Related papers: Generating Functions and Stability Study of Multiv…

Learning the influence structure of multiple time series data is of great interest to many disciplines. This paper studies the problem of recovering the causal structure in network of multivariate linear Hawkes processes. In such processes,…

Well characterized sequences of dynamical states play an important role for motor control and associative neural computation in the brain. Autonomous dynamics involving sequences of transiently stable states have been termed associative…

Solar flares, email exchanges, and many natural or social systems exhibit bursty dynamics, with periods of intense activity separated by long inactivity. These patterns often follow power- law distributions in inter-event intervals or event…

Given a collection of entities (or nodes) in a network and our intermittent observations of activities from each entity, an important problem is to learn the hidden edges depicting directional relationships among these entities. Here, we…

The paper discusses multivariate self- and cross-exciting processes. We define a class of multivariate point processes via their corresponding stochastic intensity processes that are driven by stochastic jumps. Essentially, there is a jump…

We introduce a framework to intertwine dynamical processes of different nature, each with its own distinct network topology, using a multilayer network approach. As an example of collective phenomena emerging from the interactions of…

The Hawkes process and its extensions effectively model self-excitatory phenomena including earthquakes, viral pandemics, financial transactions, neural spike trains and the spread of memes through social networks. The usefulness of these…

Hawkes process is one of the most commonly used models for investigating the self-exciting nature of earthquake occurrences. However, seismicity patterns have complicated characteristics due to heterogeneous geology and stresses, for which…

Pattern formation from homogeneity is well-studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is nontrivial to separate observed spatial patterning due to inherent spatial heterogeneity from…

In this work, we propose to catch the complexity of the membrane potential's dynamic of a motoneuron between its spikes, taking into account the spikes from other neurons around. Our approach relies on two types of data: extracellular…

In the last decade, Hawkes processes have received a lot of attention as good models for functional connectivity in neural spiking networks. In this paper we consider a variant of this process, the Age Dependent Hawkes process, which…

We characterize a comprehensive family of $d$-variate exogenous shock models. Analytically, we consider a family of multivariate distribution functions that arises from ordering, idiosyncratically distorting, and finally multiplying the…

This paper considers population processes in which general, not necessarily Markovian, multivariate Hawkes processes dictate the stochastic arrivals. We establish results to determine the corresponding time-dependent joint probability…

We propose a novel class of network models for temporal dyadic interaction data. Our goal is to capture a number of important features often observed in social interactions: sparsity, degree heterogeneity, community structure and…

We investigate numerically the collective dynamical behavior of pulse-coupled non-leaky integrate-and-fire-neurons that are arranged on a two-dimensional small-world network. To ensure ongoing activity, we impose a probability for…

It is often assumed that events cannot occur simultaneously when modelling data with point processes. This raises a problem as real-world data often contains synchronous observations due to aggregation or rounding, resulting from…

In this work, several convergence results are established for nearly critical self-excited systems in which event arrivals are described by multivariate marked Hawkes point processes. Under some mild high-frequency assumptions, the rescaled…

Epilepsy is a neurological disorder characterized by recurrent seizures affecting more than 70 million people worldwide. Often, an individual with epilepsy is more likely to experience subsequent seizures following an initial seizure, a…

Hawkes processes are a class of point processes that have the ability to model the self- and mutual-exciting phenomena. Although the classic Hawkes processes cover a wide range of applications, their expressive ability is limited due to…

Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…