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We derive various inequalities involving the intersection number of the curves contained in geodesics and tight geodesics in the curve graph. While there already exist such inequalities on tight geodesics, our method applies in the setting…

We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…

In this paper we propose a technique that assigns obstacles to clusters used for collision avoidance via Mixed-Integer Programming. This strategy enables a reduction in the number of binary variables used for collision avoidance, thus…

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using…

We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve the square of the wavenumber…

It is generally hard to count, or even estimate, how many integer points lie in a polytope P. Barvinok and Hartigan have approached the problem by way of information theory, showing how to efficiently compute a random vector which samples…

In the first part of the paper we provide a survey of recent results concerning the problem of pointwise convergence of integral kernels in Feynman path integral, obtained by means of time-frequency analysis techniques. We then focus on…

Consider the problem of inverse scattering of time-harmonic point sources from an infinite, penetrable rough interface with bounded obstacles buried in the lower half-space, where the interface is assumed to be a local perturbation of a…

As superconducting quantum circuits scale to larger sizes, the problem of frequency crowding proves a formidable task. Here we present a solution for this problem in fixed-frequency qubit architectures. By systematically adjusting qubit…

We investigate an inverse problem in time-frequency localization: the approximation of the symbol of a time-frequency localization operator from partial spectral information by the method of accumulated spectrograms (the sum of the…

Solving inverse problems with iterative algorithms is popular, especially for large data. Due to time constraints, the number of possible iterations is usually limited, potentially affecting the achievable accuracy. Given an error one is…

We prove an epiperimetric inequality for the thin obstacle problem, extending the pioneering results by Weiss on the classical obstacle problem (Invent. Math. 138 (1999), no. 1, 23-50). This inequality provides the means to study the rate…

We consider the reconstruction of the shape and the impedance function of an obstacle from measurements of the scattered field at receivers outside the object. The data is assumed to be generated by plane waves impinging on the obstacle…

Suppose that a plane wave is incident onto an impenetrable grating profile of Dirichlet or Impedance type or a penetrable grating. The grating interface is assumed to be given by a Lipschitz function in two dimensions. We derive stability…

We study several natural instances of the geometric hitting set problem for input consisting of sets of line segments (and rays, lines) having a small number of distinct slopes. These problems model path monitoring (e.g., on road networks)…

The inverse acoustic scattering problems using multi-frequency backscattering far field patterns at isolated directions are studied. The underlying object could be point like scatterers, small scatterers, extended inhomogeneities and…

In this paper we characterize sharp time-data tradeoffs for optimization problems used for solving linear inverse problems. We focus on the minimization of a least-squares objective subject to a constraint defined as the sub-level set of a…

Consider a time-harmonic elastic point source incident on a bounded obstacle which is embedded in an open space filled with a homogeneous and isotropic elastic medium. This paper is concerned with the inverse problem of recovering the…

Thin current sheets in systems of large size that exceed a critical value of the Lundquist number are unstable to a super-Alfvenic tearing instability. The scaling of the growth rate of the fastest growing instability with respect to the…

We consider the variational inequality problem over the intersection of fixed point sets of firmly nonexpansive operators. In order to solve the problem, we present an algorithm and subsequently show the strong convergence of the generated…