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Neural Processes (NPs) are a family of conditional generative models that are able to model a distribution over functions, in a way that allows them to perform predictions at test time conditioned on a number of context points. A recent…

We introduce the convolutional spectral kernel (CSK), a novel family of non-stationary, nonparametric covariance kernels for Gaussian process (GP) models, derived from the convolution between two imaginary radial basis functions. We present…

In this paper, we consider a generalization of the Stirling number sequence of both kinds by using a specialization of a new family of symmetric functions. We give combinatorial interpretations for this symmetric functions by means of…

The effectiveness of Convolutional Neural Networks (CNNs) has been substantially attributed to their built-in property of translation equivariance. However, CNNs do not have embedded mechanisms to handle other types of transformations. In…

Kuznetsov et al. (2011) and Kuznetsov and Pardo (2013) introduced the family of Hypergeometric L\'evy processes. They appear naturally in the study of fluctuations of stable processes when one analyses stable processes through the theory of…

The class of Levy processes for which overshoots are almost surely constant quantities is precisely characterized.

Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…

Graph Self-Supervised Learning (GSSL) has emerged as a powerful paradigm for generating high-quality representations for graph-structured data. While multi-scale graph contrastive learning has received increasing attention, many existing…

We describe a general scheme of derivation of the Vlasov-type equations for Markov evolutions of particle systems in continuum. This scheme is based on a proper scaling of corresponding Markov generators and has an algorithmic realization…

This paper presents a family of new integral representations and asymptotic series of the multiple gamma function. The numerical schemes for high-precision computation of the Barnes gamma function and Glaisher's constant are also discussed.

We establish a general framework for developing, efficient energy stable numerical schemes for gradient flows and develop three classes of generalized scalar auxiliary variable approaches (G-SAV). Numerical schemes based on the G-SAV…

We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to…

We study the equation $M_\Psi(z+1)=\frac{-z}{\Psi(-z)}M_\Psi(z), M_\Psi(1)=1$ defined on a subset of the imaginary line and where $\Psi$ is a negative definite functions. Using the Wiener-Hopf method we solve this equation in a two terms…

In this paper, we propose a framework for graph signal processing using category theory. The aim is to generalize a few recent works on probabilistic approaches to graph signal processing, which handle signal and graph uncertainties.

Normalizing flows have recently demonstrated the ability to learn the Boltzmann distribution of the Hubbard model, opening new avenues for generative modeling in condensed matter physics. In this work, we investigate the steps required to…

The distributional support of the sample paths of L\'evy processes is an important issue for the construction of sparse statistical models, theories of integration in infinite dimensions and the existence of generalized solutions of…

In this paper, we introduce a new subclass of close-to-convex harmonic functions. We present a sufficient coefficient condition for a function to be a member of this class. Furthermore, we establish a distortion theorem. These results lay…

This paper introduces a couple of new time-frequency transforms, designed to adapt their scale to specific features of the analyzed function. Such an adaptation is implemented via so-called focus functions, which control the window scale as…

Neural Processes (NPs; Garnelo et al., 2018a,b) are a rich class of models for meta-learning that map data sets directly to predictive stochastic processes. We provide a rigorous analysis of the standard maximum-likelihood objective used to…

It is established that general s-convex functions are a new class of generalized convex functions. In a similar vein, a new class of general s-convex sets is introduced, which are generalizations of s-convex sets. Additionally, certain…