Related papers: Two Boolean functions with five-valued Walsh spect…
In the present article, we simulate the propagation of binary signals in semi-infinite, mechanical chains of coupled oscillators harmonically driven at the end, by making use of the recently discovered process of nonlinear…
We describe a new class of Boolean functions which provide the presently best known trade-off between low computational complexity, nonlinearity and (fast) algebraic immunity. In particular, for $n\leq 20$, we show that there are functions…
The robustness of Bell's inequality (in CHSH form) violation by entangled state in the simultaneous presence of colored and white noise in the system is considered. A twophoton polarization state is modeled by twoparameter density matrix.…
The growing size of modern datasets necessitates splitting a large scale computation into smaller computations and operate in a distributed manner. Adversaries in a distributed system deliberately send erroneous data in order to affect the…
In this paper we investigate the security of a quantum cryptographic scheme which utilizes balanced homodyne detection and weak coherent pulse (WCP). The performance of the system is mainly characterized by the intensity of the WCP and…
Iterative deblurring, notably the Richardson-Lucy algorithm with and without regularization, is analyzed in the context of nuclear and high-energy physics applications. In these applications, probability distributions may be discretized…
We derive the ultimate bounds on the performance of nonlinear measurement schemes in the presence of noise. In particular, we investigate the precision of the second-order estimation scheme in the presence of the two most detrimental types…
Let $q=2^e$ with $e$ even, and let $\mathbb{F}_{q^2}$ be the finite field of order $q^2$. Put $d=(q^2+q+1)/3$, and consider the permutation polynomial $$\sigma(X)=X+X^d+X^{dq}\in\mathbb{F}_{q^2}[X].$$ For $\alpha\in\mathbb{F}_q^*$, define…
We study the computational complexity of two Boolean nonlinearity measures: the nonlinearity and the multiplicative complexity. We show that if one-way functions exist, no algorithm can compute the multiplicative complexity in time…
In this paper, a technique on constructing nonlinear resilient Boolean functions is described. By using several sets of disjoint spectra functions on a small number of variables, an almost optimal resilient function on a large even number…
Boolean functions are mathematical objects with numerous applications in domains like coding theory, cryptography, and telecommunications. Finding Boolean functions with specific properties is a complex combinatorial optimization problem…
This paper depicts an algorithm for solving the Decision Boolean Satisfiability Problem using the binary numerical properties of a Special Decision Satisfiability Problem, parallel execution, object oriented, and short termination. The two…
We present new algorithms to compute fundamental properties of a Boolean function given in truth-table form. Specifically, we give an O(N^2.322 log N) algorithm for block sensitivity, an O(N^1.585 log N) algorithm for `tree decomposition,'…
A new concept, called quasi-linear transfer functions (QLTF), which can be used to characterize the output frequency behaviour of nonlinear systems, is introduced based on the well-known Volterra series representation. By using the new…
Uncertainty quantification based on generalized polynomial chaos has been used in many applications. It has also achieved great success in variation-aware design automation. However, almost all existing techniques assume that the parameters…
We consider sensor array imaging for simultaneous noise blended sources. We study a migration imaging functional and we analyze its sensitivity to singular perturbations of the speed of propagation of the medium. We consider two kinds of…
We study noisy computation in randomly generated k-ary Boolean formulas. We establish bounds on the noise level above which the results of computation by random formulas are not reliable. This bound is saturated by formulas constructed from…
We introduce a flexible method to simultaneously infer both the drift and volatility functions of a discretely observed scalar diffusion. We introduce spline bases to represent these functions and develop a Markov chain Monte Carlo…
Recent advances in spectroscopic instrumentation and calibration methods dramatically improve the quality of quasar spectra. Supercomputer calculations show that, at high spectral resolution, procedures used in some previous analyses of…
The removal of blur from a signal, in the presence of noise, is readily accomplished if the blur can be described in precise mathematical terms. However, there is growing interest in problems where the extent of blur is known only…