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PubMed2006

Management of microbiological safety of ready-to-eat meat products by mathematical modelling: Listeria monocytogenes as an example.

The recent Commission Regulation (EC) No 2073/2005 establishes microbiological criteria in foods. For the pathogen Listeria monocytogenes in the category ready-to-eat foods able to support its growth, other than those intended for infants and for special medical purposes, two different microbiological criteria are proposed: (i) L. monocytogenes levels should be <100 cfu/g throughout the shelf-life of the product, (ii) absence in 25 g of the product at the stage before the food has left the immediate control of the food business operator, who has produced it. The application of either the first or the second of these criteria depends on whether or not the manufacturer is able to demonstrate that the level of L. monocytogenes in the food product will not exceed 100 cfu/g throughout its shelf-life. This demonstration should be based on physico-chemical characteristics of the target product and consultation of scientific literature, and, when necessary, on quantitative models and/or challenge tests. Once the characteristics of the product as well as scientific literature show that the pathogen has potential to grow on a specific food commodity, it seems adequate to use quantitative models and/or perform challenge tests to study the extent to which L. monocytogenes could grow. In this study, we aim to illustrate with an example in cooked ham the application of quantitative models as a tool to manage the compliance with these criteria. Two approaches were considered: deterministic and probabilistic, in three different commercial brands (A, B, and C). The deterministic approach showed that the limit 100 cfu/g was exceeded largely at the end of the shelf-life of all three; however, when reducing the storage time, the level of L. monocytogenes remained below 100 cfu/g in B. The probabilistic approach demonstrated very low percentiles corresponding to 100 cfu/g; when reducing the storage time, percentiles for three products increased, especially in products B and C (from 4.92% to 75.90%, and from 0.90% to 73.90%, respectively). This study shows how different storage times influence the level of L. monocytogenes at the end of the shelf-life of cooked ham, and, depending on the level reached, the microbiological criterion applied should be different, as stated above. Beside this, the choice of either point-estimate or probabilistic approach should be determined by the competent sanitary authority, and, in case of selecting the second approach, a certain percentile for the level 100 cfu/g should be established.

Animals↗
PubMed2001

Probabilistic risk assessment of cotton pyrethroids: I. Distributional analyses of laboratory aquatic toxicity data.

This is the first in a series of five papers that assess the risk of the cotton pyrethroids in aquatic ecosystems in a series of steps ranging from the analysis of effects data through modeling exposures in the landscape. Pyrethroid insecticides used on cotton have the potential to contaminate aquatic systems. The objectives of this study were to develop probabilistic estimates of toxicity distributions, to compare these among the pyrethroids, and to evaluate cypermethrin as a representative pyrethroid for the purposes of a class risk assessment of the pyrethroids. The distribution of cypermethrin acute toxicity data gave 10th centile values of 10 ng/L for all organisms, 6.4 ng/L for arthropods, and 380 ng/L for vertebrates. For bifenthrin, cyfluthrin, lambda-cyhalothrin, and deltamethrin, the 10th centile values for all organisms were 15, 12, 10, and 9 ng/L, respectively, indicating similar or somewhat lower toxicity than cypermethrin. For tralomethrin and fenpropathrin, the 10th centiles were <310 and 240 ng/L, respectively. The distribution of permethrin toxicity to all organisms, arthropods, and vertebrates gave 10th centiles of 180, 76, and 1600 ng/L, respectively, whereas those for fenvalerate were 37, 8, and 150 ng/L. With the exception of tralomethrin, the distributions of acute toxicity values had similar slopes, suggesting that the variation of sensitivity in a range of aquatic nontarget species is similar. The pyrethroids have different recommended field rates of application that are related to their efficacy, and the relationship between field rate and 10th centiles showed a trend. These results support the use of cypermethrin as a reasonable worst-case surrogate for the other pyrethroids for the purposes of risk assessment of pyrethroids as a class.

Animals↗
PubMed1996

Detecting a nonevent: Delayed presence-versus-absence discrimination in pigeons.

