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In this paper, we apply randomized algorithms to approximate the total least squares (TLS) solution of the problem $Ax\approx b$ in the large-scale discrete ill-posed problems. A regularization technique, based on the multiplicative…
This paper introduces a new formulation and solution framework for hub location problems. The formulation is based on 2-index aggregated flow variables and incorporates a set of aggregated demand constraints, which are novel in hub…
Logic-Based Benders Decomposition (LBBD) and its Branch-and-Cut variant, namely Branch-and-Check, enjoy an extensive applicability on a broad variety of problems, including scheduling. Although LBBD offers problem-specific cuts to impose…
A procedure resolving a torsion-free coherent sheaf on a nonsingular $N$-dimensional projective algebraic variety into a locally free sheaf on a projective scheme of certain class is proposed. This is a higher-dimensional analog of the…
In this work we propose a high-quality decomposition approach for qubit routing by swap insertion. This optimization problem arises in the context of compiling quantum algorithms onto specific quantum hardware. Our approach decomposes the…
We introduce low-stretch trees to the visualization community with LSQT, our novel technique that uses quasi-trees for both layout and edge bundling. Our method offers strong computational speed and complexity guarantees by leveraging the…
Kernel-free quadratic surface support vector machines (QSVM) have recently gained traction due to their flexibility in modeling nonlinear decision boundaries without relying on kernel functions. However, the introduction of a full quadratic…
This paper addresses the problem of decomposing a numerical semigroup into m-irreducible numerical semigroups. The problem originally stated in algebraic terms is translated, introducing the so called Kunz-coordinates, to resolve a series…
This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block…
Quadratic programming (QP) is a well-studied fundamental NP-hard optimization problem which optimizes a quadratic objective over a set of linear constraints. In this paper, we reformulate QPs as a mixed-integer linear problem (MILP). This…
Quantum Singular Value Transformation (QSVT) provides a unified framework for applying polynomial functions to the singular values of a block-encoded matrix. QSVT prepares a state proportional to $\bA^{-1}\bb$ with circuit depth…
Explaining generalizations and preventing over-confident predictions are central goals of studies on the loss landscape of neural networks. Flatness, defined as loss invariability on perturbations of a pre-trained solution, is widely…
Semidefinite programming (SDP) is a powerful tool for tackling a wide range of computationally hard problems such as clustering. Despite the high accuracy, semidefinite programs are often too slow in practice with poor scalability on large…
Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute…
Biclustering, also called co-clustering, block clustering, or two-way clustering, involves the simultaneous clustering of both the rows and columns of a data matrix into distinct groups, such that the rows and columns within a group display…
We present necessary and sufficient conditions for a group homomorphism between spaces of smooth sections of Lie group bundles to be a weighted composition operator. These results provide new insights into a wide range of problems related…
Neural network models are resource hungry. It is difficult to deploy such deep networks on devices with limited resources, like smart wearables, cellphones, drones, and autonomous vehicles. Low bit quantization such as binary and ternary…
We propose a method to fit arbitrarily accurate blendshape rig models by solving the inverse rig problem in realistic human face animation. The method considers blendshape models with different levels of added corrections and solves the…
In this paper we formulate and solve a robust least squares problem for a system of linear equations subject to quantization error in the data matrix. Ordinary least squares fails to consider uncertainty in the operator, modeling all noise…
We describe an efficient quantum algorithm for the quantum Schur transform. The Schur transform is an operation on a quantum computer that maps the standard computational basis to a basis composed of irreducible representations of the…