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The purpose of this paper is to suggest a formalism given by an equation suitable for simulating discrete systems with space-time variation in addition to other change variables. With such formalism, multidimensional dynamical models of discrete complex systems, such as the social systems and ecosystems, can be built.

This formalism is named as discrete multidimensional dynamic system (DMDS). The DMDS provides a way to consider the variation of the density of a state variable with regard to the variables of the change space as a function of multidimensional rates. Multidimensional rates describe this evolution as a consequence of the relation of each multidimensional-point with a given set of other points of the change space. This relation contains the accessibility domains (sets of space points with which each space point is related).

This equation is compared with both the reaction-diffusion equation written in its finite difference form and the cellular-automata model, demonstrating its compatibility with them and an increase in generality, widening the scope of application. The steps to construct models of systems with multidimensional variation based on the equation that defines the DMDS are specified and tested.

Through the DMDS and a well-stated methodology, an application case is provided in order to describe the multidimensional demographic dynamics of an urban system. In this case, the numerical evolution of the population density by districts and cohorts is determined by the DMDS based on some hypothesis about functions of population diffusion between the different districts of the system.

The scope of application of the space-time dynamic system (STDS), given by the authors in a previous work, has been extended to discrete and multidimensional systems. STDS model produces better results than the reaction-diffusion model in validation.

The purpose of this paper is to investigate the body-mind problem from a mathematical invariance principle in relation to personality dynamics in the psychological and the biological levels of description.

The relationship between the two mentioned levels of description is provided by two mathematical models as follows: the response model and the bridge model. The response model (an integro-differential equation) is capable to reproduce the personality dynamics as a consequence of a determined stimulus. The invariance principle asserts that the response model can reproduce personality dynamics at the two levels of description. The bridge model (a second-order partial differential equation) can be deduced as a consequence of this principle: it provides the co-evolution of the general factor of personality (GFP) (mind), the it is an immediate early gene (c-fos) and D3 dopamine receptor gene (DRD3) gens and the glutamate neurotransmitter (body).

An application case is presented by setting up two experimental designs: a previous pilot AB pseudo-experimental design (AB) pseudo-experimental design with one subject and a subsequent ABC experimental design (ABC) experimental design with another subject. The stimulus used is the stimulant drug methylphenidate. The response and bridge models are validated with the outcomes of these experiments.

The mathematical approach here presented is based on a holistic personality model developed in the past few years: the unique trait personality theory, which claims for a single personality trait to understand the overall human personality: the GFP.

The purpose is to present a new formal approach based on a partial integro‐differential equation, the space‐time state transition equation (STSTE), and on a set of general equations with which space‐time dynamical models of complex systems, such as social systems and ecosystems, can be built.

The STSTE provides the partial derivative of the density of a state‐variable with regard to time as a sum of time rates and space‐time rates. Time rates describe the dynamics of the system for each space‐point irrespectively of the other points, whilst space‐time rates describe this evolution as a consequence of the relation of each space‐point with a given set of other points of the space. This relation contains integrals over the accessibility domains (sets of space‐points with which each space‐point is related).

The STSTE is provided for any system of space‐coordinates and is compared with the reaction‐diffusion models (RD). The reason why it is more convenient to work with the STSTE than with the RD to model complex systems in the context of social systems and ecosystems is indicated.

An urban system (the city of Valencia, Spain) is presented as an application; an analytical solution strategy is stated under the simplest hypothesis for computing space‐time rates, and a computer program for the situation is developed to obtain numerical solutions.

A numerical comparison between the new STSTE model and the RD shows that, the STSTE model produces better results than the reaction diffusion model in validation.

The purpose of this paper is to describe a work that aims to solve contour detection problem using a planar deformable model and a swarm‐based optimization technique. Contour detection is an important task in image processing as it allows depicting boundaries of objects in an image. The proposed approach uses snakes as active contour model and adapts predator prey optimization (PPO) metaheuristic so that to define a new dynamic for evolving snakes in a way to reduce time complexity while providing good quality results.

In the proposed approach, contour detection has been cast as an optimization problem requiring function minimization. PPO has been used to develop a search strategy to handle the optimization process. PPO is a population‐based method inspired by the phenomenon of predators attack and preys evasion. It has been proposed as an improvement of particle swarm optimization (PSO) where additional particles are introduced to repel the other particles into the swarm. The introduced dynamic is intended to achieve better exploration of the search space. In the design, a representation scheme has been first defined. Each particle either a predator or a prey is represented as a curve (snake) defined by a set of control points. The idea is then to evolve a set of curves using the dynamic governed by PPO model equations. As a result, the curve that optimizes a defined energy function is identified as the contour of the target object.

Application of the proposed method to a variety of images using a multi agent platform has shown that good quality results have been obtained compared to a PSO‐based method.

Nature inspired computing is an emergent paradigm that witnesses a growing interest because it suggests a new philosophy to optimization. This work contributes in showing its suitability to solve problems even it is still at infancy. In another hand, despite the amount of work done in image processing, it is still required to define new methods for image segmentation. This work outlines a new way to deal with this problem through the use of PPO.