arXiv research

Study examines the excluded area between two-dimensional hard particles, identifying key factors affecting its magnitude.

New tools for constructing fixed point sets in digital topology.

We consider embedded, smooth curves in the plane which are either closed or asymptotic to two lines. We study their behaviour under curve shortening flow with a global forcing term. Firstly, we prove an analogue to Huisken's distance comparison principle for curve shortening flow for initial curves whose local total cu…

We developed an automated deep learning system to detect hip fractures from frontal pelvic x-rays, an important and common radiological task. Our system was trained on a decade of clinical x-rays (~53,000 studies) and can be applied to clinical data, automatically excluding inappropriate and technically unsatisfactory …

In this paper we consider minors of ribbon graphs (or, equivalently, cellularly embedded graphs). The theory of minors of ribbon graphs differs from that of graphs in that contracting loops is necessary and doing this can create additional vertices and components. Thus the ribbon graph minor relation is incompatible wi…

We explore to what extent one may hope to preserve geometric properties of three dimensional manifolds with lower scalar curvature bounds under Gromov-Hausdorff and Intrinsic Flat limits. We introduce a new construction, called sewing, of three dimensional manifolds that preserves positive scalar curvature. We then use…

Graphs with bounded anisotropic mean curvature are regular almost everywhere.

We give a reduction from {\sc clique} to establish that sparse PCA is NP-hard. The reduction has a gap which we use to exclude an FPTAS for sparse PCA (unless P=NP). Under weaker complexity assumptions, we also exclude polynomial constant-factor approximation algorithms.

For the efficient execution of deep convolutional neural networks (CNN) on edge devices, various approaches have been presented which reduce the bit width of the network parameters down to 1 bit. Binarization of the first layer was always excluded, as it leads to a significant error increase. Here, we present the novel…

Deep learning model predicts severe COVID-19 outcomes.

Study embeddability of 2-complexes in 4-space, proving Heawood family's excluded minors.

The statistical analysis of discrete data has been the subject of extensive statistical research dating back to the work of Pearson. In this survey we review some recently developed methods for testing hypotheses about high-dimensional multinomials. Traditional tests like the $χ^2$ test and the likelihood ratio test ca…

New equations reveal how cylinder power in progressive lenses depends on geodesic curvature.

Fluctuation scaling is observed phenomenon from complex networks through finance to ecology. It means that the variance and the mean of a specific quantity are related as $\ev{σ^2|n}\propto \ev{n|A}^{2α}$ with $1/2\geq α\geq 1$ when a parameter $A$ (usually the system size) is varied. $A$ can be the strength of the nod…

Support vector machine (SVM) training is an active research area since the dawn of the method. In recent years there has been increasing interest in specialized solvers for the important case of linear models. The algorithm presented by Hsieh et al., probably best known under the name of the "liblinear" implementation,…

New method finds sparse groups of input variables for neural networks.

The study characterizes embeddable 2-complexes in 3-space.

This paper argues for decolonizing AI alignment by incorporating open-source Hinduism concepts.

We initiate the mathematical study of spherical collapse of self-gravitating charged scalar fields. The main result gives a complete characterization of the future boundary of spacetime, providing a starting point for studying the cosmic censorship conjectures. In general, the boundary includes two null components, one…

Community-based system dynamics improves ML fairness by involving excluded stakeholders.

Paper excludes the lowest energy level as an accumulation point for harmonic maps into analytic manifolds.

We characterise the embeddability of simply connected locally 3-connected 2-dimensional simplicial complexes in 3-space in a way analogous to Kuratowski's characterisation of graph planarity, by excluded minors. This answers questions of Lovász, Pardon and Wagner.

A method to detect spillover effects and select valid donors for synthetic control models.

Researchers prove a Willmore conjecture for surfaces with specific symmetries.

The strong symmetric genus of a finite group G is the smallest genus of a closed orientable topological surface on which G acts faithfully as a group of orientation preserving automorphisms. In this paper we complete the calculation of the strong symmetric genus for each finite Coxeter group excluding the group E8.

Constructs finite element spaces for $(p,q)$-forms, excluding one subspace.

Proves isometric correspondence of leaves for generic rolling distributions.

We investigate the bounded cohomology of Lefschetz fibrations. If a Lefschetz fibration has regular fiber of genus at least 2 and it has at least two distinct vanishing cycles, we show that its Euler class is not bounded. As a consequence, we exclude the existence of negatively curved metrics on Lefschetz fibrations wi…

Fine particulate matter (PM$_{2.5}$) is one of the criteria air pollutants regulated by the Environmental Protection Agency in the United States. There is strong evidence that ambient exposure to (PM$_{2.5}$) increases risk of mortality and hospitalization. Large scale epidemiological studies on the health effects of P…

Line graph transformation aids graph isomorphism tests by excluding challenging graph properties.

We prove an explicit and sharp upper bound for the Castelnuovo-Mumford regularity of an FI-module V in terms of the degrees of its generators and relations. We use this to refine a result of Putman on the stability of homology of congruence subgroups, extending his theorem to previously excluded small characteristics a…

We introduce a Bernstein-type inequality which serves to uniformly control quadratic forms of gaussian variables. The latter can for example be used to derive sharp model selection criteria for linear estimation in linear regression and linear inverse problems via penalization, and we do not exclude that its scope of a…

Study certifies missed relevant items in candidate generation with audit labels.

Partial soft-matching distance improves neural representation comparison by allowing some neurons to remain unmatched.

We give a general lower bound for the normal Gromov norm of genuine laminations in terms of the topology of the complementary regions. In the special case of 3-manifolds, this yields a generalization of Agol's inequality from incompressible surfaces to tight laminations. In particular, the inequality excludes the exist…

Graphs with fat minors have a limited large-scale structure.

Decoding strategies often exclude human-like tokens, creating a detectable gap in generated text.

The positive-unlabeled (PU) classification is a common scenario in real-world applications such as healthcare, text classification, and bioinformatics, in which we only observe a few samples labeled as "positive" together with a large volume of "unlabeled" samples that may contain both positive and negative samples. Bu…

Study on inventory management under uncertainty using smooth ambiguity preference.

Minimal surfaces found in 4D space.

I classify spacelike self-similar shrinking solutions of the mean curvature flow in pseudo-euclidean space in arbitrary codimension, if the mean curvature vector is not a null vector and the principal normal vector is parallel in the normal bundle. Moreover, I exclude the existence of such self-shrinkers in several cas…

Because of the prominent position of urban rail in reducing urban transport-related problems, such as congestion and air pollution, insights into the costs of possible new urban rail projects is very relevant for those involved with cost estimations, policy makers, cost-benefit analysts, and other target groups. Knowle…

Fast method estimates variable importance for large neural networks.

Strategic feature selection in high-stakes domains like healthcare.

The aim of this paper is to collect some facts about the blowup of Jang's equation. First, we discuss how to construct solutions that blow up at an outermost MOTS. Second, we exclude the possibility that there are extra blowup surfaces in data sets with non-positive mean curvature. Then we investigate the rate of conve…

Study no-arbitrage conditions in 1D diffusion markets with interest rates.

Optimized execution model using interbank and internal liquidity.

When assessing group solvency, an important question is to what extent intragroup transfers may be considered, as this determines to which extent diversification can be achieved. We suggest a framework to describe the families of admissible transfers that range from the free movement of capital to excluding any transac…