Non-linear compartmental models

1984 ◽  
Vol 16 (1) ◽  
pp. 24-24
Author(s):  
M. J. Faddy
Keyword(s):  
Compartmental Model ◽  
Probability Distributions ◽  
Compartmental Analysis ◽  
Compartmental Models ◽  
General Will ◽  
Particle Count ◽  
Multinomial Probability ◽  
Model Independent ◽  
The Mean ◽  
Particle Counts

The linear compartmental model arises when ‘particles’ move independently between (or out of) a system of compartments in a stochastically similar way. With a given ‘initial’ particle count, the subsequent compartmental particle counts follow multinomial probability distributions (Faddy (1976)) for Markov or semi-Markov movement processes. One immediate consequence of this is that the variance of the compartmental particle count is always less than the mean, with the result that the coefficient of variation is very small for large mean counts. In applications (e.g, Faddy, Jones and Edwards (1976)) this underestimation of the variation can be a shortcoming of a compartmental analysis. Clustering, introduced by Matis and Wehrly (1981), where ‘clusters’ of particles may move together, is a way in which increased variability may be attained. Increased variability in general will result from relaxing the main assumption that gives rise to a linear model: independent behaviour of the particles. Such nonlinear compartmental models can be generally difficult to handle; in this paper some particular cases are discussed and illustrated with reference to one- and twocompartment systems.

Asteroid and Comet Impact Speeds upon Mars: Significance for Panspermia and the Supply of Organics

1997 ◽  
Vol 161 ◽  
pp. 197-201 ◽  
Author(s):  
Duncan Steel
Keyword(s):  
Probability Distributions ◽  
Regions Of Interest ◽  
Significant Fraction ◽  
Organic Chemicals ◽  
Impact Speed ◽  
The Mean ◽  
The Impact

AbstractWhilst lithopanspermia depends upon massive impacts occurring at a speed above some limit, the intact delivery of organic chemicals or other volatiles to a planet requires the impact speed to be below some other limit such that a significant fraction of that material escapes destruction. Thus the two opposite ends of the impact speed distributions are the regions of interest in the bioastronomical context, whereas much modelling work on impacts delivers, or makes use of, only the mean speed. Here the probability distributions of impact speeds upon Mars are calculated for (i) the orbital distribution of known asteroids; and (ii) the expected distribution of near-parabolic cometary orbits. It is found that cometary impacts are far more likely to eject rocks from Mars (over 99 percent of the cometary impacts are at speeds above 20 km/sec, but at most 5 percent of the asteroidal impacts); paradoxically, the objects impacting at speeds low enough to make organic/volatile survival possible (the asteroids) are those which are depleted in such species.

Partition Coefficient Ratios and Tumour Perfusion Studied with 85mKr and 133Xe

1987 ◽  
Vol 26 (06) ◽  
pp. 253-257
Author(s):  
M. Mäntylä ◽  
J. Perkkiö ◽  
J. Heikkonen
Keyword(s):  
Partition Coefficient ◽  
Partition Coefficients ◽  
Regional Blood Flow ◽  
Blood Perfusion ◽  
Compartmental Analysis ◽  
Malignant Tumour ◽  
Mean Value ◽  
Perfusion Rate ◽  
Biological Variables ◽  
The Mean

The relative partition coefficients of krypton and xenon, and the regional blood flow in 27 superficial malignant tumour nodules in 22 patients with diagnosed tumours were measured using the 85mKr- and 133Xe-clearance method. In order to minimize the effect of biological variables on the measurements the radionuclides were injected simultaneously into the tumour. The distribution of the radiotracers was assumed to be in equilibrium at the beginning of the experiment. The blood perfusion was calculated by fitting a two-exponential function to the measuring points. The mean value of the perfusion rate calculated from the xenon results was 13 ± 10 ml/(100 g-min) [range 3 to 38 ml/(100 g-min)] and from the krypton results 19 ± 11 ml/(100 g-min) [range 5 to 45 ml/(100 g-min)]. These values were obtained, if the partition coefficients are equal to one. The equations obtained by using compartmental analysis were used for the calculation of the relative partition coefficient of krypton and xenon. The partition coefficient of krypton was found to be slightly smaller than that of xenon, which may be due to its smaller molecular weight.

scholarly journals Development of Perceptual Inhibition in Adolescents—a Critical Period?