Eight pigeons were trained on a delayed presence-versus-absence discrimination paradigm in which a sample stimulus was presented on some trials but not on others. If a sample was presented, then a response to one choice key produced food. If no sample was presented, a response to the other choice key produced food. The basic finding was that performance remained constant and well above 50% correct on no-sample trials as the retention interval increased, whereas performance dropped precipitously (to below 50% correct) on sample trials. In the second phase of the experiment, all of the trials were no-sample trials, and reinforcers were delivered probabilistically for one group of pigeons and according to time-based schedules for the other group. The exact reinforcement probabilities used in Phase 2 were those calculated to be in effect on no-sample trials in Phase 1 (according to a discrete-state model of performance). Subjects did not show exclusive preference for the richer alternative on no-sample trials in the first phase, but those in the probabilistic group developed near-exclusive preference for the richer alternative during the second phase. These data are inconsistent with the predictions of the discrete-state model, but are easily accommodated by an account based on signal detection theory, which also can be applied effectively to discrimination of event duration and the "subjective shortening" effect.

Journal Article↗
PubMed2002

Continuously varying critical exponents in a sandpile model with internal disorder.

A sandpile model with an internal disorder is presented. The updating of critical sites is done according to a stochastic rule (with a probabilistic toppling q). Using a unified mean-field theory and numerical simulations, we have shown that the criticality is ensured for any value of q. The static critical exponents have been calculated and found to be the same as those obtained for the deterministic sandpile model, which is a particular case of the stochastic model. They have a universal q-independent behavior. In the limit of slow driving, we have developed a relation between our model and the branching process in order to compute the size exponent tau. It presents a continuous variation with the parameter of toppling q.

Journal Article↗
PubMed2002

Model-based cluster analysis of microarray gene-expression data.

BACKGROUND: Microarray technologies are emerging as a promising tool for genomic studies. The challenge now is how to analyze the resulting large amounts of data. Clustering techniques have been widely applied in analyzing microarray gene-expression data. However, normal mixture model-based cluster analysis has not been widely used for such data, although it has a solid probabilistic foundation. Here, we introduce and illustrate its use in detecting differentially expressed genes. In particular, we do not cluster gene-expression patterns but a summary statistic, the t-statistic. RESULTS: The method is applied to a data set containing expression levels of 1,176 genes of rats with and without pneumococcal middle-ear infection. Three clusters were found, two of which contain more than 95% genes with almost no altered gene-expression levels, whereas the third one has 30 genes with more or less differential gene-expression levels. CONCLUSIONS: Our results indicate that model-based clustering of t-statistics (and possibly other summary statistics) can be a useful statistical tool to exploit differential gene expression for microarray data.

Animals↗
PubMed2004

Probabilistic methods of identifying genes in prokaryotic genomes: connections to the HMM theory.

In this paper, we review developments in probabilistic methods of gene recognition in prokaryotic genomes with the emphasis on connections to the general theory of hidden Markov models (HMM). We show that the Bayesian method implemented in GeneMark, a frequently used gene-finding tool, can be augmented and reintroduced as a rigorous forward-backward (FB) algorithm for local posterior decoding described in the HMM theory. Another earlier developed method, prokaryotic GeneMark.hmm, uses a modification of the Viterbi algorithm for HMM with duration to identify the most likely global path through hidden functional states given the DNA sequence. GeneMark and GeneMark.hmm programs are worth using in concert for analysing prokaryotic DNA sequences that arguably do not follow any exact mathematical model. The new extension of GeneMark using the FB algorithm was implemented in the software program GeneMark.fba. Given the DNA sequence, this program determines an a posteriori probability for each nucleotide to belong to coding or non-coding region. Also, for any open reading frame (ORF), it assigns a score defined as a probabilistic measure of all paths through hidden states that traverse the ORF as a coding region. The prediction accuracy of GeneMark.fba determined in our tests was compared favourably to the accuracy of the initial (standard) GeneMark program. Comparison to the prokaryotic GeneMark.hmm has also demonstrated a certain, yet species-specific, degree of improvement in raw gene detection, ie detection of correct reading frame (and stop codon). The accuracy of exact gene prediction, which is concerned about precise prediction of gene start (which in a prokaryotic genome unambiguously defines the reading frame and stop codon, thus, the whole protein product), still remains more accurate in GeneMarkS, which uses more elaborate HMM to specifically address this task.

Algorithms↗
PubMed2006

Risk characterization and exposure assessment in arseniasis-endemic areas of Taiwan.

