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PubMed1995

Statistical basis for the determination of optical pathlength in tissue.

In this paper we show how to derive the mean and variance of the transilluminated signal obtained in models of light propagation in tissue, based both on a stochastic Monte Carlo method and on a deterministic diffusion approximation. The theoretical treatment of the Monte Carlo model applies only to integrated intensity measurements, whereas the diffusion approximation gives an estimator for the time-dependent case as well. We present results that show the accurate prediction of Monte Carlo statistics, and propose that the diffusion approximation is therefore a suitable mechanism for incorporating noise into modelling procedures.

Animals↗
PubMed2004

Analysis of sleep-stage characteristics in full-term newborns by means of spectral and fractal parameters.

STUDY OBJECTIVES: In this work, we studied the behavior of the fractal dimension during each of the neonatal electroencephalogram (EEG) sleep phases and during the awake state, comparing the results with those of the classical spectral parameters and with zero crossing values. DESIGN: Fractal dimension, zero crossing, and spectral parameters of the EEG bands were determined for each 2-second frame of the EEG sleep-time series. Eight channels of each EEG recording were examined. PARTICIPANTS: Twenty healthy full-term newborns (10 boys and 10 girls) with normal psychomotor development evaluated at 24 and 36 months of age, were chosen to participate in this study. MEASUREMENTS AND RESULTS: Fractal analysis showed that where rhythmic and regular activity are present, as during quiet sleep, the fractal dimension is low and rises when bioelectric activity is more variable and complex, reaching its maximum value during wakefulness. The discriminative value of this parameter was similar to that of some spectral bands. CONCLUSIONS: This work was an initial attempt to apply techniques derived from the nonlinear deterministic studies used to evaluate system complexity, to the neonatal EEG, in order to acquire a normative database that can be used as a reference in neurological pathologies. Fractal dimension alone or together with zero crossing and theta and delta bands could be used for computerized discrimination of neonatal EEG sleep phases.

Cerebral Cortex↗
PubMed2001

Human observer detection experiments with mammograms and power-law noise.

We determined contrast thresholds for lesion detection as a function of lesion size in both mammograms and filtered noise backgrounds with the same average power spectrum, P(f)=B/f3. Experiments were done using hybrid images with digital images of tumors added to digitized normal backgrounds, displayed on a monochrome monitor. Four tumors were extracted from digitized specimen radiographs. The lesion sizes were varied by digital rescaling to cover the range from 0.5 to 16 mm. Amplitudes were varied to determine the value required for 92% correct detection in two-alternative forced-choice (2AFC) and 90% for search experiments. Three observers participated, two physicists and a radiologist. The 2AFC mammographic results demonstrated a novel contrast-detail (CD) diagram with threshold amplitudes that increased steadily (with slope of 0.3) with increasing size for lesions larger than 1 mm. The slopes for prewhitening model observers were about 0.4. Human efficiency relative to these models was as high as 90%. The CD diagram slopes for the 2AFC experiments with filtered noise were 0.44 for humans and 0.5 for models. Human efficiency relative to the ideal observer was about 40%. The difference in efficiencies for the two types of backgrounds indicates that breast structure cannot be considered to be pure random noise for 2AFC experiments. Instead, 2AFC human detection with mammographic backgrounds is limited by a combination of noise and deterministic masking effects. The search experiments also gave thresholds that increased with lesion size. However, there was no difference in human results for mammographic and filtered noise backgrounds, suggesting that breast structure can be considered to be pure random noise for this task. Our conclusion is that, in spite of the fact that mammographic backgrounds have nonstationary statistics, models based on statistical decision theory can still be applied successfully to estimate human performance.

Female↗
PubMed2007

Stochastic simulation of chemical kinetics.

Stochastic chemical kinetics describes the time evolution of a well-stirred chemically reacting system in a way that takes into account the fact that molecules come in whole numbers and exhibit some degree of randomness in their dynamical behavior. Researchers are increasingly using this approach to chemical kinetics in the analysis of cellular systems in biology, where the small molecular populations of only a few reactant species can lead to deviations from the predictions of the deterministic differential equations of classical chemical kinetics. After reviewing the supporting theory of stochastic chemical kinetics, I discuss some recent advances in methods for using that theory to make numerical simulations. These include improvements to the exact stochastic simulation algorithm (SSA) and the approximate explicit tau-leaping procedure, as well as the development of two approximate strategies for simulating systems that are dynamically stiff: implicit tau-leaping and the slow-scale SSA.

