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This paper is a follow-up to our joint paper with I. Agol, P. Storm and K. Whyte "Finiteness of arithmetic hyperbolic reflection groups". The main purpose is to investigate the effective side of the method developed there and its possible…

A paper on ordinal partitions by Erd\H{o}s and Milner (1972) has been formalised using the proof assistant Isabelle/HOL, augmented with a library for Zermelo-Fraenkel set theory. The work is part of a project on formalising the partition…

Version 2: Corrected Section 3.3: instead of lexicographical normal forms we now use a normal form due to V. Diekert and A. Muscholl. Consequent changes made and some misprints corrected. Using an analogue of Makanin-Razborov diagrams, we…

In the note two errors in Low and Lapsley's article "Optimization Flow Control, I: Basic Algorithm and Convergence", "IEEE/ACM Transactions on Networking", 7(6), pp. 861-874, 1999, are shown. Because of these errors the proofs of both…

This paper was withdrawn by the author. The appearance of an author-written addendum [3] to the paper [2] made our correction note [1] to that paper superfluous and hence it is no longer available here. [1] Dror Bar-Natan and Ofer Ron, A…

Short review article on quantum information processing accepted for Supplement III, Encyclopaedia of Mathematics (publication expected Summer 2001). See also http://www.wkap.nl/series.htm/ENM

In this note we document a gap in an argument in the above paper, and point to new work in the literature giving a complete proof of the main result.

We start with elementary algebraic theory of factorization of linear ordinary differential equations developed in the period 1880-1930. After exposing these classical results we sketch more sophisticated algorithmic approaches developed in…

This survey is a slightly extended version of the lecture given by the author at the \emph{VI International Course of Mathematical Analysis in Andaluc\'\i a} (CIDAMA), in September 2014. Most results are contained (in a slightly less…

In the present paper, a robust approach to a special class of convex feasibility problems is considered. By techniques of convex and variational analysis, conditions for the existence of robust feasible solutions and related error bounds…

Two typos in the published paper are pointed out. Both are just typos and the calculations in that paper are based on the correct formulism.

We generalize a well known periodicity lemma from the case of free groups to the case of acylindrically hyperbolic groups. This generalization will be used later to describe solutions of certain equations in acylindrically hyperbolic groups…

We develop a theory of complexity for numerical computations that takes into account the condition of the input data and allows for roundoff in the computations. We follow the lines of the theory developed by Blum, Shub, and Smale for…

This note provides a brief guide to the current state of the literature on Tarski's problems with emphasis on features that distinguish the approach based on combinatorial and algorithmic group theory from the topological approach to…

This thesis details a class of partial orders on the space of probability distributions and the space of density operators which capture the idea of information content. Some links to domain theory and computational linguistics are also…

This is the original version of my Ph.D. thesis. The main results have been divided up between papers arXiv:2111.09784 and arXiv:2204.10924. This paper has been kept on the arXiv to preserve some proofs of elementary lemmas that will be…

The paper gives a brief review of the expectation-maximization algorithm (Dempster 1977) in the comprehensible framework of discrete mathematics. In Section 2, two prominent estimation methods, the relative-frequency estimation and the…

This work advances and substantiates the thesis that the resolution of this crisis lies in the domain of possibility theory, specifically in the axiomatic approach developed in Bychkovs article. Unlike numerous attempts to fix Dempster…

This paper is an extended version of four lectures at PIMS in Vancouver given June 27 - 30, 2016. The primary goal of these lectures was to publicize the author's recent efforts to extend to representations of linear algebraic groups the…

Using a new presentation for partition algebras (J. Algebraic Combin. 37(3):401-454, 2013), we derive explicit combinatorial formulae for the seminormal representations of the partition algebras. These results generalise to the partition…