A Simple Formula Giving the Number of Individuals Required for Obtaining One of a Given Frequency

1923 ◽  
Vol 57 (648) ◽  
pp. 66-73 ◽  
Author(s):  
H. J. Muller
Keyword(s):  
Simple Formula ◽  
Number Of Individuals

scholarly journals Predictive mathematical models for the number of individuals infected with COVID-19

2020 ◽  
Author(s):  
A.S. Fokas ◽  
N. Dikaios ◽  
G.A. Kastis
Keyword(s):  
Lower Bound ◽  
Mathematical Models ◽  
Closed Form ◽  
Upper Bound ◽  
Logistic Model ◽  
Simple Formula ◽  
Time Dependent ◽  
Sigmoidal Curve ◽  
Specific Virus ◽  
Number Of Individuals

AbstractWe model the time-evolution of the number N(t) of individuals reported to be infected in a given country with a specific virus, in terms of a Riccati equation. Although this equation is nonlinear and it contains time-dependent coefficients, it can be solved in closed form, yielding an expression for N(t) that depends on a function α(t). For the particular case that α(t) is constant, this expression reduces to the well-known logistic formula, giving rise to a sigmoidal curve suitable for modelling usual epidemics. However, for the case of the COVID-19 pandemic, the long series of available data shows that the use of this simple formula for predictions underestimates N(t); thus, the logistic formula only provides a lower bound of N(t). After experimenting with more than 50 different forms of α(t), we introduce two novel models that will be referred to as “rational” and “birational”. The parameters specifying these models (as well as those of the logistic model), are determined from the available data using an error-minimizing algorithm. The analysis of the applicability of the above models to the cases of China and South Korea suggest that they yield more accurate predictions, and importantly that they may provide an upper bound of the actual N(t). Results are presented for Italy, Spain, and France.

scholarly journals On the heat production associated with muscular work

1914 ◽  
Vol 87 (595) ◽  
pp. 311-317 ◽  
Keyword(s):  
Heat Production ◽  
Simple Formula ◽  
Mechanical Work ◽  
Muscular Work ◽  
Measured Amount ◽  
Straight Line ◽  
Number Of Individuals

On reading Prof. Macdonald’s paper it appeared that it might be interesting to see if his results connecting the heat production and muscular work could be expressed graphically or by means of some simple formula. The tables in his paper give the heat production in calories per hour of a number of individuals when doing a carefully measured amount of mechanical work on a kind of treadmill or cycle. This amount of work is kept constant for each group of observations in the paper. On plotting these as is done in fig. 1, it is clear that the points lie very approximately on a straight line, and it is easily seen that the equation to this line, may be written H = 128 + W/0·256;

Perceptual Learning of Vocoded Speech With and Without Contralateral Hearing: Implications for Cochlear Implant Rehabilitation

2020 ◽  
pp. 1-10
Author(s):  
Martin Chavant ◽  
Alexis Hervais-Adelman ◽  
Olivier Macherey
Keyword(s):  
Cochlear Implant ◽  
Perceptual Learning ◽  
Speech Signal ◽  
Training Phase ◽  
Monosyllabic Words ◽  
Low Pass ◽  
Contralateral Ear ◽  
Number Of Individuals ◽  
Insight Into ◽  
Vocoded Speech

Purpose An increasing number of individuals with residual or even normal contralateral hearing are being considered for cochlear implantation. It remains unknown whether the presence of contralateral hearing is beneficial or detrimental to their perceptual learning of cochlear implant (CI)–processed speech. The aim of this experiment was to provide a first insight into this question using acoustic simulations of CI processing. Method Sixty normal-hearing listeners took part in an auditory perceptual learning experiment. Each subject was randomly assigned to one of three groups of 20 referred to as NORMAL, LOWPASS, and NOTHING. The experiment consisted of two test phases separated by a training phase. In the test phases, all subjects were tested on recognition of monosyllabic words passed through a six-channel “PSHC” vocoder presented to a single ear. In the training phase, which consisted of listening to a 25-min audio book, all subjects were also presented with the same vocoded speech in one ear but the signal they received in their other ear differed across groups. The NORMAL group was presented with the unprocessed speech signal, the LOWPASS group with a low-pass filtered version of the speech signal, and the NOTHING group with no sound at all. Results The improvement in speech scores following training was significantly smaller for the NORMAL than for the LOWPASS and NOTHING groups. Conclusions This study suggests that the presentation of normal speech in the contralateral ear reduces or slows down perceptual learning of vocoded speech but that an unintelligible low-pass filtered contralateral signal does not have this effect. Potential implications for the rehabilitation of CI patients with partial or full contralateral hearing are discussed.

Optimal Experimental Design With Nesting of Persons in Organizations

2013 ◽  
Vol 221 (3) ◽  
pp. 145-159 ◽  
Author(s):  
Gerard J. P. van Breukelen
Keyword(s):  
Repeated Measures ◽  
Optimal Number ◽  
Health Centers ◽  
Randomized Experiments ◽  
Optimal Sample ◽  
Treatment Conditions ◽  
Sampling Cost ◽  
Nested Designs ◽  
Simple Equations ◽  
Number Of Individuals

This paper introduces optimal design of randomized experiments where individuals are nested within organizations, such as schools, health centers, or companies. The focus is on nested designs with two levels (organization, individual) and two treatment conditions (treated, control), with treatment assignment to organizations, or to individuals within organizations. For each type of assignment, a multilevel model is first presented for the analysis of a quantitative dependent variable or outcome. Simple equations are then given for the optimal sample size per level (number of organizations, number of individuals) as a function of the sampling cost and outcome variance at each level, with realistic examples. Next, it is explained how the equations can be applied if the dependent variable is dichotomous, or if there are covariates in the model, or if the effects of two treatment factors are studied in a factorial nested design, or if the dependent variable is repeatedly measured. Designs with three levels of nesting and the optimal number of repeated measures are briefly discussed, and the paper ends with a short discussion of robust design.

