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Fully homomorphic encryption (FHE) has been among the most popular research topics of the last decade. While the bootstrapping-based, public key cryptosystems that follow Gentry's original design are getting more and more efficient, their performance is st ...
We study the problem of solving a linear sensing system when the observations are unlabeled. Specifically we seek a solution to a linear system of equations y = Ax when the order of the observations in the vector y is unknown. Focusing on the setting in wh ...
Institute of Electrical and Electronics Engineers2018
Consider the problem of minimizing a convex differentiable function on the probability simplex, spectrahedron, or set of quantum density matrices. We prove that the expo-nentiated gradient method with Armijo line search always converges to the optimum, if ...
We revisit the problem of constraining the weak field limit of the gravitational lagrangian from S-matrix properties. From unitarity and Lorentz invariance of the S-matrix of massless gravitons, we derive on-shell gauge invariance to consist on the transve ...
The isodiametric inequality states that the Euclidean ball maximizes the volume among all convex bodies of a given diameter. We are motivated by a conjecture of Makai Jr. on the reverse question: Every convex body has a linear image whose isodiametric quot ...
Extreme flood simulation with synthetic extreme precipitation events raises unavoidable questions about the choice of initial conditions. State-of-the-art extreme flood estimation frameworks propose to address these questions with the help of semicontinuou ...
A Quasi Toeplitz (QT) matrix is a semi-infinite matrix of the kind A=T(a)+E whereT(a)=(aj−i)i,j∈Z+, E=(ei,j)i,j∈Z+ is compact and the norms ∥a∥W=∑i∈Z∣a∣j and $|E|_{ ...
Based on the spectral divide-and-conquer algorithm by Nakatsukasa and Higham [SIAM J. Sci. Comput., 35(3):A1325{A1349, 2013], we propose a new algorithm for computing all the eigenvalues and eigenvectors of a symmetric banded matrix. For this purpose, we c ...
We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive definite matrices i ...