Social dilemma in foraging behavior and evolution of cooperation by learning.

We consider foraging behaviors in a two-dimensional continuum space and show that a cooperative chasing strategy can emerge in a social dilemma. Predators can use two different chasing strategies: A direct chasing strategy (DCS) and a group chasing strategy (GCS). The DCS is a selfish strategy with which a chaser moves straight toward the nearest prey, and the GCS is a cooperative strategy in the sense that the chaser chooses the chasing direction for the group at a cost of its own speed. A prey flees away from the nearest hazard, either a chaser or the boundary, within its recognition range. We check the capturing activities of each strategy and find a social dilemma between the two strategies because the GCS is more efficient for the group whereas the DCS is better individually. Using a series of numerical simulations, we further show that the cooperative strategy can proliferate when a learning process of nearby successful strategies is introduced.

Vacancies in growing habitats promote the evolution of cooperation.

We study evolutionary game dynamics in a growing habitat with vacancies. Fitness is determined by the global effect of the environment and a local prisoner's dilemma among neighbors. We study population growth on a one-dimensional lattice and analyze how the environment affects evolutionary competition. As the environment becomes harsh, an absorbing phase transition from growing populations to extinction occurs. The transition point depends on which strategies are present in the population. In particular, we find a 'cooperative window' in parameter space, where only cooperators can survive. A mutant defector in a cooperative community might briefly proliferate, but over time naturally occurring vacancies separate cooperators from defectors, thereby driving defectors to extinction. Our model reveals that vacancies provide a strong boost for cooperation by spatial selection.

Emergence of cooperation through chain-reaction death.

We generalize the Bak-Sneppen model of coevolution to a game model for evolutionary dynamics which provides a natural way for the emergence of cooperation. Interaction between members is mimicked by a prisoner's dilemma game with a memoryless stochastic strategy. The fitness of each member is determined by the payoffs π of the games with its neighbors. We investigate the evolutionary dynamics using a mean-field calculation and Monte Carlo method with two types of death processes, fitness-dependent death and chain-reaction death. In the former, the death probability is proportional to e^{-ßπ} where ß is the "selection intensity." The neighbors of the death site also die with a probability R through the chain-reaction process invoked by the abrupt change of the interaction environment. When a cooperator interacts with defectors, the cooperator is likely to die due to its low payoff, but the neighboring defectors also tend to disappear through the chain-reaction death, giving rise to an assortment of cooperators. Owing to this assortment, cooperation can emerge for a wider range of R values than the mean-field theory predicts. We present the detailed evolutionary dynamics of our model and the conditions for the emergence of cooperation.

Assortative clustering in a one-dimensional population with replication strategies.

In a geographically distributed population, assortative clustering plays an important role in evolution by modifying local environments. To examine its effects in a linear habitat, we consider a one-dimensional grid of cells, where each cell is either empty or occupied by an organism whose replication strategy is genetically inherited to offspring. The strategy determines whether to have offspring in surrounding cells, as a function of the neighborhood configuration. If more than one offspring compete for a cell, then they can be all exterminated due to the cost of conflict depending on environmental conditions. We find that the system is more densely populated in an unfavorable environment than in a favorable one because only the latter has to pay the cost of conflict. This observation agrees reasonably well with a mean-field analysis which takes assortative clustering of strategies into consideration. Our finding suggests a possibility of intrinsic nonlinearity between environmental conditions and population density when an evolutionary process is involved.

Quasicrystalline phase-change memory.

