Browse
Submit Data
Databases
API
Help

Dataset Information

30 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Numerical Solution for the Extrapolation Problem of Analytic Functions.

ABSTRACT: In this work, a numerical solution for the extrapolation problem of a discrete set of n values of an unknown analytic function is developed. The proposed method is based on a novel numerical scheme for the rapid calculation of higher order derivatives, exhibiting high accuracy, with error magnitude of O(10-100) or less. A variety of integrated radial basis functions are utilized for the solution, as well as variable precision arithmetic for the calculations. Multiple alterations in the function's direction, with no curvature or periodicity information specified, are efficiently foreseen. Interestingly, the proposed procedure can be extended in multiple dimensions. The attained extrapolation spans are greater than two times the given domain length. The significance of the approximation errors is comprehensively analyzed and reported, for 5832 test cases.

SUBMITTER: Bakas NP

PROVIDER: S-EPMC6750076 | biostudies-literature | 2019

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Publications

Numerical Solution for the Extrapolation Problem of Analytic Functions.

Bakas Nikolaos P NP

Research (Washington, D.C.) 20190528

In this work, a numerical solution for the extrapolation problem of a discrete set of n values of an unknown analytic function is developed. The proposed method is based on a novel numerical scheme for the rapid calculation of higher order derivatives, exhibiting high accuracy, with error magnitude of O(10-100) or less. A variety of integrated radial basis functions are utilized for the solution, as well as variable precision arithmetic for the calculations. Multiple alt ...[more]

PMID: 31549060

Similar Datasets

Analytic approximate solution for Falkner-Skan equation.

Project description:This paper deals with the Falkner-Skan nonlinear differential equation. An analytic approximate technique, namely, optimal homotopy asymptotic method (OHAM), is employed to propose a procedure to solve a boundary-layer problem. Our method does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. The obtained results reveal that this procedure is very effective, simple, and accurate. A very good agreement was found between our approximate results and numerical solutions, which prove that OHAM is very efficient in practice, ensuring a very rapid convergence after only one iteration.

| S-EPMC4032703 | biostudies-other

Implicit Analytic Solution of Michaelis-Menten-Monod Kinetics.

Project description:An analytic solution to enzyme kinetics expressed by the Michaelis-Menten-Monod mathematical framework is presented. The analytic solution describes the implicit problem with the independent variable, normally time, substituted with the concentration of the reaction product. The analytic solution provides the substrate, enzyme, and microbial biomass concentration instantaneously and over all time domains without the use of numerical integration schemes or iterative solvers required to overcome transcendental functions. Experiments of NO2 - nitrification by Candidatus Nitrospira defluvii at temperatures ranging between 10 and 32 °C were used for validation tests with the numerical solution by finite differences and the implicit analytic solution presented here. Results showed that both finite differences and analytic solutions matched the experiments particularly well, with a correlation coefficient greater than 0.99 and residuals smaller than 2.75%.

| S-EPMC6640786 | biostudies-literature

Genetic algorithm solution for double digest problem.

Project description:The strongly NP-Hard Double Digest Problem, for reconstructing the physical map of DNA sequence, in now using for efficient genotyping. Most of the existing methods are inefficient in tackling large instances due to the large search space for the problem which grows as a factorial function (a!)(b!) of the numbers a and b of the DNA fragments generated by the two restriction enzymes. Also, none of the existing methods are able to handle the erroneous data. In this paper, we develop a novel method based on genetic algorithm for solving this problem and it is adapted to handle the erroneous data. Our genetic algorithm is implemented and compared with the other well-known existing algorithms. The obtained results show the efficiency (speedup) of our algorithm with respect to the other methods, specially for erroneous data.

| S-EPMC3374354 | biostudies-literature

Non-spherical particles in optical tweezers: A numerical solution.

Project description:We present numerical methods for modeling the dynamics of arbitrarily shaped particles trapped within optical tweezers, which improve the predictive power of numerical simulations for practical use. We study the dependence of trapping on the shape and size of particles in a single continuous wave beam setup. We also consider the implications of different particle compositions, beam types and media. The major result of the study is that for different irregular particle shapes, a range of beam powers generally leads to trapping. The trapping power range depends on whether the particle can be characterized as elongated or flattened, and the range is also limited by Brownian forces.

| S-EPMC6894773 | biostudies-literature

Solution of the Kirchhoff-Plateau Problem.

