Search Results (66 total)

We present a global payoff-based strategy updating model for studying cooperative behavior of a networked population. We adopt the Prisoner’s Dilemma game and the snowdrift game as paradigms for characterizing the interactions among individuals. We investigate the model on regular, small-world, and scale-free networks, and find multistable cooperation states depending on the initial cooperator density. In particular for the snowdrift game on small-world and scale-free networks, there exist a discontinuous phase transition and hysteresis loops of cooperator density. We explain the observed properties by theoretical predictions and simulation results of the average number of neighbors of cooperators and defectors, respectively. Our work indicates that individuals with more neighbors have a trend to preserve their initial strategies, which has strong impacts on the strategy updating of individuals with fewer neighbors; while the fact that individuals with few neighbors have to become cooperators to avoid gaining the lowest payoff plays significant roles in maintaining and spreading of cooperation strategy.

We study the effects of the existence of another type of agents, called spies, in the minority game (MG). Unlike the normal agents in the MG, the spies do not carry any strategy. Instead, they decide their action by scouting some normal agents and take the minority action of the spied group. For a few spies and when there is useful information in the normal agents’ actions, the spies can avoid the crowd effect of the normal agents and win more readily. When information becomes less useful and when more spies are present, the spies’ crowd effect hurts the success rate of the spies themselves, and the normal agents could have a higher success rate than the spies. More spies actually assist more normal agents to win, as the spies also provide more winning quotas. This leads to a nonmonotonic behavior in the total success rate of the population as a function of the fraction of spies.

The dynamical process of opinion formation within a model using a local majority opinion updating rule is studied numerically in networks with the small-world geometrical property. The network is one in which shortcuts are added to randomly chosen pairs of nodes in an underlying regular lattice. The presence of a small number of shortcuts is found to shorten the time to reach a consensus significantly. The effects of having shortcuts in a lattice of fixed spatial dimension are shown to be analogous to that of increasing the spatial dimension in regular lattices. The shortening of the consensus time is shown to be related to the shortening of the mean shortest path as shortcuts are added. Results can also be translated into that of the dynamics of a spin system in a small-world network.

Using the coupled cluster expansion with the random phase approximation, we calculate the long wavelength vacuum wave function and the vacuum state energy of 2+1 dimensional Hamiltonian SU(2) lattice gauge theory up to the seventh order. The coefficients μ₀, μ₂ of the vacuum wave function show good scaling behavior and convergence in high order calculations.

We study the effects of the presence of contrarians in an agent-based model of competing populations. Contrarians are common in societies. These contrarians are agents who deliberately prefer to hold an opinion that is contrary to the prevailing idea of the commons or normal agents. Contrarians are introduced within the context of the minority game (MG), which is a binary model for an evolving and adaptive population of agents competing for a limited resource. The average success rate among the agents is found to have a nonmonotonic dependence on the fraction a_c of contrarians. For small a_c, the contrarians systematically outperform the normal agents by avoiding the crowd effect and enhance the overall success rate. For high a_c, the antipersistent nature of the MG is disturbed and the few normal agents outperform the contrarians. Qualitative discussion and analytic results for the small a_c and high a_c regimes are presented, and the crossover behavior between the two regimes is discussed.

We provide an analytic theory to explain Anghel ’s recent numerical finding whereby a maximum in the global performance emerges for a sparsely connected competitive population [Phys. Rev. Lett. 92, 058701 (2004)]. We show that the effect originates in the highly correlated dynamics of strategy choice, and can be significantly enhanced using a simple modification to the model.

We show, both analytically and numerically, that erroneous data transmission generates a global transition within a competitive population playing the “Minority Game” on a network. This transition, which resembles a phase transition, is driven by a “temporal symmetry breaking” in the global outcome series. The phase boundary, which is a function of the network connectivity p and the error probability q, is described quantitatively by the crowd-anticrowd theory.

We formulate a theory of agent-based models in which agents compete to be in a winning group. The agents may be part of a network or not, and the winning group may be a minority group or not. An important feature of the present formalism is its focus on the dynamical pattern of strategy rankings, and its careful treatment of the strategy ties which arise during the system’s temporal evolution. We apply it to the minority game with connected populations. Expressions for the mean success rate among the agents and for the mean success rate for agents with k neighbors are derived. We also use the theory to estimate the value of connectivity p above which the binary-agent-resource system with high resource levels makes the transition into the high-connectivity state.

We propose and study an evolutionary minority game (EMG) in which the agents are allowed to choose among three possible options. Unlike the original EMG where the agents either win or lose one unit of wealth, the present model assigns one unit of wealth to the winners in the least popular option, deducts one unit from the losers in the most popular option, and awards R(−1<R<1) units for those in the third option. Decisions are made based on the information in the most recent outcomes and on the characteristic probabilities of an agent to follow the predictions based on recent outcomes. Depending on R, the population shows a transition from self-segregation in difficult situations (R<R_c) in which the agents tend to follow extreme action to cautious or less decisive action for R>R_c, where R_c(N) is a critical value for optimal performance of the system that drops to zero as the number of agents N increases.