Phase-change memory utilizing amorphous-to-crystalline phase-change processes for reset-to-set operation as a nonvolatile memory has been recently commercialized as a storage class memory. Unfortunately, designing new phase-change materials (PCMs) with low phase-change energy and sufficient thermal stability is difficult because phase-change energy and thermal stability decrease simultaneously as the amorphous phase destabilizes. This issue arising from the trade-off relationship between stability and energy consumption can be solved by reducing the entropic loss of phase-change energy as apparent in crystalline-to-crystalline phase-change process of a GeTe/Sb2Te3 superlattice structure. A paradigm shift in atomic crystallography has been recently produced using a quasi-crystal, which is a new type of atomic ordering symmetry without any linear translational symmetry. This paper introduces a novel class of PCMs based on a quasicrystalline-to-approximant crystalline phase-change process, whose phase-change energy and thermal stability are simultaneously enhanced compared to those of the GeTe/Sb2Te3 superlattice structure. This report includes a new concept that reduces entropic loss using a quasicrystalline state and takes the first step in the development of new PCMs with significantly low phase-change energy and considerably high thermal stability.

Sex-ratio bias induced by mutation.

A question in evolutionary biology is why the number of males is approximately equal to that of females in many species, and Fisher's theory of equal investment answers that it is the evolutionarily stable state. The Fisherian mechanism can be given a concrete form by a genetic model based on the following assumptions: (1) Males and females mate at random. (2) An allele acts on the father to determine the expected progeny sex ratio. (3) The offspring inherits the allele from either side of the parents with equal probability. The model is known to achieve the 1:1 sex ratio due to the invasion of mutant alleles with different progeny sex ratios. In this study, however, we argue that mutation plays a more subtle role in that fluctuations caused by mutation renormalize the sex ratio and thereby keep it away from 1:1 in general. This finding shows how the sex ratio is affected by mutation in a systematic way, whereby the effective mutation rate can be estimated from an observed sex ratio.

Long-range prisoner's dilemma game on a cycle.

We investigate evolutionary dynamics of altruism with long-range interaction on a cycle. The interaction between individuals is described by a simplified version of the prisoner's dilemma (PD) game in which the payoffs are parameterized by c, the cost of a cooperative action. In our model, the probabilities of the game interaction and competition decay algebraically with r_{AB}, the distance between two players A and B, but with different exponents: That is, the probability to play the PD game is proportional to r_{AB}^{-α}. If player A is chosen for death, on the other hand, the probability for B to occupy the empty site is proportional to r_{AB}^{-ß}. In a limiting case of ß→∞, where the competition for an empty site occurs between its nearest neighbors only, we analytically find the condition for the proliferation of altruism in terms of c_{th}, a threshold of c below which altruism prevails. For finite ß, we conjecture a formula for c_{th} as a function of α and ß. We also propose a numerical method to locate c_{th}, according to which we observe excellent agreement with the conjecture even when the selection strength is of considerable magnitude.

Duality between cooperation and defection in the presence of tit-for-tat in replicator dynamics.

The prisoner's dilemma describes a conflict between a pair of players, in which defection is a dominant strategy whereas cooperation is collectively optimal. The iterated version of the dilemma has been extensively studied to understand the emergence of cooperation. In the evolutionary context, the iterated prisoner's dilemma is often combined with population dynamics, in which a more successful strategy replicates itself with a higher growth rate. Here, we investigate the replicator dynamics of three representative strategies, i.e., unconditional cooperation, unconditional defection, and tit-for-tat, which prescribes reciprocal cooperation by mimicking the opponent's previous move. Our finding is that the dynamics is self-dual in the sense that it remains invariant when we apply time reversal and exchange the fractions of unconditional cooperators and defectors in the population. The duality implies that the fractions can be equalized by tit-for-tat players, although unconditional cooperation is still dominated by defection. Furthermore, we find that mutation among the strategies breaks the exact duality in such a way that cooperation is more favored than defection, as long as the cost-to-benefit ratio of cooperation is small.

Role of generosity and forgiveness: Return to a cooperative society.

One's reputation in human society depends on what and how one did in the past. If the reputation of a counterpart is too bad, we often avoid interacting with the individual. We introduce a selective cooperator called the goodie, who participates in the prisoner's dilemma game dependent on the opponent's reputation, and study its role in forming a cooperative society. We observe enhanced cooperation when goodies have a small but nonzero probability of playing the game with an individual who defected in previous rounds. Our finding implies that even this small generosity of goodies can provide defectors chances of encountering the better world of cooperation, encouraging them to escape from their isolated world of selfishness.

