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.
New tiles in higher dimensions are shown to be homeomorphic to balls.
Recent proofs of classical theorems in polynomial algebra and functional analysis are discussed, which use tools from the topology of real manifolds. Simpler proofs were discovered in the new century, of the Hilbert Nullstellensatz, and the Gelfand-Mazur Theorem. We give a related proof that an irreducible real polynom…
We give new tools for homotopy Brouwer theory. In particular, we describe a canonical reducing set (the set of "walls") which splits the plane into maximal translation areas and irreducible areas. We then focus on Brouwer mapping classes relatively to four orbits and describe them explicitly by adding to Handel's diagr…
Unified framework recovers and improves classical Brouwer homeomorphism results.
Study Kazdan-Warner equations on graphs using Brouwer degree theory.
We prove three theorems giving fixed points for orientation preserving homeomorphisms of the plane following forgotten results of Brouwer.
We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.
The Brouwer fixed point theorem says that any continuous function from disc to itself has a fixed point. By using simple geometrical technique we have generalized the result in manifold and proved that any continuous function on the boundary of a bounded convex domain of a -dimensional Riemannian manifold with a pol…
The proof of Brouwer's fixed-point theorem based on Sperner's lemma is often presented as an elementary combinatorial alternative to advanced proofs based on algebraic topology. The goal of this note is to show that: (i) the combinatorial proof of Sperner's Lemma can be considered as a cochain-level version, written in…
Extends Brouwer fixed point theorem with new conditions for continuous maps.
This is a mathematical commentary on Teichm{ü}ller's paper ``Bestimmung der extremalen quasikonformen Abbildungen bei geschlossenen orientierten Riemannschen Fl{ä}chen'' (Determination of extremal quasiconformal maps of closed oriented Riemann surfaces). This paper is among the last (and may be the last one) that Teich…
Paper extends Brouwer Fixed Point Theorem with amiable and almost amiable fixed sets.
We investigate the fixed point property of the group actions on a coarse space and its Higson corona. We deduce the coarse version of Brouwer's fixed point theorem.
New proof shows no flat embedding for Petersen family graphs.
We give an answer to the question given by T.Y.Kong in his article "Can 3-D Digital Topology be Based on Axiomatically Defined Digital Spaces?" In this article he asks the question, if so called "good pairs" of neighborhood relations can be found on the set Z^n such that the existence of digital manifolds of dimension …
A new technique for the study of geodesic connectedness in a class of Lorentzian manifolds is introduced. It is based on arguments of Brouwer's topological degree for the solution of functional equations. It is shown to be very useful for multiwarped spacetimes, which include different types of relativistic spacetimes.
The paper generalizes Sperner's lemma to higher dimensions and calculates a new invariant.
A new method calculates the minimum volume swept by a sphere's homotopy in 3D space.
Walraswap solves batch auction pricing by finding optimal AMM swaps.
Paper proves a new criterion for time-like geodesics in flat spacetimes.
Learning domain-invariant representation is a dominant approach for domain generalization (DG), where we need to build a classifier that is robust toward domain shifts. However, previous domain-invariance-based methods overlooked the underlying dependency of classes on domains, which is responsible for the trade-off be…
A new method improves cross-domain sentiment analysis by learning weighted domain-invariant representations.
New method improves domain generalization by aligning causal mechanisms across domains.
TAROT enhances robustness and domain adaptability with domain-invariant features.
New invariant for hyperbolic surfaces, geometric criterion for domains.
This paper investigates domain generalization: How to take knowledge acquired from an arbitrary number of related domains and apply it to previously unseen domains? We propose Domain-Invariant Component Analysis (DICA), a kernel-based optimization algorithm that learns an invariant transformation by minimizing the diss…
The paper studies invariant weighted Bergman metrics on domains.
The paper explores how to make machine learning models robust to domain shifts.
Paper develops upper-bounds for target general loss in multiple source DA and DG settings.
The paper proposes a method to create domain-invariant representations using Wasserstein distance.
New approach improves domain adaptation by enforcing cluster assumption in target domain.
Domain generalization aims to apply knowledge gained from multiple labeled source domains to unseen target domains. The main difficulty comes from the dataset bias: training data and test data have different distributions, and the training set contains heterogeneous samples from different distributions. Let denote …
A new IL framework estimates invariant predictors with single domain data.
Adversarial techniques learn invariant representations across multiple domains.
Harmonization schemes limit accuracy due to domain information.
Surgery triangles are an important computational tool in Floer homology. Given a connected oriented surface , we consider the abelian group generated by bordered 3-manifolds with boundary , modulo the relation that the three manifolds involved in any surgery triangle sum to zero. We show that is a f…
Transfer learning aims to improve learning in target domain by borrowing knowledge from a related but different source domain. To reduce the distribution shift between source and target domains, recent methods have focused on exploring invariant representations that have similar distributions across domains. However, w…
Proposes an alternative invariance penalty to address domain generalization issues.
Improves transferability of representations from source to target domains with weights and invariant representations.
Domain adaptation aims at generalizing a high-performance learner on a target domain via utilizing the knowledge distilled from a source domain which has a different but related data distribution. One solution to domain adaptation is to learn domain invariant feature representations while the learned representations sh…
SIG model identifies invariant variables for MSDA with fewer domain constraints.
Paper shows regularization improves robustness in domain generalization.
We answer the question of when a new point can be added in a continuous way to configurations of distinct points in a closed ball of arbitrary dimension. We show that this is possible given an ordered configuration of points if and only if . On the other hand, when the points are not ordered and the d…
Interventional domain adaptation improves feature transferability by removing spurious correlations.
New invariant defined for Weinstein domains, related to Kirby-Thompson's invariant.
Estimates model performance under distribution shift using domain-invariant predictors.
We prove a discrete Jordan-Brouwer-Schoenflies separation theorem telling that a (d-1)-sphere H embedded in a d-sphere G defines two different connected graphs A,B in G such a way that the intersection of A and B is H and the union is G and such that the complementary graphs A,B are both d-balls. The graph theoretic de…
M Handel has proved in [Topology 38 (1999) 235--264] a fixed point theorem for an orientation preserving homeomorphism of the open unit disk, that may be extended to the closed disk and that satisfies a linking property of orbits. We give here a new proof of Handel's fixed point theorem, based on Brouwer theory and som…