arXiv research

Given a smooth nonfocal compact Riemannian manifold, we show that the so-called Ma--Trudinger--Wang condition implies the convexity of injectivity domains. This improves a previous result by Loeper and Villani.

Hybrid framework injects TSLM insights into GRLM for robust time-series reasoning.

GNIs induce a regulariser that penalizes high-frequency components in neural network activations.

Maximal spacetimes have unique past/future sets.

New cell structure on $O(3)/O(1)^3$ derived from injectivity radius computation.

New method eliminates domain size restrictions for X-ray transform inversion.

This paper shows how integrating domain knowledge improves ML models for transprecision computing.

TensorFI injects faults in TensorFlow programs to assess their reliability.

We give sharp conditions on a local biholomorphism $F:X \to \mathbb C^{n}$ which ensure global injectivity. For $n \geq 2$, such a map is injective if for each complex line $l \subset \mathbb C^{n}$, the pre-image $F^{-1}(l)$ embeds holomorphically as a connected domain into $\mathbb C \mathbb P^{1}$, the embedding bei…

Study big mapping class groups and their co-Hopfian property, finding new examples and proving injective homomorphisms results.

Given a hyperbolic domain, the nearest point retraction is a conformally natural homotopy equivalence from the domain to the boundary of the convex core of its complement. Marden and Markovic showed that if the domain is uniformly perfect, then there exists a conformally natural quasiconformal map which admits a bounde…

Noise Injection Node Regularization improves robustness in neural networks.

The paper constructs Morse homology for functionals involving the p-Laplacian in Banach spaces.

We prove that some symetric semi-riemannian manifolds do not admit a proper domain which is divisible by the action of a discrete group of isometries. In other words, if a closed semi-riemannian manifold is locally isometric to such a model, and if its developing map is injective, then the manifold is actually geodesic…

The paper bounds radii and curvatures in Riemannian manifolds.

The study proves nearly Frobenius algebras over certain domains are Frobenius.

Latent Noise Injection improves synthetic data generation for privacy and statistical alignment.

The Fridman function is bounded by the injectivity radius for certain hyperbolic manifolds.

We give a diameter bound for fundamental domains for isometric actions of the fundamental group of a closed hyperbolic surface on a delta-hyperbolic space, where the bound depends on the hyperbolicity constant delta, the genus of the surface, and the injectivity radius of the action, which we assume to be strictly posi…

In this paper, we consider infinite-dimensional port-Hamiltonian systems with in-domain actuation by means of an approach based on Stokes-Dirac structures as well as in a framework that exploits an underlying jet-bundle structure. In both frameworks, a dynamic controller based on the energy-Casimir method is derived in…

We study the boundary and lens rigidity problems on domains without assuming the convexity of the boundary. We show that such rigidities hold when the domain is a simply connected compact Riemannian surface without conjugate points. For the more general class of non-trapping compact Riemannian surfaces with no conjugat…

We study a recent general criterion for the injectivity of the conformal immersion of a Riemannian manifold into higher dimensional Euclidean space, and show how it gives rise to important conditions for Weierstrass-Ennerper lifts defined in the unit disk $\mathbb{D}$ endowed with a conformal metric. Among the corollar…

We give lower bounds for the first Dirichilet eigenvalues for domains in submanifolds with locally bounded mean curvatures. These bounds depend on the injectivity radius, sectional curvature (upperbound) of the ambient space and on the mean curvature of the submanifold. For submanifolds fo Hadamard manifolds these lowe…

The paper extends Huber's theorem to higher dimensions using n-Laplace equations.

Stability of non-abelian X-ray transform proven in higher dimensions.

Survey of integrating domain knowledge into DL models.

Spatial processes with nonstationary and anisotropic covariance structure are often used when modelling, analysing and predicting complex environmental phenomena. Such processes may often be expressed as ones that have stationary and isotropic covariance structure on a warped spatial domain. However, the warping functi…

The basic setup consists of a complex flag manifold $Z=G/Q$ where $G$ is a complex semisimple Lie group and $Q$ is a parabolic subgroup, an open orbit $D = G_0(z) \subset Z$ where $G_0$ is a real form of $G$, and a $G_0$--homogeneous holomorphic vector bundle $\mathbb E \to D$. The topic here is the double fibration tr…

This paper proposes a deep neural network approach for predicting multiphase flow in heterogeneous domains with high computational efficiency. The deep neural network model is able to handle permeability heterogeneity in high dimensional systems, and can learn the interplay of viscous, gravity, and capillary forces fro…

A statistical test of independence may be constructed using the Hilbert-Schmidt Independence Criterion (HSIC) as a test statistic. The HSIC is defined as the distance between the embedding of the joint distribution, and the embedding of the product of the marginals, in a Reproducing Kernel Hilbert Space (RKHS). It has …

Domain knowledge helps detect adversarial examples in multi-label classification.

Injectivity of ReLU networks is characterized for generative models and inverse problems.

Classifies $π_1$-injective maps between non-compact surfaces.

Positive injectivity radius for manifolds with Lie structure at infinity.

Geometric analysis improves noise injection in GANs.

This work draws inspiration from three important sources of research on dissimilarity-based clustering and intertwines those three threads into a consistent principled functorial theory of clustering. Those three are the overlapping clustering of Jardine and Sibson, the functorial approach of Carlsson and Mémoli to par…

The paper analyzes optimal dividend and capital injection strategies under time-inconsistent preferences.

A quasi-geodesic is Morse if and only if it is strongly contracting in injective spaces.

This paper connects noise injection to Bayesian inference for neural networks, improving model uncertainty.

Invariances to translation, rotation and other spatial transformations are a hallmark of the laws of motion, and have widespread use in the natural sciences to reduce the dimensionality of systems of equations. In supervised learning, such as in image classification tasks, rotation, translation and scale invariances ar…

Compact theorem for minimal surfaces with lower injectivity radius.

Lecture notes on group actions on injective spaces and Helly graphs.

Proves polynomial injectivity of Fubini-Study map for ample line bundles.

Lower bound on boundary injectivity radius for specific tubes.

Reservoir subspace injection improves online ICA by preserving injected features.

Injective and surjective neural operators for function spaces.

Proposes a method to enhance graph models by injecting unseen connections.

The paper proves that certain spaces are injective and Helly graphs.