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World Journal of Nuclear Science and Technology 2016年第4期6卷 232-260页

作者： m. p. silverman Dep.rtm.nt of p.ysics Trinity College Hartford CT USA

A sim.le m.thod em.loying a p.ir of p.ncake-style Geiger-m.eller (Gm. counters for quantitative m.asurem.nt of radon activity concentration (activity p.r unit volum.) is described and dem.nstrated. The use of two Gm.counters, together with the basic theory derived in this p.p.r, p.rm.t the detection of alp.a p.rticles from.decay of and p.ogeny ( p.218p.p., p.214p.p.) and the conversion of the alp.a count rate into a radon concentration. A unique feature of this m.thod, in com.arison with standard m.thodologies to m.asure radon concentration, is the absence of a fixed control volum.. Advantages afforded by the rep.rted Gm.m.thod include: 1) it p.ovides a direct in-situ value of radon level, thereby elim.nating the need to send sam.les to an external testing laboratory;2) it can be ap.lied to m.nitoring radon levels exhibiting wide short-term.variability;3) it can yield short-term.m.asurem.nts of com.arable accuracy and equivalent or higher p.ecision than a com.ercial radon m.nitor sam.ling by p.ssive diffusion;4) it yields long-term.m.asurem.nts statistically equivalent to com.ercial radon m.nitors;5) it uses the m.st com.only em.loyed, overall least exp.nsive, and m.st easily op.rated typ. of nuclear instrum.ntation. As such, the m.thod is p.r-ticularly suitable for use by researchers, p.blic health p.rsonnel, and hom. dwellers who p.efer to m.nitor indoor radon levels them.elves. The results of a consecutive 30-day sequence of 24 hour m.an radon m.asurem.nts by the p.op.sed Gm.m.thod and a com.ercial state-of-the-art radon m.nitor certified for radon testing are com.ared.

关键词： Radioactivity Radon Concentration Geiger-m.eller Counter Alp.a p.rticle Diffusion Alp.a Range

Num.rical p.ocedures for Calculating the p.obabilities of Recurrent Runs

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Op.n Journal of Statistics 2014年第2期4卷 144-153页

作者： m. p. silverman Dep.rtm.nt of p.ysics Trinity College Hartford USA

Run count statistics serve a central role in tests of non-random.ess of stochastic p.ocesses of interest to a wide range of discip.ines within the p.ysical sciences, social sciences, business and finance, and other endeavors involving intrinsic uncertainty. To carry out such tests, it is often necessary to calculate two kinds of run count p.obabilities: 1) the p.obability that a certain num.er of trials results in a sp.cified m.ltip.e occurrence of an event, or 2) the p.obability that a sp.cified num.er of occurrences of an event take p.ace within a fixed num.er of trials. The use of ap.rop.iate generating functions p.ovides a system.tic p.ocedure for obtaining the distribution functions of these p.obabilities. This p.p.r exam.nes relationship. am.ng the generating functions ap.licable to recurrent runs and discusses m.thods, em.loying sym.olic m.them.tical software, for im.lem.nting num.rical extraction of p.obabilities. In addition, the asym.totic form.of the cum.lative distribution function is derived, which allows accurate runs statistics to be obtained for sequences of trials so large that com.utation tim.s for extraction of this inform.tion from.the generating functions could be im.ractically long.

关键词： Recurrent Events Theory of Runs Tim. Series Analysis Generating Functions p.obability Distributions

Crowdsourced Sam.ling of a Com.osite Random.Variable: Analysis, Sim.lation, and Exp.rim.ntal Test

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Op.n Journal of Statistics 2019年第4期9卷 494-529页

作者： m. p. silverman Dep.rtm.nt of p.ysics Trinity College Hartford CT USA

A com.osite random.variable is a p.oduct (or sum.of p.oducts) of statistically distributed quantities. Such a variable can rep.esent the solution to a m.lti-factor quantitative p.oblem.subm.tted to a large, diverse, indep.ndent, anonym.us group.of non-exp.rt resp.ndents (the “crowd”). The objective of this research is to exam.ne the statistical distribution of solutions from.a large crowd to a quantitative p.oblem.involving im.ge analysis and object counting. Theoretical analysis by the author, covering a range of conditions and typ.s of factor variables, p.edicts that com.osite random.variables are distributed log-norm.lly to an excellent ap.roxim.tion. If the factors in a p.oblem.are them.elves distributed log-norm.lly, then their p.oduct is rigorously log-norm.l. A crowdsourcing exp.rim.nt devised by the author and im.lem.nted with the assistance of a BBC (British Broadcasting Corp.ration) television show, yielded a sam.le of ap.roxim.tely 2000 resp.nses consistent with a log-norm.l distribution. The sam.le m.an was within ~12% of the true count. However, a m.nte Carlo sim.lation (m.S) of the exp.rim.nt, em.loying either norm.l or log-norm.l random.variables as factors to m.del the p.ocesses by which a crowd of 1 m.llion m.ght arrive at their estim.tes, resulted in a visually p.rfect log-norm.l distribution with a m.an resp.nse within ~5% of the true count. The results of this research suggest that a well-m.deled m.S, by sim.lating a sam.le of resp.nses from.a large, rational, and incentivized crowd, can p.ovide a m.re accurate solution to a quantitative p.oblem.than m.ght be attainable by direct sam.ling of a sm.ller crowd or an uninform.d crowd, irresp.ctive of size, that guesses random.y.

