Related papers: State-space approach to zero-modules of proper tra…
Transfer learning seeks to improve the generalization performance of a target task by exploiting the knowledge learned from a related source task. Central questions include deciding what information one should transfer and when transfer can…
As we have shown several years ago [Y2], zeros of $L(s, \Delta )$ and $L^(2)(s, \Delta )$ can be calculated quite efficiently by a certain experimental method. Here $\Delta$ denotes the cusp form of weight 12 with respect to SL$(2, Z)$ and…
The classical Maximum Power Transfer theorem of linear electrical network theory is generalized to the setting of a nonlinear state space system connected to a source. This yields a state space version of the input-output operator results…
This paper introduces a comprehensive formalism for decomposing the state space of a quantum field into several entangled subobjects, i.e., fields generating a subspace of states. Projecting some of the subobjects onto degenerate background…
We establish center manifold theorems that allow one to study the bifurcation of small solutions from a trivial state in systems of functional equations posed on the real line. The class of equations includes most importantly nonlinear…
This paper describes algorithms for the exact symbolic computation of period integrals on moduli spaces $\mathcal{M}_{0,n}$ of curves of genus $0$ with $n$ ordered marked points, and applications to the computation of Feynman integrals.
We explore the physics of two-body decay of BPS states using semiclassical analysis to construct explicit solutions that illustrate the main features of wall crossing, for both ordinary and framed BPS states. In particular we recover the…
We study the collapse transition of the lattice homopolymer on a square lattice by calculating the exact partition function zeros. The exact partition function is obtained by enumerating the number of possible conformations for each energy…
Given a measure space and a totally ordered ordered collection of measurable sets, called an ordered core, the notion of a core decreasing function is introduced and used to define the down space of a Banach function space. This is done…
We describe a general framework of functional and Fourier analysis on domains with a free action of an Abelian Lie group $G$. Namely, on a domain of the form $G\times Y$ we introduce the appropriate spaces of distributions and measurable…
The transfer of quantum states has played an important role in quantum information processing. In fact, transfer of quantum states from point $A$ to $B$ with unit fidelity is very important for us and we focus on this case. In recent years,…
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…
This paper addresses problems in functional metric geometry that arise in the study of data such as signals recorded on geometric domains or on the nodes of weighted networks. Datasets comprising such objects arise in many domains of…
Positive real odd matrix functions, often referred to as positive real lossless matrix functions, play an important role in many applications in multi-port electrical systems. In this paper we present closer analogues to some of the known…
We research the location of the zeros of the Eisenstein series and the modular functions from the Hecke type Faber polynomials associated with the normalizers of congruence subgroups which are of genus zero and of level at most twelve. In…
One of the key issues in the analysis of machine learning models is to identify the appropriate function space and norm for the model. This is the set of functions endowed with a quantity which can control the approximation and estimation…
An explicit C++ library is provided which deals with Zernike Functions over the unit circle as the main subject. The implementation includes basic means to evaluate the functions at points inside the unit circle and to convert the radial…
We study the quantum channel version of Shannon's zero-error capacity problem. Motivated by recent progress on this question, we propose to consider a certain operator space as the quantum generalisation of the adjacency matrix, in terms of…
On the basis of the transfer matrix technique an analytical method to investigate the stationary states, for an electron in one-dimensional periodic structures in an external electrical field, displaying the symmetry of the problem is…
This paper begins the study of infinite-dimensional modules defined on bicomplex numbers. It generalizes a number of results obtained with finite-dimensional bicomplex modules. The central concept introduced is the one of a bicomplex…