Extension of Leap Condition in Approximate Stochastic Simulation Algorithms of Biological Networks

Download

Saliha Demirbüken MScThesis.pdf

Date

2021-9-08

Author

Demirbüken, Saliha

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

450
views

221
downloads

The approximate stochastic simulation (ASS) algorithms are the alternative approaches to generate the complex biological systems with a loss in accuracy by gaining from computational demand. There are a number of approximate methods which can successfully simulate the systems, such as poisson tau-leap and approximate Gillespie algorithms. The common property of these approaches is that they are based on the leap conditon which controls the change in hazard functions under a time interval. By means of this interval we can find an interval for the number of simultaneous reactions k in the time interval generated from the leap condition. In this study, we propose alternative intervals for k that are dependent on the sufficient statistics and also, we derive confidence intervals for k whose parameters are obtained via maximum likelihood estimator, moment estimators and bayesian estimators. Furthermore, we extend the leap condition by using higher order Taylor expansion whose original estimators are found under the first order. In our derivations, we use the poisson tau-leap approach since it is the fundamental approximate stochastic simulation method. Moreover, we apply the approximate Gillespie algorithm since it is one of the recent approaches that is derived from the idea of the poisson tau-leap method. We consider that although the proposal approaches to these two algortihms, they can be also adapted to other algorithms whose derivation are based on the parametric assumption.

Subject Keywords

Approximate Stochastic Simulation Algorithms, Leap Condition, Confidence Interval

URI

https://hdl.handle.net/11511/92241

Collections

Graduate School of Applied Mathematics, Thesis

Suggestions

OpenMETU
Core

A neural network approach for approximate force response analyses of a bridge population Hasançebi, Oğuzhan (2013-03-01) In this paper, artificial neural networks (ANNs) are used to develop an efficient method for rapid and approximate force response analyses of a bridge population. The single-span reinforced concrete T-beam bridge population in Pennsylvania State is taken as a particular case study. First, a statistical analysis is conducted to examine implicit and explicit dependencies between various geometrical and structural parameters of the bridges, and the governing bridge parameters are identified along with their ra...
FUSION OF IMAGE SEGMENTATION ALGORITHMS USING CONSENSUS CLUSTERING Ozay, Mete; Yarman Vural, Fatoş Tunay; Kulkarni, Sanjeev R.; Poor, H. Vincent (2013-09-18) A new segmentation fusion method is proposed that ensembles the output of several segmentation algorithms applied on a remotely sensed image. The candidate segmentation sets are processed to achieve a consensus segmentation using a stochastic optimization algorithm based on the Filtered Stochastic BOEM (Best One Element Move) method. For this purpose, Filtered Stochastic BOEM is reformulated as a segmentation fusion problem by designing a new distance learning approach. The proposed algorithm also embeds th...
Computation of the Primary Decomposition of Polynomial Ideals Using Gröbner Bases Tolgay, Betül; Karayayla, Tolga; Department of Mathematics (2021-8-06) In this thesis, we investigate algorithms for computing primary decompositions of ideals in polynomial rings. Every ideal in a polynomial ring over a Noetherian commutative ring with identity has a primary decomposition, that is, it can be expressed as the intersection of primary ideals (in a unique way or not). The existence of primary decompositions in such polynomial rings is a result of the ascending chain condition and the existence proof does not suggest any construction method for the primary compone...
Application of genetic algorithms to geometry optimization of microclusters: A comparative study of empirical potential energy functions for silicon Erkoc, S; Leblebicioğlu, Mehmet Kemal; Halıcı, Uğur (Informa UK Limited, 2003-01-01) Evolutionary computation techniques (in particular, genetic algorithms) have been applied to optimize the structure of microclusters. Various empirical potential energy functions have been used to describe the interactions among the atoms in the clusters. A comparative study of silicon microclusters has been performed.
MODELLING OF KERNEL MACHINES BY INFINITE AND SEMI-INFINITE PROGRAMMING Ozogur-Akyuz, S.; Weber, Gerhard Wilhelm (2009-06-03) In Machine Learning (ML) algorithms, one of the crucial issues is the representation of the data. As the data become heterogeneous and large-scale, single kernel methods become insufficient to classify nonlinear data. The finite combinations of kernels are limited up to a finite choice. In order to overcome this discrepancy, we propose a novel method of "infinite" kernel combinations for learning problems with the help of infinite and semi-infinite programming regarding all elements in kernel space. Looking...

Citation Formats

S. Demirbüken, “Extension of Leap Condition in Approximate Stochastic Simulation Algorithms of Biological Networks,” M.S. - Master of Science, Middle East Technical University, 2021.