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 457
Author(s):  
Isabel María Introzzi ◽  
María Marta Richard’s ◽  
Yesica Aydmune ◽  
Eliana Vanesa Zamora ◽  
Florencia Stelzer ◽  
...  
Keyword(s):  
Response Time ◽  
Executive Functions ◽  
Critical Period ◽  
Search Task ◽  
Probability Distributions ◽  
Linear Trajectory ◽  
Gaussian Functions ◽  
Mean Response Time ◽  
The Mean ◽  
One Year

Recent studies suggest that the developmental curves in adolescence, related to the development of executive functions, could be fitted to a non-linear trajectory of development with progressions and retrogressions. Therefore, the present study proposes to analyze the pattern of development in Perceptual Inhibition (PI), considering all stages of adolescence (early, middle, and late) in intervals of one year. To this aim, we worked with a sample of 275 participants between 10 and 25 years, who performed a joint visual and search task (to measure PI). We have fitted ex-Gaussian functions to the probability distributions of the mean response time across the sample and performed a covariance analysis (ANCOVA). The results showed that the 10- to 13-year-old groups performed similarly in the task and differ from the 14- to 19-year-old participants. We found significant differences between the older group and all the rest of the groups. We discuss the important changes that can be observed in relation to the nonlinear trajectory of development that would show the PI during adolescence.

scholarly journals Subcritical Transmission in the Early Stage of COVID-19 in Korea

2021 ◽  
Vol 18 (3) ◽  
pp. 1265
Author(s):  
Yong Sul Won ◽  
Jong-Hoon Kim ◽  
Chi Young Ahn ◽  
Hyojung Lee
Keyword(s):  
Incubation Period ◽  
Early Stage ◽  
Probability Distributions ◽  
Likelihood Estimation ◽  
Contact Tracing ◽  
Statistical Characterization ◽  
Serial Interval ◽  
Imported Cases ◽  
The Mean ◽  
Reporting Delays

While the coronavirus disease 2019 (COVID-19) outbreak has been ongoing in Korea since January 2020, there were limited transmissions during the early stages of the outbreak. In the present study, we aimed to provide a statistical characterization of COVID-19 transmissions that led to this small outbreak. We collated the individual data of the first 28 confirmed cases reported from 20 January to 10 February 2020. We estimated key epidemiological parameters such as reporting delay (i.e., time from symptom onset to confirmation), incubation period, and serial interval by fitting probability distributions to the data based on the maximum likelihood estimation. We also estimated the basic reproduction number (R0) using the renewal equation, which allows for the transmissibility to differ between imported and locally transmitted cases. There were 16 imported and 12 locally transmitted cases, and secondary transmissions per case were higher for the imported cases than the locally transmitted cases (nine vs. three cases). The mean reporting delays were estimated to be 6.76 days (95% CI: 4.53, 9.28) and 2.57 days (95% CI: 1.57, 4.23) for imported and locally transmitted cases, respectively. The mean incubation period was estimated to be 5.53 days (95% CI: 3.98, 8.09) and was shorter than the mean serial interval of 6.45 days (95% CI: 4.32, 9.65). The R0 was estimated to be 0.40 (95% CI: 0.16, 0.99), accounting for the local and imported cases. The fewer secondary cases and shorter reporting delays for the locally transmitted cases suggest that contact tracing of imported cases was effective at reducing further transmissions, which helped to keep R0 below one and the overall transmissions small.

scholarly journals The prediction model of moisture content’s stabilization during tobacco strip drying process

2018 ◽  
Author(s):  
Mingjian Zhang ◽  
Feng Huang ◽  
Qing Chen ◽  
Le Wang ◽  
Haisheng Wang ◽  
...  
Keyword(s):  
Moisture Content ◽  
Probability Distributions ◽  
Chemical Properties ◽  
Mean Value ◽  
Drying Process ◽  
Variance Model ◽  
Initial Stage ◽  
The Mean ◽  
Agriculture Products ◽  
Physical And Chemical

A mathematical model was established to predict the mean value and variance of tobacco strip during drying processing, based that the physical and chemical properties of tobacco strip as agriculture products show probability distributions. The results show that the model can predict the mean value of moisture content at different times, and there is a certain deviation in predicting the variance of moisture content at initial stage of drying process. However, the prediction value of the variance of tobacco strip is much more accurate while the moisture content is between 8% and 10%, which is the interval of quality requirements.Keywords: tobacco strip; drying; mean value;variance model.  

