Related papers: SPM Bulletin 31
We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results…
We explore the possibility of using machine learning to identify interesting mathematical structures by using certain quantities that serve as fingerprints. In particular, we extract features from integer sequences using two empirical laws:…
Many slope filtrations occur in algebraic geometry, asymptotic analysis, ramification theory, p-adic theories, geometry of numbers... These functorial filtrations, which are indexed by rational (or sometimes real) numbers, have a lot of…
These notes started to educate ourselves and to collect some background for our future work, with the hope that perhaps they will be useful to others also. Many if not all results are more or less elementary or available in the literature,…
We study a probabilistic variant of binary session types that relate to a class of Finite-State Markov Chains. The probability annotations in session types enable the reasoning on the probability that a session terminates successfully, for…
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
This is an overview article on finite type invariants, written for the Encyclopedia of Mathematical Physics
Determinantal point processes (DPPs) are elegant probabilistic models of repulsion that arise in quantum physics and random matrix theory. In contrast to traditional structured models like Markov random fields, which become intractable and…
Structured latent attribute models (SLAMs) are a special family of discrete latent variable models widely used in social and biological sciences. This paper considers the problem of learning significant attribute patterns from a SLAM with…
Successive Subspace Learning (SSL) offers a light-weight unsupervised feature learning method based on inherent statistical properties of data units (e.g. image pixels and points in point cloud sets). It has shown promising results,…
In the paper I study properties of random polynomials with respect to a general system of functions. Some lower bounds for the mathematical expectation of the uniform and recently introduced integral-uniform norms of random polynomials are…
An important problem in the analysis of experimental data showing fractal properties, is that such samples are composed by a set of points limited by an upper and a lower cut off. We study how finite size effect due to the discreteness of…
Emerged as one of the best performing techniques for extractive summarization, determinantal point processes select the most probable set of sentences to form a summary according to a probability measure defined by modeling sentence…
Standard methods for determining the number of factors often overestimate the true number when data exhibit heavy-tailed randomness, misinterpreting noise-induced outliers as genuine factors. This paper addresses this challenge within the…
Several papers have been published recently, particularly in the field of topological insulators, that use a Fourier-transform technique in a way that can be misleading or otherwise inaccurate, and the processing is not always described in…
We describe a new class of self-similar symmetric $\alpha$-stable processes with stationary increments arising as a large time scale limit in a situation where many users are earning random rewards or incurring random costs. The resulting…
We survey the known results about simple permutations. In particular, we present a number of recent enumerative and structural results pertaining to simple permutations, and show how simple permutations play an important role in the study…
This paper introduces the Generalized Space-Time Fractional Skellam Process (GSTFSP) and the Generalized Space Fractional Skellam Process (GSFSP). We investigate their distributional properties including the probability generating function…
It has been argued by Daryl Bem in his 2011 paper that 8 out of 9 experiments yielded statistically significant results in favour of the psi effect. It is pointed out in this short communication that many of the results in the above…
This paper studies choice situations in which a decision maker can choose multiple alternatives. Given a menu of available options, the decision maker selects a subset of the menu with certain probabilities. We employ an axiomatic approach…