Comparing reactive and memory-one strategies of direct reciprocity.

Direct reciprocity is a mechanism for the evolution of cooperation based on repeated interactions. When individuals meet repeatedly, they can use conditional strategies to enforce cooperative outcomes that would not be feasible in one-shot social dilemmas. Direct reciprocity requires that individuals keep track of their past interactions and find the right response. However, there are natural bounds on strategic complexity: Humans find it difficult to remember past interactions accurately, especially over long timespans. Given these limitations, it is natural to ask how complex strategies need to be for cooperation to evolve. Here, we study stochastic evolutionary game dynamics in finite populations to systematically compare the evolutionary performance of reactive strategies, which only respond to the co-player's previous move, and memory-one strategies, which take into account the own and the co-player's previous move. In both cases, we compare deterministic strategy and stochastic strategy spaces. For reactive strategies and small costs, we find that stochasticity benefits cooperation, because it allows for generous-tit-for-tat. For memory one strategies and small costs, we find that stochasticity does not increase the propensity for cooperation, because the deterministic rule of win-stay, lose-shift works best. For memory one strategies and large costs, however, stochasticity can augment cooperation.

Nash equilibrium and evolutionary dynamics in semifinalists' dilemma.

We consider a tournament among four equally strong semifinalists. The players have to decide how much stamina to use in the semifinals, provided that the rest is available in the final and the third-place playoff. We investigate optimal strategies for allocating stamina to the successive matches when players' prizes (payoffs) are given according to the tournament results. From the basic assumption that the probability to win a match follows a nondecreasing function of stamina difference, we present symmetric Nash equilibria for general payoff structures. We find three different phases of the Nash equilibria in the payoff space. First, when the champion wins a much bigger payoff than the others, any pure strategy can constitute a Nash equilibrium as long as all four players adopt it in common. Second, when the first two places are much more valuable than the other two, the only Nash equilibrium is such that everyone uses a pure strategy investing all stamina in the semifinal. Third, when the payoff for last place is much smaller than the others, a Nash equilibrium is formed when every player adopts a mixed strategy of using all or none of its stamina in the semifinals. In a limiting case that only last place pays the penalty, this mixed-strategy profile can be proved to be a unique symmetric Nash equilibrium, at least when the winning probability follows a Heaviside step function. Moreover, by using this Heaviside step function, we study the tournament by using evolutionary replicator dynamics to obtain analytic solutions, which reproduces the corresponding Nash equilibria on the population level and gives information on dynamic aspects.

Optional games on cycles and complete graphs.

We study stochastic evolution of optional games on simple graphs. There are two strategies, A and B, whose interaction is described by a general payoff matrix. In addition, there are one or several possibilities to opt out from the game by adopting loner strategies. Optional games lead to relaxed social dilemmas. Here we explore the interaction between spatial structure and optional games. We find that increasing the number of loner strategies (or equivalently increasing mutational bias toward loner strategies) facilitates evolution of cooperation both in well-mixed and in structured populations. We derive various limits for weak selection and large population size. For some cases we derive analytic results for strong selection. We also analyze strategy selection numerically for finite selection intensity and discuss combined effects of optionality and spatial structure.

Surface scaling properties of decagonal quasicrystals under nonequilibrium vertical growth.

Restricted solid-on-solid (RSOS) growth models are studied on two different decagonal quasicrystal lattices, namely the Penrose tiling lattice and the random tiling lattice. There exist two types of growth blocks-fat and skinny tiles-which may have different sticking probabilities. We found that the RSOS growths on both lattices belong to the Kardar-Parisi-Zhang universality class when they have the same sticking probabilities in spite of the lack of periodicity in the substrates. However, when they have tile-type dependent sticking probabilities, the RSOS models on two lattices may produce different scaling behaviors. Growth on Penrose tiling shows that the roughness exponent is around 0.4 while that on random tiling is around 0.49. Our observation may provide an effective way to investigate the bulk structures of decagonal quasicrystals.