Algorithms↗
PubMed2005

Analysis of canine model of gastric electrical uncoupling using recurrence quantification analysis.

This study reports the results of recurrence quantification analysis (RQA) applied to internal gastric electrical activity (GEA) and cutaneous electrogastrographic (EGG) digital recordings obtained from acute canine models. The purpose of this chaos analysis is to differentiate three states--normal, mild, and severe induced electrical uncoupling--utilizing five quantities associated with RQA: percent recurrence, percent determinism, maximum deterministic line, entropy, and trend. The results indicate that percent recurrence and trend are the only quantities that relate the three states of gastric electrical uncoupling in any meaningful way. The ability of EGG to detect mild electrical uncoupling in the stomach appears to be limited due to the impact of numerous external factors on the signals, even if multichannel recordings are utilized.

Animals↗
PubMed1986

Identifiability, exchangeability, and epidemiological confounding.

Non-identifiability of parameters is a well-recognized problem in classical statistics, and Bayesian statisticians have long recognized the importance of exchangeability assumptions in making statistical inferences. A seemingly unrelated problem in epidemiology is that of confounding: bias in estimation of the effects of an exposure on disease risk, due to inherent differences in risk between exposed and unexposed individuals. Using a simple deterministic model for exposure effects, a logical connection is drawn between the concepts of identifiability, exchangeability, and confounding. This connection allows one to view the problem of confounding as arising from problems of identifiability, and reveals the exchangeability assumptions that are implicit in confounder control methods. It also provides further justification for confounder definitions based on comparability of exposure groups, as opposed to collapsibility-based definitions.

Bayes Theorem↗
PubMed2001

Transition between stochastic evolution and deterministic evolution in the presence of selection: general theory and application to virology.

We present here a self-contained analytic review of the role of stochastic factors acting on a virus population. We develop a simple one-locus, two-allele model of a haploid population of constant size including the factors of random drift, purifying selection, and random mutation. We consider different virological experiments: accumulation and reversion of deleterious mutations, competition between mutant and wild-type viruses, gene fixation, mutation frequencies at the steady state, divergence of two populations split from one population, and genetic turnover within a single population. In the first part of the review, we present all principal results in qualitative terms and illustrate them with examples obtained by computer simulation. In the second part, we derive the results formally from a diffusion equation of the Wright-Fisher type and boundary conditions, all derived from the first principles for the virus population model. We show that the leading factors and observable behavior of evolution differ significantly in three broad intervals of population size, N. The "neutral limit" is reached when N is smaller than the inverse selection coefficient. When N is larger than the inverse mutation rate per base, selection dominates and evolution is "almost" deterministic. If the selection coefficient is much larger than the mutation rate, there exists a broad interval of population sizes, in which weakly diverse populations are almost neutral while highly diverse populations are controlled by selection pressure. We discuss in detail the application of our results to human immunodeficiency virus population in vivo, sampling effects, and limitations of the model.

Biological Evolution↗
PubMed2004

Protein structure alignment by deterministic annealing.

MOTIVATION: Protein structure alignment is one of the most important computational problems in molecular biology and plays a key role in protein structure prediction, fold family classification, motif finding, phylogenetic tree reconstruction and so on. From the viewpoint of computational complexity, a pairwise structure alignment is also a NP-hard problem, in contrast to the polynomial time algorithm for a pairwise sequence alignment. RESULTS: We propose a method for solving the structure alignment problem in an accurate manner at the amino acid level, based on a mean field annealing technique. We define the structure alignment as a mixed integer-programming (MIP) problem. By avoiding complicated combinatorial computation and exploiting the special structure of the continuous partial problem, we transform the MIP into a reduced non-linear continuous optimization problem (NCOP) with a much simpler form. To optimize the reduced NCOP, a mean field annealing procedure is adopted with a modified Potts model, whose solution is generally identical to that of the MIP. There is no 'soft constraint' in our mean field model and all constraints are automatically satisfied throughout the annealing process, thereby not only making the optimization more efficient but also eliminating many unnecessary parameters that depend on problems and usually require careful tuning. A number of benchmark examples are tested by the proposed method with comparisons to several existing approaches.

Algorithms↗
PubMed1992

Differentiation of linearly correlated noise from chaos in a biologic system using surrogate data.

Experimental time-series of human H-reflexes were analyzed for the presence of fractal structure or deterministic chaos. Surrogate data sets consisting of stochastic time-series with preservation of selected properties of the experimental time-series were used as mathematical controls. Artifacts generated during the analysis of the experimental data are identified, and shown to be due to linear correlation in the original time-series. The method is simple and generally applicable to the non-linear analysis of time-series from any experimental system.

