Related papers: 2-Variable Boolean Operation -- its use in Pattern…
We introduce a variational theory for processes adapted to the multi-dimensional Brownian motion filtration. The theory provides a differential structure which describes the infinitesimal evolution of Wiener functionals at very small…
This work develops problem statements related to encoders and autoencoders with the goal of elucidating variational formulations and establishing clear connections to information-theoretic concepts. Specifically, four problems with varying…
Molecular self-assembly plays a very important role in various aspects of technology as well as in biological systems. Governed by the covalent, hydrogen or van der Waals interactions - self-assembly of alike molecules results in a large…
This paper is concerned mainly with the macroscopic fractal behavior of various random sets that arise in modern and classical probability theory. Among other things, it is shown here that the macroscopic behavior of Boolean coverage…
Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a…
A certain analysis of all possible associative binary operations on N is presented. This is equivalent with an analysis of all possible monoid structures on N. Several results and a conjecture in this regard are given.
We investigate the variation of the string field action under changes of the string field vertices giving rise to different decompositions of the moduli spaces of Riemann surfaces. We establish that any such change in the string action…
Variational Bayes (VB) is rapidly becoming a popular tool for Bayesian inference in statistical modeling. However, the existing VB algorithms are restricted to cases where the likelihood is tractable, which precludes the use of VB in many…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
Many-body physics of electron-electron correlations plays a central role in condensed mater physics, it governs a wide range of phenomena, stretching from superconductivity to magnetism, and is behind numerous technological applications. To…
Abstract Self-similar, fractal nature of turbulence is discussed in the context of two dimensional turbulence, by considering the fractal structure of the wave-number domain using spirals. In loose analogy with phyllotaxis in plants, each…
Following the success of Moore's predictions, we are approaching a limit in the miniaturization of semiconductors for computing materials. This has led to the exploration of various research paths to develop alternative computing paradigms,…
Generalisations of the bent property of a boolean function are presented, by proposing spectral analysis with respect to a well-chosen set of local unitary transforms. Quadratic boolean functions are related to simple graphs and it is shown…
Variational Bayes (VB) has become a widely-used tool for Bayesian inference in statistics and machine learning. Nonetheless, the development of the existing VB algorithms is so far generally restricted to the case where the variational…
The Arbitrary Pattern Formation problem asks to design a distributed algorithm that allows a set of autonomous mobile robots to form any specific but arbitrary geometric pattern given as input. The problem has been extensively studied in…
Complex systems are often modeled as Boolean networks in attempts to capture their logical structure and reveal its dynamical consequences. Approximating the dynamics of continuous variables by discrete values and Boolean logic gates may,…
The categorical distribution is a natural representation of uncertainty in multi-class segmentations. In the two-class case the categorical distribution reduces to the Bernoulli distribution, for which grayscale morphology provides a range…
This work presents a new Visual Basic 6.0 application for estimating the fractal dimension of images, based on an optimized version of the box-counting algorithm. Following the attempt to separate the real information from noise, we…
The very high multiplicity (VHM) processes are considered to investigate consequences of the dual resonance models reach (exponential) mass spectrum. The virial decomposition is developed for description of the produced particles short-rang…
A signal processing method designed for the detection of linear (coherent) behaviors among random fluctuations is presented. It is dedicated to the study of data recorded from nonlinear physical systems. More precisely the method is suited…