相关论文: Generalised Bent Criteria for Boolean Functions (I…
We present an introduction to the framework of strongly local Dirichlet forms and discuss connections between the existence of certain generalized eigenfunctions and spectral properties within this framework. The range of applications is…
In these introductory notes I give a brief overview on some theoretical aspects of light baryon spectroscopy. The first part contains a discussion of the symmetries of the baryon spectrum, the construction of flavor wave functions and some…
For each non-constant Boolean function $q$, Klapper introduced the notion of $q$-transforms of Boolean functions. The {\em $q$-transform} of a Boolean function $f$ is related to the Hamming distances from $f$ to the functions obtainable…
Bent functions of the form $\mathbb{F}_2^n\rightarrow\mathbb{Z}_q$, where $q\geqslant2$ is a positive integer, are known as generalized bent (gbent) functions. Gbent functions for which it is possible to define a dual gbent function are…
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…
We survey current term-wise techniques for quadratizing high-degree pseudo-Boolean functions and introduce a new one, which allows multiple splits of terms. We also introduce the first aggregative approach, which splits a collection of…
We determine the three-loop $\overline{\text{MS}}$ quartic $ \beta $-function for the most general renormalisable four-dimensional theories. A general parametrization of the $ \beta $-function is compared to known $ \beta $-functions for…
Logical models have been successfully used to describe regulatory and signaling networks without requiring quantitative data. However, existing data is insufficient to adequately define a unique model, rendering the parametrization of a…
We determine all composition-closed equational classes of Boolean functions. These classes provide a natural generalization of clones and iterative algebras: they are closed under composition, permutation and identification…
Beurling slow variation is generalized to Beurling regular variation. A Uniform Convergence Theorem, not previously known, is proved for those functions of this class that are measurable or have the Baire property. This permits their…
In this note, we present a generalization of some results concerning the spectral properties of a certain class of block matrices. As applications, we study some of its implications on nonnegative matrices, doubly stochastic matrices and…
The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics, and…
A Boolean function of n bits is balanced if it takes the value 1 with probability 1/2. We exhibit a balanced Boolean function with a randomized evaluation procedure (with probability 0 of making a mistake) so that on uniformly random…
For the interpolation of graph signals with generalized shifts of a graph basis function (GBF), we introduce the concept of positive definite functions on graphs. This concept merges kernel-based interpolation with spectral theory on graphs…
In this paper we introduce generalized hyperbent functions from $F_{2^n}$ to $Z_{2^k}$, and investigate decompositions of generalized (hyper)bent functions. We show that generalized (hyper)bent functions from $F_{2^n}$ to $Z_{2^k}$ consist…
We discuss ways in which tools from topology can be used to derive lower bounds for the circuit complexity of Boolean functions.
Based on the definition of generalized partially bent functions, using the theory of linear transformation, the relationship among generalized partially bent functions over ring Z N, generalized bent functions over ring Z N and affine…
This paper discusses the simplest examples of spectral zeta functions, especially those associated with graphs, a subject which has not been much studied. The analogy and the similar structure of these functions, such as their parallel…
This note contains a simple construction of complete sets of MUBs, using bent functions to write the new basis vectors as explicit linear combinations of the standard basis.
Results involving various mean value properties are reviewed for harmonic, biharmonic and metaharmonic functions. It is also considered how the standard mean value property can be weakened to imply harmonicity and belonging to other classes…