This paper examines the age-specific human health risks exposed to inorganic arsenic through arsenic-contaminated farmed fish/shrimp and groundwater consumptions in arseniasis-endemic areas of blackfoot disease (BFD)-endemic area and Lanyang Plain in Taiwan, based on an probabilistic integrated risk assessment framework. We employ an age-dependent predictive physiologically-based pharmacokinetic model to account for arsenic concentrations in target organs. We reconstruct age-specific dose-response profiles for arsenicosis and arsenic-induced cancers by best fitting a pharmacodynamics-based three-parameter Hill equation model to published epidemiological data from West Bengal and Taiwan. The predicted median arsenic concentrations in age group-specific skin, lung, and bladder ranged from 2.24-5.70, 3.76-9.46, and 5.11-20.71 micro g g(-1) in BFD-endemic area, whereas 4.98-12.04, 8.23-19.92, and 11.07-43.45 micro g g(-1) in Lanyang Plain, respectively. Risk analysis indicates that consumption of arsenic-contaminated farmed fish/shrimp and groundwater in arseniasis-endemic areas may increase threat to prevalence of arsenicosis for all age groups, whereas adults may undergo potential risks of arsenic-induced skin, lung and bladder cancers. We show that peoples in Lanyang Plain are more readily associated with higher morbidities for arsenicosis and skin cancer as well as fatalities for lung and bladder cancers than that of peoples in BFD-endemic area. Here we report the first case in which theoretical human health risks for consuming As-contaminated farmed fish/shrimp and groundwater in the arseniasis-endemic areas are alarming under a conservative condition based on a probabilistic risk assessment framework.

Adolescent↗
PubMed2003

A model for the emergence of adaptive subsystems.

We investigate the interaction of learning and evolution in a changing environment. A stable learning capability is regarded as an emergent adaptive system evolved by natural selection of genetic variants. We consider the evolution of an asexual population. Each genotype can have 'fixed' and 'flexible' alleles. The former express themselves as synaptic connections that remain unchanged during ontogeny and the latter as synapses that can be adjusted through a learning algorithm. Evolution is modelled using genetic algorithms and the changing environment is represented by two optimal synaptic patterns that alternate a fixed number of times during the 'life' of the individuals. The amplitude of the change is related to the Hamming distance between the two optimal patterns and the rate of change to the frequency with which both exchange roles. This model is an extension of that of Hinton and Nowlan in which the fitness is given by a probabilistic measure of the Hamming distance to the optimum. We find that two types of evolutionary pathways are possible depending upon how difficult (costly) it is to cope with the changes of the environment. In one case the population loses the learning ability, and the individuals inherit fixed synapses that are optimal in only one of the environmental states. In the other case a flexible subsystem emerges that allows the individuals to adapt to the changes of the environment. The model helps us to understand how an adaptive subsystem can emerge as the result of the tradeoff between the exploitation of a congenital structure and the exploration of the adaptive capabilities practised by learning.

Adaptation, Biological↗
PubMed2006

Quantification and visualization of the three-dimensional inconsistency of the subthalamic nucleus in the Schaltenbrand-Wahren brain atlas.

The Schaltenbrand-Wahren (SW) brain atlas has many limitations: the major two are three-dimensional (3D) inconsistency and spatial sparseness. In this work, we quantify and visualize the 3D inconsistency of the subthalamic nucleus (STN). The STN 3D models, 3D-A, 3D-C and 3D-S, are reconstructed from the SW axial, coronal, and sagittal microseries, respectively, by using a shape-based (NURBS) approach. All three models are placed in the SW coordinate system and compared quantitatively in terms of location (centroids), size (volumes), shape (normalized eigenvalues), orientation (eigenvectors), and mutual spatial relationships (overlaps and inclusions). Analysis is done in 3D within each orientation and across them. A dedicated tool is developed for quantitative validation of 3D modeling. The average error achieved is 0.088 mm, which is at the resolution limit of the digital SW atlas. The reconstructed 3D STN models differ in location, size, shape, orientation, overlap size, and inclusion rate. The 3D-S volume is 1.27 times larger than that of 3D-A and 1.38 times larger than that of 3D-C. The highest overlap size is found between 3D-A and 3D-S. The highest inclusion rates of 52.5 and 66.6% are for 3D-A and 3D-S. 3D-C has the lowest overlap size and results in the lowest inclusion rates (around 20-30%), meaning that 3D-C is substantially displaced in comparison to 3D-A and 3D-S. The lateral centroid coordinate of 3D-C is 9.18 mm while that of 3D-S is 12.17 mm. Each of the 3D models has some limitation: 3D-A in orientation, 3D-C in location, and 3D-S in shape realism. The STN in comparison to the actual almond is smaller, and relatively (i.e. normalized to the same height) 2.2-2.4 times wider and 3.7-5.5 times longer. 3D-C becomes more similar to 3D-S by scaling the SW coronal microseries laterally by 1.3257. Then the lateral coordinates of their centroids coincide, the difference between them in orientation is 0.11 mm, and 3D-S is only 1.06 times larger than the scaled 3D-C. This operation substantially improves registration of the SW atlas with the probabilistic functional atlas. However, 3D visualization shows that both 3D-S and scaled 3D-C models are heavily interwoven resulting in low inclusion rates of about 60%. The STN in the SW atlas shows severe 3D inaccuracy within each orientation and across them, and it has to be employed with great care and understanding of its limitations.

