Related papers: Model Checking Markov Population Models by Stochas…
We discuss the feasibility of predicting, managing and subsequently manipulating, the future evolution of a Complex Adaptive System. Our archetypal system mimics a population of adaptive, interacting objects, such as those arising in the…
We present a scalable methodology to verify stochastic hybrid systems. Using the Mori-Zwanzig reduction method, we construct a finite state Markov chain reduction of a given stochastic hybrid system and prove that this reduced Markov chain…
Agent-based models capture heterogeneity among individuals in a population and are widely used in studies of multi-cellular systems, disease, epidemics and demography to name a few. However, existing frameworks consider discrete time-step…
We propose a Markov jump process with the three-state herding interaction. We see our approach as an agent-based model for the financial markets. Under certain assumptions this agent-based model can be related to the stochastic description…
A continuous-time Markov process is proposed to analyze how a group of humans solves a complex task, consisting in the search of the optimal set of decisions on a fitness landscape. Individuals change their opinions driven by two different…
Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its…
Recent advances in large language models (LLMs) have spurred growing interest in using LLM-integrated agents for social simulation, often under the implicit assumption that realistic population dynamics will emerge once role-specified…
Population protocols are a class of algorithms for modeling distributed computation in networks of finite-state agents communicating through pairwise interactions. Their suitability for analyzing numerous chemical processes has motivated…
Single species population models and discrete stochastic gene frequency models are two standards of mathematical biology important for the evolution of populations. An agent based model is presented which reproduces these models and then…
We present a stochastic model of population dynamics exploiting cross-sectional data in trend analysis and forecasts for groups and cohorts of a population. While sharing the convenient features of classic Markov models, it alleviates the…
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,…
We present a new method for statistical verification of quantitative properties over a partially unknown system with actions, utilising a parameterised model (in this work, a parametric Markov decision process) and data collected from…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g. LSTMs) proved extremely successful in modeling complex time series…
Model predictive control strategies require to solve in an sequential manner, many, possibly non-convex, optimization problems. In this work, we propose an interacting stochastic agent system to solve those problems. The agents evolve in…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
Many analyses of resource-allocation problems employ simplistic models of the population. Using the example of a resource-allocation problem of Marecek et al. [arXiv:1406.7639], we introduce rather a general behavioural model, where the…
Applications of stochastic models often involve the evaluation of steady-state performance, which requires solving a set of balance equations. In most cases of interest, the number of equations is infinite or even uncountable. As a result,…
Given its ability to analyse stochastic models ranging from discrete and continuous-time Markov chains to Markov decision processes and stochastic games, probabilistic model checking (PMC) is widely used to verify system dependability and…
System modeling is a classical approach to ensure their reliability since it is suitable both for a formal verification and for software testing techniques. In the context of model-based testing an approach combining random testing and…