Maximum entropy algorithm with inexact upper entropy bound based on Fup basis functions with compact support

Gotovac, Hrvoje; Gotovac, Bla

doi:10.1016/j.jcp.2009.09.011

Cited by 21 publications

(28 citation statements)

References 18 publications

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“…Considering that in this case the concrete values become very large, it might be advantageous to consider central moments instead, which implies that the reconstruction procedure has to be adapted. Alternatively, we might (instead of algebraic moments) consider other functions of the random variables, such as exponential functions [Mnatsakanov and Sarkisian 2013], Fup functions [Gotovac and Gotovac 2009], and Chebyshev polynomials [Bandyopadhyay et al 2005]. Another possible extension could address the problem of truncating the support of the distribution such that the reconstruction is applied to a finite support.…”

Section: Discussionmentioning

confidence: 99%

Model Reconstruction for Moment-Based Stochastic Chemical Kinetics

Andreychenko

Mikeev

Wolf

2015

ACM Trans. Model. Comput. Simul.

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Based on the theory of stochastic chemical kinetics, the inherent randomness of biochemical reaction networks can be described by discrete-state continuous-time Markov chains. However, the analysis of such processes is computationally expensive and sophisticated numerical methods are required. Here, we propose an analysis framework in which we integrate a number of moments of the process instead of the state probabilities. This results in a very efficient simulation of the time evolution of the process. To regain the state probabilities from the moment representation, we combine the fast moment-based simulation with a maximum entropy approach for the reconstruction of the underlying probability distribution. We investigate the usefulness of this combined approach in the setting of stochastic chemical kinetics and present numerical results for three reaction networks showing its efficiency and accuracy. Besides a simple dimerization system, we study a bistable switch system and a multiattractor network with complex dynamics. ACM Reference Format:Alexander Andreychenko, Linar Mikeev, and Verena Wolf. 2015. Model reconstruction for moment-based stochastic chemical kinetics. ACM Trans. Model.

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Section: Discussionmentioning

confidence: 99%

Model Reconstruction for Moment-Based Stochastic Chemical Kinetics

Andreychenko

Mikeev

Wolf

2015

ACM Trans. Model. Comput. Simul.

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“…where f (x) is the PDF of a random variable X and mi is the ith-order origin moment as the constraint, which can be determined by the random variable X. The Lagrange method is used to work out the MaxEnt PDF from (14). (15) and (16).…”

Section: A Maxent Principlementioning

confidence: 99%

“…Among these distributions, a maximum entropy (MaxEnt) probability distribution has the largest value of entropy and the least biased estimate on the given information [13]. Many researchers have attempted to fit the MaxEnt probability distribution function (PDF) from various sampling data based on the MaxEnt principle [14][15][16][17]. Zhang et al approximated the structural performance function.…”

Section: Introductionmentioning

confidence: 99%

Reliability Evaluation of Multi-Mechanism Failure for Semiconductor Devices Using Physics-of-Failure Technique and Maximum Entropy Principle

Wan

Wang

et al. 2020

IEEE Access

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The physics-of-failure (PoF) technique is a practical approach to evaluate the reliability of semiconductor devices. However, the PoF approaches are usually insufficient in dealing with multimechanism failure and fitting the Monte Carlo (MC) sampling data. In our study, we propose an improved reliability evaluation method based on PoF technique and maximum entropy (MaxEnt) principle. The PoF models are used to generate time-to-failure samples of the failure mechanisms. Cumulative damage rules and competing failure rules are adopted to deal with multi-point and multi-mechanism failure and generate lifetime samples of the device. And the lifetime samples are fitted by MaxEnt distributions through the proposed fitting algorithm. The numerical examples given in the paper indicate that the MaxEnt distributions can describe the samples well and have a competitive advantage in dealing with multi-peak samples. A case study about a semiconductor device with multi-mechanism failure is presented to explain the workflow of the proposed reliability evaluation approach. The results show that the proposed MaxEnt distributions can yield reliable reliability evaluation results compared with Weibull and Lognormal distributions in the multi-mechanism failure process.

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“…Jednom kada je definiran proizvoljan broj n apsolutnih momenata koncentracije zagađenja, PDF se može rekonstruirati iz njih putem inverzije momenata [11] gdje se zapravo vidi direktna primjena ovako dobivenih momenata. Traženi PDF se može dobiti na osnovi principa maksimalne entropije [12] ili prilagodbom teorijske distribucije putem preklapanja momenata prema (3). Potonji postupak je primijenjen korištenjem beta-distribucije [13,14] te je radi jednostavnosti, implementiran u računalnu aplikaciju CPoRT.…”

Section: Izračun Funkcija Gustoće Vjerojatnostiunclassified

Estimation of statistical parameters of nutrients concentration generated in estuaries

Galešić¹,

Andričević²,

Divić³

2017

Zajednički Temelji 2017 - Peti Skup Mladih Istraživača Iz Područja Građevinarstva I Srodnih Tehničkih Znanosti - Zbornik Radova

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SažetakRijeke su svakako jedan od najvažnijih puteva prijenosa nutrijenata s kopna u obalne vode, koji potom u ušćima mogu izazvati čitav niz problema, od prekoračenja dopuštenih graničnih koncentracija do uzrokovanja pojave eutrofikacije. Provedeno istraživanje se bavi upravo analizom takvog pronosa u bliskoj zoni ušća za stacionarno stanje toka te domenu integriranu po dubini (2D). Iz osnovne advektivno difuzne jednadžbe su izvedeni statistički apsolutni momenti funkcije gustoće vjerojatnosti definirane u točki, te su potom pripadajuće funkcije rekonstruirane korištenjem beta-distribucije. Funkcije gustoće vjerojatnosti su ključan podatak za definiciju rizika od prekoračenja graničnih koncentracija, te ovakva metodologija omogućava izračun funkcije i pripadajućeg rizika u proizvoljnoj točki domene ušća. Razvijena metodologija je implementirana u user-friendly računalnu aplikaciju CPoRT koja je besplatna za korištenje, a koja je među ostalim namijenjena i podizanju svijesti o važnosti adekvatnog upravljanja količinama nutrijenata unesenih rijekama.Ključne riječi: koncentracija zagađenja, statistički momenti koncentracije, ušća, funkcija gustoće vjerojatnosti, alat za brzu procjenu rizika od zagađenja Estimation of statistical parameters of nutrients concentration generated in estuaries AbstractRivers are considered as one of the most influential pathways of nutrients which are generated inland and causing multiple problems when brought to estuaries, from exceeding the limit concentrations to eutrophication issues. This paper investigates such problem in estuary by analysing the steady transport of conservative pollutant in the near field zone of depth integrated domain (2D). The concentration moments are developed from fundamental advection-diffusion equation, and then are utilized to obtain the point concentration probability density function (PDF). PDFs are key data when conducting the risk assessment for exceeding the allowed concentration values, hence this methodology enables one to obtain PDF and corresponding exceedance probability at an arbitrary point in the estuary domain. The developed methodology is further implemented in a user-friendly PC application that is free to use and which is also designed to raise awareness about importance of adequate management of nutrients being generated and brought in by rivers.

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Maximum entropy algorithm with inexact upper entropy bound based on Fup basis functions with compact support

Cited by 21 publications

References 18 publications

Model Reconstruction for Moment-Based Stochastic Chemical Kinetics

Model Reconstruction for Moment-Based Stochastic Chemical Kinetics

Reliability Evaluation of Multi-Mechanism Failure for Semiconductor Devices Using Physics-of-Failure Technique and Maximum Entropy Principle

Estimation of statistical parameters of nutrients concentration generated in estuaries

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