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Large Language Model agents demonstrate potential in solving real-world problems via tools, yet generalist intelligence is bottlenecked by scarce high-quality, long-horizon data. Existing methods collect privacy-constrained API logs or…
A class of parabolic-parabolic Keller-Segel systems with degenerate diffusion and volume filling is studied in a bounded domain subject to no-flux boundary conditions. The equations are derived from a multiphase fluid model. The interplay…
We study a general class of Principal-Agent problems in continuous time under hidden action. By formulating the model as a coupled stochastic optimal control problem we are able to find a set of necessary conditions characterizing optimal…
In this paper we deal with diffusive relaxation limits of nonlinear systems of Euler type modeling chemotactic movement of cells toward Keller--Segel type systems. The approximating systems are either hyperbolic--parabolic or…
Agent-based modeling (ABM) is a well-established paradigm for simulating complex systems via interactions between constituent entities. Machine learning (ML) refers to approaches whereby statistical algorithms 'learn' from data on their…
The paper that follows describes a numerical algorithm to solve the parabolic-parabolic Keller--Segel system characterized by singular sensitivity and signal absorption in such a manner that the numerical approximations converge towards a…
We introduce stochastic models of chemotaxis generalizing the deterministic Keller-Segel model. These models include fluctuations which are important in systems with small particle numbers or close to a critical point. Following Dean's…
We investigate the one-dimensional Keller-Segel model where the diffusion is replaced by a non-local operator, namely the fractional diffusion with exponent $0<\alpha\leq 2$. We prove some features related to the classical two-dimensional…
We review existing approaches to mathematical modeling and analysis of multi-agent systems in which complex collective behavior arises out of local interactions between many simple agents. Though the behavior of an individual agent can be…
In the event that a bacteriological or chemical toxin is intro- duced to a water distribution network, a large population of consumers may become exposed to the contaminant. A contamination event may be poorly predictable dynamic process…
Proving the existence of speculative financial bubbles even a posteriori has proven exceedingly difficult so anticipating a speculative bubble ex ante would at first seem an impossible task. Still as illustrated by the recent turmoil in…
In this work, we study a stochastic system of N particles associated with the parabolic-parabolic Keller-Segel system. This particle system is singular and non Markovian in that its drift term depends on the past of the particles. When the…
We study the existence of steady states to the Keller-Segel system with linear chemotactical sensitivity function on a smooth bounded domain in $\mathbb R^N,$ $N\ge3,$ having rotational symmetry. We find three different types of…
The chapter describes the modeling of a material handling system with the production of individual units in a scheduled order. The units represent the agents in the model and are transported in the system which is abstracted as a directed…
Agent-based simulators provide granular representations of complex intelligent systems by directly modelling the interactions of the system's constituent agents. Their high-fidelity nature enables hyper-local policy evaluation and testing…
This study offers a new paradigm of individual-level modeling to address the grand challenge of incorporating human behavior in epidemic models. Using generative artificial intelligence in an agent-based epidemic model, each agent is…
We study a system of diffusing point particles in which any triplet of particles reacts and is removed from the system when the relative proximity of the constituent particles satisfies a predefined condition. Proximity-based reaction…
The steady-state and nonequilibrium properties of the model of environmental-economic interactions are studied. The interacting heterogeneous agents are simulated on the platform of the emission dynamics of cellular automaton. The model…
We rigorously derive a two-dimensional Keller-Segel type system with signal-dependent sensitivity from a stochastic interacting particle model. By employing suitably defined stopping times, we prove that the convergence of the interacting…
An optimal control problem associated to the Keller-Segel with logistic reaction system will be studied in $2D$ domains. The control acts in a bilinear form only in the chemical equation. The existence of optimal control and a necessary…