Anatomy, Artistic↗
PubMed2005

Probabilistic anatomical connectivity derived from the microscopic persistent angular structure of cerebral tissue.

Recently developed methods to extract the persistent angular structure (PAS) of axonal fibre bundles from diffusion-weighted magnetic resonance imaging (MRI) data are applied to drive probabilistic fibre tracking, designed to provide estimates of anatomical cerebral connectivity. The behaviour of the PAS function in the presence of realistic data noise is modelled for a range of single and multiple fibre configurations. This allows probability density functions (PDFs) to be generated that are parametrized according to the anisotropy of individual fibre populations. The PDFs are incorporated in a probabilistic fibre-tracking method to allow the estimation of whole-brain maps of anatomical connection probability. These methods are applied in two exemplar experiments in the corticospinal tract to show that it is possible to connect the entire primary motor cortex (M1) when tracing from the cerebral peduncles, and that the reverse experiment of tracking from M1 successfully identifies high probability connection via the pyramidal tracts. Using the extracted PAS in probabilistic fibre tracking allows higher specificity and sensitivity than previously reported fibre tracking using diffusion-weighted MRI in the corticospinal tract.

Anisotropy↗
PubMed2005

Using a probabilistic approach in an ecological risk assessment simulation tool: test case for depleted uranium (DU).

A probabilistic approach was applied in an ecological risk assessment (ERA) to characterize risk and address uncertainty employing Monte Carlo simulations for assessing parameter and risk probabilistic distributions. This simulation tool (ERA) includes a Window's based interface, an interactive and modifiable database management system (DBMS) that addresses a food web at trophic levels, and a comprehensive evaluation of exposure pathways. To illustrate this model, ecological risks from depleted uranium (DU) exposure at the US Army Yuma Proving Ground (YPG) and Aberdeen Proving Ground (APG) were assessed and characterized. Probabilistic distributions showed that at YPG, a reduction in plant root weight is considered likely to occur (98% likelihood) from exposure to DU; for most terrestrial animals, likelihood for adverse reproduction effects ranges from 0.1% to 44%. However, for the lesser long-nosed bat, the effects are expected to occur (>99% likelihood) through the reduction in size and weight of offspring. Based on available DU data for the firing range at APG, DU uptake will not likely affect survival of aquatic plants and animals (<0.1% likelihood). Based on field and laboratory studies conducted at APG and YPG on pocket mice, kangaroo rat, white-throated woodrat, deer, and milfoil, body burden concentrations observed fall into the distributions simulated at both sites.

Animals↗
PubMed2002

Asymptotic analysis of noise sensitivity in a neuronal burster.

A combination of asymptotic approaches provides a new analysis of the effect of small noise on the bursting cycle of a neuronal burster of elliptic type (type III). The analysis is applied to a stochastic model of an excitable spine, with an activity-dependent stem conductance, that exhibits conditional burst dynamics. First, we give an asymptotic approximation to the probability density for the state of the system. This density is used to compute several quantities which describe the influence of the noise on the transition from the silent to the active phase. Second, we also use a multiscale method to provide a reduced system for analysing the effect of noise on the transition out of the active phase. The combination of these two approaches results in a new framework for a quantitative description of how noise shortens the burst cycle, which measures the significant influence of small noise. For the stochastic spine model, this study suggests that small amplitude noise can significantly influence the activity-dependent morphological plasticity of dendritic spines. The techniques used in this paper combine probabilistic and asymptotic methods, and have been generalized for other noisy nonlinear systems.

Action Potentials↗
PubMed2000

How the United Nations mortality tables hang together.

The mortality statistics of 80 member states of the United Nations were used to calculate Gompertz constants. When compared with a model based on the cumulant of failures of 46 human biological functions, they were found to form essentially one set, their slopes spreading out from a constant value like spokes from the axle of a wheel. Data for the longest lived regions agree with a prediction based on the above model, and those for less long lived regions are consistent with such a model having a constant normal cumulant average but increased S.D.s. Several different approaches support the view that the data are based on a probabilistic life-span.