Optimized structures for photonic quasicrystals.

A photonic quasicrystal consists of two or more dielectric materials arranged in a quasiperiodic pattern with noncrystallographic symmetry that has a photonic band gap. We use a novel method to find the pattern with the widest TM-polarized gap for two-component materials. Patterns are obtained by computing a finite sum of density waves, assigning regions where the sum exceeds a threshold to a material with one dielectric constant, epsilon1, and all other regions to another, epsilon0. Compared to optimized crystals, optimized quasicrystals have larger gaps at low constrasts epsilon1/epsilon0 and have gaps that are much more isotropic for all contrasts. For high contrasts, optimized hexagonal crystals have the largest gaps.

Growing perfect decagonal quasicrystals by local rules.

A local growth algorithm for a decagonal quasicrystal is presented. We show that a perfect Penrose tiling (PPT) layer can be grown on a decapod tiling layer by a three dimensional (3D) local rule growth. Once a PPT layer begins to form on the upper layer, successive 2D PPT layers can be added on top resulting in a perfect decagonal quasicrystalline structure in bulk with a point defect only on the bottom surface layer. Our growth rule shows that an ideal quasicrystal structure can be constructed by a local growth algorithm in 3D, contrary to the necessity of nonlocal information for a 2D PPT growth.

Directed polymers in random media under confining force.

The scaling behavior of a directed polymer in a two-dimensional random potential under confining force is investigated. The energy of a polymer with configuration {y(x)} is given by H({y(x)}) = sigma(x=1)(N) eta(x,y(x)) + epsilonW(alpha), where eta(x,y) is an uncorrelated random potential and W is the width of the polymer. Using an energy argument, it is conjectured that the radius of gyration Rg(N) and the energy fluctuation deltaE(N) of the polymer of length N in the ground state increase as Rg(N) approximately N(nu) and deltaE(N) approximately N(omega), respectively, with nu = 1/(1+alpha) and omega = (1+2alpha)/(4+4alpha) for alpha > or = 1/2. An algorithm of finding the exact ground state, with the effective time complexity of O(N3), is introduced and used to confirm the conjecture numerically.

Growing network model for community with group structure.

We propose a growing network model for a community with a group structure. The community consists of individual members and groups, gatherings of members. The community grows as a new member is introduced by an existing member at each time step. The new member then creates a new group or joins one of the groups of the introducer. We investigate the emerging community structure analytically and numerically. The group size distribution shows a power-law distribution for a variety of growth rules, while the activity distribution follows an exponential or a power law depending on the details of the growth rule. We also present an analysis of empirical data from online communities the "Groups" in http://www.yahoo.com and the "Cafe" in http://www.daum.net, which show a power-law distribution for a wide range of group sizes.

Scaling function for surface width for free boundary conditions.

We study the restricted curvature model with both periodic and free boundary conditions and show that the scaling function of the surface width depends on the type of boundary conditions. When the free boundary condition is applied, the surface width shows a new dynamic scaling whose asymptotic behavior is different from the usual scaling behavior of the self-affine surfaces. We propose a generalized scaling function for the surface width for free boundary conditions and introduce a normalized surface width to clarify the origin of the superrough phenomena of the model.

Inflation rule for Gummelt coverings with decorated decagons and its implication for quasi-unit-cell models.

The equivalence between quasi-unit-cell models and Penrose-tile models on the level of decorations is proved using inflation rules for Gummelt coverings with decorated decagons. Owing to overlaps, Gummelt arrangement of decorated decagons gives rise to nine different (context-dependent) decagon decorations in the covering. The inflation rules for decagons for each of nine types are presented and it is shown that inflations from differently typed decagons always produce different decorations of inflated decagons. However, if the original decagon region is divided into 'equivalent' rhombus Penrose tiles, typed-decagon arrangements in the tiles (of the same shape) become identical for the fourfold inflated decagons. This implies that a decagonal quasi-unit-cell model can be reinterpreted as a Penrose-tile model with fourfold deflated supertiles.