Energy nutrients modulate the splanchnic sequestration of dietary nitrogen in humans: a compartmental analysis

2001 ◽  
Vol 281 (2) ◽  
pp. E248-E260 ◽  
Author(s):  
H. Fouillet ◽  
C. Gaudichon ◽  
F. Mariotti ◽  
C. Bos ◽  
J. F. Huneau ◽  
...  
Keyword(s):  
Compartmental Model ◽  
Compartmental Analysis ◽  
Dietary Nitrogen ◽  
Amino Acid Availability ◽  
Nutritional Conditions ◽  
Dietary Amino Acid ◽  
Single Meal ◽  
Peripheral Areas ◽  
Kinetics Of ◽  
Insight Into

We used a previously developed compartmental model to assess the postprandial distribution and metabolism of dietary nitrogen (N) in the splanchnic and peripheral areas after the ingestion of a single meal containing milk protein either alone (MP) or with additional sucrose (SMP) or fat (FMP). The addition of fat was predicted to enhance splanchnic dietary N anabolism only transiently, without significantly affecting the global kinetics of splanchnic retention and peripheral uptake. In contrast, the addition of sucrose, which induced hyperinsulinemia, was predicted to enhance dietary N retention and anabolism in the splanchnic bed, thus leading to reduced peripheral dietary amino acid availability and anabolism. The incorporation of dietary N into splanchnic proteins was thus predicted to reach 18, 24, and 35% of ingested N 8 h after MP, FMP, and SMP, respectively. Such a model provides insight into the dynamics of the system in the nonsteady postprandial state and constitutes a useful, explanatory tool to determine the region-specific utilization of dietary N under different nutritional conditions.

Calibrating compartmental models of neurons

1978 ◽  
Vol 235 (1) ◽  
pp. R93-R98 ◽  
Author(s):  
D. H. Perkel ◽  
B. Mulloney
Keyword(s):  
Steady State ◽  
Electrical Properties ◽  
Differential Equations ◽  
Compartmental Model ◽  
Compartmental Models ◽  
Electrical Measurements ◽  
Original Matrix ◽  
Systematic Procedure ◽  
The Matrix ◽  
Voltage Attenuation

Numerical parameters for a compartmental model of a neuron can be chosen to conform both to the neuron's structure and to its measured steady-state electrical properties. A systematic procedure for assigning parameters is described that makes use of the matrix of coefficients of the set of differential equations that embodies the compartmental model. The inverse of this matrix furnishes input resistances and voltage attenuation factors for the model, and an interactive modification of the original matrix and its inverse may be used to fit the model to anatomic and electrical measurements.

On the wind resource in Algeria: Probability distributions evaluation

2020 ◽  
pp. 095765092097588
Author(s):  
Houdayfa Ounis ◽  
Nawel Aries
Keyword(s):  
Wind Speed ◽  
Probability Distribution ◽  
Probability Distributions ◽  
Resource Assessment ◽  
Descriptive Statistics ◽  
The Other ◽  
Wind Speeds ◽  
Wind Resource Assessment ◽  
The Mean ◽  
Wind Resource

