Related papers: Perfect simulation for interacting Hawkes processe…

Over the past few decades, the Hawkes process has become a popular framework for modeling temporal events thanks to its flexibility to capture different dependency structures. The objective of this work is to model call sequences emitted by…

This article presents a biological neural network model driven by inhomogeneous Poisson processes accounting for the intrinsic randomness of synapses. The main novelty is the introduction of local interactions: each firing neuron triggers…

Winner-Take-All (WTA) refers to the neural operation that selects a (typically small) group of neurons from a large neuron pool. It is conjectured to underlie many of the brain's fundamental computational abilities. However, not much is…

We propose a new Kalikow decomposition for continuous time multivariate counting processes, on potentially infinite networks. We prove the existence of such a decomposition in various cases. This decomposition allows us to derive simulation…

Hyperdimensional computing (HDC) is an emerging computational framework that takes inspiration from attributes of neuronal circuits such as hyperdimensionality, fully distributed holographic representation, and (pseudo)randomness. When…

Most work on wireless network throughput ignores the temporal correlation inherent to wireless channels because it degrades tractability. To better model and quantify the temporal variations of wireless network throughput, this paper…

Hawkes process is a class of simple point processes with self-exciting and clustering properties. Hawkes process has been widely applied in finance, neuroscience, social networks, criminology, seismology, and many other fields. In this…

Human decisional processes result from the employment of selected quantities of relevant information, generally synthesized from environmental incoming data and stored memories. Their main goal is the production of an appropriate and…

An extension of the Hawkes model where the productivity is variable is considered. In particular, the case is considered where each point may have its own productivity and a simple analytic formula is derived for the maximum likelihood…

Is the brain really operating at a critical point? We study the non-equilibrium properties of a neural network which models the dynamics of the neocortex and argue for optimal quasi-critical dynamics on the Widom line where the correlation…

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…

Sample-efficient exploration is crucial not only for discovering rewarding experiences but also for adapting to environment changes in a task-agnostic fashion. A principled treatment of the problem of optimal input synthesis for system…

The Bayesian view of the brain hypothesizes that the brain constructs a generative model of the world, and uses it to make inferences via Bayes' rule. Although many types of approximate inference schemes have been proposed for hierarchical…

Neuromorphic devices represent an attempt to mimic aspects of the brain's architecture and dynamics with the aim of replicating its hallmark functional capabilities in terms of computational power, robust learning and energy efficiency. We…

The critical brain hypothesis states that there are information processing advantages for neuronal networks working close to the critical region of a phase transition. If this is true, we must ask how the networks achieve and maintain this…

Spiking neuronal networks are usually simulated with three main simulation schemes: the classical time-driven and event-driven schemes, and the more recent hybrid scheme. All three schemes evolve the state of a neuron through a series of…

Artificial neural networks built from two-state neurons are powerful computational substrates, whose computational ability is well understood by analogy with statistical mechanics. In this work, we introduce similar analogies in the context…

We prove limit theorems of an entirely new type for certain long memory regularly varying stationary infinitely divisible random processes. These theorems involve multiple phase transitions governed by how long the memory is. Apart from one…

We introduce and study an alternative form of the chaotic expansion for counting processes using the Poisson imbedding representation; we name this alternative form \textit{pseudo-chaotic expansion}. As an application, we prove that the…

The Hawkes process has garnered attention in recent years for its suitability to describe the behavior of online information cascades. Here, we present a fully tractable approach to analytically describe the distribution of the number of…