Related papers: Voevodsky's Unachieved Project
Kolmogorov complexity and algorithmic probability are defined only up to an additive resp. multiplicative constant, since their actual values depend on the choice of the universal reference computer. In this paper, we analyze a natural…
The initial value problem for the Vlasov-Poisson system is by now well understood in the case of an isolated system where, by definition, the distribution function of the particles as well as the gravitational potential vanish at spatial…
Lack of methodical support, low level of teachers' awareness of existing effective teaching technologies such as computer modeling does not allow students to form their own individual trajectory for development as well as their competence…
The purpose of this article is to lay the mathematical foundations of a well known numerical approach in computational statistical physics and molecular dynamics, namely the parallel replica dynamics introduced by A.F. Voter. The aim of the…
In 1989 H. Tverberg proposed a quite general conjecture in Discrete geometry, which could be considered as the common basis for many results in Combinatorial geometry and at the same time as a discrete analogue of the common transversal…
Many practical prediction algorithms represent inputs in Euclidean space and replace the discrete 0/1 classification loss with a real-valued surrogate loss, effectively reducing classification tasks to stochastic optimization. In this…
This article investigates the attitude toward mathematics among the students enrolled in the Foundation Year Programme at Nazarbayev University. The study is conducted quantitatively and an inventory developed by Tapia and Marsh II is…
This survey explores modern approaches for computing low-rank approximations of high-dimensional matrices by means of the randomized SVD, randomized subspace iteration, and randomized block Krylov iteration. The paper compares the…
Mathematical proof is undoubtedly the cornerstone of mathematics. The emergence, in the last years, of computing and reasoning tools, in particular automated geometry theorem provers, has enriched our experience with mathematics immensely.…
In this essay, I attempt to provide supporting evidence as well as some balance for the thesis on `Transforming socio-economics with a new epistemology' presented by Hollingworth and Mueller (2008). First, I review a personal highlight of…
After the paper of Molodtsov ( D. Molodtsov, Soft set theory first results. Computers and Mathematics with Applications, 37(4-5) (1999), 19-31), soft set theory grew at a breakneck pace. Several authors have introduced various operations,…
The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically…
In recent years, deep metric learning and its probabilistic extensions claimed state-of-the-art results in the face verification task. Despite improvements in face verification, probabilistic methods received little attention in the…
In this paper, we aim to introduce the concept of the Ouroboros space and the complimentary concept of the Ouroboros function by using the Ouroboros equation [1] as our starting point. We start with a few univariate definitions, and then…
At the intersection of what I call uncomputable art and computational epistemology, a form of experimental philosophy, we find an exciting and promising area of science related to causation with an alternative, possibly best possible,…
This paper revisits the principle of uniform convergence in statistical learning, discusses how it acts as the foundation behind machine learning, and attempts to gain a better understanding of the essential problem that current deep…
One of the primary challenges faced by deep learning is the degree to which current methods exploit superficial statistics and dataset bias, rather than learning to generalise over the specific representations they have experienced. This is…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…
The proliferation of computing devices has brought about an opportunity to deploy machine learning models on new problem domains using previously inaccessible data. Traditional algorithms for training such models often require data to be…