Turnover and Tenure in the Canadian House of Commons, 1867–1968

1970 ◽  
Vol 3 (4) ◽  
pp. 655-661 ◽  
Author(s):  
Thomas W. Casstevens ◽  
William A. Denham
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Mathematical Theory ◽  
Predictive Power ◽  
Present Model ◽  
General Election ◽  
House Of Commons ◽  
Quantitative Studies ◽  
Continuous Service ◽  
The Mean

This article presents a theoretical analysis of the turnover and tenure of the members of the Canadian House of Commons from 1867 through 1968. Previous studies of such turnover and tenure have been quantitative, but not theoretical, yielding precise measurements but no pattern. A statistical résumé is no substitute for a mathematical model. Both may be accurate, parsimonious, and elegant; but a mathematical theory is distinguished by its generality and its explanatory or predictive power. With the present model, for example, the members’ median and mean continuous service can be logically derived from the mathematical theory; but the converse is not true, that is, the mathematical theory cannot be deduced from the median and/or mean continuous service. Specifically, the theory implies that the median continuous service is approximately 0.693 times the mean continuous service. Despite a plethora of quantitative studies of legislative turnover and tenure, this equation (so far as we know) has not previously been discovered.The process to be modeled can be abstractly characterized as follows: Consider the members of the House of Commons after some particular (zero) general election. These legislators are called theoriginal members, for expository convenience. With the occurrence of deaths, resignations, political defeats, etc., only some of the original members will continue to be members of the House of Commons after the next (first) general election. These survivors are called there-elected members.

Batch Crystallization with Crystals Attrition

1993 ◽  
Vol 58 (8) ◽  
pp. 1855-1860 ◽  
Author(s):  
Jaroslav Nývlt ◽  
Stanislav Žáček
Keyword(s):  
Mathematical Model ◽  
Calcium Sulfate ◽  
Crystal Size ◽  
Theoretical Description ◽  
Secondary Nucleation ◽  
Batch Crystallization ◽  
Batch Time ◽  
The Mean

The dependence of the mean crystal size of the products from batch crystallizers on the batch time occasionally exhibits a maximum, which can be explained by secondary nucleation due to the attrition of crystals. A kinetic equatation of nucleation, comprising a term for crystal attrition, can be used for the theoretical description of such behaviour. A mathematical model of a batch crystallizer with crystal attrition has been verified on the calcium sulfate precipitation.

Explanation Plus Prediction—The Logical Focus of Project Management Research

2021 ◽  
pp. 875697282199994
Author(s):  
Joseph F. Hair ◽  
Marko Sarstedt
Keyword(s):  
Project Management ◽  
Statistical Models ◽  
Predictive Power ◽  
Mean Absolute Error ◽  
Explanatory Power ◽  
Absolute Error ◽  
Model Parameters ◽  
Mean Square ◽  
Management Research ◽  
The Mean

Most project management research focuses almost exclusively on explanatory analyses. Evaluation of the explanatory power of statistical models is generally based on F-type statistics and the R 2 metric, followed by an assessment of the model parameters (e.g., beta coefficients) in terms of their significance, size, and direction. However, these measures are not indicative of a model’s predictive power, which is central for deriving managerial recommendations. We recommend that project management researchers routinely use additional metrics, such as the mean absolute error or the root mean square error, to accurately quantify their statistical models’ predictive power.

Validation of New Mathematical Model of Flank Wear by Different Methods

2012 ◽  
Vol 729 ◽  
pp. 169-174 ◽  
Author(s):  
Zoltán Pálmai ◽  
Márton Takács ◽  
Balázs Zsolt Farkas
Keyword(s):  
Activation Energy ◽  
Mathematical Model ◽  
Flank Wear ◽  
Technological Parameters ◽  
Wear Process ◽  
Oxidation Processes ◽  
Industrial Manufacturing ◽  
Thermally Activated ◽  
Optical Electron ◽  
The Mean