The present study aims to present a contribution to the wind resource assessment in Algeria using ERA-Interim reanalysis. Firstly, the ERA-Interim reanalysis 10 m wind speed data are considered for the elaboration of the mean annual 10 m wind speed map for a period starting from 01-01-2000 to 31-12-2017. Moreover, the present study intends to highlight the importance of the descriptive statistics other than the mean in wind resource assessment. On the other hand, this study aims also to select the proper probability distribution for the wind resource assessment in Algeria. Therefore, nine probability distributions were considered, namely: Weibull, Gamma, Inverse Gaussian, Log Normal, Gumbel, Generalized Extreme Value (GEV), Nakagami, Generalized Logistic and Pearson III. Furthermore, in combination with the distribution, three parameter estimation methods were considered, namely, Method of Moment, Maximum Likelihood Method and L-Moment Method. The study showed that Algeria has several wind behaviours due to the diversified topographic, geographic and climatic properties. Moreover, the annual mean 10 m wind speed map showed that the wind speed varies from 2.3 to 5.3 m/s, where 73% of the wind speeds are above 3 m/s. The map also showed that the Algerian Sahara is windiest region, while, the northern fringe envelopes the lowest wind speeds. In addition, it has been shown that the study of the mean wind speeds for the evaluation of the wind potential alone is not enough, and other descriptive statistics must be considered. On the other hand, among the nine considered distribution, it appears that the GEV is the most appropriate probability distribution. Whereas, the Weibull distribution showed its performance only in regions with high wind speeds, which, implies that this probability distribution should not be generalized in the study of the wind speed in Algeria.

scholarly journals Al2O3 Particles on Titanium Dental Implant Systems following Sandblasting and Acid-Etching Process

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Peter Schupbach ◽  
Roland Glauser ◽  
Sebastian Bauer
Keyword(s):  
Dental Implant ◽  
Sem Analysis ◽  
Acid Etching ◽  
Mean Size ◽  
Bone Level ◽  
Titanium Dental Implant ◽  
The Mean ◽  
Particle Counts ◽  
Size Of Particles ◽  
Implant System

Dental implants with moderately rough surfaces show enhanced osseointegration and faster bone healing compared with machined surfaces. The sandblasting and acid-etching (SA) process is one technique to create moderately rough dental implant surfaces. The purpose of this study was to analyse different commercially available implant systems with a SA-modified surface and to explore the widespread notion that they have similar surface properties regarding morphology and cleanliness. SA-modified surfaces of nine implant systems manufactured by Alpha-Bio Tec Ltd, Camlog Biotechnologies AG, Dentsply Sirona Dental GmbH, Neoss Ltd, Osstem Implant Co. Ltd, Institute Straumann AG, and Thommen Medical AG were analyzed using scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDX) and examined for surface cleanliness. Six implants from three different lots were selected per each implant system. Mean particle counts for each implant and the mean size of the particles were calculated from three different regions of interest and compared using ANOVA and Tukey’s test. SEM analysis showed presence of particles on the majority of analyzed implant surfaces, and EDX evaluations determined that the particles were made of Al2O3 and thus remnants of the blasting process. SPI®ELEMENT INICELL® and Bone Level (BL) Roxolid® SLActive® implant surfaces showed the highest mean particle counts, 46.6 and 50.3 per area, respectively. The surface of BL Roxolid® SLActive® implant also showed the highest variations in the particle counts, even in samples from the same lot. The mean size of particles was 1120±1011 μm2, measured for USIII CA Fixture implants, while the biggest particle was 5900 μm2 found on a BL Roxolid® SLActive® implant. These results suggest that not all manufacturers are able to produce implant surfaces without particle contamination and highlight that the surface modification process with the SA technique should be appropriately designed and controlled to achieve a clean and consistent final medical device.

scholarly journals Imprecise Imputation as a Tool for Solving Classification Problems with Mean Values of Unobserved Features

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Lev V. Utkin ◽  
Yulia A. Zhuk
Keyword(s):  
Partial Information ◽  
Probability Distributions ◽  
Classification Problem ◽  
Support Vector ◽  
Classification Problems ◽  
Mean Values ◽  
Numerical Examples ◽  
The Standard Model ◽  
The Mean ◽  
Available Information

A method for solving a classification problem when there is only partial information about some features is proposed. This partial information comprises the mean values of features for every class and the bounds of the features. In order to maximally exploit the available information, a set of probability distributions is constructed such that two distributions are selected from the set which define the minimax and minimin strategies. Random values of features are generated in accordance with the selected distributions by using the Monte Carlo technique. As a result, the classification problem is reduced to the standard model which is solved by means of the support vector machine. Numerical examples illustrate the proposed method.

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