Project description:The Kirchhoff-Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a liquid film, with the filament being modeled as a Kirchhoff rod and the action of the spanning surface being solely due to surface tension. We establish the existence of an equilibrium shape that minimizes the total energy of the system under the physical constraint of noninterpenetration of matter, but allowing for points on the surface of the bounding loop to come into contact. In our treatment, the bounding loop retains a finite cross-sectional thickness and a nonvanishing volume, while the liquid film is represented by a set with finite two-dimensional Hausdorff measure. Moreover, the region where the liquid film touches the surface of the bounding loop is not prescribed a priori. Our mathematical results substantiate the physical relevance of the chosen model. Indeed, no matter how strong is the competition between surface tension and the elastic response of the filament, the system is always able to adjust to achieve a configuration that complies with the physical constraints encountered in experiments.

| S-EPMC5479363 | biostudies-other

A cellular solution to an information-processing problem.

Project description:Signaling receptors on the cell surface are mobile and have evolved to efficiently sense and process mechanical or chemical information. We pose the problem of identifying the optimal strategy for placing a collection of distributed and mobile sensors to faithfully estimate a signal that varies in space and time. The optimal strategy has to balance two opposing objectives: the need to locally assemble sensors to reduce estimation noise and the need to spread them to reduce spatial error. This results in a phase transition in the space of strategies as a function of sensor density and efficiency. We show that these optimal strategies have been arrived at multiple times in diverse cell biology contexts, including the stationary lattice architecture of receptors on the bacterial cell surface and the active clustering of cell-surface signaling receptors in metazoan cells.

| S-EPMC4151762 | biostudies-literature

General solution for rapid scan EPR deconvolution problem.

Project description:A general solution for the RS EPR deconvolution problem has been derived. This solution permits the use of arbitrary magnetic field scans. As a result, constraints on the current experimental designs can be lifted. For example, a trapezoidal waveform can be used to accelerate the scan rate without affecting the signal bandwidth. The assumptions made to develop the previous algorithms are mathematically validated.

| S-EPMC7575242 | biostudies-literature

A general solution for the 2-pyridyl problem.

Project description:Problem solved: an air-stable 2-pyridyl borane that can effectively couple to a wide range of aryl and heteroaryl halides and pseudohalides has evaded the synthesis community for decades. The discovery that Cu(DEA)(2) powerfully enables palladium-mediated cross-couplings with air-stable boronates 1 has finally provided a general solution to this problem. DEA=diethanolamine, DMF=N,N'-dimethylformamide, Tf=trifluoromethanesulfonyl.

| S-EPMC3433254 | biostudies-literature

Radius constants for analytic functions with fixed second coefficient.

Project description:Let f(z) = z + ∑(n=2)(∞) (a)n(z) (n) be analytic in the unit disk with the second coefficient a2 satisfying |a2| = 2b, 0 ≤ b ≤ 1. Sharp radius of Janowski starlikeness is obtained for functions f whose nth coefficient satisfies |a(n)| ≤ cn + d (c, d ≥ 0) or |a(n)| ≤ c/n (c > 0 and n ≥ 3). Other radius constants are also obtained for these functions, and connections with earlier results are made.

| S-EPMC4102033 | biostudies-other

Meta-analytic evidence for a core problem solving network across multiple representational domains.

Project description:Problem solving is a complex skill engaging multi-stepped reasoning processes to find unknown solutions. The breadth of real-world contexts requiring problem solving is mirrored by a similarly broad, yet unfocused neuroimaging literature, and the domain-general or context-specific brain networks associated with problem solving are not well understood. To more fully characterize those brain networks, we performed activation likelihood estimation meta-analysis on 280 neuroimaging problem solving experiments reporting 3166 foci from 1919 individuals across 131 papers. The general map of problem solving revealed broad fronto-cingulo-parietal convergence, regions similarly identified when considering separate mathematical, verbal, and visuospatial problem solving domain-specific analyses. Conjunction analysis revealed a common network supporting problem solving across diverse contexts, and difference maps distinguished functionally-selective sub-networks specific to task type. Our results suggest cooperation between representationally specialized sub-network and whole-brain systems provide a neural basis for problem solving, with the core network contributing general purpose resources to perform cognitive operations and manage problem demand. Further characterization of cross-network dynamics could inform neuroeducational studies on problem solving skill development.

| S-EPMC6425494 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

Tweets

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data