scholarly journals Statistics of Nascent and Mature RNA Fluctuations in a Stochastic Model of Transcriptional Initiation, Elongation, Pausing, and Termination

2020 ◽  
Vol 83 (1) ◽  
Author(s):  
Tatiana Filatova ◽  
Nikola Popovic ◽  
Ramon Grima
Keyword(s):  
Experimental Data ◽  
Fluorescence Microscopy ◽  
Stochastic Model ◽  
Explicit Dependence ◽  
Transcriptional Initiation ◽  
Estimate Parameter ◽  
Mean And Variance ◽  
The Mean ◽  
Nascent Rna ◽  
Parameter Values

AbstractRecent advances in fluorescence microscopy have made it possible to measure the fluctuations of nascent (actively transcribed) RNA. These closely reflect transcription kinetics, as opposed to conventional measurements of mature (cellular) RNA, whose kinetics is affected by additional processes downstream of transcription. Here, we formulate a stochastic model which describes promoter switching, initiation, elongation, premature detachment, pausing, and termination while being analytically tractable. We derive exact closed-form expressions for the mean and variance of nascent RNA fluctuations on gene segments, as well as of total nascent RNA on a gene. We also obtain exact expressions for the first two moments of mature RNA fluctuations and approximate distributions for total numbers of nascent and mature RNA. Our results, which are verified by stochastic simulation, uncover the explicit dependence of the statistics of both types of RNA on transcriptional parameters and potentially provide a means to estimate parameter values from experimental data.

scholarly journals Statistics of nascent and mature RNA fluctuations in a stochastic model of transcriptional initiation, elongation, pausing, and termination

2020 ◽  
Author(s):  
Tatiana Filatova ◽  
Nikola Popovic ◽  
Ramon Grima
Keyword(s):  
Experimental Data ◽  
Fluorescence Microscopy ◽  
Stochastic Model ◽  
Explicit Dependence ◽  
Transcriptional Initiation ◽  
Estimate Parameter ◽  
Mean And Variance ◽  
The Mean ◽  
Nascent Rna ◽  
Parameter Values

AbstractRecent advances in fluorescence microscopy have made it possible to measure the fluctuations of nascent (actively transcribed) RNA. These closely reflect transcription kinetics, as opposed to conventional measurements of mature (cellular) RNA, whose kinetics is affected by additional processes downstream of transcription. Here, we formulate a stochastic model which describes promoter switching, initiation, elongation, premature detachment, pausing, and termination while being analytically tractable. By computational binning of the gene into smaller segments, we derive exact closed-form expressions for the mean and variance of nascent RNA fluctuations in each of these segments, as well as for the total nascent RNA on a gene. We also derive exact expressions for the first two moments of mature RNA fluctuations, and approximate distributions for total numbers of nascent and mature RNA. Our results, which are verified by stochastic simulation, uncover the explicit dependence of the statistics of both types of RNA on transcriptional parameters and potentially provide a means to estimate parameter values from experimental data.

scholarly journals Simulating tubulin-associated unit transport in an axon: using bootstrapping for estimating confidence intervals of best-fit parameter values obtained from indirect experimental data

2017 ◽  
Vol 473 (2201) ◽  
pp. 20170045 ◽  
Author(s):  
I. A. Kuznetsov ◽  
A. V. Kuznetsov
Keyword(s):  
Experimental Data ◽  
Confidence Intervals ◽  
Surrogate Data ◽  
Model Parameters ◽  
Model Predictions ◽  
Estimate Parameter ◽  
Minimum Number ◽  
Percentile Bootstrap ◽  
Parameter Values ◽  
Best Fit

In this paper, we first develop a model of axonal transport of tubulin-associated unit (tau) protein. We determine the minimum number of parameters necessary to reproduce published experimental results, reducing the number of parameters from 18 in the full model to eight in the simplified model. We then address the following questions: Is it possible to estimate parameter values for this model using the very limited amount of published experimental data? Furthermore, is it possible to estimate confidence intervals for the determined parameters? The idea that is explored in this paper is based on using bootstrapping. Model parameters were estimated by minimizing the objective function that simulates the discrepancy between the model predictions and experimental data. Residuals were then identified by calculating the differences between the experimental data and model predictions. New, surrogate ‘experimental’ data were generated by randomly resampling residuals. By finding sets of best-fit parameters for a large number of surrogate data the histograms for the model parameters were produced. These histograms were then used to estimate confidence intervals for the model parameters, by using the percentile bootstrap. Once the model was calibrated, we applied it to analysing some features of tau transport that are not accessible to current experimental techniques.

scholarly journals Payments under the Average Crop Revenue Program: Implications for Government Costs and Producer Preferences

2009 ◽  
Vol 38 (1) ◽  
pp. 49-64 ◽  
Author(s):  
Joseph Cooper
Keyword(s):  
Stochastic Model ◽  
Coefficient Of Variation ◽  
Total Revenue ◽  
Mean And Variance ◽  
The Mean ◽  
Peripheral Production ◽  
The Impact ◽  
To Receive ◽  
Payment Rate ◽  
The U.S

