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Extraction of Information from Crowdsourcing: Experimental Test Employing Bayesian, Maximum Likelihood, and Maximum Entropy Methods

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Open Journal of Statistics 2019年第5期9卷 571-600页

作者： M. P. silverman Department of Physics Trinity College Hartford CT USA

A crowdsourcing experiment in which viewers (the “crowd”) of a British Broadcasting Corporation (BBC) television show submitted estimates of the number of coins in a tumbler was shown in an antecedent paper (Part 1) to follow a log-normal distribution ∧(m,s2). The coin-estimation experiment is an archetype of a broad class of image analysis and object counting problems suitable for solution by crowdsourcing. The objective of the current paper (Part 2) is to determine the location and scale parameters (m,s) of ∧(m,s2) by both Bayesian and maximum likelihood (ML) methods and to compare the results. One outcome of the analysis is the resolution, by means of Jeffreys’ rule, of questions regarding the appropriate Bayesian prior. It is shown that Bayesian and ML analyses lead to the same expression for the location parameter, but different expressions for the scale parameter, which become identical in the limit of an infinite sample size. A second outcome of the analysis concerns use of the sample mean as the measure of information of the crowd in applications where the distribution of responses is not sought or known. In the coin-estimation experiment, the sample mean was found to differ widely from the mean number of coins calculated from ∧(m,s2). This discordance raises critical questions concerning whether, and under what conditions, the sample mean provides a reliable measure of the information of the crowd. This paper resolves that problem by use of the principle of maximum entropy (PME). The PME yields a set of equations for finding the most probable distribution consistent with given prior information and only that information. If there is no solution to the PME equations for a specified sample mean and sample variance, then the sample mean is an unreliable statistic, since no measure can be assigned to its uncertainty. Parts 1 and 2 together demonstrate that the information content of crowdsourcing resides in the distribution of responses (very often log-normal i

关键词： Crowdsourcing Bayesian Priors Maximum Likelihood Principle of Maximum Entropy Parameter Estimation Log-Normal Distribution

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Brownian Motion of Decaying Particles: Transition Probability, Computer Simulation, and First-Passage Times

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Journal of Modern Physics 2017年第11期8卷 1809-1849页

作者： M. P. silverman Department of Physics Trinity College Hartford CT USA

Recent developments in the measurement of radioactive gases in passive diffusion motivate the analysis of Brownian motion of decaying particles, a subject that has received little previous attention. This paper reports the derivation and solution of equations comparable to the Fokker-Planck and Langevin equations for one-dimensional diffusion and decay of unstable particles. In marked contrast to the case of stable particles, the two equations are not equivalent, but provide different information regarding the same stochastic process. The differences arise because Brownian motion with particle decay is not a continuous process. The discontinuity is readily apparent in the computer-simulated trajectories of the Langevin equation that incorporate both a Wiener process for displacement fluctuations and a Bernoulli process for random decay. This paper also reports the derivation of the mean time of first passage of the decaying particle to absorbing boundaries. Here, too, particle decay can lead to an outcome markedly different from that for stable particles. In particular, the first-passage time of the decaying particle is always finite, whereas the time for a stable particle to reach a single absorbing boundary is theoretically infinite due to the heavy tail of the inverse Gaussian density. The methodology developed in this paper should prove useful in the investigation of radioactive gases, aerosols of radioactive atoms, dust particles to which adhere radioactive ions, as well as diffusing gases and liquids of unstable molecules.

关键词： Brownian Motion Random Walk Diffusion Radioactivity Transition Probability Fokker-Planck Equation Langevin Equation First Passage Fick’s Law Wiener Process

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Brownian Motion of Radioactive Particles: Derivation and Monte Carlo Test of Spatial and Temporal Distributions

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World Journal of Nuclear Science and Technology 2018年第2期8卷 86-119页

作者： M. P. silverman Akrit Mudvari Department of Physics Trinity College Hartford CT USA

Stochastic processes such as diffusion can be analyzed by means of a partial differential equation of the Fokker-Planck type (FPE), which yields a transition probability density, or by a stochastic differential equation of the Langevin type (LE), which yields the time evolution of a statistical process variable. Provided the stochastic process is continuous and certain boundary conditions are met, the two approaches yield equivalent information. However, Brownian motion of radioactively decaying particles is not a continuous process because the Brownian trajectories abruptly terminate when the particle decays. Recent analysis of the Brownian motion of decaying particles by both approaches has led to different mean-square displacements. In this paper, we demonstrate the complete equivalence of the two approaches by 1) showing quantitatively and operationally how the probability densities and statistical moments predicted by the FPE and LE relate to one another, 2) verifying that both approaches lead to identical statistical moments at all orders, and 3) confirming that the analytical solution to the FPE accurately describes the Brownian trajectories obtained by Monte Carlo simulations based on the LE. The analysis in this paper addresses both the spatial distribution of the particles (i.e. the question of displacement as a function of diffusion time) and the temporal distribution (i.e. the question of first-passage time to fixed absorbing boundaries).