关键词： Crowdsourcing Com.uter m.deling of Crowds m.nte Carlo Sim.lation Large-Scale Sam.ling Log-Norm.l Random Variable Log-Norm.l Distribution

p.ogressive Random.zation of a Deck of p.aying Cards: Exp.rim.ntal Tests and Statistical Analysis of the Riffle Shuffle

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Op.n Journal of Statistics 2019年第2期9卷 268-298页

作者： m. p. silverman Dep.rtm.nt of p.ysics Trinity College Hartford CT USA

The question of how m.ny shuffles are required to random.ze an initially ordered deck of cards is a p.oblem.that has fascinated m.them.ticians, scientists, and the general p.blic. The two p.incip.l theoretical ap.roaches to the p.oblem. which differed in how each defined random.ess, has led to statistically different threshold num.ers of shuffles. This p.p.r rep.rts a com.rehensive exp.rim.ntal analysis of the card random.zation p.oblem.for the p.rp.ses of determ.ning 1) which of the two theoretical ap.roaches m.de the m.re accurate p.ediction, 2) whether different statistical tests yield different threshold num.ers of random.zing shuffles, and 3) whether m.nual or m.chanical shuffling random.zes a deck m.re effectively for a given num.er of shuffles. p.rm.tations of 52-card decks, each subjected to sets of 19 successive riffle shuffles executed m.nually and by an auto-shuffling device were recorded sequentially and analyzed in resp.ct to 1) the theory of runs, 2) rank ordering, 3) serial correlation, 4) theory of rising sequences, and 5) entrop. and inform.tion theory. Am.ng the outcom.s, it was found that: 1) different statistical tests were sensitive to different p.tterns indicative of residual order;2) as a consequence, the threshold num.er of random.zing shuffles could vary widely am.ng tests;3) in general, m.nual shuffling random.zed a deck better than m.chanical shuffling for a given num.er of shuffles;and 4) the m.an num.er of rising sequences as a function of num.er of m.nual shuffles m.tched very closely the theoretical p.edictions based on the Gilbert-Shannon-Reed (GSR) m.del of riffle shuffles, whereas m.chanical shuffling resulted in significantly fewer rising sequences than p.edicted.

关键词： Random.zation of Cards Num.er of Riffle Shuffles Rising Sequences GSR m.del Entrop. and Inform.tion

Statistical Analysis of Subsurface Diffusion of Solar Energy with Im.lications for Urban Heat Stress

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Journal of m.dern p.ysics 2014年第9期5卷 751-762页

作者： m. p. silverman Dep.rtm.nt of p.ysics Trinity College Hartford USA

Analysis of hourly underground tem.erature m.asurem.nts at a m.dium.size (by p.p.lation) US city as a function of dep.h and extending over 5+ years revealed a p.sitive trend exceeding the rate of regional and global warm.ng by an order of m.gnitude. m.asurem.nts at dep.hs greater than ~2 m.are unaffected by daily fluctuations and sense only seasonal variability. A com.arable trend also em.rged from.the surface tem.erature record of the largest US city (New York). p.wer sp.ctral analysis of deep.and shallow subsurface tem.erature records showed resp.ctively two kinds of p.wer-law behavior: 1) a quasi-continuum.of p.wer am.litudes indicative of Brownian noise, sup.rp.sed (in the shallow record) by 2) a discrete sp.ctrum.of diurnal harm.nics attributable to the unequal heat flux between daylight and darkness. Sp.ctral am.litudes of the deep.st tem.erature tim. series (2.4 m. conform.d to a log-hyp.rbolic distribution. Up.n rem.val of seasonal variability from.the tem.erature record, the resulting sp.ctral am.litudes followed a log-exp.nential distribution. Dynam.cal analysis showed that relative am.litudes and p.ases of tem.erature records at different dep.hs were in excellent accord with a 1-dim.nsional heat diffusion m.del.

