Related papers: Sharp restriction estimates for some degenerate hi…

This paper presents an innovative approach to computational acoustic imaging of biperiodic surfaces, exploiting the capabilities of an acoustic superlens to overcome the diffraction limit. We address the challenge of imaging physical…

In this paper, a robust sequential quadratic programming method for constrained optimization is generalized to problem with an {expectation} objective function {and} deterministic equality and inequality constraints. A stochastic line…

This paper explores a new class of constrained difference programming problems, where the objective and constraints are formulated as differences of functions, without requiring their convexity. To investigate such problems, novel variants…

We establish a sharp geometric constant for the upper bound on the resonance counting function for surfaces with hyperbolic ends. An arbitrary metric is allowed within some compact core, and the ends may be of hyperbolic planar, funnel, or…

We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By…

We prove sharp local smoothing estimates for curve averages in all dimensions. As a corollary, we prove the sharp $L^p$ boundedness of the helical maximal operator in $\mathbb{R}^4$, which was previously known only for $\mathbb{R}^2$ and…

Weighted quadratic estimates are proved for certain bisectorial firstorder differential operators with bounded measurable coefficients which are (not necessarily pointwise) accretive, on complete manifolds with positive injectivity radius.…

A geometric setup for constrained variational calculus is presented. The analysis deals with the study of the extremals of an action functional defined on piecewise differentiable curves, subject to differentiable, non-holonomic…

We improve the $L^p(\mathbb{R}^n)$ bounds on Stein's square function to the best-known range of the Fourier restriction problem when $n\geq4$. Applications including certain local smoothing estimates are also discussed.

We establish an area formula for the spherical measure of intrinsic graphs of any codimension in homogeneous groups. Our approach relies on the assumption that the map defining the intrinsic graph is continuously intrinsically…

Given a real projective curve with homogeneous coordinate ring R and a nonnegative homogeneous element f in R, we bound the degree of a nonzero homogeneous sum-of-squares g in R such that the product fg is again a sum of squares. Better…

In this paper, we present a different proof on the discrete Fourier restriction. The proof recovers Bourgain's level set result on Strichartz estimates associated with Schr\"odinger equations on torus. Some sharp estimates on…

Marginal MAP inference involves making MAP predictions in systems defined with latent variables or missing information. It is significantly more difficult than pure marginalization and MAP tasks, for which a large class of efficient and…

We consider Kramers-Fokker-Planck operators with general degenerate coefficients. We prove semiclassical hypocoercivity estimates for a large class of such operators. Then, we manage to prove Eyring-Kramers formulas for the bottom of the…

We prove a variable coefficient version of the square function estimate of Guth--Wang--Zhang. By a classical argument of Mockenhaupt--Seeger--Sogge, it implies the full range of sharp local smoothing estimates for $2+1$ dimensional Fourier…

We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered…

We combine two recent ideas: cartesian differential categories, and restriction categories. The result is a new structure which axiomatizes the category of smooth maps defined on open subsets of $\R^n$ in a way that is completely algebraic.…

Following the ideas from a paper by the same author, we prove abstract maximal restriction results for the Fourier transform. Our results deal mainly with maximal operators of convolution-type and $r-$average maximal functions. As a…

This paper extends algorithms that remove the fixed point bias of decentralized gradient descent to solve the more general problem of distributed optimization over subspace constraints. Leveraging the integral quadratic constraint…

We consider a high-dimensional linear regression problem. Unlike many papers on the topic, we do not require sparsity of the regression coefficients; instead, our main structural assumption is a decay of eigenvalues of the covariance matrix…