Related papers: Voevodsky's Unachieved Project
Over the past two decades, Yuri Gurevich and his colleagues have formulated axiomatic foundations for the notion of algorithm, be it classical, interactive, or parallel, and formalized them in the new generic framework of abstract state…
This text summarizes and expands the content of a general audience talk given in 2018 at the University of Mainz. Motivated by recent developments in dependent type theory and infinity category theory, it presents a history of ideas around…
The growing disconnection of the majority of population from mathematics is becoming a phenomenon that is increasingly difficult to ignore. This paper attempts to point to deeper roots of this cultural and social phenomenon. It concentrates…
This work was originally published by the author in 1999 in a book [1] and later became part of the author's doctoral thesis in 1999 [2]. Since the original language of these works is not English, the author provides a translation of the…
In this book the authors probe into Vedic Mathematics (a concept that gained renown in the period of the religious fanatic and revivalist Hindutva rule in India): and explore whether it is really 'Vedic' in origin or 'Mathematics' in…
This article provides a conceptual and historical review of the evolution of integrable Hamiltonian systems from the Moscow School of A. T. Fomenko to the emerging Azarbaijan School of Geometric Dynamical Systems founded by the author.…
This monograph deals with adaptive supervised classification, using tools borrowed from statistical mechanics and information theory, stemming from the PACBayesian approach pioneered by David McAllester and applied to a conception of…
Inductive learning is based on inferring a general rule from a finite data set and using it to label new data. In transduction one attempts to solve the problem of using a labeled training set to label a set of unlabeled points, which are…
A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a data set of observations of this vector. The probability distribution…
This paper surveys results related to well-known works of B. Plotkin and V. Remeslennikov on the edge of algebra, logic and geometry. We start from a brief review of the paper and motivations. The first sections deal with model theory. In…
Planning under uncertainty is critical to robotics. The Partially Observable Markov Decision Process (POMDP) is a mathematical framework for such planning problems. It is powerful due to its careful quantification of the non-deterministic…
Statistical decision problems lie at the heart of statistical machine learning. The simplest problems are binary and multiclass classification and class probability estimation. Central to their definition is the choice of loss function,…
Unsupervised classification called clustering is a process of organizing objects into groups whose members are similar in some way. Clustering of uncertain data objects is a challenge in spatial data bases. In this paper we use Probability…
The dissertation describes ergodic properties of some stochastic dynamical systems generated by Markov chains with values in the state space which is a Polish space. The mathematical model describing the process of cell division is…
In 2010, Vladimir Voevodsky gave a lecture on "What If Current Foundations of Mathematics Are Inconsistent?" Among other things he said that he was seriously suspicious that an inconsistency in PA (first-order Peano arithmetic) might…
The paper deals with pedagogical heritage of A.V. Usova (1921-2014) that yields insights into problems of interdisciplinary relationship in the school science education system. Her fundamental works were used as teaching guides in the…
The goal of this thesis is twofold; introduce the fundamentals of Bayesian inference and computation focusing on astronomical and cosmological applications, and present recent advances in probabilistic computational methods developed by the…
This thesis develops and expands upon known techniques of mathematical physics relevant to the analysis of the popular Markov model of phylogenetic trees required in biology to reconstruct the evolutionary relationships of taxonomic units…
Uncertain partially observable Markov decision processes (uPOMDPs) allow the probabilistic transition and observation functions of standard POMDPs to belong to a so-called uncertainty set. Such uncertainty, referred to as epistemic…
The integration of the history and philosophy of statistics was initiated at least by Hacking (1975) and advanced by Hacking (1990), Mayo (1996), and Zabell (2005), but it has not received sustained follow-up. Yet such integration is more…