A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
This study improves quantum classifiers by optimizing data preprocessing.
This review covers AI in finance, challenges, techniques, and opportunities.
Study harmonic mappings and submanifolds using Bochner technique.
Adding a braid closure to a fibered knot makes a link ribbon concordance minimal.
Classic feature selection techniques remove those features that are either irrelevant or redundant, achieving a subset of relevant features that help to provide a better knowledge extraction. This allows the creation of compact models that are easier to interpret. Most of these techniques work over the whole dataset, b…
Study combines quantum and classical deep learning for better credit risk assessment.
The question of how to incorporate curvature information in stochastic approximation methods is challenging. The direct application of classical quasi- Newton updating techniques for deterministic optimization leads to noisy curvature estimates that have harmful effects on the robustness of the iteration. In this paper…
Recommender systems play an essential role in the modern business world. They recommend favorable items like books, movies, and search queries to users based on their past preferences. Applying similar ideas and techniques to Monte Carlo simulations of physical systems boosts their efficiency without sacrificing accura…
We give a proof of the classical Schwarz reflection principle for Jenkins-Serrin type minimal surfaces in the homogeneous three manifolds for and . In our previous paper we proved a reflection principle in Riemannian manifolds. The statements and techniques in the two papers are d…
In 2002, D. Hrencecin and L.H. Kauffman defined a filamentation invariant on oriented chord diagrams that may determine whether the corresponding flat virtual knot diagrams are non-trivial. A virtual knot diagram is non-classical if its related flat virtual knot diagram is non-trivial. Hence filamentations can be used …
This dissertation improves classical compression techniques using deep learning.
New extrinsic lower bounds are given for the classical Dirac operator on the boundary of a compact domain of a spin manifold. The main tool is to solve some boundary problems for the Dirac operator of the domain under boundary conditions of Atiyah-Patodi-Singer type. Spinorial techniques are used to give simple proofs …
In this paper, we develop a new mathematical technique which allows us to express the joint distribution of a Markov process and its running maximum (or minimum) through the marginal distribution of the process itself. This technique is an extension of the classical reflection principle for Brownian motion, and it is o…
New displacement technique vanishes bounded cohomology in all degrees.
This is survey about the classical knot concordance group, prepared for an upcoming handbook of knot theory. Topics include: the basic definitions of concordance; the theory of algebraic concordance as developed by Levine; the theory of Casson-Gordon invariants; applications of topological surgery as developed by Freed…
Explains classic quantitative strategies and their workings.
New technique prevents Q-learning collapse by maximizing diversity among ensembles.
We discuss several open problems in classical Knot Theory and we develop techniques that allow us to study them: Lagrangian tangles, skein modules and Burnside groups.
In this thesis we study the classical and quantum momentum maps and the theory of reduction. We focus on the notion of momentum map in Poisson geometry and we discuss the classification of the momentum map in this framework. Furthermore, we describe the so-called Poisson Reduction, a technique that allows us to reduce …
Recent work applying higher gauge theory to the superstring has indicated the presence of 'higher symmetry', and the same methods work for the super-2-brane. In the previous paper in this series, we used a geometric technique to construct a 'Lie 2-supergroup' extending the Poincare supergroup in precisely those spaceti…
Classical multidimensional scaling is an important dimension reduction technique. Yet few theoretical results characterizing its statistical performance exist. This paper provides a theoretical framework for analyzing the quality of embedded samples produced by classical multidimensional scaling. This lays the foundati…
New complexity measure ADL connects to classical complexity measures.
Study compares GNNs and classical molecular featurisations for molecular property and cliff prediction.
Global homotopies upgrade classical map in differential geometry.
