Related papers: Influences of monotone Boolean functions
We analyze the determination of volume effects for correlation functions that depend on an external momentum. As a specific example, we consider finite volume nucleon current correlators, and focus on the nucleon magnetic moment. Because…
Boole polynomials play an important role in the area of number theory, algebra and umbral calculus. In this paper, we investigate some properties of Boole polynomials and consider Witt-type formulas for the Boole numbers and polynomials.…
Boolean networks constitute relevant mathematical models to study the behaviours of genetic and signalling networks. These networks define regulatory influences between molecular nodes, each being associated to a Boolean variable and a…
The r-th order nonlinearity of a Boolean function is the minimum number of elements that have to be changed in its truth table to arrive at a Boolean function of degree at most r. It is shown that the (suitably normalised) r-th order…
Lattice induced threshold function is a Boolean function determined by a particular linear combination of lattice elements. We prove that every isotone Boolean function is a lattice induced threshold function and vice versa. We also…
In the present note we prove an asymptotically tight relation between additive and multiplicative complexity of Boolean functions with respect to implementation by circuits over the basis {+,*,1}.
In this paper we construct a cyclically invariant Boolean function whose sensitivity is $\Theta(n^{1/3})$. This result answers two previously published questions. Tur\'an (1984) asked if any Boolean function, invariant under some transitive…
We define a product of algebraic probability spaces equipped with two states. This product is called a conditionally monotone product. This product is a new example of independence in non-commutative probability theory and unifies the…
It is well--known that when magnetic monopoles are introduced in plasma equations the propagation of electromagnetic waves is modified. This occurs because of Maxwell equations acquire a symmetrical structure due to the existence of…
Motivated by existing results, we present some completely monotonic functions involving the polygamma functions.
We propose a notion of operator monotonicity for functions of several variables, which extends the well known notion of operator monotonicity for functions of only one variable. The notion is chosen such that a fundamental relationship…
We consider the correlations of invariant observables for the $O(N)$ and $\mathbb{C}\mathbb{P}^{N-1}$ models at zero coupling, namely, with respect to the natural group-invariant measure. In the limit where one takes a large power of the…
Whereas translating the coding of predictor variables does not change the fit of a polynomial least squares regression, penalized polynomial regressions are potentially affected. A result on which terms can be penalized to maintain the…
A real arithmetic function f is multiplicatively monotonous if f (mn) -- f (m) has constant sign for m, n positive integers. Properties and examples of such functions are discussed, with applications to positive hermitian…
Electromagnetism becomes a nonlinear theory having (effective) photon-photon interactions due at least to electron-positron fluctuations in the vacuum. We discuss the consequences of the nonlinearity for the force felt by a charge probe…
A novel polynomial expansion method of symmetric Boolean functions is described. The method is efficient for symmetric Boolean function with small set of valued numbers and has the linear complexity for elementary symmetric Boolean…
We study a form of noise-induced intermittence originated by an out of equilibrium process yielding events in time with a survival probability that in the case of an infinitely aged condition coincides with the Mittag-Leffler function. In…
A recent large deflection cantilever model is considered. The principal nonlinear effects come through the beam's inextensibility---local arc length preservation---rather than traditional extensible effects attributed to fully restricted…
Keller's theorem relates the components of the macroscopic dielectric response of a binary two-dimensional composite system with those of the reciprocal system obtained by interchanging its components. We present a derivation of the theorem…
In this paper we consider the influence of non-perturbative corrections on the large $ b $ (impact parameter) behavior of the BFKL amplitude. This is done in the framework of a model where such ``soft'' corrections are taken into account in…