A cutting edge approach to assessing physical activities occurring on sidewalks/streets (Preprint)

2018 ◽  
Author(s):  
Richard Robert Suminski Jr ◽  
Gregory Dominick ◽  
Philip Sapanaro
Keyword(s):  
Physical Activity ◽  
Environmental Conditions ◽  
Intraclass Correlation ◽  
Physical Activity Behavior ◽  
Physical Activities ◽  
Video Data ◽  
Considerable Proportion ◽  
High Definition ◽  
Deep Convolutional Neural Networks ◽  
Number Of Individuals

BACKGROUND A considerable proportion of outdoor physical activity is done on sidewalk/streets. For example, we found that ~70% of adults who walked during the previous week used the sidewalks/streets around their homes. Interventions conducted at geographical levels (e.g., community) and studies examining relationships between environmental conditions (e.g., traffic) and walking/biking, necessitate a reliable measure of physical activities performed on sidewalks/streets. The Block Walk Method (BWM) is one of the more common approaches available for this purpose. Although it utilizes reliable observation techniques and displays criterion validity, it remains relatively unchanged since its introduction in 2006. It is a non-technical, labor-intensive, first generation method. Advancing the BWM would contribute significantly to our understanding of physical activity behavior. OBJECTIVE Therefore, the objective of the proposed study is to develop and test a new BWM that utilizes a wearable video device (WVD) and computer video analysis to assess physical activities performed on sidewalks/streets. The following aims will be completed to accomplish this objective. Aim 1: Improve the BWM by incorporating a WVD into the methodology. The WVD is a pair of eyeglasses with a high definition video camera embedded into the frames. We expect the WVD to be a viable option for improving the acquisition and accuracy of data collected using the BWM. Aim 2: Advance the WVD-enhanced BWM by applying machine learning and recognition software to automatically extract information on physical activities occurring on the sidewalks/streets from the videos. METHODS Trained observers (one wearing and one not wearing the WVD) will walk together at a set pace along predetermined, 1000 ft. sidewalk/street observation routes representing low, medium, and high walkable areas. During the walks, the non-WVD observer will use the traditional BWM to record the number of individuals standing/sitting, walking, biking, and running along the routes. The WVD observer will only record a video while walking. Later, two investigators will view the videos to determine the numbers of individuals performing physical activities along the routes. For aim 2, the video data will be analyzed automatically using multiple deep convolutional neural networks (CNNs) to determine the number of humans along an observation route as well as the type of physical activities being performed. Bland Altman methods and intraclass correlation coefficients will be used to assess agreement. Potential sources of error such as occlusions (e.g., trees) will be assessed using moderator analyses. RESULTS Outcomes from this study are pending; however, preliminary studies supporting the research protocol indicate that the BWM is reliable and the number of individuals were seen walking along routes are correlated with several environmental characteristics (e.g., traffic, sidewalk defects). Further, we have used CNNs to detect cars, bikes, and pedestrians as well as individuals using park facilities. CONCLUSIONS We expect the new approach will enhance measurement accuracy while reducing the burden of data collection. In the future, the capabilities of the WVD-CNNs system will be expanded to allow for the determination of other characteristics captured by the videos such as caloric expenditure and environmental conditions.

Dynamics of Electrodiffusion Friction Probes. I. Shape-Dependent Potentiostatic Transient

1997 ◽  
Vol 62 (3) ◽  
pp. 397-419 ◽  
Author(s):  
Ondřej Wein ◽  
Václav Sobolík
Keyword(s):  
Simple Formula ◽  
Flow Direction ◽  
Voltage Step ◽  
Convex Shape ◽  
Exact Theory ◽  
Working Electrode ◽  
Arbitrary Convex

An exact theory is given of the voltage-step transient under limiting diffusion conditions for an electrodiffusion friction probe of arbitrary convex shape. The actual transient courses are given for the strip, circular, elliptic, triangular, and rectangular probes of any orientation with respect to the flow direction. A simple formula for any probe with a single working electrode of convex shape is suggested to facilitate the calibration of electrodiffusion probes based on the voltage-step transient.

Evolutionary genetics of small populations

2017 ◽  
Author(s):  
Richard Frankham ◽  
Jonathan D. Ballou ◽  
Katherine Ralls ◽  
Mark D. B. Eldridge ◽  
Michele R. Dudash ◽  
...  
Keyword(s):  
Genetic Diversity ◽  
Population Size ◽  
Evolutionary Genetics ◽  
Small Population ◽  
Small Populations ◽  
Effective Population ◽  
Genetic Management ◽  
Evolutionary Genetic ◽  
Loss Of Genetic Diversity ◽  
Number Of Individuals

Genetic management of fragmented populations involves the application of evolutionary genetic theory and knowledge to alleviate problems due to inbreeding and loss of genetic diversity in small population fragments. Populations evolve through the effects of mutation, natural selection, chance (genetic drift) and gene flow (migration). Large outbreeding, sexually reproducing populations typically contain substantial genetic diversity, while small populations typically contain reduced levels. Genetic impacts of small population size on inbreeding, loss of genetic diversity and population differentiation are determined by the genetically effective population size, which is usually much smaller than the number of individuals.

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