Related papers: Matrix Ordering through Spectral and Nilpotent Str…
We generalize classical results in spectral graph theory and linear algebra more broadly, from the case where the underlying matrix is Hermitian to the case where it is non-Hermitian. New admissibility conditions are introduced to replace…
Spectral measures arise in numerous applications such as quantum mechanics, signal processing, resonances, and fluid stability. Similarly, spectral decompositions (pure point, absolutely continuous and singular continuous) often…
This article introduces several new relations among related Hilbert space operators. In particular, we prove some L\"{o}ewner partial orderings among $T, |T|, \mathcal{R}T, \mathcal{I}T, |T|+|T^*|$ and many other related forms, as a new…
Learning maps between function spaces with a strong inductive bias is a central challenge in soft computing, especially when training data are scarce and standard deep architectures overfit. We introduce a \emph{neural integral operator}…
We develop a spectral framework for fermion mass hierarchies based on the exceptional Jordan algebra $J_3(\mathbb{O}_{\mathbb{C}})$. Starting from the octonionic realization of one Standard Model generation in $\mathbb{C}\otimes\mathbb{O}$,…
One of the major open questions in particle physics is the issue of the neutrino mass ordering (NMO). The current data of the two long-baseline experiments NO$\nu$A and T2K, interpreted in the standard 3-flavor scenario, provide a…
In this paper, the concept of generalized spectral function is introduced for finite-order tridiagonal symmetric matrices (Jacobi matrices) with complex entries. The structure of the generalized spectral function is described in terms of…
A `whole-part' theory is developed for a set of finite quantum systems $\Sigma (n)$ with variables in ${\mathbb Z}(n)$. The partial order `subsystem' is defined, by embedding various attributes of the system $\Sigma (m)$ (quantum states,…
Distributed systems, such as biological and artificial neural networks, process information via complex interactions engaging multiple subsystems, resulting in high-order patterns with distinct properties across scales. Investigating how…
This paper considers the matrix completion problem. We show that it is not necessary to assume joint incoherence, which is a standard but unintuitive and restrictive condition that is imposed by previous studies. This leads to a sample…
We introduce the new concepts of pseu\-do numerical range for operator functions and families of sesquilinear forms as well as the pseu\-do block numerical range for $n \times n$ operator matrix functions. While these notions are new even…
This paper is devoted to the study of general (Laurent) polynomial modifications of moment functionals on the unit circle, i.e., associated with hermitian Toeplitz matrices. We present a new approach which allows us to study polynomial…
In this paper, we propose Neumann Series Neural Operator (NSNO) to learn the solution operator of Helmholtz equation from inhomogeneity coefficients and source terms to solutions. Helmholtz equation is a crucial partial differential…
By learning the mappings between infinite function spaces using carefully designed neural networks, the operator learning methodology has exhibited significantly more efficiency than traditional methods in solving complex problems such as…
Motivated by potential theory on discrete spaces, we study a family of unbounded Hermitian operators in Hilbert space which generalize the usual graph-theoretic discrete Laplacian. These operators are discrete analogues of the classical…
The numerical construction of polynomials in the product representation (as used for instance in variants of the multiboson technique) can become problematic if rounding errors induce an imprecise or even unstable evaluation of the…
Recent advancements in the synthesis of anisotropic macromolecules and nanoparticles have spurred an immense interest in theoretical and computational studies of self-assembly. The cornerstone of such studies is the role of shape in…
We construct a functional model for rank one perturbations of compact normal operators acting in a certain Hilbert spaces of entire functions generalizing de Branges spaces. Using this model we study completeness and spectral synthesis…
Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However,…
Matrix functions are utilized to rewrite smooth spectral constrained matrix optimization problems as smooth unconstrained problems over the set of symmetric matrices which are then solved via the cubic-regularized Newton method. A…