This paper develops a stochastic model for comparing payments to U.S. corn producers under the U.S. Senate's Average Crop Revenue Program (ACR) versus payments under the price-based marketing loan benefit and countercyclical payment programs. Using this model, the paper examines the sensitivity of the density function for payments to changes in expected price levels. We also assess the impact of the choice of yield aggregation used in the ACR payment rate on the mean and variance of farm returns. We find that ACR payments lower the producer's coefficient of variation of total revenue more than does the price-based support, although ACR may not raise mean revenue as much. While corn farmers in the heartland states might still prefer to receive the traditional forms of support when prices are low relative to statutory loan rates and target prices, this outcome is not necessarily the case for farmers in peripheral production regions.

scholarly journals Analysis of Single Bacterium Dynamics in a Stochastic Model of Toxin-Producing Bacteria

2021 ◽  
pp. 210-225
Author(s):  
Jamie Paterson ◽  
Martín López-García ◽  
Joseph Gillard ◽  
Thomas R. Laws ◽  
Grant Lythe ◽  
...  
Keyword(s):  
Experimental Data ◽  
Stochastic Model ◽  
Biological System ◽  
Toxin Production ◽  
Bacterial Toxin ◽  
Bacterial Populations ◽  
The Mean ◽  
First Time ◽  
Number Of Bacteria

AbstractWe stochastically model two bacterial populations which can produce toxins. We propose to analyse this biological system by following the dynamics of a single bacterium during its lifetime, as well as its progeny. We study the lifespan of a single bacterium, the number of divisions that this bacterium undergoes, and the number of toxin molecules that it produces during its lifetime. We also compute the mean number of bacteria in the genealogy of the original bacterium and the number of toxin molecules produced by its genealogy. We illustrate the applicability of our methods by considering the bacteria Bacillus anthracis and antibiotic treatment, making use of in vitro experimental data. We quantify, for the first time, bacterial toxin production by exploiting an in vitro assay for the A16R strain, and make use of the resulting parameterised model to illustrate our techniques.

The global dynamics of stochastic Holling type II predator-prey models with non constant mortality rate

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5811-5825
Author(s):  
Xinhong Zhang
Keyword(s):  
Mortality Rate ◽  
Stochastic Model ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Global Dynamics ◽  
Type Ii ◽  
Predator Prey ◽  
Persistence In The Mean ◽  
The Mean ◽  
Predator Prey Models

In this paper we study the global dynamics of stochastic predator-prey models with non constant mortality rate and Holling type II response. Concretely, we establish sufficient conditions for the extinction and persistence in the mean of autonomous stochastic model and obtain a critical value between them. Then by constructing appropriate Lyapunov functions, we prove that there is a nontrivial positive periodic solution to the non-autonomous stochastic model. Finally, numerical examples are introduced to illustrate the results developed.

Stochastic model of nonideal mixer. Boundary conditions in batch system

1984 ◽  
Vol 49 (2) ◽  
pp. 490-505
Author(s):  
Vladimír Kudrna ◽  
Pavel Hasal ◽  
Jiří Vlček
Keyword(s):  
Experimental Data ◽  
Stochastic Model ◽  
Boundary Conditions ◽  
Closed System ◽  
Batch System ◽  
Ideal Mixer

The earlier proposed general approach for description of the non-ideal mixer is coupled with corresponding boundary conditions for the closed system. Some simplifications in this procedure result in relations which are in agreement with experimental data.

scholarly journals Weighted statistical binary patterns for facial feature representation

2021 ◽  
Author(s):  
Hung Phuoc Truong ◽  
Thanh Phuong Nguyen ◽  
Yong-Guk Kim
Keyword(s):  
Comprehensive Evaluation ◽  
Facial Feature ◽  
Input Image ◽  
Feature Representation ◽  
Illumination Variation ◽  
Straight Line ◽  
Mean And Variance ◽  
The Mean ◽  
Face Datasets ◽  
Degraded Images

AbstractWe present a novel framework for efficient and robust facial feature representation based upon Local Binary Pattern (LBP), called Weighted Statistical Binary Pattern, wherein the descriptors utilize the straight-line topology along with different directions. The input image is initially divided into mean and variance moments. A new variance moment, which contains distinctive facial features, is prepared by extracting root k-th. Then, when Sign and Magnitude components along four different directions using the mean moment are constructed, a weighting approach according to the new variance is applied to each component. Finally, the weighted histograms of Sign and Magnitude components are concatenated to build a novel histogram of Complementary LBP along with different directions. A comprehensive evaluation using six public face datasets suggests that the present framework outperforms the state-of-the-art methods and achieves 98.51% for ORL, 98.72% for YALE, 98.83% for Caltech, 99.52% for AR, 94.78% for FERET, and 99.07% for KDEF in terms of accuracy, respectively. The influence of color spaces and the issue of degraded images are also analyzed with our descriptors. Such a result with theoretical underpinning confirms that our descriptors are robust against noise, illumination variation, diverse facial expressions, and head poses.

