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Hybrid systems whose mode dynamics are governed by non-linear ordinary differential equations (ODEs) are often a natural model for biological processes. However such models are difficult to analyze. To address this, we develop a…
We study a matrix product state (MPS) algorithm to approximate excited states of translationally invariant quantum spin systems with periodic boundary conditions. By means of a momentum eigenstate ansatz generalizing the one of \"Ostlund…
We study complex networks of stochastic two-state units. Our aim is to model discrete stochastic excitable dynamics with a rest and an excited state. Both states are assumed to possess different waiting time distributions. The rest state is…
Many applications in medical statistics as well as in other fields can be described by transitions between multiple states (e.g. from health to disease) experienced by individuals over time. In this context, multi-state models are a popular…
Random graph mixture models are now very popular for modeling real data networks. In these setups, parameter estimation procedures usually rely on variational approximations, either combined with the expectation-maximisation (\textsc{em})…
We introduce a simple model of opinion dynamics in which binary-state agents evolve due to the influence of agents in a local neighborhood. In a single update step, a fixed-size group is defined and all agents in the group adopt the state…
We consider the task of filtering a dynamic parameter evolving as a diffusion process, given data collected at discrete times from a likelihood which is conjugate to the marginal law of the diffusion, when a generic dual process on a…
We study stochastic pairwise interaction network systems whereby a finite population of agents, identified with the nodes of a graph, update their states in response to both individual mutations and pairwise interactions with their…
We show that the dynamics of simple disordered models, like the directed Trap Model and the Random Energy Model, takes place at a coexistence point between active and inactive dynamical phases. We relate the presence of a dynamic phase…
In the standard $q$-voter model, a given agent can change its opinion only if there is a full consensus of the opposite opinion within a group of influence of size $q$. A more realistic extension is the threshold $q$-voter, where a minimal…
In the problem of asymptotic binary i.i.d. state discrimination, the optimal asymptotics of the type I and the type II error probabilities is in general an exponential decrease to zero as a function of the number of samples; the set of…
Background: A common modelling approach in public health and epidemiology divides the population under study into compartments containing persons that share the same status. Here we consider a three-state model with the compartments: A, B…
Analytical complexity of quantum wavefunction whose argument is extended into the complex plane provides an important information about the potentiality of manifesting complex quantum dynamics such as time-irreversibility, dissipation and…
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…
The precise characterization of dynamics in open quantum systems often presents significant challenges, leading to the introduction of various approximations to simplify a model. One commonly used strategy involves Markovian approximations,…
We propose and study a model for the interplay between two different dynamical processes --one for opinion formation and the other for decision making-- on two interconnected networks $A$ and $B$. The opinion dynamics on network $A$…
We develop two approximate theories to describe the miscible and immiscible droplets that can occur in a binary mixture of highly magnetic bosonic atoms. In addition to allowing simpler calculations, the approximate theories provide insight…
The $q$-neighbor Ising model for the opinion formation on multiplex networks with two layers in the form of random graphs (duplex networks), the partial overlap of nodes, and LOCAL\&AND spin update rule was investigated by means of the pair…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
Maximum entropy (maxEnt) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic dynamical systems, the effect of state space topology and path-dependent constraints on…