关键词： Brownian Motion Diffusion Radioactive Decay Fokker-Planck Equation Langevin Equation Monte Carlo Simulation First-Passage Time Wiener Process Bernoulli Process Survival Function Moment-Generating Function

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Bending of a Tapered Rod: Modern Application and Experimental Test of Elastica Theory

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World Journal of Mechanics 2018年第7期8卷 272-300页

作者： M. P. silverman Joseph Farrah Department of Physics Trinity College Hartford USA

A tapered rod mounted at one end (base) and subject to a normal force at the other end (tip) is a fundamental structure of continuum mechanics that occurs widely at all size scales from radio towers to fishing rods to micro-electromechanical sensors. Although the bending of a uniform rod is well studied and gives rise to mathematical shapes described by elliptic integrals, no exact closed form solution to the nonlinear differential equations of static equilibrium is known for the deflection of a tapered rod. We report in this paper a comprehensive numerical analysis and experimental test of the exact theory of bending deformation of a tapered rod. Given the rod geometry and elastic modulus, the theory yields virtually all the geometric and physical features that an analyst, experimenter, or instrument designer might want as a function of impressed load, such as the exact curve of deformation (termed the elastica), maximum tip displacement, maximum tip deflection angle, distribution of curvature, and distribution of bending moment. Applied experimentally, the theory permits rapid estimation of the elastic modulus of a rod, which is not easily obtainable by other means. We have tested the theory by photographing the shapes of a set of flexible rods of different lengths and tapers subject to a range of impressed loads and using digital image analysis to extract the coordinates of the elastica curves. The extent of flexure in these experiments far exceeded the range of applicability of approximations that linearize the equations of equilibrium or neglect tapering of the rod. Agreement between the measured deflection curves and the exact theoretical predictions was excellent in all but several cases. In these exceptional cases, the nature of the anomalies provided important information regarding the deviation of the rods from an ideal Euler-Bernoulli cantilever, which thereby permitted us to model the deformation of the rods more accurately.

关键词： Elastica Deflection of Tapered Cantilever Euler-Bernoulli Beam Elastic Modulus Flexure Formula

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Exact Statistical Distribution of the Body Mass Index (BMI): Analysis and Experimental Confirmation

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Open Journal of Statistics 2022年第3期12卷 324-356页

作者： Mark P. silverman Trevor C. Lipscombe Department of Physics Trinity College Hartford CT USA The Catholic University of America Washington DC USA

Body Mass Index (BMI), defined as the ratio of individual mass (in kilograms) to the square of the associated height (in meters), is one of the most widely discussed and utilized risk factors in medicine and public health, given the increasing obesity worldwide and its relation to metabolic disease. Statistically, BMI is a composite random variable, since human weight (converted to mass) and height are themselves random variables. Much effort over the years has gone into attempts to model or approximate the BMI distribution function. This paper derives the mathematically exact BMI probability density function (PDF), as well as the exact bivariate PDF for human weight and height. Taken together, weight and height are shown to be correlated bivariate lognormal variables whose marginal distributions are each lognormal in form. The mean and variance of each marginal distribution, together with the linear correlation coefficient of the two distributions, provide 5 nonadjustable parameters for a given population that uniquely determine the corresponding BMI distribution, which is also shown to be lognormal in form. The theoretical analysis is tested experimentally by gender against a large anthropometric data base, and found to predict with near perfection the profile of the empirical BMI distribution and, to great accuracy, individual statistics including mean, variance, skewness, kurtosis, and correlation. Beyond solving a longstanding statistical problem, the significance of these findings is that, with knowledge of the exact BMI distribution functions for diverse populations, medical and public health professionals can then make better informed statistical inferences regarding BMI and public health policies to reduce obesity.

