ph↗

arXiv2007

Evolutionary game dynamics with three strategies in finite populations

We propose a model for evolutionary game dynamics with three strategies $A$, $B$ and $C$ in the framework of Moran process in finite populations. The model can be described as a stochastic process which can be numerically computed from a system of linear equations. Furthermore, to capture the feature of the evolutionary process, we define two essential variables, the {\em global} and the {\em local} fixation probability. If the {\em global} fixation probability of strategy $A$ exceeds the neutral fixation probability, the selection favors $A$ replacing $B$ or $C$ no matter what the initial ratio of $B$ to $C$ is. Similarly, if the {\em local} fixation probability of $A$ exceeds the neutral one, the selection favors $A$ replacing $B$ or $C$ only in some appropriate initial ratios of $B$ to $C$. Besides, using our model, the famous game with AllC, AllD and TFT is analyzed. Meanwhile, we find that a single individual TFT could invade the entire population under proper conditions.

physics.soc-ph↗