Having reviewed the literature on cutting and based on the optical, electron-optical and morphological examinations of wear processes we have reached the conclusion that it is possible to describe the abrasive, adhesive and thermally activated diffusion, oxidation processes in a single mathematical model. The model is a non-linear autonomous differential equation, which can be solved by simple numerical methods. The complex wear equation was validated by the results of the cutting tests performed with P20 carbide on C45 carbon steel. If we have this data, we can calculate the activation energy of the process determining the nature of the wear process. The apparent activation energy of wear is Q=151,7kJ/mol. The model can even be used with changing technological parameters, and the data necessary for the constants of the wear equation may as well be determined even by measurements performed on the tool during industrial manufacturing. By the mean of this data, we can calculate the activation energy determining the nature of the wear process.

Mathematical Model Establishment and Analysis on the Pipe Deformation under External Pressure with the Ovality

2013 ◽  
Vol 760-762 ◽  
pp. 2263-2266
Author(s):  
Kang Yong ◽  
Wei Chen
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Yield Strength ◽  
Residual Stresses ◽  
Numerical Simulations ◽  
Significant Influence ◽  
External Pressure ◽  
Pipe Diameter ◽  
Axial Loads ◽  
The Stability

Beside the residual stresses and axial loads, other factors of pipe like ovality, moment could also bring a significant influence on pipe deformation under external pressure. The Standard of API-5C3 has discussed the influences of deformation caused by yield strength of pipe, pipe diameter and pipe thickness, but the factor of ovality degree is not included. Experiments and numerical simulations show that with the increasing of pipe ovality degree, the anti-deformation capability under external pressure will become lower, and ovality affecting the stability of pipe shape under external pressure is significant. So it could be a path to find out the mechanics relationship between ovality and pipe deformation under external pressure by the methods of numerical simulations and theoretical analysis.

Non-invasive determination of the systolic peak-to-peak gradient in children with aortic stenosis: validation of a mathematical model

2000 ◽  
Vol 10 (2) ◽  
pp. 115-119 ◽  
Author(s):  
Valter C. Lima ◽  
Evan Zahn ◽  
Christine Houde ◽  
Jeffrey Smallhorn ◽  
Robert M. Freedom ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Pulse Pressure ◽  
Linear Regression Analysis ◽  
Systolic Pressure ◽  
Pressure Gradients ◽  
Non Invasive ◽  
The Mean ◽  
Congenital Aortic Valvar Stenosis ◽  
Peak Gradient

AbstractDoppler derived systolic pressure gradients have become widely applied as noninvasively obtained estimates of the severity of aortic valvar stenosis. There is little correlation, however, between the Doppler derived peak instantaneous gradient and the peak-to-peak gradient obtained at catheterisation, the latter being the most applied variable to determine severity in children. The purpose of this study was to validate a mathematical model based on data from catheterisation which estimates the peak-to-peak gradient from variables which can be obtained by noninvasive means (Doppler derived mean gradient and pulse pressure), according to the formula: peak-to-peak systolic gradient=6.02+1.49*(mean gradient)−0.44*(pulse pressure). Simultaneous cardiac catheterization and Doppler studies were performed on 10 patients with congenital aortic valvar stenosis. Correlations between the gradients measured at catheter measured, and those derived by Doppler, were performed using linear regression analysis. The mean gradients correlated well (y=0.67 × + 11.11, r=0.87, SEE=6 mm Hg, p=0.001). The gradients predicted by the formula also correlated well with the peak-to-peak gradients measured at catheter (y=0.66 × + 14.44, r=0.84, SEE=9 mm Hg, p=O.002). The data support the application of the model, allowing noninvasive prediction of the peak-to-peak gradient across the aortic valvar stenosis.