关键词： Tim. Series Analysis Heat Conduction Therm.l Diffusion p.wer Laws Clim.te Change Heat-Island Effect

Reaction Forces on a Fixed Ladder in Static Equilibrium. Analysis and Definitive Exp.rim.ntal Test of the Ladder p.oblem

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World Journal of m.chanics 2018年第9期8卷 311-342页

作者： m. p. silverman Dep.rtm.nt of p.ysics Trinity College Hartford USA

The develop.0}nt of a theoretical m.del to p.edict the four equilibrium.forces of reaction on a sim.le ladder of non-adjustable length leaning against a wall has long rem.ined an unresolved m.tter. The difficulty is that the p.oblem.is statically indeterm.nate and therefore requires com.lem.ntary inform.tion to obtain a unique solution. This p.p.r rep.rts 1) a com.rehensive theoretical analysis of the three fundam.ntal m.dels based on treating the ladder as a single Euler-Bernoulli beam. and 2) a detailed exp.rim.ntal investigation of the forces of reaction as a function of ap.lied load and location of load. In contrast to p.evious untested p.op.sals that the solution to the ladder p.oblem.lay in the axial constraint on com.ression or the transverse constraint on flexure, the exp.rim.ntal outcom. of the p.esent work showed unam.iguously that 1) the ladder could be m.deled the best by a p.nned sup.ort at the base (on the ground) and a roller sup.ort at the top.(at the wall), and 2) the only com.lem.ntary relation needed to resolve the static indeterm.nacy is the force of friction at the wall. m.asurem.nts were also m.de on the im.act loading of a ladder by rap.d ascent and descent of a clim.er. The results obtained were consistent with a sim.le dynam.cal m.del of the ladder as a linear elastic m.dium.subject to a p.lse p.rturbation. The solution to the ladder p.oblem.herein p.esented p.ovides a basis for theoretical extension to other typ.s of ladders. Of p.rticular im.ortance, given that accidents involving ladders in the workp.ace com.rise a significant fraction of all industrial accidents, the theoretical relations rep.rted here can help.determ.ne whether a collap.ed structure, against which a ladder was ap.lied, m.t regulatory safety lim.ts or not.

关键词： Reaction Forces on a Ladder Reaction Forces on a Beam Im.ulse Load on a Ladder Ladder in Static Equilibrium Statically Indeterm.nate Forces

Effects of a p.riodic Decay Rate on the Statistics of Radioactive Decay: New m.thods to Search for Violations of the Law of Radioactive Change

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Journal of m.dern p.ysics 2015年第11期6卷 1533-1553页

作者： m. p. silverman Dep.rtm.nt of p.ysics Trinity College Hartford USA

It is a long-held tenet of nuclear p.ysics, from.the early work of Rutherford and Soddy up.to p.esent tim.s that the disintegration of each sp.cies of radioactive nuclide occurs random.y at a constant rate unaffected by interactions with the external environm.nt. During the p.st 15 years or so, rep.rts have been p.blished of som. 10 or m.re unstable nuclides with non-exp.nential, p.riodic decay rates claim.d to be of geop.ysical, astrop.ysical, or cosm.logical origin. Deviations from.standard exp.nential decay are weak, and the claim. are controversial. This p.p.r exam.nes the effects of a p.riodic decay rate on the statistical distributions of 1) nuclear activity m.asurem.nts and 2) nuclear lifetim. m.asurem.nts. It is dem.nstrated that the m.difications to these distributions are ap.roxim.tely 100 tim.s m.re sensitive to non-standard radioactive decay than m.asurem.nts of the decay curve, p.wer sp.ctrum. or autocorrelation function for corresp.nding system.p.ram.ters.

关键词： Radioactive Decay Non-Exp.nential Decay Tim.-Dep.ndent Decay Half-Life Lifetim. Decay Curve

Cheating or Coincidence? Statistical m.thod Em.loying the p.incip.e of m.xim.m.Entrop. for Judging Whether a Student Has Com.itted p.agiarism

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Op.n Journal of Statistics 2015年第2期5卷 143-157页

作者： m. p. silverman Dep.rtm.nt of p.ysics Trinity College Hartford CT USA

Elem.nts of corresp.ndence (“coincidences”) between a student’s solutions to an assigned set of quantitative p.oblem. and the solutions m.nual for the course textbook m.y suggest that the stu-dent cop.ed the work from.an illicit source. p.agiarism.of this kind, which occurs p.im.rily in fields such as the natural sciences, engineering, and m.them.tics, is often difficult to establish. This p.p.r derives an exp.ession for the p.obability that alleged coincidences in a student’s p.p.r could be attributable to p.re chance. The analysis em.loys the p.incip.e of m.xim.m.Entrop. (p.0}), which, m.them.tically, is a variational p.ocedure requiring m.xim.zation of the Shannon-Jaynes entrop. function augm.nted by the com.leteness relation for p.obabilities and known inform.tion in the form.of exp.ctation values. The virtue of the p.0} as a general m.thod of inferential reasoning is that it generates the m.st objective (i.e. least biased) p.obability distribution consistent with the given inform.tion. Num.rical exam.nation of test cases for a range of p.ausible conditions can yield outcom.s that tend to exonerate a student who otherwise m.ght be wrongfully judged guilty of cheating by adjudicators unfam.liar with the surp.ising p.op.rties of random.p.ocesses.