We observe that any knot invariant extends to virtual knots. The isotopy classification problem for virtual knots is reduced to an algebraic problem formulated in terms of an algebra of arrow diagrams. We introduce a new notion of finite type invariant and show that the restriction of any such invariant of degree n to …
Classical Delaunay surfaces are highly symmetric constant mean curvature (CMC) submanifolds of space forms. We prove the existence of Delaunay-type hypersurfaces in a large class of compact manifolds, using the geometry of cohomogeneity one group actions and variational bifurcation techniques. Our construction speciali…
This is the first in a series Of papers in which we initiate the study Of very rough solutions to the initial value problem for the Einstein Vacuum equations expressed relative to wave coordinates. By very rough we mean solutions which cannot be constructed by the classical techniques Of energy estimates and Sobolev in…
Paper compares neural networks and classical statistics for dementia prediction, highlighting interpretability of classical methods.
It is well-known that the monoid of long virtual knots is not commutative. This contrasts with the case of classical long knots, where for all . In the present paper, we present a new proof that two inequivalent non-classical prime long virtual knots never commute. The original r…
Quantum annealing (QA) is a generic method for solving optimization problems using fictitious quantum fluctuation. The current device performing QA involves controlling the transverse field; it is classically simulatable by using the standard technique for mapping the quantum spin systems to the classical ones. In this…
The paper calculates bridge numbers for knots using machine learning.
Extends folding techniques to study subgroups of CAT(0) cube complexes.
Collaborative filtering is a rapidly advancing research area. Every year several new techniques are proposed and yet it is not clear which of the techniques work best and under what conditions. In this paper we conduct a study comparing several collaborative filtering techniques -- both classic and recent state-of-the-…
Torsion sensitive intersection homology was introduced to unify several versions of Poincare duality for stratified spaces into a single theorem. This unified duality theorem holds with ground coefficients in an arbitrary PID and with no local cohomology conditions on the underlying space. In this paper we consider for…
In this paper, we try to generalize to the case of compact Riemannian orbifolds some classical results about the existence of closed geodesics of positive length on compact Riemannian manifolds . We shall also consider the problem of the existence of infinitely many geometrically distinct closed geodesics. In th…
Update: The Cosmetic Surgery Conjecture modulo finitely many Dehn-filling coefficients has been a well-known classical result, so the first main result of this paper is not new. (But the author was initially unaware of this fact, and the tools and techniques used here are very different from all the classically known m…
We prove several vanishing theorems for a class of generalized elliptic genera on foliated manifolds, by using classical equivariant index theory. The main techniques are the use of the Jacobi theta-functions and the construction of a new class of elliptic operators associated to foliations.
Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks. Despite these successes, the proximity to the physical limits of chip fabrication al…
Paper presents a faster classical algorithm for principal component regression.
Improved sales forecasting at various levels using ensemble methods.
Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Since quantum systems produce counter-intuitive patterns believed not to be efficiently produced by classical systems, it is reasonable to postulate that quantum computers …
We present proofs of classical results in Poisson geometry using techniques from Dirac geometry. This article is based on mini-courses at the Poisson summer school in Geneva, June 2016, and at the workshop "Quantum Groups and Gravity" at the University of Waterloo, April 2016.
The linear Support Vector Machine (SVM) is a classic classification technique in machine learning. Motivated by applications in modern high dimensional statistics, we consider penalized SVM problems involving the minimization of a hinge-loss function with a convex sparsity-inducing regularizer such as: the L1-norm on t…
Machine learning (ML) is quickly emerging as a powerful tool with diverse applications across an extremely broad spectrum of disciplines and commercial endeavors. Typically, ML is used as a black box that provides little illuminating rationalization of its output. In the current work, we aim to better understand the ge…
Research proves the semi-classical limit of Liouville conformal field theory, describing deterministic geometry from random fluctuations.
This study compares feature importance and explainability in quantum vs classical ML models.
New DR method uses Gromov-Wasserstein distance for high-dimensional data.
For the existence of a branched covering Sigma~ --> Sigma between closed surfaces there are easy necessary conditions in terms of chi(Sigma~), chi(Sigma), orientability, the total degree, and the local degrees at the branching points. A classical problem dating back to Hurwitz asks whether these conditions are also suf…