Quantitative studies of the reactions to horizontal angular accelerations in axolotls. I. The head-turning reflexes of normal animals

1977 ◽  
Vol 66 (1) ◽  
pp. 1-14
Author(s):  
K. Brandle
Keyword(s):  
Stimulus Intensity ◽  
Time Course ◽  
Maximum Velocity ◽  
Afferent Input ◽  
Head Turning ◽  
Mean Values ◽  
Quantitative Studies ◽  
The Mean ◽  
Negative Exponential ◽  
Total Angle

1. Artifically metamorphosed axolotls were exposed to both brief (impulse) and long-lasting horizontal angular accelerations on a turn-table. The animals responded with a head-turning reaction. 2. The general course of the reaction to impulse acceleration was independent of stimulus intensity. The velocity of the head movement first increased to a maximum exponentially and then decreased in a negative exponential manner. Stimulus intensity had a linear relationship to the mean maximum velocity and mean total angle covered by head-turning. The average velocity-time curves at various stimulus intensities differed only by a velocity factor. 3. During long-lasting constant accelerations the velocity of the head-turning increased to a maximum velocity in a sigmoid time-course and then decreased, first to a constant velocity, and then further. Mean values of the maximum velocity were correlated linearly with the stimulus intensity. 4. It was concluded that the head-turning reflexes in axolotls do not agree with the accepted movements of the vertebrate cupula and therefore are not a simple ‘copy’ of the afferent input. It is also suggested that the reaction threshold differes from that for the labyrinthine input.

Attenuation of pulsations in the reciprocating compressor piping system with an elbow-shaped surge tank

2018 ◽  
Vol 233 (5) ◽  
pp. 1677-1689
Author(s):  
Quyang Ma ◽  
Guoan Yang ◽  
Mengjun Li
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Frequency Analysis ◽  
Transfer Matrix Method ◽  
Piping System ◽  
Pulsation Frequency ◽  
Reciprocating Compressor ◽  
Pressure Pulsations ◽  
Surge Tank ◽  
The Mathematical Model

An elbow-shaped surge tank is proposed to suppress the pressure pulsations. The transfer matrix method was developed and the mathematical model was established to predict the distribution of pressure pulsations in the piping system (on which a surge tank was already installed) with an elbow-shaped surge tank. Simulation work of the whole piping system was performed. The results show that the elbow-shaped surge tank has good performance to attenuate the pressure pulsations. The frequency analysis shows that the amplitude for the first pulsation frequency is attenuated to a low level. The impulse response was analyzed to examine the efficiency of suppressing pulsations by using the suppressor. The theoretical analysis showed that there exists the optimal suppression performance when setting the distance between the elbow-shaped surge tank and the existing one. Meanwhile, modifying the ratio of length to diameter with a fixed surge volume could also impact the pressure pulsations. The analysis results can be used as a reference in designing and installing the elbow-shaped surge tank.

scholarly journals XII. On the cause of the discrepancies observed by Mr. Baily with the Cavendish apparatus for determining the mean density of the earth

1847 ◽  
Vol 137 ◽  
pp. 217-229 ◽  
Keyword(s):  
Mathematical Theory ◽  
Full Account ◽  
Astronomical Society ◽  
Royal Astronomical Society ◽  
The Earth ◽  
Singular Source ◽  
The Mean ◽  
The Masses ◽  
Source Of Error ◽  
Different Parts

In the Fourteenth Volume of the Transactions of the Royal Astronomical Society will be found a full account of the Cavendish apparatus, and of the mode of experimenting followed by Mr. Baily. It will therefore not be necessary for me, in this place, to enter into any detail as to the different parts of the instrument, and the various precautions adopted in order to avoid that singular source of error 'currents of air in the torsion box arising from unequal temperature,’ which had been discovered by Cavendish. It will be sufficient for me to state that all the arrangements are of a highly satisfactory kind, and that I am of opinion that no aerial currents could have existed in the torsion box. The deduction of the mean density of the earth from the observed vibrations of the balls influenced by the torsion force and the attraction of the masses, is founded on a mathematical theory of the motion of the balls given by the Astronomer Royal, Mr. Airy ; and as this theory is certainly insufficient to account for the discrepancies, it will here be necessary to give a brief sketch of it.

