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Let $\Lambda$ be the collection of all probability distributions for $(X,\widetilde{X})$, where $X$ is a fixed random vector and $\widetilde{X}$ ranges over all possible knockoff copies of $X$ (in the sense of \cite{CFJL18}). Three topics…
Time-reversal invariant three-dimensional topological insulators can be defined fundamentally by a topological field theory with a quantized axion angle theta of zero or pi. It was recently shown that fractional quantized values of theta…
Finding upper and lower bounds to integrals with respect to copulas is a quite prominent problem in applied probability. In their 2014 paper, Hofer and Iaco showed how particular two dimensional copulas are related to optimal solutions of…
Topological insulators show important properties, such as topological phase transitions and topological edge states. Although these properties and phenomena can be simulated by well-designed circuits, it is undoubtedly difficult to design…
In this work, we introduce a novel evaluation framework for generative models of graphs, emphasizing the importance of model-generated graph overlap (Chanpuriya et al., 2021) to ensure both accuracy and edge-diversity. We delineate a…
We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely…
A large number of commonly used parametric Archimedean copula (AC) families are restricted to a single parameter, connected to a concordance measure such as Kendall's tau. This often leads to poor statistical fits, particularly in the joint…
In this paper, we consider the conditional generation problem by guiding off-the-shelf unconditional diffusion models with differentiable loss functions in a plug-and-play fashion. While previous research has primarily focused on balancing…
The algebra of invariants of several 3 x 3 matrices under the action of the orthogonal group by simultaneous conjugation is considered over a field of characteristic different from two. The maximal degree of elements of minimal system of…
Bivariate generating functions for various subsets of the class of permutations containing no descending sequence of length three or more are determined. The notion of absolute indecomposability of a permutation is introduced, and used in…
Copulas are mathematical objects that fully capture the dependence structure among random variables and hence, offer a great flexibility in building multivariate stochastic models. In statistics, a copula is used as a general way of…
Any nested Archimedean copula is defined starting from a rooted phylogenetic tree, for which a new class of nonparametric estimators is presented. An estimator from this new class relies on a two-step procedure where first a binary tree is…
We introduce a new family of copula densities constructed from univariate distributions on $[0,1]$. Although our construction is structurally simple, the resulting family is versatile: it includes both smooth and irregular examples, and…
We develop factor copula models for analysing the dependence among mixed continuous and discrete responses. Factor copula models are canonical vine copulas that involve both observed and latent variables, hence they allow tail, asymmetric…
The omnipotence of copulas when modeling dependence given marg\-inal distributions in a multivariate stochastic situation is assured by the Sklar's theorem. Montes et al.\ (2015) suggest the notion of what they call an \emph{imprecise…
Handling highly dependent data is crucial in clinical trials, particularly in fields related to ophthalmology. Incorrectly specifying the dependency structure can lead to biased inferences. Traditionally, models rely on three fixed…
We present a new kind of generator of internal waves which has been designed for three purposes. First, the oscillating boundary conditions force the fluid particles to travel in the preferred direction of the wave ray, hence reducing the…
In this paper, a method to generate permutations of a string under a set of constraints decided by the user is presented. The required permutations are generated without generating all the permutations.
This work concerns with the following problem. Given a two-dimensional domain whose boundary is a closed polygonal line with internal boundaries defined also by polygonal lines, it is required to generate a grid consisting only of…
We discuss diffeomorphism and gauge invariant theories in three dimensions motivated by the fact that some models of interest do not have a suitable action description yet. The construction is based on a canonical representation of symmetry…