Related papers: What Is Boolean Valued Analysis?
We show (almost) separation between certain important classes of Boolean functions. The technique that we use is to show that the total influence of functions in one class is less than the total influence of functions in the other class. In…
An effective method to obtain exact analytical solutions of equations describing the coherent dynamics of multilevel systems is presented. The method is based on the usage of orthogonal polynomials, integral transforms and their discrete…
We define a notion which contains numerous basic notions of Analysis as special cases, for example limit, continuity, differential, Riemann and Lebesgue integral, root and exponential functions. Properties like additivity or linearity of…
Since its introduction 25 years ago, the quantum weak value has gradually transitioned from a theoretical curiosity to a practical laboratory tool. While its utility is apparent in the recent explosion of weak value experiments, its…
In this article, we introduce a procedure for selecting variables in principal components analysis. The procedure was developed to identify a small subset of the original variables that best explain the principal components through…
A Boolean function of n bits is balanced if it takes the value 1 with probability 1/2. We exhibit a balanced Boolean function with a randomized evaluation procedure (with probability 0 of making a mistake) so that on uniformly random…
In this tutorial, I will discuss the details about how Probabilistic Latent Semantic Analysis (PLSA) is formalized and how different learning algorithms are proposed to learn the model.
This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.
In the field of Business Process Management formal models for the control flow of business processes have been designed since more than 15 years. Which methods are best suited to verify the bulk of these models? The first step is to select…
Obtaining more accurate equity value estimates is the starting point for stock selection, value-based indexing in a noisy market, and beating benchmark indices through tactical style rotation. Unfortunately, discounted cash flow, method of…
A list of open problems in the field of analysis of boolean functions, compiled February 2012 for the Simons Symposium.
We present a novel approach, which is based on multiple-valued logic (MVL), to the verification and analysis of digital hardware designs, which extends the common ternary or quaternary approaches for simulations. The simulations which are…
A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.
$P$-values have been the focus of considerable criticism based on various considerations. Still, the $P$-value represents one of the most commonly used statistical tools. When assessing the suitability of a single hypothesized distribution,…
Polymorphic circuits are a special kind of circuits which possess multiple build-in functions, and these functions are activated by environment parameters, like temperature, light and VDD. The behavior of a polymorphic circuit can be…
We study groups, exponential groups and ordered groups equipped with valuations. We investigate algebraic and topological features of such valued structures, and apply our findings in order to solve regular equations over groups using…
Tuning parameters in supervised learning problems are often estimated by cross-validation. The minimum value of the cross-validation error can be biased downward as an estimate of the test error at that same value of the tuning parameter.…
It is time to renew old ways of thinking about dimensional analysis. Specifically, more than $n-r$ invariants and more than one functional relation between invariants need to be considered simultaneously. Thus generalized, dimensional…
The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…
Weighted mean value identities over balls are considered for harmonic functions and their derivatives. Logarithmic and other weights are involved in these identities for functions. Some applications of weighted identities are presented.…