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PubMed2002

Chaotic probability density in two periodically driven and weakly coupled Bose-Einstein condensates.

Using the idea of the macroscopic quantum wave function and the definition of the classical chaos, we analytically reveal that the probability density of two periodically driven and weakly coupled Bose-Einstein condensates is deterministic but not predictable. Numerical calculation for the time evolutions of the chaotic probability density demonstrates the analytical result and exhibits the nonphysical implosions and ultimate unboundedness. A method for controlling the implosions and unboundedness is proposed through adjustment of the initial conditions that leads the probability density to periodically oscillate.

Journal Article↗

PubMed2003

Nucleation probability in binary heterogeneous nucleation of water-n-propanol vapor mixtures on insoluble and soluble nanoparticles.

Nucleation probabilities for binary heterogeneous nucleation have been measured quantitatively. Heterogeneous nucleation of binary n-propanol-water vapor mixtures on partially soluble 6.9-nm NaCl particles and on nonsoluble oxidized and nonoxidized 8-nm Ag particles at a constant nucleation temperature of 288 K (NaCl) or 285 K (Ag) has been investigated experimentally and theoretically. An expansion chamber was applied to generate supersaturated vapor mixtures. Number concentrations of particles activated to condensational growth were determined optically for various vapor phase activities at constant temperature. Nucleation probabilities have been measured as functions of the vapor phase activities for several n-propanol-water vapor mixing ratios. Beyond certain vapor phase activities a sharp onset of heterogeneous nucleation was observed both for NaCl and for Ag particles. For insoluble particle surfaces the theoretical slopes of the nucleation probability versus vapor phase activity curves were found to be somewhat steeper as compared to the experiment. On the other hand, for soluble particles the experimental slopes were found to be in satisfactory agreement with theory. The onset of the nucleation process is defined at an activity value where 50% of the particles were activated to condensational growth. Onset activities were obtained for various mixing ratios of the binary vapor mixtures. In the case of NaCl nuclei for n-propanol rich mixtures, the heterogeneous nucleation calculations based on a thermodynamically consistent version of Fletcher theory and an experimentally determined contact angle provide a reasonable approximation of the experimental data. However, it appears that the Fletcher theory is not applicable in the region of transition from n-propanol rich to water rich mixtures. Based on the Köhler theory of activation of soluble particles, a theory was formulated accounting for the presence of two condensable vapors and limited solubility of NaCl in water-propanol liquid mixtures. This approach provides a satisfactory description of the transition from activation of soluble particles to nucleation of vapors on insoluble particles. In the case of silver particles Fletcher theory with macroscopic experimental contact angles as well as with contact angle zero results in strong deviations from experimental data. A significant improvement was achieved by introducing fit contact angles, which are substantially lower than the macroscopic experimental values and may be considered as approximate values of the microscopic contact angles.

Journal Article↗

PubMed2003

Analytical solution of space probability distributions of particles in a one-dimensional ring.

Spatial probability distributions of a few particles having nonidentical masses in one-dimensional space with both periodic and fixed boundary conditions are analytically computed in statistical equilibrium states, and explicit solutions of the probability distributions are obtained. Some nontrivial interesting features of the probability distributions are predicted and fully confirmed by numerical simulations. The realization of a microcanonical equilibrium state of the system is justified by the agreement between the theoretical predictions and numerical observations.

Journal Article↗

PubMed2003

Universality of the crossing probability for the Potts model for q=1, 2, 3, 4.

The universality of the crossing probability pi(hs) of a system to percolate only in the horizontal direction was investigated numerically by a cluster Monte Carlo algorithm for the q-state Potts model for q=2, 3, 4 and for percolation q=1. We check the percolation through Fortuin-Kasteleyn clusters near the critical point on the square lattice by using representation of the Potts model as the correlated site-bond percolation model. It was shown that probability of a system to percolate only in the horizontal direction pi(hs) has the universal form pi(hs)=A(q)Q(z) for q=1,2,3,4 as a function of the scaling variable z=[b(q)L(1/nu(q))[p-p(c)(q,L)]](zeta(q)). Here, p=1-exp(-beta) is the probability of a bond to be closed, A(q) is the nonuniversal crossing amplitude, b(q) is the nonuniversal metric factor, nu(q) is the correlation length index, and zeta(q) is the additional scaling index. The universal function Q(x) approximately equal exp(-/z/). The nonuniversal scaling factors were found numerically.

