arXiv research

An extra large metric is a spherical cone metric with all cone angles greater than 2 pi and every closed geodesic longer than 2pi. We show that every two-dimensional extra large metric can be triangulated with vertices at cone points only. The argument implies the same result for Euclidean and hyperbolic cone metrics, …

Study shows large extra dimensions are hidden from view by black holes.

Improved clustering of extra-financial data using NMF with data separation.

New singularity theorems are derived for generic warped-product spacetimes of any dimension. The main purpose is to analyze the stability of (compact or large) extra dimensions against dynamical perturbations. To that end, the base of the warped product is assumed to be our visible 4-dimensional world, while the extra …

We describe a simple locally CAT(0) classifying space for extra extra large type Artin groups (with all labels at least 5). Furthermore, when the Artin group is not dihedral, we describe a rank 1 periodic geodesic, thus proving that extra large type Artin groups are acylindrically hyperbolic. Together with Property RD …

Three hard diagrams of the unknot require extra crossings to simplify.

In this work we present a novel approach for transfer-guided exploration in reinforcement learning that is inspired by the human tendency to leverage experiences from similar encounters in the past while navigating a new task. Given an optimal policy in a related task-environment, we show that its bisimulation distance…

A TQFT is a functor from a cobordism category to the category of vector spaces, satisfying certain properties. An important property is that the vector spaces should be finite dimensional. For the WRT TQFT, the relevant 2+1-cobordism category is built from manifolds which are equipped with an extra structure such as a …

Smooth isotopy on cube saves energy with extra dimensions.

We consider a set of gauge-theoretic equations on closed oriented four-manifolds, which was introduced by Vafa and Witten. The equations involve a triple consisting of a connection and extra fields associated to a principal bundle over a closed oriented four-manifold. They are similar to Hitchin's equations over compac…

Extract anomalies from 5D SCFTs using extra-dimensional η-invariants.

Study extra-special quotients of surface braid groups and construct double Kodaira fibrations.

A new method detects unknown classes and adapts to extra dimensions in high-dimensional classification.

In the present work, it is shown that, the application of the Bazanski approach to Lagrangians, written in AP-geometry and including the basic vector of the space, gives rise to a new class of path equations. The general equation representing this class contains four extra terms, whose vanishing reduces this equation t…

Math proves gravity can be localized near branes in extra dimensions.

Data augmentation is usually used by supervised learning approaches for offline writer identification, but such approaches require extra training data and potentially lead to overfitting errors. In this study, a semi-supervised feature learning pipeline was proposed to improve the performance of writer identification b…

Semichiral $(2,2)$ sigma models with $4d$ target space are discussed. A novel description in $(1,1)$ superspace allows an analysis of possible extended supersymmetries. It is argued that a manifest semichiral realization of an extra supersymmetry is only possible for hyperkähler target geometry. A semichiral formulatio…

Initial data for $pp$-wave spacetimes constructed in 4D.

This paper analyzes OGDA and EG methods for nonconvex minimax problems.

Paper tackles leveraging unlabeled data for PU classification and robust generation.

The generalized 5D Black-Scholes differential equation with stochastic volatility is derived. The projections of the stochastic evolutions associated with the random variables from an enlarged space or superspace onto an ordinary space can be achieved via higher-dimensional operators. The stochastic nature of the secur…

In this paper we consider solving saddle point problems using two variants of Gradient Descent-Ascent algorithms, Extra-gradient (EG) and Optimistic Gradient Descent Ascent (OGDA) methods. We show that both of these algorithms admit a unified analysis as approximations of the classical proximal point method for solving…

In this note we generalize an extension theorem in [5] and [9] of the mean curvature flow to the H^{k} mean curvature flow under some extra conditions. The main difficult problem in proving the extension theorem is to find a suitable version of Michael-Simon inequality for the H^{k} mean curvature flow, and to do a sui…

Joint training improves model accuracy by selectively using privileged information.

Mutant knots, in the sense of Conway, are known to share the same Homfly polynomial. Their 2-string satellites also share the same Homfly polynomial, but in general their m-string satellites can have different Homfly polynomials for m>2. We show that, under conditions of extra symmetry on the constituent 2-tangles, the…

Study shows that splitting links requires an arbitrarily large number of extra crossings.

Federated Extra-Trees protects privacy while improving machine learning performance.

Unified framework for decentralized bilevel optimization with various heterogeneity-correction strategies.

Riera proved at arXiv:1412.6964 that the diffeomorphism group of particular compact manifolds are not Jordan by exhibiting subgroups isomorphic to extra-special $p$-groups of exponent $p$ for primes $p$ satisfying some conditions. Generalising the methods of that paper, we construct a compact connected smooth real mani…

We define a type of biquandle which is a generalization of symplectic quandles. We use the extra structure of these bilinear biquandles to define new knot and link invariants and give some examples.

Spectral clustering adapted for mixed data types without preprocessing.

This paper proposes a method to gain extra supervision via multi-task learning for multi-modal video question answering. Multi-modal video question answering is an important task that aims at the joint understanding of vision and language. However, establishing large scale dataset for multi-modal video question answeri…

We consider an American contingent claim on a financial market where the buyer has additional information. Both agents (seller and buyer) observe the same prices, while the information available to them may differ due to some extra exogenous knowledge the buyer has. The buyer's information flow is modeled by an initial…

We show that smooth isoperimetric profiles are exceptional for real analytic Riemannian manifolds. For instance, under some extra assumption, this can happen only on topological spheres.

New MCMC method corrects bias without extra cost.

Let M be an oriented compact 3-manifold and let T be a (loose) triangulation of M, with ideal vertices at the components of the boundary of M and possibly internal vertices. We show that any spin structure s on M can be encoded by extra combinatorial structures on T. We then analyze how to change these extra structures…

We discuss pluripotential aspects of the Monge-Ampère equations on compact Hermitian manifolds and prove $L^{\infty}$ estimates for any metric, as well as the existence of weak solutions under an extra assumption.

Data-driven modeling increasingly requires to find a Nash equilibrium in multi-player games, e.g. when training GANs. In this paper, we analyse a new extra-gradient method for Nash equilibrium finding, that performs gradient extrapolations and updates on a random subset of players at each iteration. This approach prova…

New algorithms solve monotone inclusions and convex-concave minimax problems.

Bootstrap bounds on Einstein manifolds using semidefinite programming.

We review the relation between homotopy algebras of conformal field theory and geometric structures arising in sigma models. In particular we formulate conformal invariance conditions, which in the quasi-classical limit are Einstein equations with extra fields, as generalized Maurer-Cartan equations.

Paper examines how income support affects retirement decisions for low-income individuals.

New method uses off-the-shelf classifiers to improve diffusion generation without extra training.

Sampling more can make models more confident in wrong answers, not better.

AdaGrad converges under heavy-tailed noise without extra operations.

Random learning rate improves neural network training without extra cost.

We prove a $C^0$ a priori estimate on a solution of the quaternionic Calabi problem on an arbitrary compact connected HKT-manifold. This generalizes earlier works where this result was proven under certain extra assumptions on the manifold.

We introduce an extra filtration of $\CFK(Y,K)$ and use it in order to obtain formulas for Floer homology of $(Y,K)$, which is obtained from $(Y_i,K_i), i=1,2$ by gluing the knot complements on the framed torus boundaries.