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Masahiko Ueda

Publications and source records attributed to Masahiko Ueda.

27 records · Page 2Linked to original sources

Effect of information asymmetry in Cournot duopoly game with bounded rationality

We investigate the effect of information asymmetry on a dynamic Cournot duopoly game with bounded rationality. Concretely, we study how one player's possession of information about the other player's behavior in a duopoly affects the stability of the Cournot-Nash equilibrium. We theoretically and numerically show that the information stabilizes the Cournot-Nash equilibrium and suppresses chaotic behavior in the duopoly.

cs.GT↗

Numerical calculation of overlap distribution of $(2+1)$-dimensional directed polymer in random media

We investigate $(2+1)$-dimensional discretized directed polymers in Gaussian random media. By numerically calculating the probability distribution function of overlap between two independent and identical systems on a common random potential, we show that there is no replica symmetry breaking. We also show that while the mean-squared displacement of one polymer end exhibits superdiffusive behavior, the mean-squared relative distance of two polymer ends exhibits subdiffusive behavior.

cond-mat.dis-nn↗

Replica symmetry breaking in trajectory space for diffusion in logarithmically correlated random potentials

We study the dynamics of a particle in a one-dimensional Gaussian random potential with logarithmic correlations. It was shown in previous studies that the model exhibits a dynamical transition between two subdiffusive phases. We numerically investigate both phases by focusing on overlap between trajectories of two independent particles in a common random potential, and show that replica symmetry breaking in trajectory space occurs in the low-temperature phase.

cond-mat.stat-mech↗

Stronger selection can slow down evolution driven by recombination on a smooth fitness landscape

Stronger selection implies faster evolution---that is, the greater the force, the faster the change. This apparently self-evident proposition, however, is derived under the assumption that genetic variation within a population is primarily supplied by mutation (i.e.\ mutation-driven evolution). Here, we show that this proposition does not actually hold for recombination-driven evolution, i.e.\ evolution in which genetic variation is primarily created by recombination rather than mutation. By numerically investigating population genetics models of recombination, migration and selection, we demonstrate that stronger selection can slow down evolution on a perfectly smooth fitness landscape. Through simple analytical calculation, this apparently counter-intuitive result is shown to stem from two opposing effects of natural selection on the rate of evolution. On the one hand, natural selection tends to increase the rate of evolution by increasing the fixation probability of fitter genotypes. On the other hand, natural selection tends to decrease the rate of evolution by decreasing the chance of recombination between immigrants and resident individuals. As a consequence of these opposing effects, there is a finite selection pressure maximizing the rate of evolution. Hence, stronger selection can imply slower evolution if genetic variation is primarily supplied by recombination.

q-bio.PE↗

Replica symmetry breaking in trajectory space for the trap model

We study the localization in the one-dimensional trap model in terms of statistical mechanics of trajectories. By numerically investigating overlap between trajectories of two particles on a common disordered potential, we find that there is a phase transition in the path ensemble. We characterize the low temperature phase as a replica symmetry breaking phase in trajectory space.

cond-mat.stat-mech↗

Replica symmetry breaking in trajectories of a driven Brownian particle

We study a Brownian particle passively driven by a field obeying the noisy Burgers equation. We demonstrate that the system exhibits replica symmetry breaking in the path ensemble with the initial position of the particle being fixed. The key step of the proof is that the path ensemble with a modified boundary condition can be exactly mapped to the canonical ensemble of directed polymers.

cond-mat.stat-mech↗

Replica analysis of Franz-Parisi potential for sparse systems

We propose a method for calculating the Franz-Parisi potential for spin glass models on sparse random graphs using the replica method under the replica symmetric ansatz. The resulting self-consistent equations have the solution with the characteristic structure of multi-body overlaps, and the self-consistent equations under this solution are equivalent to the one-step replica symmetry breaking (1RSB) cavity equation with Parisi parameter $x=1$. This method is useful for the evaluation of transition temperatures of the $p$-spin model on regular random graphs under a uniform magnetic field.

cond-mat.dis-nn↗

Calculation of 1RSB transition temperature of spin glass models on regular random graphs under the replica symmetric ansatz

We study $p$-spin glass models on regular random graphs. By analyzing the Franz-Parisi potential with a two-body cavity field approximation under the replica symmetric ansatz, we obtain a good approximation of the 1RSB transition temperature for $p=3$. Our calculation method is much easier than the 1RSB cavity method because the result is obtained by solving self-consistent equations with Newton's method.

cond-mat.stat-mech↗