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Motivated by the growing interest in today's massive parallel computing capabilities we analyze a queueing network with many servers in parallel to which jobs arrive a according to a Poisson process. Each job, upon arrival, is split into…
We consider a family of distributions on spatial random partitions that provide a coupling between different models of interest: the ideal Bose gas; the zero-range process; particle clustering; and spatial permutations. These distributions…
Let $\{X_{1},\ldots,X_{N_1}\}$ and $\{Y_{1},\ldots,Y_{N_2}\}$ be two sequences of interdependent heterogeneous samples, where for $i=1,\ldots,N_{1},$ $X_{i}\sim \text{Kw-G}(x, \alpha_{i}, \gamma_{i};G)$ and for $i=1,\ldots,N_{2},$…
A probabilistic approach of computing geometric rate of convergence of stochastic processes is introduced in this paper. The goal is to quantitatively compute both upper and lower bounds of the exponential rate of convergence to the…
We study the probability distribution of the ratio of consecutive level spacings for embedded one plus two-body random matrix ensembles with and without spin degree of freedom and for both fermion and boson systems. The agreement between…
In any Markov chain Monte Carlo analysis, rapid convergence of the chain to its target probability distribution is of practical and theoretical importance. A chain that converges at a geometric rate is geometrically ergodic. In this paper,…
The fractional order system, which is described by the fractional order derivative and integral, has been studied in many engineering areas. Recently, the concept of fractional order has been generalized to the distributed order concept,…
The paper presents a systematic theory for asymptotic inference of autocovariances of stationary processes. We consider nonparametric tests for serial correlations based on the maximum (or ${\cal L}^\infty$) and the quadratic (or ${\cal…
We formulate and analyze a graphical model selection method for inferring the conditional independence graph of a high-dimensional nonstationary Gaussian random process (time series) from a finite-length observation. The observed process…
Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Under sufficient permanent random covalent bonding, a fluid of atoms or small molecules is transformed into an amorphous solid network. Being amorphous, local structural properties in such networks vary across the sample. A natural order…
Heterogeneity of many building materials complicates numerical modelling of structural behaviour. The material randomicity can be manifested by different values of material parameters of each material specimen. To capture inherent…
Suppose X is a frequency vector that follows a central multiple hyper-geometric distribution, such as arises in random sampling of an m-category attribute from a finite population without replacement. We show that the probability that X…
We discuss the possibility of simultaneous and sequential synchronisation in vertical and horizontal arrays of unidirectionally coupled discrete systems. This is realized for the specific case of two dimensional Gumowski-Mira maps. The…
Data-driven control strategies for dynamical systems with unknown parameters are popular in theory and applications. An essential problem is to prevent stochastic linear systems becoming destabilized, due to the uncertainty of the…
Sensor-based sorting systems enable the physical separation of a material stream into two fractions. The sorting decision is based on the image data evaluation of the sensors used and is carried out using actuators. Various process…
This paper generalizes stochastic collocation methods to handle correlated non-Gaussian random parameters. The key challenge is to perform a multivariate numerical integration in a correlated parameter space when computing the coefficient…
The likelihood for the parameters of a generalized linear mixed model involves an integral which may be of very high dimension. Because of this intractability, many approximations to the likelihood have been proposed, but all can fail when…