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It is often of interest to perform clustering on longitudinal data, yet it is difficult to formulate an intuitive model for which estimation is computationally feasible. We propose a model-based clustering method for clustering objects that…
While recent advances in next-generation neural mass models provide exact descriptions of densely coupled neural populations in the thermodynamic limit, populations in vivo remain strictly finite in size. Finite-size effects introduce…
This paper considers the problem of inference in cluster randomized experiments when cluster sizes are non-ignorable. Here, by a cluster randomized experiment, we mean one in which treatment is assigned at the cluster level. By…
The goal of this paper is to propose and analyze a differentially private randomized mechanism for the $K$-means query. The goal is to ensure that the information received about the cluster-centroids is differentially private. The method…
We discuss the development of cluster algorithms from the viewpoint of probability theory and not from the usual viewpoint of a particular model. By using the perspective of probability theory, we detail the nature of a cluster algorithm,…
The failure of the Euclidean norm to reliably distinguish between nearby and distant points in high dimensional space is well-known. This phenomenon of distance concentration manifests in a variety of data distributions, with iid or…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…
Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…
We present a fluid-mechanical model of the coalescence of a number of elastic objects due to surface tension. We consider an array of spring-block elements separated by thin liquid films, whose dynamics are modelled using lubrication…
10,000 simulations of 1000-particle realisations of the same cluster are computed by direct force summation. Over three crossing times the original Poisson noise is amplified more than tenfold by self-gravity. The cluster's fundamental…
Properties of arrival times are studied for a Cox process with independent (and stationary) increments. Under a reasonable setting the directing random measure is shown to take over independent (and stationary) increments of the process,…
A new approach to describe comminution processes in general ball mills as a macroscopic canonical ensemble is proposed. Using hamiltonian method, the model is able to take simultaneously into account the internal dynamics from mechanical…
There are multiple cluster randomised trial designs that vary in when the clusters cross between control and intervention states, when observations are made within clusters, and how many observations are made at that time point. Identifying…
Dirichlet process mixtures are flexible non-parametric models, particularly suited to density estimation and probabilistic clustering. In this work we study the posterior distribution induced by Dirichlet process mixtures as the sample size…
Recently, the so-called next-generation neural mass models have received a lot of attention of the researchers in the field of mathematical neuroscience. The ability of these models to account for the degree of synchrony in neural…
In this paper we presented a stochastic version mean-shift clustering algorithm. In the stochastic version the data points "climb" to the modes of the distribution collectively, while in the deterministic mean-shift, each datum "climbs"…
The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point patterns. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the…
Cluster analysis has become one of the most exercised research areas over the past few decades in computer science. As a consequence, numerous clustering algorithms have already been developed to find appropriate partitions of a set of…
The noise of signals or currents consisting from a sequence of pulses, elementary events or moving discrete objects (particles) is analyzed. A simple analytically solvable model is investigated in detail both analytically and numerically.…
The classical $k$-means algorithm for partitioning $n$ points in $\mathbb{R}^d$ into $k$ clusters is one of the most popular and widely spread clustering methods. The need to respect prescribed lower bounds on the cluster sizes has been…