First-order stochastic chemical reactions and oscillations in the variance

1980 ◽  
Vol 17 (4) ◽  
pp. 1087-1093 ◽  
Author(s):  
Richard C. Hertzberg ◽  
Vincent F. Gallucci
Keyword(s):  
General Solution ◽  
Markov Model ◽  
Random Processes ◽  
Numerical Examples ◽  
First Order ◽  
Variance Functions ◽  
First Order Kinetics ◽  
Component Systems ◽  
Mean And Variance ◽  
The Mean

The general solution of a Markov model for first-order kinetics is developed as a sum of independent, multinomially distributed random processes. Fluctuations in the mean and variance functions are discussed and shown to be unrelated in time during the early phase of the reaction. Numerical examples are presented for two- and three-component systems.

First-order stochastic chemical reactions and oscillations in the variance

1980 ◽  
Vol 17 (04) ◽  
pp. 1087-1093 ◽  
Author(s):  
Richard C. Hertzberg ◽  
Vincent F. Gallucci
Keyword(s):  
General Solution ◽  
Markov Model ◽  
Random Processes ◽  
Numerical Examples ◽  
First Order ◽  
Variance Functions ◽  
First Order Kinetics ◽  
Component Systems ◽  
Mean And Variance ◽  
The Mean

The general solution of a Markov model for first-order kinetics is developed as a sum of independent, multinomially distributed random processes. Fluctuations in the mean and variance functions are discussed and shown to be unrelated in time during the early phase of the reaction. Numerical examples are presented for two- and three-component systems.

Characterization of a Fibrin Glue-Gdnf Slow-Release Preparation

1998 ◽  
Vol 7 (1) ◽  
pp. 53-61
Author(s):  
Henrich Cheng ◽  
Matt Fraidakis ◽  
Birger Blombäck ◽  
Paul Lapchak ◽  
Barry Hoffer ◽  
...  
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Fibrin Glue ◽  
Trophic Factor ◽  
Adult Rats ◽  
First Order ◽  
First Order Kinetics ◽  
Implantation Sites ◽  
The Mean ◽  
Over Time

One novel method to deliver trophic factor locally in the CNS is to mix it into fibrin glue. In the present studies, [125I]-labeled GDNF-containing fibrin glue balls were used to determine binding and spread of the trophic factor. First, the binding of different concentrations of [125I]-labelèd GDNF in fibrin glue was determined in vitro. Within the six concentrations used (from 200 nM to 0.004 nM, 0 M as control), there was a strong linear correlation between the [125I]-GDNF concentration and the recovered radioactivity (r = 0.992). The mean bound radioactivity in 16 samples with 4 nM [125I]-GDNF was 71262 + 2710 CPM, and accounted for 89.8% of the mean initial count of free [125I]-GDNF (79369 + 3499 CPM). Second, [125I]-GDNF-containing glue balls were implanted into the anterior chamber of adult rats. The implanted fibrin glue balls decreased in size with time, but could still be identified on the irises 2 wk after implantation. Radioactivity was concentrated at the implantation sites in the early stages with a distribution in the surrounding iris tissue, which became separated into focal radioactive spots at the third week. Counts of radioactivity were significantly higher in the [125I]-GDNF glue ball-implanted irises than controls until 14 days after implantation. A study of the [125I] decay over time using least-squares linear regression demonstrated first-order kinetics (r = —0.98, p < 0.02) with k = 0.0091 and T 1/2 = 76 h. Finally, [125I]-GDNF–containing glue balls were implanted in the spinal cord of adult rats. Radioactivity was concentrated at the implantation sites in the early stages and was later distributed more widely in the surrounding thoracic cord. The [125I]-GDNF–containing glue degraded over time and became a porous meshwork with decreasing radioactivity at the later time points. Radioactivity in the spinal cords subjected to implantation of [125I]-GDNF–containing glue balls was higher than in controls for 14 days. Study of the [125I] decay by time with least-squares linear regression demonstrated first-order kinetics (r = -0.97, p = 0.001) with T 1/2 = 75.6 h. We conclude that the trophic factor GDNF becomes bound in the fibrin glue matrix from which it is gradually released. Our results suggest that fibrin glue is an effective substrate for keeping a trophic factor localized in situ for a finite period, protected from the circulation, surrounding aqueous humor or CSF.

