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A new method is described that permits quickly and easily, a 2-dimensional search for TeV gamma-ray sources over large fields of view ~6deg with instruments utilising the imaging atmospheric Cerenkov technique. It employs as a background…
We describe a set of novel methods for efficiently sampling high-dimensional parameter spaces of physical theories defined at high energies, but constrained by experimental measurements made at lower energies. Often, theoretical models such…
A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
All parallel algorithms for directed reachability and shortest paths crucially rely on efficient shortcut constructions. These constructions find directed paths and shortcut them by adding edges, with the goal to reduce the diameter of the…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
Optimal Experiment Design for parameter estimation in water networks has been traditionally formulated to maximize either hydraulic model accuracy or spatial coverage. Because a unique sensor configuration that optimizes both objectives may…
The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…
We derive a procedure for computing an upper bound on the number of equiangular lines in various Euclidean vector spaces by generalizing the classical pillar decomposition developed by (Lemmens and Seidel, 1973); namely, we use linear…
This work proposes a method for model reduction of finite-volume models that guarantees the resulting reduced-order model is conservative, thereby preserving the structure intrinsic to finite-volume discretizations. The proposed…
State-of-the-art methods in convex and non-convex optimization employ higher-order derivative information, either implicitly or explicitly. We explore the limitations of higher-order optimization and prove that even for convex optimization,…
The total least squares problem with the general Tikhonov regularization can be reformulated as a one-dimensional parametric minimization problem (PM), where each parameterized function evaluation corresponds to solving an n-dimensional…
In this paper, we focus on developing randomized algorithms for the computation of low multilinear rank approximations of tensors based on the random projection and the singular value decomposition. Following the theory of the singular…
Projective Norms are a class of tensor norms that map on the input and output spaces. These norms are useful for providing a measure of entanglement. Calculating the projective norms is an NP-hard problem, which creates challenges in…
We introduce a new criterion which tests if a given decomposition of a given ternary form $T$ of even degree is unique. The criterion is based on the analysis of the Hilbert function of the projective set of points $Z$ associated to the…
A complete reduction on a difference field is a linear operator that enables one to decompose an element of the field as the sum of a summable part and a remainder such that the given element is summable if and only if the remainder is…
Higher-order tensor methods were recently proposed for minimizing smooth convex and nonconvex functions. Higher-order algorithms accelerate the convergence of the classical first-order methods thanks to the higher-order derivatives used in…
We derive new estimates for distances between optimal matchings of eigenvalues of non-normal matrices in terms of the norm of their difference. We introduce and estimate a hyperbolic metric analogue of the classical spectral-variation…
Given an edge-weighted graph, how many minimum $k$-cuts can it have? This is a fundamental question in the intersection of algorithms, extremal combinatorics, and graph theory. It is particularly interesting in that the best known bounds…
Projection-based Reduced Order Models minimize the discrete residual of a "full order model" (FOM) while constraining the unknowns to a reduced dimension space. For problems with symmetric positive definite (SPD) Jacobians, this is…