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Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
The notion of quasi boundary triples and their Weyl functions from extension theory of symmetric operators is extended to the general framework of adjoint pairs of operators under minimal conditions on the boundary maps. With the help of…
We introduce a new model for investigating spectral properties of quantum graphs, a quantum circulant graph. Circulant graphs are the Cayley graphs of cyclic groups. Quantum circulant graphs with standard vertex conditions maintain…
An essential feature of genuine quantum correlation is the simultaneous existence of correlation in complementary bases. We reveal this feature of quantum correlation by defining measures based on invariance under a basis change. For a…
The theory of quasirandomness has greatly expanded from its inaugural graph theoretical setting to several different combinatorial objects such as hypergraphs, tournaments, permutations, etc. However, these quasirandomness variants have…
We analyze qubit channels by exploiting the possibility of representing two-level quantum systems in terms of characteristic functions. To do so, we use functions of non-commuting variables (Grassmann variables), defined in terms of…
In the present paper, several properties concerning generalized derivatives of multifunctions implicitly defined by set-valued inclusions are studied by techniques of variational analysis. Set-valued inclusions are problems formalizing the…
An important facet of the inverse eigenvalue problem for graphs is to determine the minimum number of distinct eigenvalues of a particular graph. We resolve this question for the join of a connected graph with a path. We then focus on…
Generalization is an important feature of neural network, and there have been many studies on it. Recently, with the development of quantum compu-ting, it brings new opportunities. In this paper, we studied a class of quantum neural network…
We discuss Neumann problems for self-adjoint Laplacians on (possibly infinite) graphs. Under the assumption that the heat semigroup is ultracontractive we discuss the unique solvability for non-empty subgraphs with respect to the vertex…
We define several new types of quantum chromatic numbers of a graph and characterise them in terms of operator system tensor products. We establish inequalities between these chromatic numbers and other parameters of graphs studied in the…
We study a combinatorial model of the quantum scalar field with polynomial potential on a graph. In the first quantization formalism, the value of a Feynman graph is given by a sum over maps from the Feynman graph to the spacetime graph…
In this article we construct zeta functions of quantum graphs using a contour integral technique based on the argument principle. We start by considering the special case of the star graph with Neumann matching conditions at the center of…
Given a digraph D, the complementarity spectrum of the digraph is defined as the set of complementarity eigenvalues of its adjacency matrix. This complementarity spectrum has been shown to be useful in several fields, particularly in…
In this letter, we give a characterization for a generic construction of bent functions. This characterization enables us to obtain another efficient construction of bent functions and to give a positive answer on a problem of bent…
The form factor of a quantum graph is a function measuring correlations within the spectrum of the graph. It can be expressed as a double sum over the periodic orbits on the graph. We propose a scheme which allows one to evaluate the…
In this paper we will study the set of parameters in which certain partial derivatives of the Green's function, related to a $n$-order linear operator $T_{n}[M]$, depending on a real parameter $M$, coupled to different two-point boundary…
In this paper we argue that boundary condition may run with energy scale. As an illustrative example, we consider one-dimensional quantum mechanics for a spinless particle that freely propagates in the bulk yet interacts only at the origin.…
Many computational problems are unchanged under some symmetry operation. In classical machine learning, this can be reflected with the layer structure of the neural network. In quantum machine learning, the ansatz can be tuned to correspond…
This contribution extends linear models for feature vectors to sublinear models for graphs and analyzes their properties. The results are (i) a geometric interpretation of sublinear classifiers, (ii) a generic learning rule based on the…