scholarly journals A MORPHOMETRIC STUDY ON THE THICKNESS OF THE PULMONARY AIR-BLOOD BARRIER

1964 ◽  
Vol 21 (3) ◽  
pp. 367-384 ◽  
Author(s):  
Ewald R. Weibel ◽  
Bruce W. Knight

A reliable knowledge of the thickness of the alveolo-capillary "membrane" or air-blood barrier is of physiologic interest since it is intimately related to a quantitative estimation of such functional events as gas diffusion or tissue metabolism in the lung. The characteristic thickness of the air-blood barrier with respect to gas diffusion is its harmonic mean thickness, while the arithmetic mean thickness is related to the mass of tissue building the barrier and consuming oxygen in the lung. Two morphometric methods are proposed by which these two dimensions can be estimated from random measurements in the electron microscope in a reliable, simple, and efficient manner. By applying these methods to three rat lungs the arithmetic mean thickness of the barrier was found to measure 1.25 µ, the harmonic mean thickness, 0.57 µ. On the basis of these measurements a geometric model of the barrier in the form of a corrugated membrane was derived. Its dimensions showed close similarity to those of the natural barrier. This analysis suggested furthermore that the gas conductance of the barrier is nearly optimal if one considers the mass of tissue and the minimal barrier thickness as fixed properties which are determined by other functional requirements on the alveolo-capillary membrane.

Genetics ◽  
2002 ◽  
Vol 161 (1) ◽  
pp. 381-388
Author(s):  
Masaru Iizuka ◽  
Hidenori Tachida ◽  
Hirotsugu Matsuda

Abstract We consider a diffusion model with neutral alleles whose population size is fluctuating randomly. For this model, the effects of fluctuation of population size on the effective size are investigated. The effective size defined by the equilibrium average heterozygosity is larger than the harmonic mean of population size but smaller than the arithmetic mean of population size. To see explicitly the effects of fluctuation of population size on the effective size, we investigate a special case where population size fluctuates between two distinct states. In some cases, the effective size is very different from the harmonic mean. For this concrete model, we also obtain the stationary distribution of the average heterozygosity. Asymptotic behavior of the effective size is obtained when the population size is large and/or autocorrelation of the fluctuation is weak or strong.


1976 ◽  
Vol 64 (2) ◽  
pp. 447-460
Author(s):  
G. M. Huges ◽  
S. F. Perry

1. Methods are described for the morphometric estimation of parameters of the gill system of trout which are relevant to its function in gas exchange. The methods have been used with 1 mum sections viewed under the light microscope. 2. In particular the diffusion distances between water and blood are measured, which together with determinations of gill area, provide figures for the morphometrically estimated diffusing capacity. 3. The methods have been used to compare the diffusing capacity of gills from control fish and those treated in polluted waters. The concept of relative diffusing capacity (Drel) is introduced which enables comparisons to be made without the need to determine the absolute diffusing capacity. 4. Quantitative estimation of changes in relative volumes and surface areas of components of the secondary lamellae were determined, and employed to explain the possible anatomical causes of changes in Drel. 5. It is suggested that these methods can be of value in the comparison of the gills of fish treated in different waters.


Author(s):  
Oluyori P. Dare ◽  
Eteje S. Okiemute

<p class="abstract"><strong>Background:</strong> Orthometric height, as well as geoid modelling using the geometric method, requires centroid computation. And this can be obtained using various models, as well as methods. These methods of centroid mean computation have impacts on the accuracy of the geoid model since the basis of the development of the theory of each centroid mean type is different. This paper presents the impact of different centroid means on the accuracy of orthometric height modelling by geometric geoid method.</p><p class="abstract"><strong>Methods:</strong> DGPS observation was carried out to obtain the coordinates and ellipsoidal heights of selected points. The centroid means were computed with the coordinates using three different centroid means models (arithmetic mean, root mean square and harmonic mean). The computed centroid means were entered accordingly into a Microsoft Excel program developed using the Multiquadratic surface to obtain the model orthometric heights at various centroid means. The root means square error (RMSE) index was applied to obtain the accuracy of the model using the known and the model orthometric heights obtained at various centroid means.  </p><p class="abstract"><strong>Results:</strong> The computed accuracy shows that the arithmetic mean method is the best among the three centroid means types.</p><p class="abstract"><strong>Conclusions:</strong> It is concluded that the arithmetic mean method should be adopted for centroid computation, as well as orthometric height modelling using the geometric method.</p>


2021 ◽  
Vol 40 (2) ◽  
pp. 61-67
Author(s):  
Gilbert E. Matthews

This article posits that using the arithmetic mean to average multiples is mathematically inferior. A multiple is an inverted ratio with price in the numerator. The harmonic mean is a statistically sound method for averaging inverted ratios. It should be used as a measure of central tendency for multiples, along with the median. Empirically, the harmonic mean and the median of a set of multiples are usually similar. Because the harmonic mean can be overly affected by abnormally low multiples, the valuator must use judgment to exclude outliers.


