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Derivation of computational formulas for certain class of finite sums: Approach to generating functions arising from p$$ p $$-adic integrals and special functions

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2022年第16期45卷 9520-9544页

作者： Simsek, Yilmaz Univ Akdeniz Dept Math Fac Sci TR-07058 Antalya Turkey

The aim of this paper is to construct generating functions for certain families of special finite sums by using the Newton-Mercator series, hypergeometric functions, and p$$ p $$-adic integral. By using these generating functions with their functional and partial derivative equations, many novel computational formulas involving the special finite sums of (inverse) binomial coefficients, the Bernoulli type polynomials and numbers, Euler polynomials and numbers, the Stirling numbers, the (alternating) harmonic numbers, the Leibnitz polynomials, and others are derived. We also develop a computation algorithm for these finite sums and provide some of their special values. By using these finite sums and combinatorial numbers, we find some formulas involving multiple alternating zeta functions, the Bernoulli polynomials of higher order and the Euler polynomials of higher order. We then obtain a decomposition from these formulas, which are related to the multiple Hurwitz zeta functions.

关键词： computational algorithm finite sums generating function multiple alternating zeta functions p-adic integral special functions and special numbers

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COMPUTER-BASED TECHNIQUES FOR SOLVING PROBLEMS OF APPLIED AND computational MATHEMATICS WITH GIVEN QUALITY CHARACTERISTICS

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CYBERNETICS AND SYSTEMS ANALYSIS 2006年第5期42卷 641-648页

作者： Sergienko, I. V. Zadiraka, V. K. Babich, M. D. Berezovskii, A. I. Besarab, P. N. Lyudvichenko, V. A. Natl Acad Sci Ukraine VM Glushkov Inst Cybernet Kiev Ukraine 2Ukrainian Acad Foreign Trade Kiev Ukraine Int Acad Human Resource Management MAUP Kiev Ukraine

The paper is concerned with computer-based techniques for the choice and development of computational resources and their efficient use to find an approximate solution with a given accuracy in a limited processor time.

关键词： computer-based techniques mathematical model of applied problem computational model computational process computational algorithm estimates of quality characteristics of computational algorithm

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Bootstrapping the lexicon: A computational model of infant speech segmentation

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COGNITION 2002年第2期83卷 167-206页

作者： Batchelder, EO CUNY Grad Ctr New York NY USA

Prelinguistic infants must find a way to isolate meaningful chunks from the continuous streams of speech that they hear. BootLex, a new model which uses distributional cues to build a lexicon, demonstrates how much can be accomplished using this single source of information. This conceptually simple probabilistic algorithm achieves significant segmentation results on various kinds of language corpora - English, Japanese, and Spanish: child- and adult-directed speech, and written texts;and several variations in coding structure - and reveals which statistical characteristics of the input have an influence on segmentation performance. BootLex is then compared, quantitatively and qualitatively, with three other groups of computational models of the same infant segmentation process, paying particular attention to functional characteristics of the models and their similarity to human cognition. Commonalities and contrasts among the models are discussed, as well as their implications both for theories of the cognitive problem of segmentation itself, and for the general enterprise of computational cognitive modeling. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： speech segmentation infants computational algorithm probabilistic cues cognitive models

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A Novel computational Approach "BP-STOCH" to Study ligand Binding to Finite Lattice

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BIOPOLYMERS 2011年第3期95卷 208-216页

作者： Beshnova, Daria A. Bereznyak, Ekaterina G. Shestopalova, Anna V. Evstigneev, Maxim P. Sevastopol Natl Tech Univ Dept Phys Sevastopol Ukraine Natl Acad Sci Ukraine Inst Radiophys & Elect Dept Biophys Kharkov Ukraine

