相关论文: Generating Functions and Stability Study of Multiv…

In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world…

Many complex systems exhibit extreme events far more often than expected for a normal distribution. This work examines how self-similar bursts of activity across several orders of magnitude can emerge from first principles in systems that…

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…

Sequences of events including infectious disease outbreaks, social network activities, and crimes are ubiquitous and the data on such events carry essential information about the underlying diffusion processes between communities (e.g.,…

This paper considers the robustness of event-triggered control of general linear systems against additive or multiplicative frequency-domain uncertainties. It is revealed that in static or dynamic event triggering mechanisms, the sampling…

We study bifurcations in networks of integrate-and-fire neurons with stochastic spike emission, focusing on the effects of the spatial and temporal structure of the synaptic interactions. Using a deterministic mean-field approximation of…

Aggressive behavior in autistic inpatient youth often arises in temporally clustered bursts complicating efforts to distinguish external triggers from internal escalation. The sample population branching factor-the expected number of new…

Voltage stability in modern power systems involves coupled dynamics across multiple time scales. Conventional methods based on time-scale separation or static stability margins may overlook instabilities caused by the coupling of slow and…

We study the relaxation response of a social system after endogenous and exogenous bursts of activity using the time-series of daily views for nearly 5 million videos on YouTube. We find that most activity can be described accurately as a…

This work introduces a self and mutually exciting point process that embeds flexible residuals and intensity with discretely Markovian dynamics. By allowing the integration of diverse residual distributions, this model serves as an…

Human behavior drives a range of complex social, urban, and economic systems, yet understanding its structure and dynamics at the individual level remains an open question. From credit card transactions to communications data, human…

We consider a network of event-based systems that use a shared wireless medium to communicate with their respective controllers. These systems use a contention resolution mechanism to arbitrate access to the shared network. We identify…

Locally stationary Hawkes processes have been introduced in order to generalise classical Hawkes processes away from stationarity by allowing for a time-varying second-order structure. This class of self-exciting point processes has…

We develop a generalized stability framework for stochastic discrete-time systems, where the generality pertains to the ways in which the distribution of the state energy can be characterized. We use tools from finance and operations…

Hawkes Processes are a type of point process for modeling self-excitation, i.e., when the occurrence of an event makes future events more likely to occur. The corresponding self-triggering function of this type of process may be inferred…

We performed an extensive numerical study of a two-dimensional reaction-diffusion system of the activator-inhibitor type in which domain patterns can form. We showed that both multidomain and labyrinthine patterns may form spontaneously as…

Traditionally, Hawkes processes are used to model time--continuous point processes with history dependence. Here we propose an extended model where the self--effects are of both excitatory and inhibitory type and follow a Gaussian Process.…

We consider a new class of non Markovian processes with a countable number of interacting components, both in discrete and continuous time. Each component is represented by a point process indicating if it has a spike or not at a given…

Modeling event patterns is a central task in a wide range of disciplines. In applications such as studying human activity patterns, events often arrive clustered with sporadic and long periods of inactivity. Such heterogeneity in event…

Complex systems with multiple processes evolving on different temporal scales are naturally described by multilayer networks, where each layer represents a different timescale. In this work, we show how the multilayer structure shapes the…