Related papers: A crossinggram for random fields on lattices
The uncertainties in material and other properties of structures are usually spatially correlated. We introduce an efficient technique for representing and processing spatially correlated random fields in robust topology optimisation of…
An important source of high clustering coefficient in real-world networks is transitivity. However, existing approaches for modeling transitivity suffer from at least one of the following problems: i) they produce graphs from a specific…
Random intersection graphs containing an underlying community structure are a popular choice for modelling real-world networks. Given the group memberships, the classical random intersection graph is obtained by connecting individuals when…
We propose a novel framework for learning time-varying graphs from spatiotemporal measurements. Given an appropriate prior on the temporal behavior of signals, our proposed method can estimate time-varying graphs from a small number of…
We study the geometry of stable maximal hypersurfaces in a variety of spacetimes satisfying various physically relevant curvature assumptions, for instance the Timelike Convergence Condition (TCC). We characterize stability when the target…
In this note we introduce a hierarchy of phase spaces for static friction, which give a graphical way to systematically quantify the directional dependence in static friction via subregions of the phase spaces. We experimentally plot these…
We consider branching random walks on the Euclidean lattice in dimensions five and higher. In this non-Markovian setting, we first obtain a relationship between the equilibrium measure and Green's function, in the form of an approximate…
Mean-field approximation is often used to explore the qualitative behaviour of phase transitions in classical spin models before employing computationally costly methods such as the Monte-Carlo techniques. We implement a 'lattice…
In the paper we present simple examples of linear random fields defined on $\ZZ^2$ and $\ZZ^3$ which exhibit the scaling transition phenomenon. These examples lead to more general definition of the scaling transition and allow to understand…
Ridge regression with random coefficients provides an important alternative to fixed coefficients regression in high dimensional setting when the effects are expected to be small but not zeros. This paper considers estimation and prediction…
We establish scaling limits for the random walk whose state space is the range of a simple random walk on the four-dimensional integer lattice. These concern the asymptotic behaviour of the graph distance from the origin and the spatial…
In this paper, we consider the direct and inverse problems of the description of lattice positive random fields by various systems of finite-dimensional (as well as one-point) probability distributions parameterized by boundary conditions.…
Consider a sequence of i.i.d. random variables $X_n$ where each random variable is refreshed independently according to a Poisson clock. At any fixed time $t$ the law of the sequence is the same as for the sequence at time 0 but at random…
We propose a new approach to represent nonparametrically the linear dependence structure of a spatio-temporal process in terms of latent common factors. Though it is formally similar to the existing reduced rank approximation methods…
Random fields in nature often have, to a good approximation, Gaussian characteristics. We present the mathematical framework for a new and simple method for investigating the non-Gaussian contributions, based on counting the maxima and…
An intrinsic branching structure within the transient random walk on a strip in a random environment is revealed. As applications, which enables us to express the hitting time explicitly, and specifies the density of the absolutely…
We consider continuous time random interlacements on $\mathbb{Z}^d$, $d \ge 3$, and characterize the distribution of the corresponding stationary random field of occupation times. When d = 3, we relate this random field to the…
We create a framework to analyse the timing and frequency of instantaneous interactions between pairs of entities. This type of interaction data is especially common nowadays, and easily available. Examples of instantaneous interactions…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
We consider random rectangles in $\mathbb{R}^2$ that are distributed according to a Poisson random measure, i.e., independently and uniformly scattered in the plane. The distributions of the length and the width of the rectangles are…