Mathematics

In the following paper, a new approach for de signing high-performance arithmetic circuits based on the new “Weighted Logic” family is presented while demonstrating the new technique's performance advantage an d relatively low-energy characteristics. It will be shown by the means of a 64-bit comparator and a 64-bit adder that using the new approach, arithmetic functions can be implemented more

The paper deals with approaches utilized for adjustment of well known Method of Aggregate Indices (MAI) to uncertainty conditions. The necessity for such adjustments occurs because of the shortage of numeric information. It appears at any stage of estimation of the aggregate quality index for operating electricity units when respective measure (index) integrates a system of object’s parameters. Each parameter is required for ultimate quality appraisal, and taken together they are supposed to be sufficient for estimating quality level of the analyzed unit. The Baye's uncertainty randomization procedure is proposed as a tool to simulate the shortage of numeric information. Through this procedure separate indices, weight coefficients and aggregated indices are transformed into correspondent random magnitudes. Then, comparing the qualities of any two objects is converted in the problem of revealing a certain type of stochastic dominance between respective randomized aggregate indice...

The paper starts with the task of assessing different qualities (security, efficiency, matching ecological standards, etc.) of the complex units operating in electricity sector (power plants, current generators, electricity transmission lines, generating companies, etc.). Then the task considered as the problem of multi criteria assessment of the multidimensional objects, which are identified with a finite bundles of initial parameters. The

The paper deals with approaches utilized for adjustment of well known Method of Aggregate Indices (MAI) to uncertainty conditions. The necessity for such adjustments occurs because of the shortage of numeric information. It appears at any stage of estimation of the aggregate quality index for operating electricity units when respective measure (index) integrates a system of object’s parameters. Each parameter is required for ultimate quality appraisal, and taken together they are supposed to be sufficient for estimating quality level of the analyzed unit. The Baye's uncertainty randomization procedure is proposed as a tool to simulate the shortage of numeric information. Through this procedure separate indices, weight coefficients and aggregated indices are transformed into correspondent random magnitudes. Then, comparing the qualities of any two objects is converted in the problem of revealing a certain type of stochastic dominance between respective randomized aggregate indi...

: A central goal of mathematical linguistics is to precisely determine the power of a linguistic theory. Traditionally, formal language theory (the Chomsky hierarchy) and its generative power analyses have translated this question into the narrower question of how unrestricted the rule format of a theory is. Modern computational complexity theory offers another, more useful, translation: how much of what computational resources does a theory consume? Complexity theory also offers a new perspective on descriptive adequacy. In a descriptively adequate linguistic theory, the structural descriptions and computational power of the theory match those of an ideal speaker-hearer. The primary goal of this paper is to demonstrate how considerations from computational complexity theory can inform grammatical theorizing. To this end, the paper revises generalized phrase structure grammar (GPSG) linguistic theory so that its computational power more closely matches the limited computational abil...

Expectation maximization (EM) provides a simple and elegant approach to the problem of optimizing the parameters of a normal mixture on an unlabeled dataset. To accomplish this, EM iteratively reweights the elements of the dataset until a locally optimal normal mixture is obtained. This paper explores the intriguing question of whether such an EM-style algorithm exists for the related and apparently more difficult problem of finding a normal mixture that maximizes the a posteriori class probabilities of a labeled dataset. We expose a fundamental degeneracy in the relationship between a normal mixture and the a posteriori class probability functions that it induces, and use this degeneracy to prove that reweighting a dataset can almost always give rise to a normal mixture that exhibits any desired class function behavior. This establishes that EM-style approaches are sufficiently expressive for a posteriori optimization problems and opens the way to the design of new algorithms for t...

ABSTRACT In this paper, a new numerical scheme is constructed to solve a class of Infinite Horizon Optimal Control Problems (IHOCPs). The idea is to extend the spectral Ritz method to solve an IHOCP directly by a proper approximation of the state and control functions. We solve the IHOCP on the original time interval. Applying the new constructed operational Laguerre matrix and substituting the estimated functions into the performance index yields a system of algebraic equations. Notably, the choice of Laguerre polynomials along with the spectral Ritz method provides to impose all the given initial and boundary conditions easily. By rigorous proofs, the convergence of the new method is investigated. The numerical technique is also examined by adding three illustrative application problems to show the applicability and effectiveness of the proposed technique. Furthermore, our results are compared with the outlets of other works to show superiority of the proposed methodology.

