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PubMed2003

Free energy of liquid water on the basis of quasichemical theory and ab initio molecular dynamics.

We use ab initio molecular dynamics as a basis for quasichemical theory evaluation of the free energy of water near conventional liquid thermodynamic states. The Perdew-Wang-91 (PW91), Perdew-Burke-Ernzerhof (PBE), and revised PBE (rPBE) functionals are employed. The oxygen radial density distribution using the rPBE functional is in reasonable agreement with current experiments, whereas the PW91 and PBE functionals predict a more structured oxygen radial density distribution. The diffusion coefficient with the rPBE functional is in reasonable accord with experiments. Using a maximum entropy procedure, we obtain x0 from the coordination number distribution xn for oxygen atoms having n neighbors. Likewise, we obtain p0 from pn, the probability of observing cavities of specified radius containing n water molecules. The probability x0 is a measure of the local chemical interactions and is central to the quasichemical theory of solutions. The probability p0, central to the theory of liquids, is a measure of the free energy required to open cavities of defined sizes in the solvent. Using these values and a reasonable model for electrostatic and dispersion effects, the hydration free energy of water in water at 314 K is calculated to be -5.1 kcal/mole with the rPBE functional, in encouraging agreement with the experimental value of -6.1 kcal/mole.

Computer Simulation↗
PubMed2003

Detection and false-alarm probabilities for laser radars that use Geiger-mode detectors.

For a direct-detection laser radar that uses a Geiger-mode detector, theory shows that the single-pulse detection probability is reduced by a factor exp(-K), where K is the mean number of primary electrons created by noise in the interval t between detector turn-on and arrival of laser photons reflected from the target. The corresponding false-alarm probability is at least 1 - exp(-K). For fixed-rate noise, one can improve the detection and false-alarm probabilities by reducing t. Moreover, when background-light noise is significant and dominates dark-current noise and when the laser signal is of the order of ten photoelectrons or more, the probabilities can be improved by reducing the amount of light falling on the detector, even if the laser signal is reduced by the same factor as the background light is. Additional analytical calculations show that identifying coincidences in data from as few as three pulses canreduce the false-alarm probability by orders of magnitude and, for some conditions, can also improve the detection probability.

Journal Article↗
PubMed1985

Gene genealogy and variance of interpopulational nucleotide differences.

A mathematical theory is developed for computing the probability that m genes sampled from one population (species) and n genes sampled from another are derived from l genes that existed at the time of population splitting. The expected time of divergence between the two most closely related genes sampled from two different populations and the time of divergence (coalescence) of all genes sampled are studied by using this theory. It is shown that the time of divergence between the two most closely related genes can be used as an approximate estimate of the time of population splitting (T) only when T identical to t/(2N) is small, where t and N are the number of generations and the effective population size, respectively. The variance of Nei and Li's estimate (d) of the number of net nucleotide differences between two populations is also studied. It is shown that the standard error (Sd) of d is larger than the mean when T is small (T much less than 1). In this case, Sd is reduced considerably by increasing sample size. When T is large (T greater than 1), however, a large proportion of the variance of d is caused by stochastic factors, and increase in the sample size does not help to reduce Sd. To reduce the stochastic variance of d, one must use data from many independent unlinked gene loci.

Analysis of Variance↗
PubMed1983

Membrane fluidity and the probability of complement fixation.

We develop a mathematical theory of the role of membrane fluidity in the initiation of the IgG mediated complement cascade. The basic assumption is that C1q must be at least doubly bound to activate C1r, but that once C1q is doubly bound, C1r still requires some mean finite time tau to become enzymatically active. If C1q dissociates during this time interval, C1r cannot be activated. We consider the consequences of the simplest model of fluidity--one in which the difference between "fluid phase" lipids and "non-fluid phase" lipids is to allow protein mobility, but not a change in protein conformation. We show that under these conditions fluidity will effect C1r activation only if the rate of formation of multiply bound C1q is limited by diffusion in the membrane. If diffusion in the membrane is not rate-limiting, then, within the framework of this model, fluidity has no effect whatsoever on C1r activation. Thus, an experimental determination that C1q binding is not rate-limited by diffusion in the surface, but that fluidity does effect activation, would suggest a protein conformational change resulting perhaps from altered lipid composition. If diffusion in the surface does rate limit multiple C1q binding, we predict the possibility of an optimum diffusion coefficient for activation. For suitably chosen and reasonable parameter values this optimum will occur in the range (10(-11) less than or equal to D less than or equal to 10(-8) cm2/sec. We predict further, under these circumstances, a precipitous drop in the probability of activation above the optimum. The abrupt switch from a high probability of activation to essentially no probability of activation suggests the possibility of a very sensitive control mechanism exploitable by relatively small changes in membrane lipid composition.

Animals↗
PubMed2003

Alcohol and error processing.

A recent study indicates that alcohol consumption reduces the amplitude of the error-related negativity (ERN), a negative deflection in the electroencephalogram associated with error commission. Here, we explore possible mechanisms underlying this result in the context of two recent theories about the neural system that produces the ERN - one based on principles of reinforcement learning and the other based on response conflict monitoring.

