Related papers: Markovian Dynamics on Complex Reaction Networks

We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe networks of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is…

We present a simple Markov model of spiking neural dynamics that can be analytically solved to characterize the stochastic dynamics of a finite-size spiking neural network. We give closed-form estimates for the equilibrium distribution,…

We consider a broad class of stochastic imitation dynamics over networks, encompassing several well known learning models such as the replicator dynamics. In the considered models, players have no global information about the game…

We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each…

The last decade has witnessed a surge of theoretical and computational models to describe the dynamics of complex gene regulatory networks, and how these interactions can give rise to multistable and heterogeneous cell populations. As the…

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…

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…

Ideas, behaviors, and opinions spread through social networks. If the probability of spreading to a new individual is a non-linear function of the fraction of the individuals' affected neighbors, such a spreading process becomes a "complex…

Localized perturbations in a real-world network have the potential to trigger cascade failures at the whole system level, hindering its operations and functions. Standard approaches analytically tackling this problem are mostly based either…

In this paper, we model a decision-making process involving a set of interacting agents. We use Markovian opinion dynamics, where each agent switches between decisions according to a continuous time Markov chain. Existing opinion dynamics…

Multistate dynamical processes on networks, where nodes can occupy one of a multitude of discrete states, are gaining widespread use because of their ability to recreate realistic, complex behaviour that cannot be adequately captured by…

The investigation of community structure in networks is a task of great importance in many disciplines, namely physics, sociology, biology and computer science where systems are often represented as graphs. One of the challenges is to find…

Chemical reaction network theory provides powerful tools for rigorously understanding chemical reactions and the dynamical systems and differential equations that represent them. A frequent issue with mathematical analyses of these networks…

Robustness of biochemical systems has become one of the central questions in systems biology although it is notoriously difficult to formally capture its multifaceted nature. Maintenance of normal system function depends not only on the…

In communication networks structure and dynamics are tightly coupled. The structure controls the flow of information and is itself shaped by the dynamical process of information exchanged between nodes. In order to reconcile structure and…

Understanding how complex behaviors, opinions, and innovations spread in online social networks remains a central challenge in computational social science. Existing models of complex contagion typically rely on stylized threshold…

Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…

The main subject of the thesis is the study of stationary nonequilibrium states trough the use of microscopic stochastic models that encode the physical interaction in the rules of Markovian dynamics for particles configurations. These…

An emerging paradigm proposes that neural computations can be understood at the level of dynamical systems that govern low-dimensional trajectories of collective neural activity. How the connectivity structure of a network determines the…

Markov chains are a common framework for individual-based state and time discrete models in ecology and evolution. Their use, however, is largely limited to systems with a low number of states, since the transition matrices involved pose…