We propose and study a model of scale-free growing networks that gives a degree distribution dominated by a power-law behavior with a model-dependent, hence tunable, exponent. The model represents a hybrid of the growing networks based on popularity-driven and fitness-driven preferential attachments. As the network grows, a newly added node establishes m new links to existing nodes with a probability p based on popularity of the existing nodes and a probability 1−p based on fitness of the existing nodes. An explicit form of the degree distribution P(p,k) is derived within a mean field approach. For reasonably large k, P(p,k)∼k^−γ(p)F(k,p), where the function F is dominated by the behavior of 1∕ln(k∕m) for small values of p and becomes k independent as p→1, and γ(p) is a model-dependent exponent. The degree distribution and the exponent γ(p) are found to be in good agreement with results obtained by extensive numerical simulations.

We study a version of the minority game in which one agent is allowed to join the game in a random fashion. It is shown that in the crowded regime, i.e., for small values of the memory size m of the agents in the population, the agent performs significantly well if she decides to participate the game randomly with a probability q and she records the performance of her strategies only in the turns that she participates. The information, characterized by a quantity called the inefficiency, embedded in the agent’s strategies performance turns out to be very different from that of the other agents. Detailed numerical studies reveal a relationship between the success rate of the agent and the inefficiency. The relationship can be understood analytically in terms of the dynamics in which the various possible histories are being visited as the game proceeds. For a finite fraction of randomly participating agents up to 60% of the population, it is found that the winning edge of these agents persists.

Thin films of (1-x)PbMg_1/3Nb_2/3O₃-xPbTiO₃ (PMN-PT) with x=0, 0.1, 0.3, 0.35, and 0.4 have been fabricated on (001)MgO single-crystal substrates by pulsed laser deposition (PLD). X-ray diffraction (XRD), scanning electron microscopy (SEM), and atomic force microscopy (AFM) were employed to characterize the structural properties of these PMN-PT films. Our results show that these films possess excellent structural properties and are cube-on-cube grown on (001)MgO substrates. Spectroellipsometry (SE) was used to characterize the depth profiles, the microstructural inhomogeneities, including void and surface roughness, refractive indices and extinction coefficients of the films. In the analysis of the measured SE spectra, a double-layer Lorentz model with four oscillators was adopted to represent the optical properties of the PMN-PT films. In this model, the films were assumed to consist of two layers—a bottom bulk PMN-PT layer and a surface layer composed of bulk PMN-PT as well as void. Good agreement was obtained between the measured spectra and the model calculations. The film thickness measured by SEM is consistent with that obtained by SE while the root mean square (rms) surface roughness determined by AFM is also close to our fitted effective surface layer thickness obtained by SE. Our measurements show that the refractive indices of the PMN-PT films increase with PbTiO₃ contents. This dependence is consistent with our optical transmittance measurements which revealed that the energy band gaps of PMN-PT films decrease with increasing PbTiO₃ contents. The correlation between the energy band gap and the refractive index is discussed.

We derive an expression for the effective second-harmonic coefficient of a dilute suspension of coated spherical particles. It is assumed that the coating material, but not the core or the host, has a nonlinear susceptibility for second-harmonic generation (SHG). The resulting compact expression shows the various factors affecting the effective SHG coefficient. The effective SHG per unit volume of nonlinear coating material is found to be greatly enhanced at certain frequencies, corresponding to the surface-plasmon resonance of the coated particles. Similar expression is also derived for a dilute suspension of coated discs. For coating materials with third-harmonic (THG) coefficient, results for the effective THG coefficients are given for the cases of coated particles and coated discs.

The effective nonlinear response of films of random composites consisting of a binary composite with nonlinear particles randomly embedded in a linear host is theoretically and numerically studied. A theoretical expression for the effective second-harmonic generation susceptibility, incorporating the thickness of the film, is obtained by combining a modified effective-medium approximation with the general expression for the effective second-harmonic generation susceptibility in a composite. The validity of the theoretical results is tested against results obtained by numerical simulations on random resistor networks. Numerical results are found to be well described by our theory. The result implies that the effective-medium approximation provides a convenient way for the estimation of the nonlinear response in films of random dielectrics.

We propose a model of weighted scale-free networks incorporating a stochastic scheme for weight assignments to the links, taking into account both the popularity and fitness of a node. As the network grows, the weights of links are driven either by the connectivity with probability p or by the fitness with probability 1-p. Numerical results show that the total weight exhibits a power-law distribution with an exponent σ that depends on the probability p. The exponent σ decreases continuously as p increases. For p=0, the scaling behavior is the same as that of the connectivity distribution. An analytical expression for the total weight is derived so as to explain the features observed in the numerical results. Numerical results are also presented for a generalized model with a fitness-dependent link formation mechanism.