Journal Article↗

PubMed2004

Survival probabilities in time-dependent random walks.

We analyze the dynamics of random walks in which the jumping probabilities are periodic time-dependent functions. In particular, we determine the survival probability of biased walkers who are drifted towards an absorbing boundary. The typical lifetime of the walkers is found to decrease with an increment in the oscillation amplitude of the jumping probabilities. We discuss the applicability of the results in the context of complex adaptive systems.

Journal Article↗

PubMed2004

Survival probability of a diffusing test particle in a system of coagulating and annihilating random walkers.

We calculate the survival probability of a diffusing test particle in an environment of diffusing particles that undergo coagulation at rate lambda(c) and annihilation at rate lambda(a) . The test particle is annihilated at rate lambda(') on coming into contact with the other particles. The survival probability decays algebraically with time as t(-theta;) . The exponent theta; in d<2 is calculated using the perturbative renormalization group formalism as an expansion in epsilon=2-d . It is shown to be universal, independent of lambda(') , and to depend only on delta , the ratio of the diffusion constant of test particles to that of the other particles, and on the ratio lambda(a) / lambda(c) . In two dimensions we calculate the logarithmic corrections to the power law decay of the survival probability. Surprisingly, the logarithmic corrections are nonuniversal. The one-loop answer for theta; in one dimension obtained by setting epsilon=1 is compared with existing exact solutions for special values of delta and lambda(a) / lambda(c) . The analytical results for the logarithmic corrections are verified by Monte Carlo simulations.

Journal Article↗

PubMed2006

Spatial survival probability for one-dimensional fluctuating interfaces in the steady state.

We report numerical and analytic results for the spatial survival probability for fluctuating one-dimensional interfaces with Edwards-Wilkinson or Kardar-Parisi-Zhang dynamics in the steady state. Our numerical results are obtained from analysis of steady-state profiles generated by integrating a spatially discretized form of the Edwards-Wilkinson equation to long times. We show that the survival probability exhibits scaling behavior in its dependence on the system size and the "sampling interval" used in the measurement for both "steady-state" and "finite" initial conditions. Analytic results for the scaling functions are obtained from a path-integral treatment of a formulation of the problem in terms of one-dimensional Brownian motion. A "deterministic approximation" is used to obtain closed-form expressions for survival probabilities from the formally exact analytic treatment. The resulting approximate analytic results provide a fairly good description of the numerical data.

Journal Article↗

PubMed2000

Sticking probabilities in adsorption from liquid solutions: alkylthiols on gold

The sticking probability, defined as the rate of adsorption per molecular collision with the surface, directly expresses the difficulty encountered by a molecule in scaling the barrier to adsorption. Its prior use has been restricted to adsorption of gases. A method extending this concept to adsorption from liquid solutions is applied to transient measurements of alkylthiol adsorption onto gold from ethanol solutions. The initial sticking probability increases from approximately 10(-8) to approximately 10(-6) with alkyl chain length, implying a stabilization of the transition state by approximately 0.65 kJ/mol per CH2. Since their sticking probabilities in the gas phase are approximately 1.0, the solvent increases the activation free energy by approximately 40 kJ/mol.

Journal Article↗

PubMed2005

Distribution functions, loop formation probabilities, and force-extension relations in a model for short double-stranded DNA molecules.

We obtain, using transfer-matrix methods, the distribution function P(R) of the end-to-end distance, the loop formation probability, and force-extension relations in a model for short double-stranded DNA molecules. Accounting for the appearance of "bubbles," localized regions of enhanced flexibility associated with the opening of a few base pairs of double-stranded DNA in thermal equilibrium, leads to dramatic changes in P(R) and unusual force-extension curves. An analytic formula for the loop formation probability in the presence of bubbles is proposed. For short heterogeneous chains, we demonstrate a strong dependence of loop formation probabilities on sequence.

DNA↗

PubMed2006

Holographic probabilities in eternal inflation.

In the global description of eternal inflation, probabilities for vacua are notoriously ambiguous. The local point of view is preferred by holography and naturally picks out a simple probability measure. It is insensitive to large expansion factors or lifetimes and so resolves a recently noted paradox. Any cosmological measure must be complemented with the probability for observers to emerge in a given vacuum. In lieu of anthropic criteria, I propose to estimate this by the entropy that can be produced in a local patch. This allows for prior-free predictions.