scholarly journals Groups and Individuals: Optical Flow Patterns of Broiler Chicken Flocks Are Correlated with the Behavior of Individual Birds

Animals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 568
Author(s):  
Sabine G. Gebhardt-Henrich ◽  
Ariane Stratmann ◽  
Marian Stamp Dawkins
Keyword(s):  
Optical Flow ◽  
Broiler Chicken ◽  
Average Length ◽  
Flow Patterns ◽  
Group Level ◽  
Positive Correlation ◽  
Water Test ◽  
Mean And Variance ◽  
The Mean

Group level measures of welfare flocks have been criticized on the grounds that they give only average measures and overlook the welfare of individual animals. However, we here show that the group-level optical flow patterns made by broiler flocks can be used to deliver information not just about the flock averages but also about the proportion of individuals in different movement categories. Mean optical flow provides information about the average movement of the whole flock while the variance, skew and kurtosis quantify the variation between individuals. We correlated flock optical flow patterns with the behavior and welfare of a sample of 16 birds per flock in two runway tests and a water (latency-to-lie) test. In the runway tests, there was a positive correlation between the average time taken to complete the runway and the skew and kurtosis of optical flow on day 28 of flock life (on average slow individuals came from flocks with a high skew and kurtosis). In the water test, there was a positive correlation between the average length of time the birds remained standing and the mean and variance of flock optical flow (on average, the most mobile individuals came from flocks with the highest mean). Patterns at the flock level thus contain valuable information about the activity of different proportions of the individuals within a flock.

scholarly journals A New Model for the Stochastic Point Reactor: Development and Comparison with Available Models

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 955
Author(s):  
Alamir Elsayed ◽  
Mohamed El-Beltagy ◽  
Amnah Al-Juhani ◽  
Shorooq Al-Qahtani
Keyword(s):  
Kinetic Model ◽  
Differential Equations ◽  
Test Cases ◽  
System Of Differential Equations ◽  
Reactor Model ◽  
Time System ◽  
New Model ◽  
Reactor Dynamics ◽  
Mean And Variance ◽  
The Mean

The point kinetic model is a system of differential equations that enables analysis of reactor dynamics without the need to solve coupled space-time system of partial differential equations (PDEs). The random variations, especially during the startup and shutdown, may become severe and hence should be accounted for in the reactor model. There are two well-known stochastic models for the point reactor that can be used to estimate the mean and variance of the neutron and precursor populations. In this paper, we reintroduce a new stochastic model for the point reactor, which we named the Langevin point kinetic model (LPK). The new LPK model combines the advantages, accuracy, and efficiency of the available models. The derivation of the LPK model is outlined in detail, and many test cases are analyzed to investigate the new model compared with the results in the literature.

scholarly journals Rapid review of available evidence on the serial interval and generation time of COVID-19

BMJ Open ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. e040263
Author(s):  
John Griffin ◽  
Miriam Casey ◽  
Áine Collins ◽  
Kevin Hunt ◽  
David McEvoy ◽  
...  
Keyword(s):  
Generation Time ◽  
Social Contact ◽  
Careful Consideration ◽  
Rapid Review ◽  
Eligibility Criteria ◽  
Reproduction Numbers ◽  
Serial Interval ◽  
Scientific Papers ◽  
The Mean ◽  
Parameter Values

The serial interval is the time between symptom onsets in an infector–infectee pair. The generation time, also known as the generation interval, is the time between infection events in an infector–infectee pair. The serial interval and the generation time are key parameters for assessing the dynamics of a disease. A number of scientific papers reported information pertaining to the serial interval and/or generation time for COVID-19. Objective Conduct a review of available evidence to advise on appropriate parameter values for serial interval and generation time in national COVID-19 transmission models for Ireland and on methodological issues relating to those parameters. Methods We conducted a rapid review of the literature covering the period 1 January 2020 and 21 August 2020, following predefined eligibility criteria. Forty scientific papers met our inclusion criteria and were included in the review. Results The mean of the serial interval ranged from 3.03 to 7.6 days, based on 38 estimates, and the median from 1.0 to 6.0 days (based on 15 estimates). Only three estimates were provided for the mean of the generation time. These ranged from 3.95 to 5.20 days. One estimate of 5.0 days was provided for the median of the generation time. Discussion Estimates of the serial interval and the generation time are very dependent on the specific factors that apply at the time that the data are collected, including the level of social contact. Consequently, the estimates may not be entirely relevant to other environments. Therefore, local estimates should be obtained as soon as possible. Careful consideration should be given to the methodology that is used. Real-time estimations of the serial interval/generation time, allowing for variations over time, may provide more accurate estimates of reproduction numbers than using conventionally fixed serial interval/generation time distributions.

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