arXiv research

The paper improves conditions for unique recovery in homomorphic sensing of subspaces.

We derive precise transformation formulas for synthetic lower Ricci bounds under time change. More precisely, for local Dirichlet forms we study how the curvature-dimension condition in the sense of Bakry-Emery will transform under time change. Similarly, for metric measure spaces we study how the curvature-dimension c…

Improved compressed sensing using a generator that learns from measurements.

We present sufficient conditions for the cohomology of a closed aspherical manifold to be proper Lipschitz in sense of Connes-Gromov-Moscovici [CGM]. The conditions are stated in terms of the Stone-Čech compactification of the universal cover of a manifold. We show that these conditions are formally weaker than the suf…

Improved convergence for overparameterized low-rank matrix sensing.

Study shows tori metrics converging to flat under specific conditions.

We present an information-theoretic framework for sequential adaptive compressed sensing, Info-Greedy Sensing, where measurements are chosen to maximize the extracted information conditioned on the previous measurements. We show that the widely used bisection approach is Info-Greedy for a family of $k$-sparse signals b…

The present paper deals with the study of pseudo parallel (in the sense of Chaki and in the sense of Deszcz) contact CR-submanifolds with respect to Levi-Civita connection as well as semisymmetric metric connection of Kenmotsu manifolds and prove that these corresponding two classes are equivalent with a certain condit…

Study of Dirac-Witten operator on Lorentzian manifolds under dominant energy condition.

The problem of replicating the flexibility of human common-sense reasoning has captured the imagination of computer scientists since the early days of Alan Turing's foundational work on computation and the philosophy of artificial intelligence. In the intervening years, the idea of cognition as computation has emerged …

Study surfaces with nonnegative curvature in spectral sense, proving inequalities and bounds.

Improved subgradient method tackles ill-conditioned composite optimization problems.

In this paper we describe the notion of a weak lipschitzianity of a mapping on a $C^{q}$ stratification. We also distinguish a class of regularity conditions that are in some sense invariant under definable, locally Lipschitz and weakly bi-Lipschitz homeomorphisms. This class includes the Whitney (B) condition and the …

Ricci flow solves curvature-bound initial spaces to smooth manifolds.

Along a Ricci flow solution on a closed manifold, we show that if Ricci curvature is uniformly bounded from below, then a scalar curvature integral bound is enough to extend flow. Moreover, this integral bound condition is optimal in some sense.

In this paper, we study the problem of compressed sensing using binary measurement matrices and $\ell_1$-norm minimization (basis pursuit) as the recovery algorithm. We derive new upper and lower bounds on the number of measurements to achieve robust sparse recovery with binary matrices. We establish sufficient conditi…

AdaBoost improves binary classification in robust one-bit compressed sensing with adversarial errors.

This paper establishes information-theoretic limits in estimating a finite field low-rank matrix given random linear measurements of it. These linear measurements are obtained by taking inner products of the low-rank matrix with random sensing matrices. Necessary and sufficient conditions on the number of measurements …

Video analytics requires operating with large amounts of data. Compressive sensing allows to reduce the number of measurements required to represent the video using the prior knowledge of sparsity of the original signal, but it imposes certain conditions on the design matrix. The Bayesian compressive sensing approach r…

Extends phase retrieval methods to handle sensing vector errors.

In this paper we present two new approaches to efficiently solve large-scale compressed sensing problems. These two ideas are independent of each other and can therefore be used either separately or together. We consider all possibilities. For the first approach, we note that the zero vector can be taken as the initial…

Let M be a smooth compact manifold without boundary. We consider two smooth Sub-Semi-Riemannian metrics on M. Under suitable conditions, we show that they are almost conformally isometric in an Lp sense. Assume also that M carries a Riemannian metric with parallel Ricci curvature. Then an equation of Ricci type, is in …

Study shows Fredholmness of a Lorentzian Dirac operator on spacetimes.

Paper uses SGLD to recover signals from generative models, proving convergence under mild conditions.