scholarly journals CATION EXCHANGE BETWEEN CELLS AND PLASMA OF MAMMALIAN BLOOD

1950 ◽  
Vol 33 (6) ◽  
pp. 703-722 ◽  
Author(s):  
C. W. Sheppard ◽  
W. R. Martin
Keyword(s):  
Exchange Rate ◽  
Radioactive Isotope ◽  
Specific Activity ◽  
Compartment System ◽  
First Order ◽  
First Order Kinetics ◽  
Mammalian Blood ◽  
The Mean ◽  
Pseudo First Order

The exchange of potassium between cells and plasma of heparinized human blood has been studied in vitro using the radioactive isotope K42. The changes in cell and plasma specific activity are characteristic of a simple two-compartment system. The mean of seven determinations of the exchange rate at 38°C. is 1.8 per cent of the cellular potassium per hour. The results indicate that at 38°C. the rate is relatively insensitive to oxygenation or reduction of the hemoglobin, and to 1200 r of gamma radiation. With varying temperature the rate follows pseudo first order kinetics with a Q10 of 2.35. Below 15°C. the rate of loss of potassium exceeds the rate of uptake.

scholarly journals EVALUASI NUMERIK PENDUGA FUNGSI NILAI HARAPAN DAN FUNGSI RAGAM PROSES POISSON MAJEMUK DENGAN INTENSITAS EKSPONENSIAL FUNGSI LINEAR

2018 ◽  
Vol 17 (2) ◽  
pp. 157
Author(s):  
S. UTAMI ◽  
I W. MANGKU ◽  
I G. P. PURNABA
Keyword(s):  
Monte Carlo ◽  
Confidence Intervals ◽  
Observation Interval ◽  
Compound Poisson Process ◽  
Intensity Function ◽  
Significance Level ◽  
Variance Functions ◽  
Mean And Variance ◽  
The Mean ◽  
Strongly Consistent

<em>Performances of estimators for the mean and variance functions of a compound Poisson process having intensity obtained as an exponential of linear function are investigated using Monte Carlo simulations. The intensity function of this process is assumed to be </em>𝑒𝑥𝑝(𝛼+𝛽𝑠) <em>with </em>0&lt;𝛽&lt;<em>∞</em>, <em>where </em>𝛽 <em>is assumed to be known. In [8], estimators of the mean and variance functions of this process have been constructed and have been proved to be unbiased, weakly and strongly consistent. The objectives of this research are to check distributions of these estimators using Monte Carlo simulation and to check the convergence to </em>1−𝛼 <em>of the probabilities that the parameters are contained in the confidence intervals constructed in [11]. Results of the research are as follows. Distribution of estimators for the mean and variance functions are approximately normal. For a given significance level </em>𝛼<em>, the larger the size of observation interval, the closer the probabilities that the parameters are contained in the confidence intervals to </em>1−𝛼<em>.</em>

Reliability-Based Design of Reinforced Earth Retaining Walls

1996 ◽  
Vol 1526 (1) ◽  
pp. 64-78 ◽  
Author(s):  
Imad A. Basheer ◽  
Yacoub M. Najjar
Keyword(s):  
Order Approximation ◽  
Retaining Walls ◽  
Design Parameters ◽  
Physical Parameters ◽  
Statistical Parameters ◽  
First Order ◽  
Reliability Based Design ◽  
Reinforced Earth ◽  
Mean And Variance ◽  
The Mean

Reliability of an earth structure can be assessed from the knowledge of the governing probability distribution and its related statistical parameters, namely, the mean and variance. In this study, the mean and variance for the design parameters (width and length of the reinforcing ties) of reinforced earth retaining walls supporting sandy soils are determined using the first-order Taylor series approximation. Design diagrams that enable estimation of both mean and variance also are developed to avoid extensive computations that involve partial differentiation. Errors associated with truncating second-order terms are also evaluated. It is found that for soils with moderately variable physical parameters, the first-order approximation is adequate for estimating both the mean and variance.

