Related papers: Generalised Bent Criteria for Boolean Functions (I…
We study the beta functions for four-dimensional conformal gravity using two different parametrizations of metric fluctuation, linear split and exponential parametrization. We find that after imposing the traceless conditions, the beta…
We examine a hierarchy of equivalence classes of quasi-random properties of Boolean Functions. In particular, we prove an equivalence between a number of properties including balanced influences, spectral discrepancy, local strong…
We study the quantum query complexity of the Boolean hidden shift problem. Given oracle access to f(x+s) for a known Boolean function f, the task is to determine the n-bit string s. The quantum query complexity of this problem depends…
The Walsh--Hadamard spectrum of a bent function uniquely determines a dual function. The dual of a bent function is also bent. A bent function that is equal to its dual is called a self-dual function. The Hamming distance between a bent…
This is the second part of a work dedicated to the study of Bernstein-Sato polynomials for several analytic functions depending on parameters. In this part, we give constructive results generalizing previous ones obtained by the author in…
Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…
Suppose that f is a boolean function from F_2^n to {0,1} with spectral norm (that is the sum of the absolute values of its Fourier coefficients) at most M. We show that f may be expressed as +/- 1 combination of at most 2^(2^(O(M^4)))…
The subject of this textbook is the analysis of Boolean functions. Roughly speaking, this refers to studying Boolean functions $f : \{0,1\}^n \to \{0,1\}$ via their Fourier expansion and other analytic means. Boolean functions are perhaps…
A general analytical approach to the statistical description of quantum graph spectra based on the exact periodic orbit expansions of quantum levels is discussed. The exact and approximate expressions obtained in \cite{Anima} for the…
We give a Herglotz-type representation of an arbitrary generalized spectral measure. As an application, a new proof of the classical Naimark's dilation theorem is given. The same approach is used to describe the spectrum of all unitary…
In this paper an algorithm is designed which generates in-equivalent Boolean functions of any number of variables from the four Boolean functions of single variable. The grammar for such set of Boolean function is provided. The Turing…
Boolean functions on the space $F_{2}^m$ are not only important in the theory of error-correcting codes, but also in cryptography, where they occur in private key systems. In these two cases, the nonlinearity of these function is a main…
In this paper we shall describe some correlation function computations in perturbative heterotic strings that, for example, in certain circumstances can lend themselves to a heterotic generalization of quantum cohomology calculations.…
We describe the dynamics of a single fermion in a dispersionless band coupled to the 2+1 dimensional conformal field theory (CFT) describing the quantum phase transition of a bosonic order parameter with N components. The fermionic spectral…
Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…
We will study some important properties of Boolean functions based on newly introduced concepts called Special Decomposition of a Set and Special Covering of a Set. These concepts enable us to study important problems concerning Boolean…
In this paper, several new classes of Boolean functions with few Walsh transform values, including bent, semi-bent and five-valued functions, are obtained by adding the product of two or three linear functions to some known bent…
Quantum-classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations that quantum mechanical wave functions present around the classical…
Our main result is a generalized Dillon-type theorem, giving graph-theoretic conditions which guarantee that a $p$-ary function in an even number of variables is bent, for $p$ a prime number greater than 2. The key condition is that the…
In this paper some classes of local polynomial functions on abelian groups are characterized by the properties of their variety. For this characterization we introduce a numerical quantity depending on the variety of the local polynomial…