arXiv research

Aims to find efficient neural architectures under resource constraints.

Predict genetic inheritance patterns using hypergraphs and latent models.

The study examines Ricci solitons and curvature inheritance on Robinson-Trautman spacetimes.

Maxwell fields inherit stationarity from stationary metrics.

Parallel unlearning framework for inherited models reduces computational overhead.

In a previous article, we defined a very flexible notion of suborbifold and characterized those suborbifolds which can arise as the images of orbifold embeddings. In particular, suborbifolds are images of orbifold embeddings precisely when they are saturated and split. This article addresses the problem of orbifold str…

Adversarial robustness improved by sparsity in network weights.

Invariant reduction preserves Poisson structures in PDEs.

Model projection transfers convolutional network properties to feedforward networks.

Curvature bounds preserved in length-minimizing disks.

Researchers infer gene activity in dividing cells, accounting for protein inheritance and division history.

This paper studies how key tensor properties are inherited in subtensors of tensor train decompositions.

Kähler manifold loop space inherits Kähler structure and is complete.

Proves limit of free boundary minimal hypersurfaces inherit non-trivial Jacobi fields.

A new framework decouples instance representation learning from subject-level supervision in EEG-based disease diagnosis.

The authors find a Kähler structure for a specific configuration space of points in $S^3$.

Let n>1 and G be the group SU(n) or Sp(n). This paper constructs compact symplectic manifolds whose symplectic quotient under a Hamiltonian G-action does not inherit the strong Lefschetz property.

A new method combines metrics for shape registration, inheriting advantages from both curve and surface approaches.

We prove that any compact Kähler manifold bearing a holomorphic Cartan geometry contains a rational curve just when the Cartan geometry is inherited from a holomorphic Cartan geometry on a lower dimensional compact Kähler manifold.

Endowed with quotient topology inherited from the space of based loops, the fundamental group of the Hawaiian earring fails to be metrizable. The fundamental group of any space which retracts to the Hawaiian earring is also nonmetrizable.

Study shows racial bias in health data, which can be reduced with simple techniques.

A technique called 'prior laundering' uses legacy reconstructions to create uncertainty in Bayesian inverse problems.

In this article, I prove that full subcomplexes of CAT(0) simplicial 3-complexes inherit the non positive curvature condition, and describe a family of counterexamples that prove this result can not be extended to higher dimensions.

Curvature of 2D subsets preserved in their space.

We construct helicoid-like embedded minimal disks with axes along self-similar curves modeled on logarithmic spirals. The surfaces have a self-similarity inherited from the curves and the nature of the construction. Moreover, inside of a "logarithmic cone", the surfaces are embedded.

The paper examines geometric properties of a unique spacetime model.

We show how the existing proof of the Farrell-Jones Conjecture for virtually poly-$\mathbb{Z}$-groups can be improved to rely only on the usual inheritance properties in combination with transfer reducibility as a sufficient criterion for the validity of the conjecture.

Study shows asphericity isn't inherited in certain arrangements.

Improved convergence speed of principal component analysis through modified learning rules.

An open subset U of a complex surface can be topologically perturbed to yield an open subset whose inherited complex structure is Stein, if and only if U is homeomorphic to the interior of a handlebody whose handles all have index equal or less than 2.

Neural networks improve cancer risk prediction from family history data.

New graph properties inherited by Frechet mean and median.

Theoretical study shows adversarial training improves robustness in deep learning models.

Label noise in adversarial training leads to robust overfitting, explained and mitigated.

We derive a local curvature estimate for four-dimensional stationary solutions to the inheriting Einstein-Maxwell-Klein-Gordon equations. In particular, it implies that any such stationary geodesically complete solution with vanishing Poynting vector and proper coupling constants (like dark energy) is flat. We also gen…

The first aim of the present paper is to compare various sub-Riemannian structures over the three dimensional sphere $S^3$ originating from different constructions. Namely, we describe the sub-Riemannian geometry of $S^3$ arising through its right Lie group action over itself, the one inherited from the natural complex…

Study shows certain surface homeomorphisms groups can't be precompact.

In this article we study Ammann tilings from the perspective of symplectic geometry. Ammann tilings are nonperiodic tilings that are related to quasicrystals with icosahedral symmetry. We associate to each Ammann tiling two explicitly constructed highly singular symplectic spaces and we show that they are diffeomorphic…

Given a closed, oriented surface M, the algebraic intersection of closed curves induces a symplectic form Int(.,.) on the first homology group of M. If M is equipped with a Riemannian metric g, the first homology group of M inherits a norm, called the stable norm. We study the norm of the bilinear form Int(.,.), with r…

We define Lie and Courant algebroids on Fréchet manifolds. Moreover, we construct a Dirac structure on the generalized tangent bundle of a Fréchet manifold and show that it inherits a Fréchet Lie algebroid structure. We show that the Lie algebroid cohomology of the $\bb$-cotangent bundle Lie algebroid of a weakly sympl…

Study on surface geometry in Lie groups with CR structures.

Link prediction is a fundamental task in statistical network analysis. Recent advances have been made on learning flexible nonparametric Bayesian latent feature models for link prediction. In this paper, we present a max-margin learning method for such nonparametric latent feature relational models. Our approach attemp…

Different approaches to defining dynamic market risk measures are available in the literature. Most are focused or derived from probability theory, economic behavior or dynamic programming. Here, we propose an approach to define and implement dynamic market risk measures based on recursion and state economy representat…

We show that if a smooth multiplicative subbundle $S\subseteq TG$ on a groupoid $G\rr P$ is involutive and satisfies completeness conditions, then its leaf space $G/S$ inherits a groupoid structure over the space of leaves of $TP\cap S$ in $P$. As an application, a special class of Dirac groupoids is shown to project b…

In homogenous space Sol we study compact surfaces with constant mean curvature and with non-empty boundary. We ask how the geometry of the boundary curve imposes restrictions over all possible configurations that the surface can adopt. We obtain a flux formula and we establish results that assert that, under some restr…

We prove that pseudo-holomorphic discs attached to a maximal totally real submanifold inherit their regularity from the regularity of the submanifold and of the almost complex structure. The proof is based on the computation of an explicit lower bound for the Kobayashi metric in almost complex manifolds, which also yie…

We study affine maps between affine manifolds. Even when the fibers are compact and diffeomorphic, two of them can inherit different affine structures from the source space. This leads to a fixed linear holonomy deformation theory of the affine structure of an affine manifold. We found various conditions which make the…

GPDNNs inherit robustness from GPs and DNNs, outputting high entropy for adversarial examples.