arXiv research

InSphereNet uses infilling spheres for 3D object classification, improving accuracy with fewer parameters.

Derives new orthogonal coordinates for evolving surfaces and curves.

A new algorithm solves signed Fréchet regression on manifolds with bounded curvature.

Novel neural network approximates exact distance for robust classification.

SLIM model predicts social network polarization using signed links.

We extend the topological field theory (``itsy bitsy topological field theory"') of our previous work from mod-2 to twisted coefficients. This topological field theory is derived from sutured Floer homology but described purely in terms of surfaces with signed points on their boundary (occupied surfaces) and curves on …

Lowered regularity assumption for a phase-dependent Helfrich energy equation.

Signed seminorms linked to real tropical spaces and matroids.

New simulation method tackles sign problem in quantum fields.

Paper extends MLFD to signed measures via bilevel approach.

Refines d'Alembertian for signed Lorentz distance functions in metric measure spacetimes.

A formula that relates triple points, branch points, and their distances from infinity is presented. We recover trivial normal Euler classes for oriented surfaces, and formulas on signed triple points.

The paper bounds solutions to complex optimization problems with uncertain data.

Let $F: [0, \infty) \to [0, \infty)$ be a strictly increasing $C^2$ function with $F(0)=0$. We unify the concepts of $F$-harmonic maps, minimal hypersurfaces, maximal spacelike hypersurfaces, and Yang-Mills Fields, and introduce $F$-Yang-Mills fields, $F$-degree, $F$-lower degree, and generalized Yang-Mills-Born-Infeld…

Differentiable pipeline replaces non-differentiable CAE components for shape optimization.

The paper proves the existence of infinite sign-changing solutions to a Hardy-Sobolev equation on Riemannian manifolds.

DKMD is a fast signed statistic for comparing univariate distributions.

Learning a distance function or metric on a given data manifold is of great importance in machine learning and pattern recognition. Many of the previous works first embed the manifold to Euclidean space and then learn the distance function. However, such a scheme might not faithfully preserve the distance function if t…

Derives curvature conditions for spatial isotropy without field equations.

A projective parameter of a geodesic on a Finsler space is defined to be solution of a certain ODE. Using projective parameter and Funk metric, one can construct a projectively invariant intrinsic pseudo-distance on a Finsler space. In the present work, solutions of the projective parameter's ODE are characterized with…

In this paper, we propose a game theoretical adversarial intervention detection mechanism for reliable smart road signs. A future trend in intelligent transportation systems is ``smart road signs" that incorporate smart codes (e.g., visible at infrared) on their surface to provide more detailed information to smart veh…

The Pearson distance between a pair of random variables $X,Y$ with correlation $ρ_{xy}$, namely, 1-$ρ_{xy}$, has gained widespread use, particularly for clustering, in areas such as gene expression analysis, brain imaging and cyber security. In all these applications it is implicitly assumed/required that the distance …

Semantic Embeddings are a popular way to represent knowledge in the field of zero-shot learning. We observe their interpretability and discuss their potential utility in a safety-critical context. Concretely, we propose to use them to add introspection and error detection capabilities to neural network classifiers. Fir…

New neural architectures invariant to sign flips and basis symmetries for graph representation learning.

For a domain $Ω\subset\mathbb R^n$, we introduce the concept of a uniformly $C^m$ defining function. We characterize uniformly $C^m$ defining functions in terms of the signed distance function for the boundary and provide a large class of examples of unbounded domains with uniformly $C^m$ defining functions. Some of ou…

We consider a neural network architecture with randomized features, a sign-splitter, followed by rectified linear units (ReLU). We prove that our architecture exhibits robustness to the input perturbation: the output feature of the neural network exhibits a Lipschitz continuity in terms of the input perturbation. We fu…

We show that for a simple surface with boundary the attenuated ray transform in the presence of a unitary connection and a skew-Hermitian Higgs field is injective modulo the natural obstruction for functions and vector fields. We also show that the connection and the Higgs field are uniquely determined by the scatterin…

The paper examines convergence of distances in Lipschitz structures on manifolds.

Paper introduces length measures for curves and convex shapes, proving isoperimetric and distance properties.

Study on function sensitivity in random DNNs using large deviation theory.

Paper connects surface shape analysis and unbalanced optimal transport.

For any compact oriented manifold $M$, we show that that the top degree multi-vector fields transverse to the zero section of $\wedge^{\text{top}}TM$ are classified, up to orientation preserving diffeomorphism, in terms of the topology of the arrangement of its zero locus and a finite number of numerical invariants. Th…

Consider a random vector with finite second moments. If its precision matrix is an M-matrix, then all partial correlations are non-negative. If that random vector is additionally Gaussian, the corresponding Markov random field (GMRF) is called attractive. We study estimation of M-matrices taking the role of inverse sec…

The paper proves a Basmajian identity for non-Archimedean local fields.

Study projective symmetries in Finsler spaces, showing reductions and constant flag curvature.

Study uses Wasserstein distance to identify causal orders and unmix sources.

The paper explores generalized quasi-Einstein manifolds and their properties.

Hypothesis tests are a crucial statistical tool for data mining and are the workhorse of scientific research in many fields. Here we present a differentially private analogue of the classic Wilcoxon signed-rank hypothesis test, which is used when comparing sets of paired (e.g., before-and-after) data values. We present…

Spider GAN accelerates GAN training with a new approach.

This work proposes a model for geodesic distances and flows on manifolds.

New theory connects string theory to swampland distance conjecture.

The liquid shape between two vertical parallel plates in a gravity field due to capillary forces is studied. When the physical system achieves its mechanical equilibrium, the capillary surface has mean curvature proportional to its height above a horizontal reference plane and it meets the vertical walls in a prescribe…

We consider the signed density of the extremal points of (two-dimensional) scalar fields with a Gaussian distribution. We assign a positive unit charge to the maxima and minima of the function and a negative one to its saddles. At first, we compute the average density for a field in half-space with Dirichlet boundary c…

We prove an existence theorem for positive solutions to Lichnerowicz-type equations on complete manifolds with boundary and nonlinear Neumann conditions. This kind of nonlinear problems arise quite naturally in the study of solutions for the Einstein-scalar field equations of General Relativity in the framework of the …

We present a string inspired 3D Euclidean field theory as the starting point for a modified Ricci flow analysis of the Thurston conjecture. In addition to the metric, the theory contains a dilaton, an antisymmetric tensor field and a Maxwell-Chern Simons field. For constant dilaton, the theory appears to obey a Birkhof…

A new metric learning framework for signed graphs using Gershgorin disc alignment.

We use a Riemannnian approximation scheme to define a notion of $\textit{sub-Riemannian Gaussian curvature}$ for a Euclidean $C^{2}$-smooth surface in the Heisenberg group $\mathbb{H}$ away from characteristic points, and a notion of $\textit{sub-Riemannian signed geodesic curvature}$ for Euclidean $C^{2}$-smooth curve…

Revisits shallow neural networks using Lipschitz norms and measures.