scholarly journals Quantitative Analysis of a Transient Dynamics of a Gene Regulatory Network

2018 ◽  
Author(s):  
JaeJun Lee ◽  
Julian Lee
Keyword(s):  
Fixed Point ◽  
Quantitative Analysis ◽  
Rate Equation ◽  
Regulatory Network ◽  
Mean Field ◽  
Extinction Time ◽  
Stochastic Noise ◽  
Stable Fixed Point ◽  
The Mean ◽  
Gene Regulatory

AbstractIn a stochastic process, noise often modifies the picture offered by the mean field dynamics. In particular, when there is an absorbing state, the noise erases a stable fixed point of the mean field equation from the stationary distribution, and turns it into a transient peak. We make a quantitative analysis of this effect for a simple genetic regulatory network with positive feedback, where the proteins become extinct in the presence of stochastic noise, contrary to the prediction of the deterministic rate equation that the protein number converges to a non-zero value. We show that the transient peak appears near the stable fixed point of the rate equation, and the extinction time diverges exponentially as the stochastic noise approaches zero. We also show how the baseline production from the inactive gene ameliorates the effect of the stochastic noise, and interpret the opposite effects of the noise and the baseline production in terms of the position shift of the unstable fixed point. The order of magnitude estimates using biological parameters suggest that for a real gene regulatory network, the stochastic noise is sufficiently small so that not only is the extinction time much larger than biologically relevant time-scales, but also the effect of the baseline production dominates over that of the stochastic noise, leading to the protection from the catastrophic rare event of protein extinction.

scholarly journals Insensitivity of the mean field limit of loss systems under SQ(d) routeing

2019 ◽  
Vol 51 (4) ◽  
pp. 1027-1066
Author(s):  
Thirupathaiah Vasantam ◽  
Arpan Mukhopadhyay ◽  
Ravi R. Mazumdar
Keyword(s):  
Fixed Point ◽  
Service Time ◽  
Mean Field ◽  
Service Time Distribution ◽  
Field Limit ◽  
Mean Field Limit ◽  
Mean Field Equations ◽  
The Mean ◽  
Loss Systems ◽  
Exponential Case

AbstractIn this paper, we study a large multi-server loss model under the SQ(d) routeing scheme when the service time distributions are general with finite mean. Previous works have addressed the exponential service time case when the number of servers goes to infinity, giving rise to a mean field model. The fixed point of the limiting mean field equations (MFEs) was seen to be insensitive to the service time distribution in simulations, but no proof was available. While insensitivity is well known for loss systems, the models, even with state-dependent inputs, belong to the class of linear Markov models. In the context of SQ(d) routeing, the resulting model belongs to the class of nonlinear Markov processes (processes whose generator itself depends on the distribution) for which traditional arguments do not directly apply. Showing insensitivity to the general service time distributions has thus remained an open problem. Obtaining the MFEs in this case poses a challenge due to the resulting Markov description of the system being in positive orthant as opposed to a finite chain in the exponential case. In this paper, we first obtain the MFEs and then show that the MFEs have a unique fixed point that coincides with the fixed point in the exponential case, thus establishing insensitivity. The approach is via a measure-valued Markov process representation and the martingale problem to establish the mean field limit.

scholarly journals Quantitative analysis of the ThrbCRM1-centered gene regulatory network

Biology Open ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. bio039115 ◽  
Author(s):  
Benjamin Souferi ◽  
Mark M. Emerson
Keyword(s):  
Quantitative Analysis ◽  
Gene Regulatory Network ◽  
Regulatory Network ◽  
Gene Regulatory

scholarly journals Mean field analysis of a spatial stochastic model of a gene regulatory network

2014 ◽  
Vol 71 (4) ◽  
pp. 921-959 ◽  
Author(s):  
M. Sturrock ◽  
P. J. Murray ◽  
A. Matzavinos ◽  
M. A. J. Chaplain
Keyword(s):  
Stochastic Model ◽  
Gene Regulatory Network ◽  
Regulatory Network ◽  
Mean Field ◽  
Field Analysis ◽  
Gene Regulatory ◽  
Spatial Stochastic Model

Performance Analysis of Work Stealing in Large-scale Multithreaded Computing

2021 ◽  
Vol 6 (2) ◽  
pp. 1-28
Author(s):  
Nikki Sonenberg ◽  
Grzegorz Kielanski ◽  
Benny Van Houdt
Keyword(s):  
Fixed Point ◽  
Large Scale ◽  
Field Model ◽  
Unique Fixed Point ◽  
Mean Field ◽  
Response Time Distribution ◽  
Mean Field Model ◽  
Work Stealing ◽  
Poisson Arrivals ◽  
The Mean