Parameters representing three‐dimensional (3D) biofilm structure are quantified from confocal laser‐scanning microscope (CLSM) images. These 3D parameters describe the distribution of biomass pixels within the space occupied by a biofilm; however, they lack a direct connection to biofilm activity. As a result, researchers choose a handful of parameters without there being a consensus on a standard set of parameters. We hypothesized that a select 3D parameter set could be used to reconstruct a biofilm image and that the reconstructed and original biofilm images would have similar activities. To test this hypothesis, an algorithm was developed to reconstruct a biofilm image with parameters identical to those of the original CLSM image. We introduced an objective method to assess the reconstruction algorithm by comparing the activities of the original and reconstructed biofilm images. We found that biofilm images with identical structural parameters showed nearly identical activities and substrate concentration profiles. This implies that the set containing all common structural parameters can successfully describe biofilm structure. This finding is significant, as it opens the door to the next step, of finding a smaller standard set of biofilm structural parameters that can be used to compare biofilm structure.

he study proposed identifying and assessing virology journals’ quality by virtue of internationally accepted bibliometric indicators, namely, JIF, CS, SJR, and h5-index. The data collected from Web of Science, Scopus, and Google metrics for the year 2018 under the category ‘Virology’. Thirty-six journals retrieved, then ranks and values of journals compared with each indicator’s metrics. To assess the compatibility, the bivariate correlation coefficient calculated using SPSS. Microsoft Excel and Microsoft access 2010 used to analyze and visualize the journal’s ranking with each indicator. The results exclaim except Cell Host and Microbe, none of the journals shows a similar ranking in all four indicators. Only seven journals are open access, and the rest of the 29 closed access—the USA leading ‘Virology’ researches. The calculation of the correlation coefficient indicates that all the indicators are compatible and can be used as an alternative to others to assess the journals’ quali...

The study proposed identifying and assessing virology journals’ quality by virtue of internationally accepted bibliometric indicators, namely, JIF, CS, SJR, and h5-index. The data collected from Web of Science, Scopus, and Google metrics for the year 2018 under the category ‘Virology’. Thirty-six journals retrieved, then ranks and values of journals compared with each indicator’s metrics. To assess the compatibility, the bivariate correlation coefficient calculated using SPSS. Microsoft Excel and Microsoft access 2010 used to analyze and visualize the journal’s ranking with each indicator. The results exclaim except Cell Host and Microbe, none of the journals shows a similar ranking in all four indicators. Only seven journals are open access, and the rest of the 29 closed access—the USA leading ‘Virology’ researches. The calculation of the correlation coefficient indicates that all the indicators are compatible and can be used as an alternative to others to assess the journals’ qual...

In this paper, the Fractional Laplace Differential Transform Method is presented firstly in the literature and applied to the fractional partial differential equations to obtain approximate analytical solutions. This method is a combined form of the Laplace transform and Differential Transform Method. The obtained numerical solutions by the Fractional Laplace Differential Transform Method show that this method is easy to carry out and has high accuracy. These results reveal that the proposed method is a promising tool for solving fractional partial differential equations. The described method in this study is expected to be employed to more problems in fractional calculus.

In this paper, we present approximation algorithms for combinatorial optimization problems under probabilistic constraints. Specifically, we focus on stochastic variants of two important combinatorial optimization problems: the k-center problem and the set cover problem, with uncertainty characterized by a probability distribution over set of points or elements to be covered. We consider these problems under adaptive and non-adaptive settings, and present efficient approximation algorithms for the case when underlying distribution is a product distribution. In contrast to the expected cost model prevalent in stochastic optimization literature, our problem definitions support restrictions on the probability distributions of the total costs, via incorporating constraints that bound the probability with which the incurred costs may exceed a given threshold.