Related papers: Numerical approximation of a coagulation-Fragmenta…
We translate a coagulation-framentation model, describing the dynamics of animal group size distributions, into a model for the population distribution and associate the \blue{nonlinear} evolution equation with a Markov jump process of a…
We study coagulation-fragmentation equations inspired by a simple model proposed in fisheries science to explain data for the size distribution of schools of pelagic fish. Although the equations lack detailed balance and admit no…
The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov chain. The simulations of this stochastic process and its invariant measure are…
In this paper we study the discrete coagulation--fragmentation models with growth, decay and sedimentation. We demonstrate the existence and uniqueness of classical global solutions provided the linear processes are sufficiently strong.…
This paper studies a distributed algorithm for constrained consensus optimization that is obtained by fusing the Arrow-Hurwicz-Uzawa primal-dual gradient method for centralized constrained optimization and the Wang-Elia method for…
Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the…
A central task of artificial intelligence is the design of artificial agents that act towards specified goals in partially observed environments. Since such environments frequently include interaction over time with other agents with their…
This paper proposes a thorough theoretical analysis of Stochastic Gradient Descent (SGD) with non-increasing step sizes. First, we show that the recursion defining SGD can be provably approximated by solutions of a time inhomogeneous…
We study the coupled dynamics of two populations of random replicators by means of statistical mechanics methods, and focus on the effects of relative population size, strategy correlations and heterogeneities in the respective co-operation…
A hierarchical system of equations is introduced to describe dynamics of `sizes' of infinite clusters which coagulate and fragmentate with homogeneous rates of certain form. We prove that this system of equations is solved weakly by…
In this article, we are concerned with the analysis on the numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation. This ill-posed problem is solved through a stabilized nonlinear…
In this paper we consider first order differential models of collective behaviors of groups of agents based on the mass conservation equation. Models are formulated taking the spatial distribution of the agents as the main unknown,…
In 1986, Dixon and McKee developed a discrete fractional Gr\"{o}nwall inequality [Z. Angew. Math. Mech., 66 (1986), pp. 535--544], which can be seen as a generalization of the classical discrete Gr\"{o}nwall inequality. However, this…
We establish sufficient conditions for the quick relaxation to kinetic equilibrium in the classic Vicsek-Cucker-Smale model of bird flocking. The convergence time is polynomial in the number of birds as long as the number of flocks remains…
Under the condition of detailed balance and some additional restrictions on the size of the coefficients, we identify the equilibrium distribution to which solutions of the discrete coagulation-fragmentation system of equations converge for…
We derive a new method to infer from data the out-of-equilibrium alignment dynamics of collectively moving animal groups, by considering the maximum entropy distribution consistent with temporal and spatial correlations of flight direction.…
We propose and analyse numerical schemes for a system of quasilinear, degenerate evolution equations modelling biofilm growth as well as other processes such as flow through porous media and the spreading of wildfires. The first equation in…
The Collective Graphical Model (CGM) models a population of independent and identically distributed individuals when only collective statistics (i.e., counts of individuals) are observed. Exact inference in CGMs is intractable, and previous…
Systems of reaction-diffusion equations are commonly used in biological models of food chains. The populations and their complicated interactions present numerous challenges in theory and in numerical approximation. In particular,…
We present a generalization of the dynamical model of information transmission and herd behavior proposed by Eguiluz and Zimmermann. A characteristic size of group of agents $s_{0}$ is introduced. The fragmentation and coagulation rates of…