We prove that a class of asymptotically nonnegatively curved manifolds (in the sense of Abresch) satisfying some uniform Euclidean type volume growth conditions contains only finitely many homeomorphism types.

We prove that the "generic condition" used in singularity theorems of general relativity is generic in the space of Lorentzian metrics on a given manifold, in the sense that it is satisfied for all metrics in a residual set in the Whitney $C^k$-topology, for $k$ depending on the dimension of the manifold.

We study the value of information in sequential compressed sensing by characterizing the performance of sequential information guided sensing in practical scenarios when information is inaccurate. In particular, we assume the signal distribution is parameterized through Gaussian or Gaussian mixtures with estimated mean…

Given a complex of groups over a finite simplicial complex in the sense of Haefliger, we give conditions under which it is possible to build an EZ-structure in the sense of Farrell-Lafont for its fundamental group out of such structures for its local groups. As an application, we prove a combination theorem that yields…

The study establishes a curvature-dimension condition for discrete Markov chains.

New method uses generative priors for compressive sensing with sparse solutions.

Faster reconstruction of compressed signals using conditional GAN and NPGD.

ARHT algorithm improves sparsity guarantees in convex optimization.

A-DLISTA and VLISTA learn dictionaries and sparse representations under varying sensing matrices.

We investigate the integral conditions to extend the mean curvature flow in a Riemannian manifold. We prove that the mean curvature flow solution with finite total mean curvature on a finite time interval $[0,T)$ can be extended over time $T$. Moreover, we show that the condition is optimal in some sense.

Local Kan conditions enable differentiation of simplicial manifolds.

Stability conditions on K3 surfaces are linked to the masses of spherical objects.

We present an introduction to boundary value problems for Dirac-type operators on complete Riemannian manifolds with compact boundary. We introduce a very general class of boundary conditions which contains local elliptic boundary conditions in the sense of Lopatinskij and Shapiro as well as the Atiyah-Patodi-Singer bo…

Study shows MDA's effectiveness even when more components are assumed than in actual data.

In this paper we prove necessary and sufficient conditions for the Kobayashi metric on a convex domain to be Gromov hyperbolic. In particular we show that for convex domains with $C^\infty$ boundary being of finite type in the sense of D'Angelo is equivalent to the Gromov hyperbolicity of the Kobayashi metric. We also …

We prove Gray--Moser stability theorems for complementary pairs of forms of constant class defining symplectic pairs, contact-symplectic pairs and contact pairs. We also consider the case of contact-symplectic and contact-contact structures, in which the constant class condition on a one-form is replaced by the conditi…

Investigates conditions for non-rigidity in extremal metrics involving scalar curvature.

Study improves distributed linear estimation under adversarial conditions.

Paper tackles 1-bit compressed sensing, presenting efficient algorithm for sparse signal estimation.

We define an abstract notion of double Lie algebroid, which includes as particular cases: (1) the double Lie algebroid of a double Lie groupoid in the sense of the author, such as the iterated tangent bundle of an ordinary manifold, and various iterated tangent/cotangent constructions in symplectic and Poisson geometry…

State-space systems generate probabilistic dependencies between inputs and outputs.

We extend the well-known result that any $f \in W^{1,n}(Ω,\mathbb{R}^n)$, $Ω\subset \mathbb{R}^n$ with strictly positive Jacobian is actually continuous: it is also true for fractional Sobolev spaces $W^{s,\frac{n}{s}}(Ω)$ for any $s \geq \frac{n}{n+1}$, where the sign condition on the Jacobian is understood in a distr…

Recall that Federer-Fleming defined the notion of flat convergence of submanifolds of Euclidean space to solve the Plateau problem. Here we prove the upper semicontinuity of Neumann eigenvalues of the submanifolds when they converge in the flat sense without losing volume. With an additional condition on the boundaries…

In this paper, we study a special type of compact Hermitian manifolds that are Strominger Kähler-like, or SKL for short. This condition means that the Strominger connection (also known as Bismut connection) is Kähler-like, in the sense that its curvature tensor obeys all the symmetries of the curvature of a Kähler mani…