Adolescent↗
PubMed2005

VTE Risk assessment - a prognostic Model: BATER Cohort Study of young women.

BACKGROUND: Community-based cohort studies are not available that evaluated the predictive power of both clinical and genetic risk factors for venous thromboembolism (VTE). There is, however, clinical need to forecast the likelihood of future occurrence of VTE, at least qualitatively, to support decisions about intensity of diagnostic or preventive measures. MATERIALS AND METHODS: A 10-year observation period of the Bavarian Thromboembolic Risk (BATER) study, a cohort study of 4337 women (18-55 years), was used to develop a predictive model of VTE based on clinical and genetic variables at baseline (1993). The objective was to prepare a probabilistic scheme that discriminates women with virtually no VTE risk from those at higher levels of absolute VTE risk in the foreseeable future. A multivariate analysis determined which variables at baseline were the best predictors of a future VTE event, provided a ranking according to the predictive power, and permitted to design a simple graphic scheme to assess the individual VTE risk using five predictor variables. RESULTS: Thirty-four new confirmed VTEs occurred during the observation period of over 32,000 women-years (WYs). A model was developed mainly based on clinical information (personal history of previous VTE and family history of VTE, age, BMI) and one composite genetic risk markers (combining Factor V Leiden and Prothrombin G20210A Mutation). Four levels of increasing VTE risk were arbitrarily defined to map the prevalence in the study population: No/low risk of VTE (61.3%), moderate risk (21.1%), high risk (6.0%), very high risk of future VTE (0.9%). In 10.6% of the population the risk assessment was not possible due to lacking VTE cases. The average incidence rates for VTE in these four levels were: 4.1, 12.3, 47.2, and 170.5 per 104 WYs for no, moderate, high, and very high risk, respectively. CONCLUSION: Our prognostic tool - containing clinical information (and if available also genetic data) - seems to be worthwhile testing in medical practice in order to confirm or refute the positive findings of this study. Our cohort study will be continued to include more VTE cases and to increase predictive value of the model.

Journal Article↗
PubMed2006

Reasoning with conditionals: a test of formal models of four theories.

The four dominant theories of reasoning from conditionals are translated into formal models: The theory of mental models (Johnson-Laird, P. N., & Byrne, R. M. J. (2002). Conditionals: a theory of meaning, pragmatics, and inference. Psychological Review, 109, 646-678), the suppositional theory (Evans, J. S. B. T., & Over, D. E. (2004). If. Oxford: Oxford University Press), a dual-process variant of the model theory (Verschueren, N., Schaeken, W., & d'Ydewalle, G. (2005). A dual-process specification of causal conditional reasoning. Thinking &Reasoning, 11, 278-293), and the probabilistic theory (Oaksford, M., Chater, N., & Larkin, J. (2000). Probabilities and polarity biases in conditional inference. Journal of Experimental Psychology: Learning, Memory, and Cognition, 26, 883-899). The first three theories are formalized as multinomial models. The models are applied to the frequencies of patterns of acceptance or rejection across the four basic inferences modus ponens, acceptance of the consequent, denial of the antecedent, and modus tollens. Model fits are assessed for two large data sets, one representing reasoning with abstract, basic conditionals, the other reflecting reasoning with pseudo-realistic causal and non-causal conditionals. The best account of the data was provided by a modified version of the mental-model theory, augmented by directionality, and by the dual-process model.

Adolescent↗
PubMed1989

Analysis of surveillance data: a rationale for statistical tests with comments on confidence intervals and statistical models.

In the examination of differences between subgroups in surveillance data, whether through simple counting or through sophisticated statistical modelling, the comparison is not between simple random samples from two or more populations. The rationale for statistical tests rests on an appeal to a model of random permutation of demographic and disease factors for the observed population during the surveillance period. The testing evaluates chance as a possible explanation for the observed results. In the analysis of internal structure in a surveillance data set, statistical tests produce a conceptually simple result that lends itself to concise presentation and flexible interpretation. Tests limit emphasis on probabilistic manipulation and on parameter estimates. They cannot stand alone, and thus encourage descriptive presentation of observations. In contrast, statistical models and confidence intervals emphasize parameters rather than distributions and compete with the data for limited space.

Data Interpretation, Statistical↗