关键词： p.agiarism Cheating Coincidence Inform.tion Entrop.

The Role of Friction in the Static Equilibrium.of a Fixed Ladder: Theoretical Analysis and Exp.rim.ntal Test

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World Journal of m.chanics 2018年第12期8卷 445-463页

作者： m. p. silverman Dep.rtm.nt of p.ysics Trinity College Hartford CT USA

In a recent p.blication the author derived and exp.rim.ntally tested several theoretical m.dels, distinguished by different boundary conditions at the contacts with horizontal and vertical sup.orts, that p.edicted the forces of reaction on a fixed (i.e. inextensible) ladder. This p.oblem.is statically indeterm.nate since there are 4 forces of reaction and only 3 equations of static equilibrium. The m.del that p.edicted the em.irical reactions correctly used a law of static friction to com.lem.nt the equations of static equilibrium. The p.esent p.p.r exam.nes in greater theoretical and exp.rim.ntal detail the role of friction in accounting for the forces of reaction on a fixed ladder. The rep.rted m.asurem.nts confirm.that forces p.rallel and norm.l to the sup.ort at the top.of the ladder are linearly p.op.rtional with a constant coefficient of friction irresp.ctive of the m.gnitude or location of the load, as assum.d in the theoretical m.del. However, m.asurem.nts of forces p.rallel and norm.l to the sup.ort at the base of the ladder are linearly p.op.rtional with coefficients that dep.nd sensitively on the location (although not the m.gnitude) of the load. This p.p.r accounts quantitatively for the different effects of friction at the top.and base of the ladder under conditions of usual use whereby friction at the vertical sup.ort alone is insufficient to keep.the ladder from.sliding. A theoretical m.del is also p.op.sed for the unusual circum.tance in which friction at the vertical sup.ort can keep.the ladder from.sliding.

关键词： Forces on a Ladder Static Equilibrium Law of Static Friction Statically Indeterm.nate Forces of Reaction

Extraction of Inform.tion from.Crowdsourcing: Exp.rim.ntal Test Em.loying Bayesian, m.xim.m.Likelihood, and m.xim.m.Entrop. m.thods

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Op.n Journal of Statistics 2019年第5期9卷 571-600页

作者： m. p. silverman Dep.rtm.nt of p.ysics Trinity College Hartford CT USA

A crowdsourcing exp.rim.nt in which viewers (the “crowd”) of a British Broadcasting Corp.ration (BBC) television show subm.tted estim.tes of the num.er of coins in a tum.ler was shown in an antecedent p.p.r (p.rt 1) to follow a log-norm.l distribution ∧(m.s2). The coin-estim.tion exp.rim.nt is an archetyp. of a broad class of im.ge analysis and object counting p.oblem. suitable for solution by crowdsourcing. The objective of the current p.p.r (p.rt 2) is to determ.ne the location and scale p.ram.ters (m.s) of ∧(m.s2) by both Bayesian and m.xim.m.likelihood (m.) m.thods and to com.are the results. One outcom. of the analysis is the resolution, by m.ans of Jeffreys’ rule, of questions regarding the ap.rop.iate Bayesian p.ior. It is shown that Bayesian and m. analyses lead to the sam. exp.ession for the location p.ram.ter, but different exp.essions for the scale p.ram.ter, which becom. identical in the lim.t of an infinite sam.le size. A second outcom. of the analysis concerns use of the sam.le m.an as the m.asure of inform.tion of the crowd in ap.lications where the distribution of resp.nses is not sought or known. In the coin-estim.tion exp.rim.nt, the sam.le m.an was found to differ widely from.the m.an num.er of coins calculated from.∧(m.s2). This discordance raises critical questions concerning whether, and under what conditions, the sam.le m.an p.ovides a reliable m.asure of the inform.tion of the crowd. This p.p.r resolves that p.oblem.by use of the p.incip.e of m.xim.m.entrop. (p.0}). The p.0} yields a set of equations for finding the m.st p.obable distribution consistent with given p.ior inform.tion and only that inform.tion. If there is no solution to the p.0} equations for a sp.cified sam.le m.an and sam.le variance, then the sam.le m.an is an unreliable statistic, since no m.asure can be assigned to its uncertainty. p.rts 1 and 2 together dem.nstrate that the inform.tion content of crowdsourcing resides in the distribution of resp.nses (very often log-norm.l i

关键词： Crowdsourcing Bayesian p.iors m.xim.m Likelihood p.incip.e of m.xim.m Entrop. p.ram.ter Estim.tion Log-Norm.l Distribution