We have studied the electronic transport properties of open Sierpinski gasket systems in the presence of a magnetic field. The real-space renormalization-group scheme combined with the generalized eigenfunction method is used to calculate the transmission and reflection coefficients. Three kinds of electronic exits are investigated upto the thirtieth generation Sierpinski lattice. Some resonant-transmission features and the symmetry of the transmission coefficient T to the magnetic flux Φ are observed and discussed.

The random-phase approximation is applied to coupled cluster expansions for (2+1)-dimensional SU(3) lattice gauge theory. The 0⁺⁺ glueball mass is calculated up to the fourth order. The result agrees with the recent Monte Carlo result.

The Eguíluz and Zimmermann model of information transmission and herd formation in a financial market is studied analytically. Starting from a formal description on the rate of change of the system from one partition of agents in the system to another, a mean-field theory is systematically developed. The validity of the mean-field theory is carefully studied against fluctuations. When the number of agents N is sufficiently large and the probability of making a transaction a≪1/N ln N, finite-size effect is found to be significant. In this case, the system has a large probability of becoming a single cluster containing all the agents. For small clusters of agents, the cluster size distribution still obeys a power law but with a much reduced magnitude. The exponent is found to be modified to the value of -3 by the fluctuation effects from the value of -5/2 in the mean-field theory.

We show analytically how the fluctuations (i.e., standard deviation σ) in the minority game can decrease below the random coin-toss limit if the agents use more general, stochastic strategies. This suppression of σ results from a cancellation between the actions of a crowd, in which agents act collectively and make the same decision, and those of an anticrowd, in which agents act collectively by making the opposite decision to the crowd.

We present a theory describing a recently introduced model of an evolving, adaptive system in which agents compete to be in the minority. The agents themselves are able to evolve their strategies over time in an attempt to improve their performance. The theory explicitly demonstrates the self-interaction, or market impact, that agents in such systems experience.

We propose a scheme to improve the coupled cluster expansion in lattice gauge theory (LGT), based on the application of the random phase approximation, in order to approximate a wave function in terms of a linear combination of Wilson loops. Using this method, we study the vacuum energy and vacuum wave function in (2+1)D SU(3) LGT up to fourth order. The vacuum energy is lower than that obtained by the unimproved approach. The coefficients μ₀,μ₂ of the vacuum wave function show good scaling behavior and convergence.

We have studied the electronic transport properties of open Sierpinski gasket systems connected to two electron reservoirs in the presence of a magnetic field. In the framework of a tight-binding model, the systems are composed of one-dimensional ordered chains. A generalized eigenfunction method, which allows one to deal with finite systems consisting of a large number of lattice sites (nodes), is used to calculate the transmission and reflection coefficients of the studied systems. The numerical results show that there are two kinds of symmetries of the transmission coefficient T to magnetic flux Φ, and there are antiresonant state regions (T=0) and resonant states (T=1). It is different from the open ring systems now the electronic energies of resonant states do not coincide with the eigenenergies of the isolated Sierpinski gasket systems. It is also found that the transmission behavior of the single exit systems is much more complicated than that of two exit systems.

Three cellular automaton models of increasing complexity are introduced to model driven diffusive systems related to the generalized Frenkel-Kontorova (FK) models recently proposed by Braun et al. [Phys. Rev. E 58, 1311 (1998)]. The models are defined in terms of parallel updating rules. Simulation results are presented for these models. The features are qualitatively similar to those models defined previously in terms of sequentially updating rules. Essential features of the FK model such as phase transitions, jamming due to atoms in the immobile state, and hysteresis in the relationship between the fraction of atoms in the running state and the bias field are captured. Formulating in terms of parallel updating rules has the advantage that the models can be treated analytically by following the time evolution of the occupation on every site of the lattice. Results of this analytical approach are given for the two simpler models. The steady state properties are found by studying the stable fixed points of a closed set of dynamical equations obtained within the approximation of retaining spatial correlations only up to two nearest-neighboring sites. Results are found to be in good agreement with numerical data.

An evolving population, in which individual members (“agents”) adapt their behavior according to past experience, is of central importance to many disciplines. Because of their limited knowledge and capabilities, agents are forced to make decisions based on inductive, rather than deductive, thinking. We show that a population of competing agents with similar capabilities and knowledge will tend to self-segregate into opposing groups characterized by extreme behavior. Cautious agents perform poorly and tend to become rare.

Using the charge exchange facility and second arm spectrometer at TRIUMF, we have measured the ³¹P(n,p) double differential cross section for 198 MeV incident neutrons, at scattering angles of 0–30°, and excitation energies up to 30 MeV. Via a multipole decomposition analysis we have extracted both the Gamow-Teller strength distribution and the GT transition probabilities to low-lying ³¹Si bound states. Comparison to a shell model calculation, using the full 1s-0d space and universal SD interaction, shows reasonable agreement in the strength distribution, but reduced summed strength in the experiment (∑B_GT=2.32±0.20 for E_x<~10 MeV) relative to the theory (∑B_GT=3.33 for E_x<~10 MeV). We discuss the role of configuration mixing and Pauli blocking on the ³¹P³¹Si GT strength distribution.