We report a novel computational algorithm "BP-STOCH" to be used for studying single-type ligand binding with biopolymers of finite lengths, such as DNA oligonucleotides or oligopeptides. It is based on an idea to represent any type of ligand biopolymer complex in a form of binary number, where "0" and "1" bits stand for vacant and engaged monomers of the biopolymer, respectively. Cycling over all binary numbers from the lowest 0 up to the highest 2(N) - 1 means a sequential generating of all possible configurations of vacant/ engaged monomers, which, after proper filtering, results in a full set of possible types of complexes in solution between the ligand and the N-site lattice. The principal advantage of BP-STOCH algorithm is the possibility to incorporate into this cycle any conditions on computation of the concentrations and observed experimental parameters of the complexes in solution, and programmatic access to each monomer of the biopolymer within each binding site of every binding configuration. The latter is equivalent to unlimited extension of the basic reaction scheme and allows to use BP-STOCH algorithm as an alternative to conventional computational approaches. (C) 2010 Wiley Periodicals, Inc. Biopolymers 95: 208-216, 2011.

关键词： ligand-biopolymer complexation computational algorithm binding occupancy fitting titration data

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On the Use of Computation Optimization Opportunities in Computer Technologies for Applied and computational Mathematics Problems with Prescribed Quality Characteristics

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computational MATHEMATICS AND MATHEMATICAL PHYSICS 2010年第12期50卷 2166-2174页

作者： Babich, M. D. Zadiraka, V. K. Lyudvichenko, V. A. Sergienko, I. V. Natl Acad Sci Ukraine Glushkov Inst Cybernet UA-03187 Kiev Ukraine

The use of various opportunities for computation optimization in computer technologies for applied and computational mathematics problems with prescribed quality characteristics is investigated. More precisely, the choice and determination of computational resources and methods of their efficient use for finding an approximate solution of problems up to prescribed accuracy in a limited amount of processor time are investigated.

关键词： computer technology mathematical model of applied problem model of computations computation procedure computational algorithm estimates of computational algorithm quality

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HFS-based computational method for weighted fuzzy time series forecasting model using techniques of adaptive radius clustering and grey wolf optimization

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GRANULAR COMPUTING 2024年第1期9卷 1-24页

作者： Pant, Shivani Kumar, Sanjay GB Pant Univ Agr & Technol Dept Math Stat & Comp Sci Pantnagar 263145 Uttarakhand India

Recently, hesitant fuzzy sets (HFSs) have been used extensively in time series forecasting. HFSs have inherent characteristics of addressing problem of non-stochastic hesitancy that is developed as a result of the availability of numerous techniques for fuzzification of time series data. In the present study, we have developed an HFS-based computational method for weighted fuzzy time series (WFTS) forecasting. The proposed method addresses the three main issues of appropriate partitioning of the universe of discourse (UOD) into unequal-length intervals, inclusion of hesitancy during fuzzification of time series data, recurrence, and weighting of fuzzy logical relation (FLR) in fuzzy time series forecasting. The proposed method uses a non-parametric clustering approach of adaptive radius clustering for accurate partitioning of UOD and HFS for inclusion of hesitancy in time series during process of fuzzification. The recurrence and weighting of FLRs are handled using Markov weights, which are then subsequently optimized by utilizing the popular swarm intelligence technique of grey wolf optimization. A simple computational method is provided that incorporates the optimized weights, thus simplifying the forecasting process. The proposed WFTS forecasting method is implemented in the Python programming language to forecast benchmark time series data of the University of Alabama and financial time series data of Taiwan stock exchange (TAIEX), market price of State Bank of India (SBI) at Bombay Stock Exchange (BSE), India. The model's performance is measured by means of root-mean-square error (RMSE), and its reduced amount demonstrates the model's outperformance in forecasting of three diversified time series data taken in the study.

