相关论文: An Analytical Framework to Describe the Interactio…
We perform an analysis of a recent spatial version of the classical Lotka-Volterra model, where a finite scale controls individuals' interaction. We study the behavior of the predator-prey dynamics in physical spaces higher than one,…
This paper deals with the Cauchy Problem for a PDE-ODE model, where a system of two conservation laws, namely the Two-Phase macroscopic model, is coupled with an ordinary differential equation describing the trajectory of an autonomous…
This essay provides a critical overview of the mathematical kinetic theory of active particles, which is used to model and study collective systems consisting of interacting living entities, such as those involved in behavior and evolution.…
The necessity and utility of considering the interaction of a quantum system with its environment when describing its time evolution have been recognized in several branches of physics and of other sciences. The Kraus' representation is a…
In multiagent systems autonomous agents interact with each other to achieve individual and collective goals. Typical interactions concern negotiation and agreement on resource exchanges. Modeling and formalizing these agreements pose…
We develop an operator-theoretical method for the analysis on well posedness of partial differential equations that can be modeled in the form \begin{equation*} \left\{ \begin{array}{rll} \Delta^{\alpha} u(n) &= Au(n+2) + f(n,u(n)), \quad n…
The dynamics of a prey-predator system with foraging facilitation among predators are investigated. The analysis involves the computation of many semi-algebraic systems of large degrees. We apply the pseudo-division reduction, real-root…
How large ecosystems can create and maintain the remarkable biodiversity we see in nature is probably one of the biggest open questions in science, attracting attention from different fields, from Theoretical Ecology to Mathematics and…
This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…
If one isolated species is supposed to evolve following the logistic mapping, then we are tempted to think that the dynamics of two species can be expressed by a coupled system of two discrete logistic equations. As three basic…
This paper analyzes general spatially-coupled (SC) systems with multi-dimensional coupling. A continuum approximation is used to derive potential functions that characterize the performance of the SC systems. For any dimension of coupling,…
We introduce an extended mathematical programming framework for specifying equilibrium problems and their variational representations, such as generalized Nash equilibrium, multiple optimization problems with equilibrium constraints, and…
We propose a new variant of the strategic classification problem: a principal reveals a classifier, and $n$ agents report their (possibly manipulated) features to be classified. Motivated by real-world applications, our model crucially…
We use a combination of perturbation theory and numerical techniques to study the equilibration of two interacting fields which are initially at thermal equilibrium at different temperatures. Using standard rules of quantum field theory, we…
Intersectionality is a framework that analyzes how interlocking systems of power and oppression affect individuals along overlapping dimensions including race, gender, sexual orientation, class, and disability. Intersectionality theory…
In two papers we proposed a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities and discussed some of its properties. The model aims to be analogous to a discrete algorithm…
Recent work in the field of multi-agent systems has sought to use techniques and concepts from the field of formal methods to provide rigorous theoretical analysis and guarantees on complex systems where multiple agents strategically…
We create a framework to analyse the timing and frequency of instantaneous interactions between pairs of entities. This type of interaction data is especially common nowadays, and easily available. Examples of instantaneous interactions…
This paper proposes distributed omniscient observers for both heterogeneous and homogeneous linear multi-agent systems, such that each agent can correctly estimate the states of all agents. The observer design is based on local input-output…
Consider the coupling of $2$ evolution equations, each generating a global process. We prove that the resulting system generates a new global process. This statement can be applied to differential equations of various kinds. In particular,…