Related papers: Optimizing certain combinations of spectral and li…
In this paper, we study the properties of Connes spectral distances between quantum states under unitary transformations. We mainly focus on spectral triples with matrix algebras acting on finite dimensional Hilbert spaces via some linear…
We study an optimal transport problem with a backward martingale constraint in a pseudo-Euclidean space $S$. We show that the dual problem consists in the minimization of the expected values of the Fitzpatrick functions associated with…
We consider general (not necessarily Hamiltonian) first-order symmetric system $J y'-B(t)y=\D(t) f(t)$ on an interval $\cI=[a,b) $ with the regular endpoint $a$. A distribution matrix-valued function $\Si(s), \; s\in\bR,$ is called a…
The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT)…
This paper discusses the use of absolutely one-homogeneous regularization functionals in a variational, scale space, and inverse scale space setting to define a nonlinear spectral decomposition of input data. We present several theoretical…
We develop further the theory of symmetrization of fractional Laplacian operators contained in recent works of two of the authors. The theory leads to optimal estimates in the form of concentration comparison inequalities for both elliptic…
This paper proposes an intrinsic pseudospectral convexification framework for optimal control problems with manifold constraints. While successive pseudospectral convexification combines spectral collocation with successive convexification,…
The paper analyzes and compares some spectral filtering methods as truncated singular/eigen-value decompositions and Tikhonov/Re-blurring regularizations in the case of the recently proposed Reflective [M.K. Ng, R.H. Chan, and W.C. Tang, A…
The Unified Transform provides a novel method for analyzing boundary value problems for linear and for integrable nonlinear PDEs. The numerical implementation of this method to linear elliptic PDEs formulated in the {\it interior} of a…
In this paper, we study the decentralized optimization problem of minimizing a finite sum of continuously differentiable and possibly nonconvex functions over a fixed-connected undirected network. We propose a unified decentralized…
Controlling the spectral norm of the Jacobian matrix, which is related to the convolution operation, has been shown to improve generalization, training stability and robustness in CNNs. Existing methods for computing the norm either tend to…
We study a class of spectral design problems in which a prior positive semidefinite information matrix is updated by a sum of rank-one matrices constructed from chosen design vectors subject to a bound on their Euclidean norm. The objective…
Computationally efficient solutions for pseudometrics quantifying deviation from topological conjugacy between dynamical systems are presented. Deviation from conjugacy is quantified in a Pareto optimal sense that accounts for spectral…
We propose a Forward-Backward Truncated-Newton method (FBTN) for minimizing the sum of two convex functions, one of which smooth. Unlike other proximal Newton methods, our approach does not involve the employment of variable metrics, but is…
The paper introduces a new adaptive version of the Frank-Wolfe algorithm for relatively smooth convex functions. It is proposed to use the Bregman divergence other than half the square of the Euclidean norm in the formula for step-size.…
A novel method for distributed estimation of the frequency of power systems is introduced based on the cooperation between multiple measurement nodes. The proposed distributed widely linear complex Kalman filter (D-ACKF) and the distributed…
We analyze the compatibility of the hypothesis of third-family quark-lepton unification at the TeV scale with electroweak precision data, lepton flavor universality tests, and high-$p_T$ constraints. We work within the framework of the UV…
We develop a novel variant of the classical Frank-Wolfe algorithm, which we call spectral Frank-Wolfe, for convex optimization over a spectrahedron. The spectral Frank-Wolfe algorithm has a novel ingredient: it computes a few eigenvectors…
Measuring the similarity between data points often requires domain knowledge, which can in parts be compensated by relying on unsupervised methods such as latent-variable models, where similarity/distance is estimated in a more compact…
In the noncommutative geometry approach to the standard model we discuss the possibility to derive the extra scalar field sv- initially suggested by particle physicist to stabilize the electroweak vacuum - from a "grand algebra" that…