arXiv research

New research finds 145 infinite families of CS spheres are standard.

New Einstein metric found on non-standard solvmanifold.

We consider Killing vector fields on standard static space-times and obtain equations for a vector field on a standard static space-time to be Killing. We also provide a characterization of Killing vector fields on standard static space-times with compact Riemannian parts.

Standardizes surfaces in 3D handlebodies using Morse theory.

Regardless of the gold-standard being considered as outdated, it provides valuable signs concerning the development of novel monetary standards, better adjusted to the current macroeconomic environment. By using a point of view of classical physics, the intent of this work is doing a review of the concept of monetary s…

Study compact plane waves, showing they are essentially standard.

Standard trisection diagrams found for a specific type of knot.

The paper examines trisection diagrams of spun knots and shows they are standard for certain cases.

Study non-standard bi-orders on punctured torus bundles, matching standard ones in key subgroups.

The paper classifies compact homogeneous Finsler manifolds with positive flag curvature.

Algorithm converts plat to standard closure of braids in 3D and related spaces.

Adversarial training augments the training set with perturbations to improve the robust error (over worst-case perturbations), but it often leads to an increase in the standard error (on unperturbed test inputs). Previous explanations for this tradeoff rely on the assumption that no predictor in the hypothesis class ha…

Derives energy-momentum tensor from Standard Model, examines energy conditions.

Essentially, some conditions for the Riemannian factor and the warping function of a standard static space-time are obtained in order to guarantee that no nontrivial warping function on the Riemannian factor can make the standard static space-time Einstein.

This paper describes a method to construct standard 4-balls from homotopy 4-balls in $\mathbb{C}^2$.

Paper classifies pseudomanifolds over stratified spaces.

Interestingness measures provide information that can be used to prune or select association rules. A given value of an interestingness measure is often interpreted relative to the overall range of the values that the interestingness measure can take. However, properties of individual association rules restrict the val…

Ricci flow preserves standard sphere's curvature for certain conditions.

Study minimal networks on spheres and balls near standard metrics.

In this paper, we introduce the notion of standard homogeneous $(α_1,α_2)$-metrics, as a natural non-Riemannian deformation for the normal homogeneous Riemannian metrics. We prove that with respect to the given bi-invariant inner product and orthogonal decompositions for $\mathfrak{g}$, if there exists one generic stan…

A new method for CT using graph-based regularization.

This study proves new financial market theorems breaking standard risk definitions.

The Standard Model of elementary particles is a theory unifying three of the four basic forces of the Nature: electromagnetic, weak, and strong interactions. In this paper we consider the Standard Model in the presence of a classical (non-quantized) gravitation field and apply a bundle approach for describing it.

Automates standards design through machine learning.

Study proves existence of global solutions for Standard Model on expanding spacetimes.

We propose iSCMs to standardize SCM data, improving causal inference.

Paper shows adversarial training can be fooled by new type of noise.

Let $\F$ be a compact surface and let $I$ be the unit interval. This paper gives a standard form for all 2-sided incompressible surfaces in the 3-manifold $\F \times I$. Since $\F \times I$ is a handlebody when $\F$ has boundary, this standard form applies to incompressible surfaces in a handlebody.

Develops non-standard analysis for coherent risk estimation.

Standardizes Dunfield-Gong's 4-sphere, solves knot sliceness problem.

The paper studies geodesic orbit properties in Finsler spaces.

We study cosmetic contact surgeries along transverse knots in the standard contact 3-sphere, i.e. contact surgeries that yield again the standard contact 3-sphere. The main result is that we can exclude non-trivial cosmetic contact surgeries along all transverse knots not isotopic to the transverse unknot with self-lin…

Calegari's 4-spheres from fibered knots are proven standard.

The study explores deformations of standard locally homogeneous spaces.

Akbulut has recently shown that an infinite family of Cappell-Shaneson homotopy 4-spheres is diffeomorphic to the standard 4-sphere. In the present paper, a strictly larger family is shown to be standard by a simpler method. This new approach uses no Kirby calculus except through the relatively simple 1979 paper of Akb…

We prove that the classical set of moves for standard spines of 3-manifolds (i.e. the MP-move and the V-move) does not suffice to relate to each other any two standard skeleta of a 3-manifold with marked boundary. We also describe a condition on the 3-manifold with marked boundary that tells whether the generalised set…

Many unsupervised kernel methods rely on the estimation of the kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). Both kernel CO and kernel CCO are sensitive to contaminated data, even when bounded positive definite kernels are used. To the best of our knowledge, there are few well…

The standard Laplace operator is a generalization of the Hodge Laplace operator on differential forms to arbitrary geometric vector bundles, alternatively it can be seen as generalization of the Casimir operator acting on sections of homogeneous vector bundles over symmetric spaces to general Riemannian manifolds. Stre…

The standard interpretation of importance-weighted autoencoders is that they maximize a tighter lower bound on the marginal likelihood than the standard evidence lower bound. We give an alternate interpretation of this procedure: that it optimizes the standard variational lower bound, but using a more complex distribut…

The enumeration of normal surfaces is a crucial but very slow operation in algorithmic 3-manifold topology. At the heart of this operation is a polytope vertex enumeration in a high-dimensional space (standard coordinates). Tollefson's Q-theory speeds up this operation by using a much smaller space (quadrilateral coord…

Standard $S^4$ proved to be diffeomorphic to a curious homotopy sphere.

This paper addresses GE estimation in non-standard settings using various resampling methods.

Recent works on adversarial perturbations show that there is an inherent trade-off between standard test accuracy and adversarial accuracy. Specifically, they show that no classifier can simultaneously be robust to adversarial perturbations and achieve high standard test accuracy. However, this is contrary to the stand…

We discuss when and why custom multi-factor risk models are warranted and give source code for computing some risk factors. Pension/mutual funds do not require customization but standardization. However, using standardized risk models in quant trading with much shorter holding horizons is suboptimal: 1) longer horizon …

Division algorithm for surface group rings yields standard complexes and cohomological dimensions.

There are currently two parameterizations used to derive fixed kernels corresponding to infinite width neural networks, the NTK (Neural Tangent Kernel) parameterization and the naive standard parameterization. However, the extrapolation of both of these parameterizations to infinite width is problematic. The standard p…

Standardized fairness measures for continuous risk scores using Wasserstein distance.

Standard bubbles and partitions are stable in various model spaces.