Author(s):  
Zhipeng Zhang ◽  
Kang Zhou ◽  
Xiang Liu

Abstract Broken-rail prevention and risk management have been being a major activity for a long time for the railroad industry. The major objective of this research is to evaluate and analyze the broken rail-caused derailment risk using Artificial Intelligence (AI) approaches. The risk model is primarily built upon 1) broken rail probability; 2) probability of broken-rail derailment given a broken rail; and 3) derailment severity, measured by the number of cars derailed. The train derailment risk accounts for derailment probability and derailment consequences simultaneously. Due to the low frequency of broken-rail derailments, it is desirable to estimate the probability of broken rail-caused derailments through the broken rail occurrence. The estimation of the probability of broken rail-caused derailment includes the conditional probability of derailment given broken rail occurrence and the probability of broken rail occurrence. More specially, the probability of broken-rail derailment given a broken rail can be estimated by the statistical relationship between broken-rail derailment and broken rail, given specific variables (e.g., track curvature, signal condition, and annual traffic). The probability of broken rails can be estimated using machine learning techniques based on railroad big data, including maintenance, track layout, traffic and historical inspection records. In terms of derailment consequence, it is defined as the number of cars (both loaded and empty) derailed per derailment that would be estimated based on potentially affecting factors, such as train length, train speed, and train tonnage. The quantitative estimation and analysis of broken rail-caused derailments are based upon the historical records from one Class I railroad company from 2012 to 2016, covering over 20,000 track miles on mainlines. The developed integrated risk model is able to contribute to the prediction of location-centric broken rail-caused derailment risk. Ultimately, the identification of high-risk locations can ultimately aid the railroads to mitigate broken rail risk in a cost-efficient manner and improve railroad safety.


1986 ◽  
Vol 75 (4) ◽  
pp. 427-429 ◽  
Author(s):  
L.J. Schaaf ◽  
F.C. Lam ◽  
D.G. Perrier

1973 ◽  
Vol 66 (3) ◽  
pp. 253-255
Author(s):  
Joseph L. Ercolano

The harmonic mean of two positive, real numbers was known to early Greek mathematicians. In fact, it is alleged that “Pythagoras learned in Mesopotamia of three means—the arithmetic, the geometric, and the subcontrary (later called the harmonic)—and of the ‘golden proportion’ relating two of these: the first of two numbers is to their arithmetic mean as their harmonic mean is to the second of the numbers” (Boyer 1968). Archytas, a disciple of Pythagoras (whose most important contribution to mathematics may very well have been his intervention with Dionysius to save the life of his friend, Plato), wrote on the application of these three means to music, and is possibly the one who is responsible for renaming the suhcontrary mean the harmonic mean (Boyer 1968).


Author(s):  
Staffan Lindskog ◽  
Rolf Sjo¨blom

On November 1st 2008, a new ordinance came into force in Sweden. It extends the implementation of nuclear liability to all nuclear facilities and companies, regardless of size. The Government has authorized the Swedish Radiation Safety Authority (SSM) to issue further regulation as warranted and appropriate, and commissioned the same Authority to oversee the implementation. Consequently, SSM is presently conducting research in order to establish a basis for the implementation of the ordinance to smaller facilities and enterprises. The goal is to enable finance to be assured in an efficient manner so that any burden on the companies is as small as possible. Thus, “functional requirements” are identified, and used as a basis for various investigations. The aspects include technical and cost calculation prerequisites, as well as various domains of law: the environmental code, radiation and nuclear safety, financial reporting, and criminal law. It is found that the basis for the differentiation among the facility operators and owners should be the cost and the associated uncertainty. Thus, a cost calculation will have to be carried out by all. It should be based on available standards and guidance documents. It is found that this is a requirement that already exists elsewhere in the legislation, and thus no additional burden is imposed on the companies. It is found that segregated funds is the preferred option for long-term liabilities. Securities are suitable for short-term liabilities provided that the economy of the company in question is sound. Securities might also be used for long-term liabilities to cover uncertainty. It is proposed that a de minimis limit of at least kSEK 25 (about k€ 2, 4 and k$ 3, 4) is used. An important reason for this is that lower limits might be incompatible with the rules for financial reporting. It is also proposed that securities might be used also for long-term commitments if the total environmental liability does not exceed 1,00 MSEK (about k€ 96 and k$ 135). It is found that the “general advice” that must be used by smaller companies lacks proper instructions on how to account for environmental liability whilst at the same time it prohibits the use of e g the international reporting standards IFRS/IAS. It is also found that the “general advice” prohibits distribution of costs for research and development over time. This might be incompatible with a fund system where considerable research may be necessary at the early stages of the work and often many years before the actual decommissioning is to take place. The rules in the penal code require that an annual report presents an “essentially correct financial situation”. One of the interpretations to this statement is that a deviance of at most 30% might be tolerated. Although previous work has indicated that the error in cost estimates need not be higher than about 15%, even for research facilities, concealed cost raisers may from time to time lead to much larger errors, even when best practices are being used. It is therefore essential that decommissioning planning and cost predictions are made in accordance with state of the art, and that the estimating methods as well as the results are properly documented.


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