Algorithms↗
PubMed2003

Individual-based vs deterministic models for macroparasites: host cycles and extinction.

Our understanding of the qualitative dynamics of host-macroparasite systems is mainly based on deterministic models. We study here an individual-based stochastic model that incorporates the same assumptions as the classical deterministic model. Stochastic simulations, using parameter values based on some case studies, preserve many features of the deterministic model, like the average value of the variables and the approximate length of the cycles. An important difference is that, even when deterministic models yield damped oscillations, stochastic simulations yield apparently sustained oscillations. The amplitude of such oscillations may be so large to threaten parasites' persistence.With density-dependence in parasite demographic traits, persistence increases somewhat. Allowing instead for infections from an external parasite reservoir, we found that host extinction may easily occur. However, the extinction probability is almost independent of the level of external infection over a wide intermediate parameter region.

Animals↗
PubMed2004

Dense motion estimation using regularization constraints on local parametric models.

This paper presents a method for dense optical flow estimation in which the motion field within patches that result from an initial intensity segmentation is parametrized with models of different order. We propose a novel formulation which introduces regularization constraints between the model parameters of neighboring patches. In this way, we provide the additional constraints for very small patches and for patches whose intensity variation cannot sufficiently constrain the estimation of their motion parameters. In order to preserve motion discontinuities, we use robust functions as a regularization mean. We adopt a three-frame approach and control the balance between the backward and forward constraints by a real-valued direction field on which regularization constraints are applied. An iterative deterministic relaxation method is employed in order to solve the corresponding optimization problem. Experimental results show that the proposed method deals successfully with motions large in magnitude, motion discontinuities, and produces accurate piecewise-smooth motion fields.

Algorithms↗
PubMed2005

Dynamic optimization of bioprocesses: efficient and robust numerical strategies.

The dynamic optimization (open loop optimal control) of non-linear bioprocesses is considered in this contribution. These processes can be described by sets of non-linear differential and algebraic equations (DAEs), usually subject to constraints in the state and control variables. A review of the available solution techniques for this class of problems is presented, highlighting the numerical difficulties arising from the non-linear, constrained and often discontinuous nature of these systems. In order to surmount these difficulties, we present several alternative stochastic and hybrid techniques based on the control vector parameterization (CVP) approach. The CVP approach is a direct method which transforms the original problem into a non-linear programming (NLP) problem, which must be solved by a suitable (efficient and robust) solver. In particular, a hybrid technique uses a first global optimization phase followed by a fast second phase based on a local deterministic method, so it can handle the nonconvexity of many of these NLPs. The efficiency and robustness of these techniques is illustrated by solving several challenging case studies regarding the optimal control of fed-batch bioreactors and other bioprocesses. In order to fairly evaluate their advantages, a careful and critical comparison with several other direct approaches is provided. The results indicate that the two-phase hybrid approach presents the best compromise between robustness and efficiency.

Algorithms↗
PubMedDate not supplied

Robust spectrotemporal reverse correlation for the auditory system: optimizing stimulus design.

The spectrotemporal receptive field (STRF) is a functional descriptor of the linear processing of time-varying acoustic spectra by the auditory system. By cross-correlating sustained neuronal activity with the dynamic spectrum of a spectrotemporally rich stimulus ensemble, one obtains an estimate of the STRF. In this article, the relationship between the spectrotemporal structure of any given stimulus and the quality of the STRF estimate is explored and exploited. Invoking the Fourier theorem, arbitrary dynamic spectra are described as sums of basic sinusoidal components--that is, moving ripples. Accurate estimation is found to be especially reliant on the prominence of components whose spectral and temporal characteristics are of relevance to the auditory locus under study and is sensitive to the phase relationships between components with identical temporal signatures. These and other observations have guided the development and use of stimuli with deterministic dynamic spectra composed of the superposition of many temporally orthogonal moving ripples having a restricted, relevant range of spectral scales and temporal rates. The method, termed sum-of-ripples, is similar in spirit to the white-noise approach but enjoys the same practical advantages--which equate to faster and more accurate estimation--attributable to the time-domain sum-of-sinusoids method previously employed in vision research. Application of the method is exemplified with both modeled data and experimental data from ferret primary auditory cortex (AI).

Acoustic Stimulation↗
PubMed2001

Balanced branching in transcription termination.

