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Rhythmic activities that alternate between coherent and incoherent phases are ubiquitous in chemical, ecological, climate, or neural systems. Despite their importance, general mechanisms for their emergence are little understood. In order…

Theoretical developments in sequential Bayesian analysis of multivariate dynamic models underlie new methodology for causal prediction. This extends the utility of existing models with computationally efficient methodology, enabling routine…

We propose a branching process based on a dynamical scaling hypothesis relating time and mass. In the context of earthquake occurrence, we show that experimental power laws in size and time distribution naturally originate solely from this…

Stochastic spreading models defined on complex network topologies are used to mimic the diffusion of diseases, information, and opinions in real-world systems. Existing theoretical approaches to the characterization of the models in terms…

We demonstrate the effectiveness of the categorical distribution as a neural network output for next event prediction. This is done for both discrete-time and continuous-time event sequences. To model continuous-time processes, the…

Many-variable differential equations with random coefficients provide powerful models for the dynamics of many interacting species in ecology. These models are known to exhibit a dynamical phase transition from a phase where population…

Evolutionary game theory has been successfully used to investigate the dynamics of systems, in which many entities have competitive interactions. From a physics point of view, it is interesting to study conditions under which a coordination…

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…

This work interprets and generalizes consensus-type algorithms as switching dynamics leading to symmetrization of some vector variables with respect to the actions of a finite group. We show how the symmetrization framework we develop…

We extend the synthetic theories of discrete and Gaussian categorical probability by introducing a diagrammatic calculus for reasoning about hybrid probabilistic models in which continuous random variables, conditioned on discrete ones,…

While "complexity science" has achieved significant successes in several interdisciplinary fields such as economics and biology, it is only a very recent observation that legal systems -- from the way legal texts are drafted and connected…

In this paper we review some general properties of probability distributions which exibit a singular behavior. After introducing the matter with several examples based on various models of statistical mechanics, we discuss, with the help of…

We introduce a class of continuous-time bivariate phase-type distributions for modeling dependencies from common shocks. The construction uses continuous-time Markov processes that evolve identically until an internal common-shock event,…

This paper suggests that business cycles may be a manifestation of coupled real economy and stock market dynamics and describes a mechanism that can generate economic fluctuations consistent with observed business cycles. To this end, we…

These lecture notes cover basic automata-theoretic concepts and logical formalisms for the modeling and verification of concurrent and distributed systems. Many of these concepts naturally extend the classical automata and logics over…

In this paper continuous time random walk models approximating fractional space-time diffusion processes are studied. Stochastic processes associated with the considered equations represent time-changed processes, where the time-change…

In the present paper we introduce positive flows and processes, which generalize the ordinary dynamical systems and stochastic processes. We develop a branch of theory of positive operators based on the concepts of phase and positive…

The process of fluctuations of trajectory observables of stochastic systems is related to processes with independent increments from the risk theory. The first-passage times of variables of the thermodynamics of trajectories, in particular,…

We solve a simple model that supports a dynamic phase transition and show conditions for the existence of the transition. Using methods of large deviation theory we analytically compute the probability distribution for activity and entropy…

In the past few decades considerable effort has been expended in characterizing and modeling financial time series. A number of stylized facts have been identified, and volatility clustering or the tendency toward persistence has emerged as…