关键词： Hesitant fuzzy set Adaptive radius clustering computational algorithm Grey wolf optimization Weighted fuzzy time series

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computational Implementation of a Mixed-Dimensional Model of Heat Transfer in the Soil-Pipe System in Cryolithic Zone

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computational MATHEMATICS AND MATHEMATICAL PHYSICS 2021年第12期61卷 2054-2067页

作者： Vasil'ev, V., I Vasil'eva, M. V. Nikiforov, D. Ya Sidnyaev, N., I Stepanov, S. P. Tseeva, A. N. North Eastern Fed Univ Yakutsk 677000 Russia Bauman State Tech Univ Moscow 105005 Russia Yakutsk Design Res Inst Construct Yakutsk 677000 Russia

A mathematical model of heat transfer between the permafrost foundation of a building with a system of freezing pipes and atmospheric air is constructed and numerically implemented. As a mathematical model of heat transfer in the building foundation, the Stefan problem in the enthalpy statement with smoothed coefficients and a smeared temperature source is used. The heat transfer in the system of pipes is described by a one-dimensional convection-conduction equation. Numerical results obtained on model problems showed that the proposed numerical method significantly reduces the computational complexity of the problem.

关键词： cryolithic zone heat and mass transfer Stefan problem finite element method computational algorithm

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computational methods for constructing protein structure models from 3D electron microscopy maps

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JOURNAL OF STRUCTURAL BIOLOGY 2013年第1期184卷 93-102页

作者： Esquivel-Rodriguez, Juan Kihara, Daisuke Purdue Univ Dept Comp Sci Coll Sci W Lafayette IN 47907 USA Purdue Univ Dept Biol Sci Coll Sci W Lafayette IN 47907 USA Purdue Univ Markey Ctr Struct Biol Coll Sci W Lafayette IN 47907 USA

Protein structure determination by cryo-electron microscopy (EM) has made significant progress in the past decades. Resolutions of EM maps have been improving as evidenced by recently reported structures that are solved at high resolutions close to 3 angstrom. computational methods play a key role in interpreting EM data. Among many computational procedures applied to an EM map to obtain protein structure information, in this article we focus on reviewing computational methods that model protein three-dimensional (3D) structures from a 3D EM density map that is constructed from two-dimensional (2D) maps. The computational methods we discuss range from de novo methods, which identify structural elements in an EM map, to structure fitting methods, where known high resolution structures are fit into a low-resolution EM map. A list of available computational tools is also provided. (C) 2013 Elsevier Inc. All rights reserved.

关键词： Electron microscopy Structure fitting Macromolecular structure modeling Electron density map computational algorithm

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computational Scheme for Invariantly Unbiased Estimation of Linear Operators in a Given Class

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computational MATHEMATICS AND MATHEMATICAL PHYSICS 2008年第4期48卷 549-560页

作者： Bulychev, Yu. G. Eliseev, A. V. Rostov Mil Inst Missile Forces Rostov Na Donu 344027 Russia

The values of linear operators of a given class are estimated in the case of measurements including piecewise continuous noise of deterministic structure with unknown parameters. A computational scheme producing unbia... 详细信息

关键词： estimation of linear operators invariance of linear estimates least squares method computational algorithm statistical methods for error estimation

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On matching confidence intervals and tests for some discrete distributions: methodological and computational aspects

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computational STATISTICS 2021年第3期36卷 1775-1790页

作者： Klaschka, Jan Reiczigel, Jeno Czech Acad Sci Inst Comp Sci Prague Czech Republic Univ Vet Med Budapest Budapest Hungary

Exact two-tailed tests and two-sided confidence intervals (CIs) for a binomial proportion or Poisson parameter by Sterne (Biometrika 41:117-129, 1954) or Blaker (Can J Stat 28(4):783-798, 2000) are successful in reducing conservatism of the Clopper-Pearson method. However, the methods suffer from an inconsistency between the tests and the corresponding CIs: In some cases, a parameter value is rejected by the test, though it lies in the CI. The problem results from non-unimodality of the test p value functions. We propose a slight modification of the tests that avoids the inconsistency, while preserving nestedness and exactness. Fast and accurate algorithms for both the test modification and calculation of confidence bounds are presented together with their theoretical background.

关键词： Exact test Sterne's and Blaker's exact confidence interval Binomial model Poisson model computational algorithm

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