Related papers: Discrete Complex Analysis and Probability
With the widespread success of deep neural networks in science and technology, it is becoming increasingly important to quantify the uncertainty of the predictions produced by deep learning. In this paper, we introduce a new method that…
Most of the characterizations of probability distributions are based on properties of functions of possibly independent random variables. We investigate characterizations of probability distributions through properties of minima or maxima…
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…
In this note, we explore a simple approach to composition estimation, using penalized likelihood density estimation on a nominal discrete domain. Practical issues such as smoothing parameter selection and the use of prior information are…
This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…
Recent developments in theory and phenomenology relevant to deep inelastic lepton scattering are reviewed, concentrating on the following topics: Predicted behaviour of non-singlet and polarized structure functions at small $x$; Theoretical…
Since the introduction of strong anticipation by D.~Dubois the numerous investigations of concrete systems have been proposed. In proposed paper the new examples of discrete dynamical systems with anticipation are considered. The…
We introduce a new class of multiplications of distributions in one dimension merging together two different regularizations of distributions. Some of the features of these multiplications are discussed in a certain detail. We use our…
As the use of differential privacy (DP) becomes widespread, the development of effective tools for reasoning about the privacy guarantee becomes increasingly critical. In pursuit of this goal, we demonstrate novel relationships between DP…
In this paper, we extend to polarization the method we have recently employed to treat spin. We are led to a generalization of its treatment. Thus, we are able to connect its matrix treatment to first principles, and we obtain the most…
The two parameter Poisson-Dirichlet Process (PDP), a generalisation of the Dirichlet Process, is increasingly being used for probabilistic modelling in discrete areas such as language technology, bioinformatics, and image analysis. There is…
A number of complexity measures for Boolean functions have previously been introduced. These include (1) sensitivity, (2) block sensitivity, (3) witness complexity, (4) subcube partition complexity and (5) algorithmic complexity. Each of…
In this thesis we study convolutions that arise from noncommutative probability theory. We prove several regularity results for free convolutions, and for measures in partially defined one-parameter free convolution semigroups. We discuss…
We illustrate the general principle that complex analysis can be a good setting for posing problems that are best solved using techniques from other mathematical disciplines. Several examples are provided.
Abstraction is a fundamental tool for reasoning about complex systems. Program abstraction has been utilized to great effect for analyzing deterministic programs. At the heart of program abstraction is the relationship between a concrete…
We investigate properties of the set of discrete Morse functions on a simplicial complex as defined by Forman. It is not difficult to see that the pairings of discrete Morse functions of a finite simplicial complex again form a simplicial…
This paper provides closed-form expansions for the log-likelihood function of multivariate diffusions sampled at discrete time intervals. The coefficients of the expansion are calculated explicitly by exploiting the special structure…
The LMC-complexity introduced by Lopez-Ruiz, Mancini and Calbet [Phys. Lett. A 209, 321-326 (1995)] is calculated for different physical situations: one instance of classical statistical mechanics, normal and exponential distributions, and…
A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…
We study tail probabilities via some Gaussian approximations. Our results make refinements to large deviation theory. The proof builds on classical results by Bahadur and Rao. Binomial distributions and their tail probabilities are…