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In the context of functional data analysis, probability density functions as non-negative functions are characterized by specific properties of scale invariance and relative scale which enable to represent them with the unit integral…
Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter, are considered. Using an interior Dirichlet heat kernel lower bound estimate for…
The notion of o-polynomial comes from finite projective geometry. In 2011 and later, it has been shown that those objects play an important role in symmetric cryptography and coding theory to design bent Boolean functions, bent vectorial…
In this article, we study the properties of the nonlinear Fourier spectrum in order to gain better control of the temporal support of the signals synthesized using the inverse nonlinear Fourier transform (NFT). In particular, we provide…
cryptographic hash function is a deterministic procedure that compresses an arbitrary block of numerical data and returns a fixed-size bit string. There exist many hash functions: MD5, HAVAL, SHA, ... It was reported that these hash…
This work presents a study of perturbations of symmetric Boolean functions. In particular, it establishes a connection between exponential sums of these perturbations and Diophantine equations of the form $$ \sum_{l=0}^n \binom{n}{l}…
A divide-and-conquer cryptanalysis can often be mounted against some keystream generators composed of several (nonlinear) independent devices combined by a Boolean function. In particular, any parity-check relation derived from the periods…
We provide analytic solutions of the optical Bloch equations for a two-level system interacting with a broadband light field. We will focus on two special examples: incident light with a Lorentzian spectral density and the limit of incident…
A function defined on the Boolean hypercube is $k$-Fourier-sparse if it has at most $k$ nonzero Fourier coefficients. For a function $f: \mathbb{F}_2^n \rightarrow \mathbb{R}$ and parameters $k$ and $d$, we prove a strong upper bound on the…
We observe deterministic chaos in a simple network of electronic logic gates that are not regulated by a clocking signal. The resulting power spectrum is ultra-wide-band, extending from dc to beyond 2 GHz. The observed behavior is…
A nonlinear algebraic equation system of two variables is numerically solved, which is derived from a nonlinear algebraic equation system of four variables, that corresponds to a mathematical model related to investment under conditions of…
We provide new single-integral formulas of the power spectral density of single-channel and cross-channel nonlinear interference in highly-dispersed coherent optical links for which the Gaussian Noise model [1], [2] applies.
We develop a new technique for proving concentration inequalities which relate between the variance and influences of Boolean functions. Using this technique, we 1. Settle a conjecture of Talagrand [Tal97] proving that $$\int_{\left\{…
The relation between the boolean functions and Bell inequalities for qubits is analyzed. The connection between the maximal quantum violation of a Bell inequality and the nonlinearity of the corresponding boolean function is discussed. A…
Higher-order spectra (or polyspectra), defined as the Fourier Transform of a stationary process' autocumulants, are useful in the analysis of nonlinear and non Gaussian processes. Polyspectral means are weighted averages over Fourier…
The implementation of Bayesian predictive procedures under standard normal models is considered. Two distributions are of particular interest, the K-prime and K-square distributions. They also give exact inferences for simple and multiple…
Accurate uncertainty quantification is critical for reliable predictive modeling. Existing methods typically address either aleatoric uncertainty due to measurement noise or epistemic uncertainty resulting from limited data, but not both in…
This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…
We propose a linear algorithm for determining two function parameters by their linear combination. These functions must satisfy the first order differential equations with polynomial coefficients and our parameters are the coefficients of…
This paper discusses the application of known techniques, knowledge and technology in a novel way for encryption. Two distinct and separate methods are presented. Method 1: Alter the symbol set of the language by adding additional redundant…