Related papers: Perfect simulation for interacting Hawkes processe…
In computer simulations of spiking neural networks, often it is assumed that every two neurons of the network are connected by a probability of 2\%, 20\% of neurons are inhibitory and 80\% are excitatory. These common values are based on…
Driven by the recent surge in neural-inspired modeling, point processes have gained significant traction in systems and control. While the Hawkes process is the standard model for characterizing random event sequences with memory,…
We propose an efficient strategy to suppress epidemic explosion in heterogeneous metapopulation networks, wherein each node represents a subpopulation with any number of individuals and is assigned a curing rate that is proportional to…
We prove a law of large numbers and a functional central limit theorem for multivariate Hawkes processes observed over a time interval $[0,T]$ in the limit $T \rightarrow \infty$. We further exhibit the asymptotic behaviour of the…
Hawkes point processes are first-order non-Markovian stochastic models of intermittent bursty dynamics with applications to physical, seismic, epidemic, biological, financial, and social systems. While accounting for positive feedback loops…
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…
Recently proposed encoder-decoder structures for modeling Hawkes processes use transformer-inspired architectures, which encode the history of events via embeddings and self-attention mechanisms. These models deliver better prediction and…
The research work outlined in the present note highlights the essential role played by the simulation procedures implemented by us on CINECA supercomputers to complement the mathematical investigations carried within our group over the past…
In this paper we prove scalar and sample path large deviation principles for a large class of Poisson cluster processes. As a consequence, we provide a large deviation principle for ergodic Hawkes point processes.
We present a neuronal network model inspired by the Ising model, where each neuron is a binary spin ($s_i = \pm1$) interacting with its neighbors on a 2D lattice. Updates are asynchronous and follow Metropolis dynamics, with a…
State-of-the-art simulations of detailed neural models follow the Bulk Synchronous Parallel execution model. Execution is divided in equidistant communication intervals, equivalent to the shortest synaptic delay in the network. Neurons…
We present a perfect simulation algorithm for stationary processes indexed by Z, with summable memory decay. Depending on the decay, we construct the process on finite or semi-infinite intervals, explicitly from an i.i.d. uniform sequence.…
In this paper, we design a nonparametric online algorithm for estimating the triggering functions of multivariate Hawkes processes. Unlike parametric estimation, where evolutionary dynamics can be exploited for fast computation of the…
Temporal networks are characterised by interdependent link events between nodes, forming ordered sequences of links that may represent specific information flows in the system. Nevertheless, representing temporal networks using discrete…
The order flow in high-frequency financial markets has been of particular research interest in recent years, as it provides insights into trading and order execution strategies and leads to better understanding of the supply-demand…
Many events occur in the world. Some event types are stochastically excited or inhibited---in the sense of having their probabilities elevated or decreased---by patterns in the sequence of previous events. Discovering such patterns can help…
We consider a fully-connected network of leaky integrate-and-fire neurons with spike-timing-dependent plasticity. The plasticity is controlled by a parameter representing the expected weight of a synapse between neurons that are firing…
Numerous studies grounded on Hawkes processes have been carried out in many fields including finance, biology and social network. Hawkes processes form a class of selfexciting simple point processes. In this article, we consider a general…
This paper addresses nonparametric estimation of nonlinear multivariate Hawkes processes, where the interaction functions are assumed to lie in a reproducing kernel Hilbert space (RKHS). Motivated by applications in neuroscience, the model…
We study a stochastic system of interacting neurons and its metastable properties. The system consists of $N$ neurons, each spiking randomly with rate depending on its membrane potential. At its spiking time, the neuron potential is reset…