Theoretical analysis and simulation of pedestrian evacuation under invisible conditions

SIMULATION ◽  
2012 ◽  
Vol 88 (9) ◽  
pp. 1138-1148 ◽  
Author(s):  
Ren-Yong Guo ◽  
Hai-Jun Huang
Keyword(s):  
Theoretical Analysis ◽  
Numerical Examples ◽  
Pedestrian Evacuation ◽  
Mean And Variance ◽  
The Mean

We study a class of pedestrian evacuation process in rooms without visibility by analytical and simulative methods. First, the moving distance of pedestrians for leaving the rooms is analyzed using the mean and variance theory. A microscopic pedestrian model is then extended to simulate pedestrian evacuation in the rooms. By numerical examples, the distributions of single individual’s evacuation efficiency in the rooms and the improvement by increasing the number of exits for the individual’s evacuation efficiency are demonstrated. Pedestrians’ moving distances obtained by analytical and simulative methods are also compared. The study is helpful for assessing the efficiency of evacuation and the safety of buildings under conditions of invisibility.

scholarly journals Semiparametric Smoothing Spline in Joint Mean and Dispersion Models with Responses from the Biparametric Exponential Family: A Bayesian Perspective

2021 ◽  
Vol 9 (2) ◽  
pp. 351-367
Author(s):  
Héctor Zárate ◽  
Edilberto Cepeda
Keyword(s):  
Exponential Family ◽  
Parametric Models ◽  
Efficient Estimation ◽  
Smoothing Methods ◽  
Markov Chain Sampling ◽  
Variance Functions ◽  
Natural Connection ◽  
Mean And Variance ◽  
The Mean ◽  
Two Parameter

This article extends the fusion among various statistical methods to estimate the mean and variance functions in heteroscedastic semiparametric models when the response variable comes from a two-parameter exponential family distribution. We rely on the natural connection among smoothing methods that use basis functions with penalization, mixed models and a Bayesian Markov Chain sampling simulation methodology. The significance and implications of our strategy lies in its potential to contribute to a simple and unified computational methodology that takes into account the factors that affect the variability in the responses, which in turn is important for an efficient estimation and correct inference of mean parameters without the requirement of fully parametric models. An extensive simulation study investigates the performance of the estimates. Finally, an application using the Light Detection and Ranging technique, LIDAR, data highlights the merits of our approach.

SIMULTANEOUS SPECIFICATION TESTING OF MEAN AND VARIANCE STRUCTURES IN NONLINEAR TIME SERIES REGRESSION

2011 ◽  
Vol 27 (4) ◽  
pp. 792-843 ◽  
Author(s):  
Song Xi Chen ◽  
Jiti Gao
Keyword(s):  
Time Series ◽  
Empirical Likelihood ◽  
Goodness Of Fit ◽  
Test Procedure ◽  
Single Pair ◽  
Test Statistic ◽  
Time Series Regression ◽  
Variance Functions ◽  
Mean And Variance ◽  
The Mean

This paper proposes a nonparametric simultaneous test for parametric specification of the conditional mean and variance functions in a time series regression model. The test is based on an empirical likelihood (EL) statistic that measures the goodness of fit between the parametric estimates and the nonparametric kernel estimates of the mean and variance functions. A unique feature of the test is its ability to distribute natural weights automatically between the mean and the variance components of the goodness-of-fit measure. To reduce the dependence of the test on a single pair of smoothing bandwidths, we construct an adaptive test by maximizing a standardized version of the empirical likelihood test statistic over a set of smoothing bandwidths. The test procedure is based on a bootstrap calibration to the distribution of the empirical likelihood test statistic. We demonstrate that the empirical likelihood test is able to distinguish local alternatives that are different from the null hypothesis at an optimal rate.

Sign in / Sign up

Export Citation Format

Share Document