Journal Article↗

PubMed2006

Estimating the probability of the presence of a signal of interest in multiresolution single- and multiband image denoising.

We develop three novel wavelet domain denoising methods for subband-adaptive, spatially-adaptive and multivalued image denoising. The core of our approach is the estimation of the probability that a given coefficient contains a significant noise-free component, which we call "signal of interest." In this respect, we analyze cases where the probability of signal presence is 1) fixed per subband, 2) conditioned on a local spatial context, and 3) conditioned on information from multiple image bands. All the probabilities are estimated assuming a generalized Laplacian prior for noise-free subband data and additive white Gaussian noise. The results demonstrate that the new subband-adaptive shrinkage function outperforms Bayesian thresholding approaches in terms of mean-squared error. The spatially adaptive version of the proposed method yields better results than the existing spatially adaptive ones of similar and higher complexity. The performance on color and on multispectral images is superior with respect to recent multiband wavelet thresholding.

Algorithms↗

PubMed2005

A model selection algorithm for a posteriori probability estimation with neural networks.

This paper proposes a novel algorithm to jointly determine the structure and the parameters of a posteriori probability model based on neural networks (NNs). It makes use of well-known ideas of pruning, splitting, and merging neural components and takes advantage of the probabilistic interpretation of these components. The algorithm, so called a posteriori probability model selection (PPMS), is applied to an NN architecture called the generalized softmax perceptron (GSP) whose outputs can be understood as probabilities although results shown can be extended to more general network architectures. Learning rules are derived from the application of the expectation-maximization algorithm to the GSP-PPMS structure. Simulation results show the advantages of the proposed algorithm with respect to other schemes.

Algorithms↗

PubMed2003

Analyzing EEG signals using the probability estimating guarded neural classifier.

This paper introduces a neural network architecture for classifying feature vectors symbolizing portions (or segments) of an electroencephalogram (EEG) trace of a human subject. This classification task is the one that is typically required when developing a so-called brain-computer interface (BCI), which analyzes the EEG signals of a subject in order to "understand" the subject's thoughts. However, instead of merely saying which "category of thoughts" (i.e., which class) the respective input feature vector belongs to, the network described here estimates the probabilities of an EEG segment being associated with each individual class. The network, which is called PeGNC (for probability estimating guarded neural classifier), is tested with two kinds of experiments. In the first experiment, the alpha-rhythm associated with a human subject closing the eyes is detected online with the help of a frequency-based representation. Since the EEG signal is, in general, always a mixture of numerous action potentials generated simultaneously and it is, thus, very likely that mental activities result in overlapping classes, it is reasonable to believe that the PeGNC network--which does not select any one single class, but determines probability values for each mental category--is particularly suitable for this kind of EEG analysis. The second experiment deals with this issue on the basis of an offline analysis of simulated data.

Adult↗

PubMed2005

Crystal structure of the probable haloacid dehalogenase PH0459 from Pyrococcus horikoshii OT3.

PH0459, from the hyperthermophilic archaeon Pyrococcus horikoshii OT3, is a probable haloacid dehalogenase with a molecular mass of 26,725 Da. Here, we report the 2.0 A crystal structure of PH0459 (PDB ID: 1X42) determined by the multiwavelength anomalous dispersion method. The core domain has an alpha/beta structure formed by a six-stranded parallel beta-sheet flanked by six alpha-helices and three 3(10)-helices. One disulfide bond, Cys186-Cys212, forms a bridge between an alpha-helix and a 3(10)-helix, although PH0459 seems to be an intracellular protein. The subdomain inserted into the core domain has a four-helix bundle structure. The crystal packing suggests that PH0459 exists as a monomer. A structural homology search revealed that PH0459 resembles the l-2-haloacid dehalogenases l-DEX YL from Pseudomonas sp. YL and DhlB from Xanthobacter autotrophicus GJ10. A comparison of the active sites suggested that PH0459 probably has haloacid dehalogenase activity, but its substrate specificity may be different. In addition, the disulfide bond in PH0459 probably facilitates the structural stabilization of the neighboring region in the monomeric form, although the corresponding regions in l-DEX YL and DhlB may be stabilized by dimerization. Since heat-stable dehalogenases can be used for the detoxification of halogenated aliphatic compounds, PH0459 will be a useful target for biotechnological research.