关键词： Body Mass Index Obesity Distribution of Weight Distribution of Height Correlation of Weight and Height

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家庭用药手册

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作者： Harold M. silverman

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超声治疗青光眼

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国外医学（物理医学与康复学分册） 1992年第3期12卷 116-117页

作者： silverman RH 林玉平

美国有20个医疗中心应用超声疗法治疗青光眼。现已对880只眼共治疗1117次。本文仅总结经常规和手术方法治疗无效的顽固性青光眼病人。资料与方法技术参数—换能器外径80mm,焦距90mm,频率4.6MHz,包括A 型扫描诊断部件(测距用)

关键词：青光眼超声波疗法

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Quantum Stabilization of General-Relativistic Variable-Density Degenerate Stars

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Journal of Modern Physics 2012年第7期3卷 561-569页

作者： David Eric Cox Ronald L. Mallett MP silverman Department of Physics Trinity College Hartford CT Department of Physics University of Connecticut Storrs CT

Research by one of the authors suggested that the critical mass of constant-density neutron stars will be greater than eight solar masses when the majority of their neutrons group into bosons that form a Bose-Einstein condensate, provided the bosons interact with each other and have scattering lengths on the order of a picometer. That analysis was able to use Newtonian theory for the condensate with scattering lengths on this order, but general relativity provides a more fundamental analysis. In this paper, we determine the equilibrium states of a static, spherically-symmetric variable-density mixture of a degenerate gas of noninteracting neutrons and a Bose-Einstein condensate using general relativity. We use a Klein-Gordan Lagrangian density with a Gross-Pitaevskii term for the condensate and an effective field for the neutrons. We show that a new class of compact stars can exist with masses above the Oppenheimer-Volkoff limit, provided the scattering length of the bosons is large enough. These stars have no internal singularities, obey causality, and demonstrate a quantum mechanism consistent with general relativity that could prevent collapsed stars from becoming black holes.

关键词： Gravity General Relativity Neutron Stars Black Holes Bose-Einstein Condensates Numerical Physics

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苯妥英的皮肤反应及免疫反应

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国外医学（皮肤性病学分册） 1989年第3期15卷 155-158页

作者： silverman AK 钱恒林

苯妥英又名二苯乙内酰脲或大仑丁,它是临床上应用广泛的抗惊厥及抗心律失常药物。最近几年皮肤病学家又利用它治疗隐性遗传性营养不良型大疱性表皮松解症、带状硬皮病和先天性厚甲症等。相对来说,其并发症是很少的,但对其所引起的多种... 详细信息

苯妥英又名二苯乙内酰脲或大仑丁,它是临床上应用广泛的抗惊厥及抗心律失常药物。最近几年皮肤病学家又利用它治疗隐性遗传性营养不良型大疱性表皮松解症、带状硬皮病和先天性厚甲症等。相对来说,其并发症是很少的,但对其所引起的多种皮肤及免疫反应已有报道,现综述如下。苯妥英的药理学在成年人苯妥英经胃肠道吸收很快,肌注则吸收较慢,其半衰期为22小时,而且容易保持稳定的治疗水平(10～20μg/ml)。在婴儿及儿童,由于解毒系统发育不成熟,苯妥英的半衰期及血浆水平变化很大,因此在治疗时。

关键词：苯妥英皮肤免疫

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THE EFFECT OF TISSUE DISAGGREGATION METHODS ON THE CLONOGENICITY OF SOLID HUMAN TUMOR CELLS

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中华医学杂志(英文版) 1992年第2期105卷 126-131页

作者：李同光 Lisa D Blackburn Ronnie D Horner Jan F silverman Albert L Wiley Jr. Departments of Radiation Oncology Family Medicine Clinical Pathology and Diagnostic Medicine East Carolina University School of Medicine Greenville NC 27858 USA

The effect of mechanical,enzymatic and com-bined disaggregations on the same tumor tissue(n=154)to define variables related to clonogenic effi-ciency (CE) of human tumor clonogenic assay(HTCA)was ***,CE was highly asso-ciated with the percentage of malignant cells in theinoculative suspensions(P<0.001)and the total cellconcentration plated(P=0.03).However,there was nosignificant correlation between CE and thedisaggregation method,type of tumor,cell viability,proportion of macrophages in the inoculum,or lengthof incubation(10 or 20 days).In addition,a higher CEwas found in some nonadherent fractions when com-paring the CE of the original plating suspensions tothat of their nonadherent *** is concluded thatmechanical disaggregation is the simplest technique forobtaining the highest yield of malignant cells,which isa decisive factor for colony growth,and that anincubation time of 10 days and 1×10～6cells per plate is the best condition for the human tu-mor clonogenic assay.

关键词： SOFT-AGAR GROWTH ASSAY

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