scholarly journals Building a mechanistic mathematical model of hepatitis C virus entry

2018 ◽  
Author(s):  
Mphatso Kalemera ◽  
Dilyana Mincheva ◽  
Joe Grove ◽  
Christopher J. R. Illingworth
Keyword(s):  
Mathematical Model ◽  
Hepatitis C Virus ◽  
Hepatitis C ◽  
Viral Entry ◽  
Productive Infection ◽  
Virus Particles ◽  
Quantitative Studies ◽  
Receptor Dynamics ◽  
Viral Lifecycle ◽  
The Impact

AbstractThe mechanism by which hepatitis C virus (HCV) gains entry into cells is a complex one, involving a broad range of host proteins. Entry is a critical phase of the viral lifecycle, and a potential target for therapeutic or vaccine-mediated intervention. However, the mechanics of HCV entry remain poorly understood. Here we describe a novel computational model of viral entry, encompassing the relationship between HCV and the key host receptors CD81 and SR-B1. We conduct experiments to thoroughly quantify the influence of an increase or decrease in receptor availability upon the extent of viral entry. We use these data to build and parameterise a mathematical model, which we then validate by further experiments. Our results are consistent with sequential HCV-receptor interactions, whereby initial interaction between the HCV E2 glycoprotein and SR-B1 facilitates the accumulation CD81 receptors, leading to viral entry. However, we also demonstrate that a small minority of virus can achieve entry in the absence of SR-B1. Our model estimates the impact of the different obstacles that viruses must surmount to achieve entry; among virus particles attaching to the cell surface, 20-35% accumulate sufficient CD81 receptors, of these 4-8% then complete the subsequent steps to achieve productive infection. Furthermore, we make estimates of receptor stoichiometry; between 3 and 6 CD81 receptors are likely to be required to achieve viral entry. Our model provides a tool to investigate the entry characteristics of HCV variants and outlines a framework for future quantitative studies of the multi-receptor dynamics of HCV entry.

Evaluation of a method for noninvasive intracranial pressure assessment during infusion studies in patients with hydrocephalus

2000 ◽  
Vol 92 (5) ◽  
pp. 793-800 ◽  
Author(s):  
Bernhard Schmidt ◽  
Marek Czosnyka ◽  
Jens Jürgen Schwarze ◽  
Dirk Sander ◽  
Werner Gerstner ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Intracranial Pressure ◽  
Time Course ◽  
Cerebral Blood Flow Velocity ◽  
Absolute Error ◽  
Content Type ◽  
Arterial Blood ◽  
Potential Clinical Benefit ◽  
The Mean ◽  
Fine Print

Object. A mathematical model previously introduced by the authors allowed noninvasive intracranial pressure (nICP) assessment. In the present study the authors investigated this model as an aid in predicting the time course of raised ICP during infusion tests in patients with hydrocephalus and its suitability for estimating the resistance to outflow of cerebrospinal fluid (Rcsf).Methods. Twenty-one patients with hydrocephalus were studied. The nICP was calculated from the arterial blood pressure (ABP) waveform by using a linear signal transformation, which was dynamically modified by the relationship between ABP and cerebral blood flow velocity. This model was verified by comparison of nICP with “real” ICP measured during lumbar infusion tests. In all simulations, parallel increases in real ICP and nICP were evident. The simulated Rcsf was computed using nICP and then compared with Rcsf computed from real ICP. The mean absolute error between real and simulated Rcsf was 4.1 ± 2.2 mm Hg minute/ml. By the construction of simulations specific to different subtypes of hydrocephalus arising from various causes, the mean error decreased to 2.7 ± 1.7 mm Hg minute/ml, whereas the correlation between real and simulated Rcsf increased from R = 0.73 to R = 0.89 (p < 0.001).Conclusions. The validity of the mathematical model was confirmed in this study. The creation of type-specific simulations resulted in substantial improvements in the accuracy of ICP assessment. Improvement strategies could be important because of a potential clinical benefit from this method.

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