We propose a novel communication design, termed random orthogonalization , for federated learning (FL) in massive multiple-input and multiple-output (MIMO) wireless system. The key novelty of random orthogonalization comes from the tight coupling FL two unique characteristics MIMO - channel har...

‎‎for any group $g$‎, ‎we define an equivalence relation $thicksim$ as below‎: ‎[forall g‎, ‎h in g gthicksim h longleftrightarrow |g|=|h|]‎ ‎the set of sizes of equivalence classes with respect to this relation is called the same-order type of $g$ and denote by $alpha{(g)}$‎. ‎in this paper‎, ‎we give a partial answer to a conjecture raised by shen‎. ‎in fact‎, ‎we show that if $g$ is a nilpot...

We present an Out-of-Core Filter-Diagonalization method which can be used to solve very large electronic structure problems within the framework of the one-electron pseudopotentialbased methods. The approach is based on the following three steps: First, nonorthogonal states in a desired energy range are generated using the filter-diagonalization method. Next, these states are orthogonalized usi...

We present in detail the recently derived ab initio molecular dynamics (AIMD) formalism [Alonso et al. Phys. Rev. Lett. 2008, 101, 096403], which due to its numerical properties, is ideal for simulating the dynamics of systems containing thousands of atoms. A major drawback of traditional AIMD methods is the necessity to enforce the orthogonalization of the wave functions, which can become the ...

We propose a new uniform framework of Compact Rational Krylov (CORK) methods for solving large-scale nonlinear eigenvalue problems: A(λ)x = 0. For many years, linearizations are used for solving polynomial and rational eigenvalue problems. On the other hand, for the general nonlinear case, A(λ) can first be approximated by a (rational) matrix polynomial and then a convenient linearization is us...

We find a canonical form for pure states of a general multipartite system, in which the constraints on the coordinates (with respect to a factorisable orthonormal basis) are simply that certain ones vanish and certain others are real. For identical particles they are invariant under permutations of the particles. As an application, we find the dimension of the generic local equivalence class.

two symmetric matrices, where one matrix has a restricted rank. A comparison of the two cases reveals a remarkable similarity between Eckhart-Young theorem and Ky Fan’s maximum principle. The extremum principles of Ky Fan consider sums and products of eigenvalues of Hermitian matrices. The third part of the talk derives extended rules for rectangular matrices. In this case singular values take ...

We consider the problem of constructing an optimal set of orthogonal vectors from a given set of vectors in a real Hilbert space. The vectors are chosen to minimize the sum of the squared norms of the errors between the constructed vectors and the given vectors. We show that the design of the optimal vectors, referred to as the least-squares (LS) orthogonal vectors, can be formulated as a semid...