The theory of stochastic transcription termination based on free-energy competition [von Hippel, P. H. & Yager, T. D. (1992) Science 255, 809-812 and von Hippel, P. H. & Yager, T. D. (1991) Proc. Natl. Acad. Sci. USA 88, 2307-2311] requires two or more reaction rates to be delicately balanced over a wide range of physical conditions. A large body of work on glasses and large molecules suggests that this balancing should be impossible in such a large system in the absence of a new organizing principle of matter. We review the experimental literature of termination and find no evidence for such a principle, but do find many troubling inconsistencies, most notably, anomalous memory effects. These effects suggest that termination has a deterministic component and may conceivably not be stochastic at all. We find that a key experiment by Wilson and von Hippel [Wilson, K. S. & von Hippel, P. H. (1994) J. Mol. Biol. 244, 36-51] thought to demonstrate stochastic termination was an incorrectly analyzed regulatory effect of Mg(2+) binding.

Bacteriophages↗
PubMed1984

Evolutionary principles for polynomial models of frequency-dependent selection.

A one-locus two-allele deterministic model of frequency-dependent selection is analyzed, where genotypic fitnesses [w(i)(q)] are assumed to be nth-degree polynomial functions of allelic frequency (q). The model encompasses many modes of selection, including intraspecies competitive interaction, brood selection, meiotic drive, cyclical selection, and mixed models. Allelic frequencies converge monotonically to locally stable equilibria provided that dw(i)(q)/dq is not large. There exists a function T(q) that is nondecreasing and locally maximized at locally stable equilibria. The rate of change of T(q) per generation is approximately equal to the additive genetic variance in fitness. T(q) is a simple function of the average effect of an allelic substitution and is closely related to Wright's "fitness function." These results define "evolutionary landscapes" for some complex selection processes and enlarge the scope of the classical methods embodied in Wright's "mean fitness principle" and Fisher's "fundamental theorem."

Journal Article↗
PubMed2002

Comparison of the pollutant loads in dry and wet weather runoff in a southern California urban watershed.

This research compares the relative contributions of potential contaminants discharged in dry weather flow (DWF) and wet weather flow (WWF) from the highly urbanized Ballona Creek watershed (BCW) in southern California using empirical and deterministic models. These models were used to compare the loading of the following pollutants: total suspended solids, biochemical oxygen demand, total nitrogen, total inorganic nitrogen, total Kjeldahl nitrogen, total phosphorus, copper, lead, arsenic, nickel, cadmium, and chromium. The results indicate DWF contributes approximately 10-30% of the total annual flow discharged from Ballona Creek. The annual DWF volume was fairly consistent; the variation in DWF percentage contribution was dependent on the highly variable volume of WWF. The relative contribution to the annual pollutant load varied considerably between each pollutant. In general, the DWF load was found to be significant, especially in years with lower precipitation totals. The results from this investigation have identified the relative relationship between DWF and WWF loads in the BCW and will aid in the decision-making process during the development of an integrated DWF-WWF management plan and allocation of water pollution control funds between DWF and WWF management.

California↗
PubMed2002

Exemplar and prototype models revisited: response strategies, selective attention, and stimulus generalization.

J. D. Smith and colleagues (J. P. Minda & J. D. Smith, 2001; J. D. Smith & J. P. Minda, 1998,2000; J. D. Smith, M. J. Murray, & J. P. Minda, 1997) presented evidence that they claimed challenged the predictions of exemplar models and that supported prototype models. In the authors' view, this evidence confounded the issue of the nature of the category representation with the type of response rule (probabilistic vs. deterministic) that was used. Also, their designs did not test whether the prototype models correctly predicted generalization performance. The present work demonstrates that an exemplar model that includes a response-scaling mechanism provides a natural account of all of Smith et al.'s experimental results. Furthermore, the exemplar model predicts classification performance better than the prototype models when novel transfer stimuli are included in the experimental designs.

Attention↗
PubMed1992

The spread of a parasitic infection in a spatially distributed host population.

Starting from a stochastic model for the spread of a parasitic infection in a spatially distributed host population we describe the way to a continuum formulation by a deterministic model in terms of a nonlinear partial differential equation and an integro-differential equation. The hosts are assumed to occupy fixed spatial positions, whereas the parasites are mobile, however can propagate only within the hosts. To perform the continuum limit we suppose that the size Nh of the host population, the size Np of the parasite population, and the ratio Np/Nh tend to infinity. Accordingly, the parameters determining the time evolution of the host and parasite populations are rescaled suitably.

Cells, Cultured↗