Related papers: Lecture notes on "Combinatorial Criteria for Uniqu…
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.
This work addresses certain ambiguities in the Dirac approach to constrained systems. Specifically, we investigate the space of so-called ``rigging maps'' associated with Refined Algebraic Quantization, a particular realization of the Dirac…
We give a quick survey of the various fixed point theorems in computability theory, partial combinatory algebra, and the theory of numberings, as well as generalizations based on those. We also point out several open problems connected to…
Partially exchangeable sequences representable as mixtures of Markov chains are completely specified by de Finetti's mixing measure. The paper characterizes, in terms of a subclass of hidden Markov models, the partially exchangeable…
A recent parameterisation scheme developed for the quark mixing matrix is shown to be easily applicable to the lepton mixing matrix as well.
In this paper, we study dependence coefficients for copula-based Markov chains. We provide new tools to check the convergence rates of mixing coefficients of copula-based Markov chains. We study Markov chains generated by the…
These are the notes of the lectures delivered by the author at CIME in June 2018. The main purpose of the notes is to provide an overview of the techniques used in the construction of the triply graded link homology. The homology is space…
We review different notions of cuts appearing throughout the literature on scattering amplitudes. Despite similar names, such as unitarity cuts or generalized cuts, they often represent distinct computations and distinct physics. We…
The successes and shortcomings of the Standard Model are reviewed, with emphasis on the reasons motivating the need to extend it. The basic elements of grand unification and supersymmetry are described, exploring their phenomenological…
In this paper we consider the notions of binomial thinning, binomial mixing, their generalizations, certain interplay between them, associated limit theorems and provide various examples.
Query answering routinely employs knowledge graphs to assist the user in the search process. Given a knowledge graph that represents entities and relationships among them, one aims at complementing the search with intuitive but effective…
This document is a collection of comments that I wrote down while reading the first four chapters of the book "Discrete Groups, Expanding Graphs and Invariant Measures" by Alexander Lubotzky. Most of them are more detailed versions of…
We introduce a new combinatorial object called tower diagrams and prove fundamental properties of these objects. We also introduce an algorithm that allows us to slide words to tower diagrams. We show that the algorithm is well-defined only…
We consider two examples for a well-known method for obtaining concentration of measure (COM) bounds for a given observable in a given measure. The method is to consider an auxiliary Markov chain for which the invariant distribution is the…
The goal of these notes is to provide an informal introduction to Gromov-Witten theory with an emphasis on its role in counting curves in surfaces. These notes are based on a talk given at the Fields Institute during a week-long conference…
Review of results from lattice QCD of relevance to standard-model phenomenology, to appear in Annual Review of Nuclear and Particle Science. KEY WORDS: hadron masses, quark mixing (CKM) matrix, weak matrix elements, strong coupling…
Wojcik's hypothesis has been mentioned on page 32 of the text S.Piekarski, "Galilean-Invariant Formulation of the Fluid Mechanics", IFTR REPORTS, 7/2007. Here we discuss it in more detail. Our main is to show that the form of the…
We provide an information-theoretic framework for studying the generalization properties of machine learning algorithms. Our framework ties together existing approaches, including uniform convergence bounds and recent methods for adaptive…
We extend the synthetic theories of discrete and Gaussian categorical probability by introducing a diagrammatic calculus for reasoning about hybrid probabilistic models in which continuous random variables, conditioned on discrete ones,…
We address the problem of characterising the compatible tuples of measurements that admit a unique joint measurement. We derive a uniqueness criterion based on the method of perturbations and apply it to show that extremal points of the set…