Randomized work stealing is used in distributed systems to increase performance and improve resource utilization. In this article, we consider randomized work stealing in a large system of homogeneous processors where parent jobs spawn child jobs that can feasibly be executed in parallel with the parent job. We analyse the performance of two work stealing strategies: one where only child jobs can be transferred across servers and the other where parent jobs are transferred. We define a mean-field model to derive the response time distribution in a large-scale system with Poisson arrivals and exponential parent and child job durations. We prove that the model has a unique fixed point that corresponds to the steady state of a structured Markov chain, allowing us to use matrix analytic methods to compute the unique fixed point. The accuracy of the mean-field model is validated using simulation. Using numerical examples, we illustrate the effect of different probe rates, load, and different child job size distributions on performance with respect to the two stealing strategies, individually, and compared to each other.

scholarly journals On the Critical Value for ‘Percolation’ of Minimum-Weight Trees in the Mean-Field Distance Model

1998 ◽  
Vol 7 (1) ◽  
pp. 1-10 ◽  
Author(s):  
DAVID ALDOUS
Keyword(s):  
Fixed Point ◽  
Probability Distributions ◽  
Minimum Weight ◽  
Mean Field ◽  
Critical Value ◽  
Edge Weight ◽  
Maximal Size ◽  
Distance Model ◽  
The Mean

Consider the complete n-graph with independent exponential (mean n) edge-weights. Let M(c, n) be the maximal size of subtree for which the average edge-weight is at most c. It is shown that M(c, n) makes the transition from o(n) to Ω(n) around some critical value c(0), which can be specified in terms of a fixed point of a mapping on probability distributions.

scholarly journals GREMA: modelling of emulated gene regulatory networks with confidence levels based on evolutionary intelligence to cope with the underdetermined problem

2020 ◽  
Vol 36 (12) ◽  
pp. 3833-3840
Author(s):  
Ming-Ju Tsai ◽  
Jyun-Rong Wang ◽  
Shinn-Jang Ho ◽  
Li-Sun Shu ◽  
Wen-Lin Huang ◽  
...  
Keyword(s):  
Gene Regulatory Network ◽  
Confidence Level ◽  
Regulatory Network ◽  
Supplementary Information ◽  
Experimental Measurements ◽  
Confidence Levels ◽  
Benchmark Datasets ◽  
The Mean ◽  
Gene Regulatory ◽  
Evolutionary Intelligence

Abstract Motivation Non-linear ordinary differential equation (ODE) models that contain numerous parameters are suitable for inferring an emulated gene regulatory network (eGRN). However, the number of experimental measurements is usually far smaller than the number of parameters of the eGRN model that leads to an underdetermined problem. There is no unique solution to the inference problem for an eGRN using insufficient measurements. Results This work proposes an evolutionary modelling algorithm (EMA) that is based on evolutionary intelligence to cope with the underdetermined problem. EMA uses an intelligent genetic algorithm to solve the large-scale parameter optimization problem. An EMA-based method, GREMA, infers a novel type of gene regulatory network with confidence levels for every inferred regulation. The higher the confidence level is, the more accurate the inferred regulation is. GREMA gradually determines the regulations of an eGRN with confidence levels in descending order using either an S-system or a Hill function-based ODE model. The experimental results showed that the regulations with high-confidence levels are more accurate and robust than regulations with low-confidence levels. Evolutionary intelligence enhanced the mean accuracy of GREMA by 19.2% when using the S-system model with benchmark datasets. An increase in the number of experimental measurements may increase the mean confidence level of the inferred regulations. GREMA performed well compared with existing methods that have been previously applied to the same S-system, DREAM4 challenge and SOS DNA repair benchmark datasets. Availability and implementation All of the datasets that were used and the GREMA-based tool are freely available at https://nctuiclab.github.io/GREMA. Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals Non-perturbative effects in spin glasses

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Michele Castellana ◽  
Giorgio Parisi
Keyword(s):  
Fixed Point ◽  
Ising Model ◽  
Spin Glasses ◽  
Numerical Study ◽  
Mean Field ◽  
Critical Dimension ◽  
Upper Critical Dimension ◽  
Ising Spin ◽  
Ferromagnetic Ising Model ◽  
The Mean

Abstract We present a numerical study of an Ising spin glass with hierarchical interactions—the hierarchical Edwards-Anderson model with an external magnetic field (HEA). We study the model with Monte Carlo (MC) simulations in the mean-field (MF) and non-mean-field (NMF) regions corresponding to d ≥ 4 and d < 4 for the d-dimensional ferromagnetic Ising model respectively. We compare the MC results with those of a renormalization-group (RG) study where the critical fixed point is treated as a perturbation of the MF one, along the same lines as in the "Equation missing"-expansion for the Ising model. The MC and the RG method agree in the MF region, predicting the existence of a transition and compatible values of the critical exponents. Conversely, the two approaches markedly disagree in the NMF case, where the MC data indicates a transition, while the RG analysis predicts that no perturbative critical fixed point exists. Also, the MC estimate of the critical exponent ν in the NMF region is about twice as large as its classical value, even if the analog of the system dimension is within only ~2% from its upper-critical-dimension value. Taken together, these results indicate that the transition in the NMF region is governed by strong non-perturbative effects.

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