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We show how one can trace in a systematic way the coarse-grained solutions of individual-based stochastic epidemic models evolving on heterogeneous complex networks with respect to their topological characteristics. In particular, we have…

Many epidemic processes in networks spread by stochastic contacts among their connected vertices. There are two limiting cases widely analyzed in the physics literature, the so-called contact process (CP) where the contagion is expanded at…

Sequential processes in real-world often carry a combination of simple subsystems that interact with each other in certain forms. Learning such a modular structure can often improve the robustness against environmental changes. In this…

In many applications, linear models fit the data poorly. This article studies an appealing alternative, the generalized regression model. This model only assumes that there exists an unknown monotonically increasing link function connecting…

Transitivity is a central, generative principle in social and other complex networks, capturing the tendency for two nodes with a common neighbor to form a direct connection. We propose a new model for highly dense, complex networks based…

In this paper, we prove functional central limit theorems (FCLTs) for a stochastic epidemic model with varying infectivity and general infectious periods recently introduced in Forien, Pang and Pardoux (2020).The infectivity process (total…

Because of its mathematical tractability, the Gaussian mixture model holds a special place in the literature for clustering and classification. For all its benefits, however, the Gaussian mixture model poses problems when the data is skewed…

This work is motivated by an original dataset of reported mumps cases across nine regions of England, and focuses on the modeling of temporal dynamics and time-varying dependency patterns between the observed time series. The goal is to…

In statistics, generalized linear models (GLMs) are widely used for modeling data and can expressively capture potential nonlinear dependence of the model's outcomes on its covariates. Within the broad family of GLMs, those with binary…

Recent research on social contagion processes has revealed the limitations of traditional networks, which capture only pairwise relationships, to characterize complex multiparty relationships and group influences properly. Social contagion…

Dose-finding studies in oncology often include an up-and-down dose transition rule that assigns a dose to each cohort of patients based on accumulating data on dose-limiting toxicity (DLT) events. In making a dose transition decision, a key…

We consider stochastic approximations of sampling algorithms, such as Stochastic Gradient Langevin Dynamics (SGLD) and the Random Batch Method (RBM) for Interacting Particle Dynamcs (IPD). We observe that the noise introduced by the…

One of the most defining features of the global financial network is its inherent complex and intertwined structure. From the perspective of systemic risk it is important to understand the influence of this network structure on default…

Diffusion of information in networks is at the core of many problems in AI. Common examples include the spread of ideas and rumors as well as marketing campaigns. Typically, information diffuses at a non-linear rate, for example, if markets…

Fitting generative models to sequential data typically involves two recursive computations through time, one forward and one backward. The latter could be a computation of the loss gradient (as in backpropagation through time), or an…

We propose an asymptotic theory for distribution forecasting from the log normal chain-ladder model. The theory overcomes the difficulty of convoluting log normal variables and takes estimation error into account. The results differ from…

I present three models of plant--pathogen interactions. The models are stochastic and spatially explicit at the scale of individual plants. For each model, I use a version of pair approximation or moment closure along with a separation of…

We show that the recently introduced logarithmic metrics used to predict disease arrival times on complex networks are approximations of more general network-based measures derived from random walks theory. Using the daily air-traffic…

We study two simple mathematical models of the epidemic. At first, we study the repetitive infection spreading in a simplified SIRS model including the effect of the decay of the acquired immune. The model is an intermediate model of the…

In order to simulate the spread of infectious diseases, many epidemiological models use systems of ordinary differential equations (ODEs) to describe the underlying dynamics. These models incorporate the implicit assumption, that the stay…