Alcohol Drinking↗
PubMed2003

Pressure wave propagation in fluid-filled co-axial elastic tubes. Part 1: Basic theory.

Our work is motivated by ideas about the pathogenesis of syringomyelia. This is a serious disease characterized by the appearance of longitudinal cavities within the spinal cord. Its causes are unknown, but pressure propagation is probably implicated. We have developed an inviscid theory for the propagation of pressure waves in co-axial, fluid-filled, elastic tubes. This is intended as a simple model of the intraspinal cerebrospinal-fluid system. Our approach is based on the classic theory for the propagation of longitudinal waves in single, fluid-filled, elastic tubes. We show that for small-amplitude waves the governing equations reduce to the classic wave equation. The wave speed is found to be a strong function of the ratio of the tubes' cross-sectional areas. It is found that the leading edge of a transmural pressure pulse tends to generate compressive waves with converging wave fronts. Consequently, the leading edge of the pressure pulse steepens to form a shock-like elastic jump. A weakly nonlinear theory is developed for such an elastic jump.

Animals↗
PubMed2005

Statistical-overlap theory for elliptical zones of high aspect ratio in comprehensive two-dimensional separations.

The low prediction by statistical-overlap theory of the numbers of singlets and peaks in two-dimensional separations containing zones represented by either circles of small number or eccentric ellipses of any number is shown to result from use of probability expressions for unbound spaces of infinite extent. An exact theory is derived for the probability of singlet formation in a reduced two-dimensional space of unit length, width, and area. The probability is a weighted sum of the probabilities of singlet formation in the interior, edge, and corner regions of the space, which depend only on saturation. The weighting factors are the fractions of area associated with each region and depend on the number of zones, the aspect ratio, the saturation, and the ellipse's spatial orientation. The average numbers of doublets, triplets, and peaks in the space are approximated by combining these results with Roach's equations describing the clustering of circles in an unbound two-dimensional space. Simulations show that theory predicts the number of singlets, doublets, triplets, and peaks, when the number of zones is 25 or more, the aspect ratio is 100 or less, and the saturation is 2 or less. The relationship is derived between the aspect ratios of ellipses in the reduced space and actual separation space. Calculations are presented for comprehensive two-dimensional gas chromatography.

Journal Article↗
PubMed2004

Density functional response theory calculations of three-photon absorption.

Three-photon absorption probabilities delta(3PA) have been calculated through application of a recently derived method for cubic response functions within density functional theory (DFT). Calculations are compared with Hartree-Fock (HF) and with a coupled cluster hierarchy of models in a benchmarking procedure. Except for cases having intermediate states near resonance, density functional theory is demonstrated to be in sufficient agreement with the highly correlated methods in order to qualify for predictions of delta(3PA). For the larger systems addressed, a set of acceptor A and donor D substituted pi-conjugated systems formed by trans-stilbene and dithienothiophene (DTT), we find noticeable differences in the magnitude of delta(3PA) between HF and DFT, although similar trends are followed. It is shown that the dipolar structures, TS-AD and DTT-AD, have substantially larger delta(3PA) than other types of modifications which is in accordance with observations for two-photon absorption. This is the first application of density functional theory to three-photon absorption beyond the use of few-state models.

Journal Article↗
PubMedDate not supplied

Probabilistic linkage of large public health data files.

Probabilistic linkage technology makes it feasible and efficient to link large public health databases in a statistically justifiable manner. The problem addressed by the methodology is that of matching two files of individual data under conditions of uncertainty. Each field is subject to error which is measured by the probability that the field agrees given a record pair matches (called the m probability) and probabilities of chance agreement of its value states (called the u probability). Fellegi and Sunter pioneered record linkage theory. Advances in methodology include use of an EM algorithm for parameter estimation, optimization of matches by means of a linear sum assignment program, and more recently, a probability model that addresses both m and u probabilities for all value states of a field. This provides a means for obtaining greater precision from non-uniformly distributed fields, without the theoretical complications arising from frequency-based matching alone. The model includes an iterative parameter estimation procedure that is more robust than pre-match estimation techniques. The methodology was originally developed and tested by the author at the U.S. Census Bureau for census undercount estimation. The more recent advances and a new generalized software system were tested and validated by linking highway crashes to Emergency Medical Service (EMS) reports and to hospital admission records for the National Highway Traffic Safety Administration (NHTSA).

Adult↗
PubMed2004

Error-rate and decision-theoretic methods of multiple testing: which genes have high objective probabilities of differential expression?

Given a multiple testing situation, the null hypotheses that appear to have sufficiently low probabilities of truth may be rejected using a simple, nonparametric method based on decision theory. This applies not only to posterior levels of belief, but also to conditional probabilities in the sense of relative frequencies, as seen from their equality to local false discovery rates (dFDRs). This approach neither requires the estimation of probability densities, nor of their ratios. Decision theory can also inform the selection of false discovery rate weights. An application to gene expression microarrays is presented with a discussion of the applicability of the assumption of "clumpy dependence."

Journal Article↗
PubMed2005

The probability of parallel evolution.

