Related papers: A Mixed Self-Exciting Process to Model Epileptic S…
Fueled in part by recent applications in neuroscience, the multivariate Hawkes process has become a popular tool for modeling the network of interactions among high-dimensional point process data. While evaluating the uncertainty of the…
Objective: Epilepsy, a prevalent neurological disease, demands careful diagnosis and continuous care. Seizure detection remains challenging, as current clinical practice relies on expert analysis of electroencephalography, which is a…
An extension of the Hawkes process, the Marked Hawkes process distinguishes itself by featuring variable jump size across each event, in contrast to the constant jump size observed in a Hawkes process without marks. While extensive…
The neural Hawkes process (Mei & Eisner, 2017) is a generative model of irregularly spaced sequences of discrete events. To handle complex domains with many event types, Mei et al. (2020a) further consider a setting in which each event in…
The degree of synchronization and the amount of dynamical cluster formation in electroencephalographic (EEG) signals are characterized by employing two order parameters introduced in the context of coupled chaotic systems subject to…
Hawkes process models are used in settings where past events increase the likelihood of future events occurring. Many applications record events as counts on a regular grid, yet discrete-time Hawkes models remain comparatively underused and…
Epilepsy is a neurological disorder identified by sudden and recurrent seizures, which are believed to be accompanied by distinct changes in brain dynamics. Exploring the dynamic changes of brain network states during seizures can pave the…
We present the first exact analysis of some of the temporal properties of multivariate self-excited Hawkes conditional Poisson processes, which constitute powerful representations of a large variety of systems with bursty events, for which…
Excessively high, neural synchronisation has been associated with epileptic seizures, one of the most common brain diseases worldwide. A better understanding of neural synchronisation mechanisms can thus help control or even treat epilepsy.…
To predict an epileptic event means the ability to determine in advance the time of the seizure with the highest possible accuracy. A correct prediction benchmark for epilepsy events in clinical applications is a typical problem in…
Accurate classification of seizure types plays a crucial role in the treatment and disease management of epileptic patients. Epileptic seizure types not only impact the choice of drugs but also the range of activities a patient can safely…
Epilepsy represents the most prevalent neurological disease in the world. One-third of people suffering from mesial temporal lobe epilepsy (MTLE) exhibit drug resistance, urging the need to develop new treatments. A key part in anti-seizure…
In the present work, we introduce a general class of mean-field interacting nonlinear Hawkes processes modelling the reciprocal interactions between two neuronal populations, one excitatory and one inhibitory. The model incorporates two…
Due to its clustering and self-exciting properties, the Hawkes process has been used extensively in numerous fields ranging from sismology to finance. Since data is often aquired on regular time intervals, we propose a piece-wise constant…
Epilepsy is a brain disorder due to abnormalactivity of neurons and recording of seizures is of primary interest in the evaluation of epileptic patients. A seizureis the phenomenon of rhythmicity discharge from either a local area or the…
Modern health care systems are conducting continuous, automated surveillance of the electronic medical record (EMR) to identify adverse events with increasing frequency; however, many events such as sepsis do not have elucidated prodromes…
The human brain is a directional network system of brain regions involving directional connectivity. Seizures are a directional network phenomenon as abnormal neuronal activities start from a seizure onset zone (SOZ) and propagate to…
Earthquakes in seismological catalogs and acoustic emission events in lab experiments can be statistically described as a linear Hawkes point process, where the spatio-temporal rate of events is a linear superposition of background…
Epileptic seizure detection and classification in clinical electroencephalogram data still is a challenge, and only low sensitivity with a high rate of false positives has been achieved with commercially available seizure detection tools,…
We introduce the Hyperedge-triggered Hawkes (HTH) process for inferring higher-order interaction structure in multi-cellular systems from asynchronous event-time data. Beyond standard pairwise excitation, the HTH intensity includes a term…