Amino Acid Sequence↗

PubMed2002

What number is "fifty-fifty"?: redistributing excessive 50% responses in elicited probabilities.

Studies using open-ended response modes to elicit probabilistic beliefs have sometimes found an elevated frequency (or blip) at 50 in their response distributions. Our previous research suggests that this is caused by intrusion of the phrase "fifty-fifty," which represents epistemic uncertainty, rather than a true numeric probability of 50%. Such inappropriate responses pose a problem for decision analysts and others relying on probabilistic judgments. Using an explicit numeric probability scale (ranging from 0-100%) reduces thinking about uncertain events in verbal terms like "fifty-fifty," and, with it, exaggerated use of the 50 response. Here, we present two procedures for adjusting response distributions for data already collected with open-ended response modes and hence vulnerable to an exaggerated presence of 50%. Each procedure infers the prevalence of 50s had a numeric probability scale been used, then redistributes the excess. The two procedures are validated on some of our own existing data and then applied to judgments elicited from experts in groundwater pollution and bioremediation.

Journal Article↗

PubMed2002

A statistical model for investigating binding probabilities of DNA nucleotide sequences using microarrays.

There is considerable scientific interest in knowing the probability that a site-specific transcription factor will bind to a given DNA sequence. Microarray methods provide an effective means for assessing the binding affinities of a large number of DNA sequences as demonstrated by Bulyk et al. (2001, Proceedings of the National Academy of Sciences, USA 98, 7158-7163) in their study of the DNA-binding specificities of Zif268 zinc fingers using microarray technology. In a follow-up investigation, Bulyk, Johnson, and Church (2002, Nucleic Acid Research 30, 1255-1261) studied the interdependence of nucleotides on the binding affinities of transcription proteins. Our article is motivated by this pair of studies. We present a general statistical methodology for analyzing microarray intensity measurements reflecting DNA-protein interactions. The log probability of a protein binding to a DNA sequence on an array is modeled using a linear ANOVA model. This model is convenient because it employs familiar statistical concepts and procedures and also because it is effective for investigating the probability structure of the binding mechanism.

Analysis of Variance↗

PubMed2003

The shapes of neutral gene genealogies in two species: probabilities of monophyly, paraphyly, and polyphyly in a coalescent model.

The genealogies of samples of orthologous regions from multiple species can be classified by their shapes. Using a neutral coalescent model of two species, I give exact probabilities of each of four possible genealogical shapes: reciprocal monophyly, two types of paraphyly, and polyphyly. After the divergence that forms two species, each of which has population size N, polyphyly is the most likely genealogical shape for the lineages of the two species. At approximately 1.300N generations after divergence, paraphyly becomes most likely, and reciprocal monophyly becomes most likely at approximately 1.665N generations. For a given species, the time at which 99% of its loci acquire monophyletic genealogies is approximately 5.298N generations, assuming all loci in its sister species are monophyletic. The probability that all lineages of two species are reciprocally monophyletic given that a sample from the two species has a reciprocally monophyletic genealogy increases rapidly with sample size, as does the probability that the most recent common ancestor (MRCA) for a sample is also the MRCA for all lineages from the two species. The results have potential applications for the testing of evolutionary hypotheses.

Computer Simulation↗

PubMed1995

Probability of random sire exclusion using microsatellite markers for parentage verification.

Many microsatellite sequences have been described in the bovine genome. Being highly polymorphic these have been suggested as markers for parentage verification and individual identification in cattle. We have evaluated the use of five highly polymorphic microsatellite markers for parentage verification in 14 breeds of cattle in the UK. Three of the microsatellite loci occur within introns in genes: BoLA DRB3, steroid 21-hydroxylase, and the beta subunit of the follicle-stimulating hormone. The other two are anonymous sites ETH131 and HEL6. Results were analysed by a statistical approach that takes in to account deviations from Hardy-Wienberg equilibrium and linkage disequilibrium for multiple loci. The method of determining the probability of random sire exclusion uses observed genotype frequencies instead of allele frequencies. Independently, the markers used have a probability of between 0.72 and 0.62 of identifying a parentage error, while used together the five markers give, on average across breeds, a probability of 0.99 of excluding an incorrect sire.

Animals↗