How often will natural selection drive parallel evolution at the DNA sequence level? More precisely, what is the probability that selection will cause two populations that live in identical environments to substitute the same beneficial mutation? Here I show that, under fairly general conditions, the answer is simple: if a wild-type sequence can mutate to n different beneficial mutations, replicate populations will on average fix the same mutation with probability P = 2/(n + 1). This probability, which is derived using extreme value theory, is independent of most biological details, including the length of the gene in question and the precise distribution of fitness effects among alleles. I conclude that the probability of parallel evolution under natural selection is nearly twice as large as that under neutrality.

Adaptation, Biological↗
PubMed2002

Generalized quantum Fokker-Planck, diffusion, and Smoluchowski equations with true probability distribution functions.

Traditionally, quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasiprobability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using true probability distribution functions is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their coordinates and momenta, we derive a generalized quantum Langevin equation in c numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion, and Smoluchowski equations are the exact quantum analogs of their classical counterparts. The present work is independent of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (the Smoluchowski equation being considered in the overdamped limit).

Journal Article↗
PubMed2001

Optimal nonlinear codes for the perception of natural colours.

We discuss how visual nonlinearity can be optimized for the precise representation of environmental inputs. Such optimization leads to neural signals with a compressively nonlinear input-output function the gradient of which is matched to the cube root of the probability density function (PDF) of the environmental input values (and not to the PDF directly as in histogram equalization). Comparisons between theory and psychophysical and electrophysiological data are roughly consistent with the idea that parvocellular (P) cells are optimized for precision representation of colour: their contrast-response functions span a range appropriately matched to the environmental distribution of natural colours along each dimension of colour space. Thus P cell codes for colour may have been selected to minimize error in the perceptual estimation of stimulus parameters for natural colours. But magnocellular (M) cells have a much stronger than expected saturating nonlinearity; this supports the view that the function of M cells is mainly to detect boundaries rather than to specify contrast or lightness.

Algorithms↗
PubMed1983

Evaluation of diagnostic audiometric tests.

Five diagnostic audiometric procedures - acoustic reflexes, performance-intensity functions for monosyllabic (phonetically balanced) words, Békésy audiometry, Békésy comfortable loudness audiometry and suprathreshold adaptation test - were critically evaluated by decision matrix analysis and information theory analysis. The subjects were 20 patients with surgically confirmed eighth nerve disorders and 20 patients with presumed cochlear disorders. Each patient completed all test procedures. In terms of decision matrix analysis, sensitivity (correct identification of eighth nerve site) ranged from 45 to 85%. Specificity (correct rejection of patients with cochlear site) ranged from 70 to 100%. Predictive value ranged from 74 to 100% for positive results and from 62 to 82% for negative results. The efficiency of the five tests ranged from 68 to 78%. In terms of information theory, positive test results increased the probability of eighth nerve disorder in any subject from 50% (a priori) to 74-100%. Negative test results decreased the probability of eighth nerve disorder from 50% to 18-38%. Relative differences among the diagnostic effectiveness of the five individual test procedures were not pronounced. However, the suprathreshold adaptation test (results confined to 500, 1 000 and 2 000 Hz) was less efficient than the other four diagnostic techniques.

Adult↗
PubMed1995

Communication theory and the search for effective feedback.

If messages transmitted to the public, patients and health professionals could be assured of being received, understood and acted on as intended by the senders of messages, there would be little need to focus on communications and feedback. That the physician's office, the healthcare system and the community are littered with messages that 'never got through' attests to the problem of ineffective communications and the absence of effective feedback. Communication theorists, health psychologists and thoughtful health professionals, particularly those working in community hypertension programmes, have developed approaches that improve the probabilities of 'getting the message through'. Theory-based communications with built-in feedback and 'feed-forward' enhance the probabilities of success considerably. This presentation explores these problems using the SMCR model of communication. Differences between linear models and transactional models are discussed. On the assumption that the health message environments of the future will be increasingly complex with highly differentiated target audiences in a rapid paced computer and electronically driven world, 'getting the message through' will become an even greater challenge than in the recent past. Specific steps to change communication approaches in this setting are proposed.

Communication↗
PubMed2006

Seeing the forest when entry is unlikely: probability and the mental representation of events.

Conceptualizing probability as psychological distance, the authors draw on construal level theory (Y. Trope & N. Liberman, 2003) to propose that decreasing an event's probability leads individuals to represent the event by its central, abstract, general features (high-level construal) rather than by its peripheral, concrete, specific features (low-level construal). Results indicated that when reported probabilities of events were low rather than high, participants were more broad (Study 1) and inclusive (Study 2) in their categorization of objects, increased their preference for general rather than specific activity descriptions (Study 3), segmented ongoing behavior into fewer units (Study 4), were more successful at abstracting visual information (Study 5), and were less successful at identifying details missing within a coherent visual whole (Study 6). Further, after exposure to low-probability as opposed to high-probability phrases, participants increasingly preferred to identify actions in ends-related rather than means-related terms (Study 7). Implications for probability assessment and choice under uncertainty are discussed.

Choice Behavior↗