Nobuoki Eshima

The Cauchy problem for the system of equations describing migration motivated by regional economic disparity

We prove that there exists a unique global solution to the Cauchy problem for the system of nonlinear integro-partial differential equations describing migration motivated by regional economic disparity.

The behavior of solutions to the Cauchy problem for the master equation

We deal with the master equation, which is a nonlinear integro-partial differential equation. The equation plays a very important role in quantitative sociodynamics. The purpose of this paper is to investigate how solutions to the Cauchy problem for the equation behave as the time variable increases.

The nonlinear integro-partial differential equation describing the logistic growth of human population with migration

We derive a nonlinear integro-partial differential equation which describes the logistic growth of human population with migration. The equation is based upon the theory of logistic growth of population and upon the theory of migration in quantitative sociodynamics. We prove that the Cauchy problem for the equation has a unique global solution, and we obtain fundamental estimates for the solution.

Blowing-up solutions to the Cauchy problem for the master equation

The master equation is a nonlinear integro-partial differential equation that plays a very important role in investigating various sociodynamic phenomena. The purpose of this paper is to fully study blowing-up solutions to the Cauchy problem for the equation.

The Cauchy problem for the nonlinear integro-partial differential equation in quantitative sociodynamics

The master equation is a nonlinear integro-partial differential equation, which describes the evolution of various quantities in quantitative sociodynamics. For example, the master equation can describe interregional migration. The purpose of this paper is to obtain asymptotic estimates for solutions to the Cauchy problem for the equation.

An infinite continuous model which derives from a finite discrete model describing the time evolution of the density of firms

We derive a continuous model from a discrete model describing the time evolution of the density of firms which attempt to relocate within a bounded domain in order to obtain higher desirability in business. The discrete model consists of a finite number of firms, and is discretized with respect to both the time variable and the space variable. In the mathematical level of rigor, we derive the continuous model from the finite discrete model, by making use of a certain method frequently employed in statistical physics. We can consider that the continuous model thus obtained consists of an infinite number of firms. The infinite continuous model is represented by a non-linear integro-partial differential equation called the master equation.

The behavior of stochastic agent-based models when the number of agents and the time variable tend to infinity

In order to quantitatively describe interregional migration, we construct two stochastic agent-based models that consist of a large number of agents relocating to obtain higher utility in a discrete bounded domain. In one model we assume that the utility is defined as an increasing affine function of the density of agents. In the other model we assume that the utility is equal to a concave quadratic function of the density of agents. The purpose of the paper is to obtain estimates for the behavior of the models when the number of agents and the time variable tend to infinity.

Self-organization exhibited by a stochastic agent-based model of firms seeking higher desirability in business expressed by the market potential

We consider an agent-based model consisting of a finite number of firms that move stochastically within a discrete bounded domain in order to obtain higher business profits. The desirability in business is expressed by a certain exogenous random variable and a linear integral operator called market potential. If the number of firms is extremely large and the domain is very wide, then it is almost impossible to fully investigate the model by only doing numerical simulations. In order to overcome the difficulty, we employ a deterministic continuous model that is derived from the stochastic agent-based model by taking the scaling limit. By making use of the continuous model thus derived, we can fully observe self-organization exhibited by the original agent-based model.

An Entropy-Based Approach for Measuring Factor Contributions in Factor Analysis Models

In factor analysis, factor contributions of latent variables are assessed conventionally by the sums of the squared factor loadings related to the variables. First, the present paper considers issues in the conventional method. Second, an alternative entropy-based approach for measuring factor contributions is proposed. The method measures the contribution of the common factor vector to the manifest variable vector and decomposes it into contributions of factors. A numerical example is also provided to demonstrate the present approach.

A self-referential agent-based model that consists of a large number of agents moving stochastically in a discrete bounded domain

In order to describe interregional migration, we construct two models that consist of a large number of agents who relocate stochastically within a bounded discrete domain. Each agent of the models moves in order to obtain higher desirability. One is a model whose agents take only the present behavior of agents into account. The other is a model that contains agents relocating on the basis of a conjecture about the behavior (in the future) of agents. We assume that the agents of the latter model form the conjecture by making use of the model containing themselves. In this sense, we can say that the latter model has self-reference. The purpose of the present paper is to study the asymptotic behavior of these two models.