arXiv subjects

Juan G. Diaz Ochoa

Publications and source records attributed to Juan G. Diaz Ochoa.

7 recordsLinked to original sources

arXiv2026

The point is a trap: Mathematics of Elastic States in Complex Multiscale Systems

Observables in complex biological systems are often reduced in their inherent complexity, resulting in abstract, a priori mathematical representations based on simple concepts such as points in spaces or interconnected nodes in lattices or networks. This reduction is relevant not only for the formulation of multiscale mathematical models and field theories but also for experimental planning and data collection to gain systematic evidence for the nature of such systems, thus extracting robust causal relationships that would lead to better control of the system. However, mathematical abstraction remains challenging and problematic, especially given the tightly intertwined elements between objects and their environment, the system's affordance, and the fact that all these aspects limit fundamental mathematical concepts such as set theory, thus hindering the definition of phase spaces in extreme cases. In this work, I introduce a potential axiomatic representing a nonreducible representation of high order structures representing entanglement between observables in complex systems and their environment, considering not only their coupling but also their affordance in relation to the overall system and context, and thus intend to formalize concepts already used in complex systems such as Kantian wholes. In light of this axiomatic, I identify states that are rather less elastic with respect to their environment, discuss how low elasticity enables the application of set theory, while high elasticity limits the mathematical representation of complex systems, and present an exemplary Ising model with a network of elastic states with respect to different contexts as a limiting case for mathematical modelling in this context.

physics.bio-ph↗

arXiv2008

Diversity under variability and extreme variability of environments

We conducted an investigation of the effect that extreme variability of the individual's environment has in the individual's adaptability and, in general, in the co-evolution of a population. First we assume that the individuals are a kind of perceptrons with a given memory size that adapt to their environment; second we consider co-evolution not only of the individual actions but also of the memory size, depending on the individual's fitness; and third we assume strong variability of the environment. We show that changes in the intensity of the environmental fluctuations introduce a phase transition in the frequency of cooperators and the diversity of the population. We also find out that extreme variability of the environment induces changes in the critical exponents and that this variability can promote more diversity in the population.

physics.bio-ph↗

arXiv2007

Evolutionary dynamics and diversity in populations

The dynamics of populations is rich, taking into account that both, the individual's actions and the population's fitness are coupled. The way in which an individual chooses a strategy depends off course on the interaction with other individuals and the relation between selection and mutation within the population. The present model considers individuals with {\it memory}. This memory is represented by a device where information of past actions is stored as bits in a 1D Ising chain. The selection of a new individual action depends on the individual's memory. If the selection of a strategy does not improve the individual's fitness, a new individual with different memory size replaces it. Both, actions and memory are observables that characterize the population. They can change in time, and both depend on the fitness of the population. This model allows the implementation of {\it learning} parameters as well as an {\it external information source}, acting as an {\it external field} which drives individuals to select one preferred action. In particular we show that the {\it diversity} of the population, measured as a {\it Shannon's diversity index} (equivalent to a neg-entropy), is not only related to the {\it energy consumption and size} of the system, but is also related to the way in which the individuals are influenced by the {\it external field}.

physics.bio-ph↗

arXiv2007

General multistate models for agents with internal bias

We present a model of interpersonal comparisons appearing as a generalization of a multi-state model for elements with internal bias. Within this model agents suffering under dissatisfaction compare them with their neighbors. The internal bias are the pre-formed preferences, and the states are represented by the visual contacts that an agent makes to the baskets of her/his neighbors. The topology of the comparisons is a random network. We compare the behavior between altruistic and non-altruistic agents and we find out that altruistic behavior alters the robustness of the network.

physics.soc-ph↗

arXiv2007

Memory distribution in complex fitness landscapes

In a co-evolutionary context, the survive probability of individual elements of a system depends on their relation with their neighbors. The natural selection process depends on the whole population, which is determined by local events between individuals. Particular characteristics assigned to each individual, as larger memory, usually improve the individual fitness, but an agent possess also endogenous characteristics that induce to re-evaluate her fitness landscape and choose the best-suited kind of interaction, inducing a non absolute value of the outcomes of the interaction. In this work, a novel model with agents combining memory and rational choice is introduced, where individual choices in a complex fitness landscape induce changes in the distribution of the number of agents as a function of the time. In particular, the tail of this distribution is fat compared with distributions for agents interacting only with memory.

physics.bio-ph↗

arXiv2006

Fairness State with Plastic Preferences

The definition of preferences assigned to individuals is a concept that concerns many disciplines, from economics, with the search of an acceptable outcome for an ensemble of individuals, to decision making an analysis of vote systems. We are concerned in the phenomena of good selection and economic fairness. In Arrow's theorem this situation is expressed as the impossibility of aggregate preferences among individuals falling down into some unfairness state. This situation was also analyzed in a previous model in a network of individuals with a random allocation. Both analysis are based on static preferences. In a real society the individuals are confronted to information exchange which can modify the way that they think. Also, the preference formation of each individual is influenced by this exchange. This consideration reveals why the actual theory is not able to make an accurate analysis of the influence of the individual, or cluster of individuals, in the fairness state. The aim of this investigation is to consider the coupling of two systems, one for the formation of preferences and a second where an allocation of goods is done in an evolutionary environment.

physics.soc-ph↗

arXiv2006

General Relativity at an interface

In this work a simple toy model for a free interface between bulk phases in space and time is presented, derived from the balance equations for extensive thermodynamic variables of Meinhold-Heerlein. In this case the free interface represents geodesics in the space-time, allowing the derivation of the Einstein's equations for gravitational fields. The effect of the balance equation is examined and a simple expression for cold dark matter is derived. The thermodynamically meaning of this model is also discussed.

gr-qc↗