On Equilibrium Distribution of a Reversible Growth Model

We study a probabilistic model of interacting spins indexed by elements of a finite subset of the d-dimensional integer lattice, da parts per thousand yen1. Conditions of time reversibility are examined. It is shown that the model equilibrium distribution converges to a limit distribution as the indexing set expands to the whole lattice. The occupied site percolation problem is solved for the limit distribution. Two models with similar dynamics are also discussed.

A review on probabilistic graphical models in evolutionary computation

Thanks to their inherent properties, probabilistic graphical models are one of the prime candidates for machine learning and decision making tasks especially in uncertain domains. Their capabilities, like representation, inference and learning, if used effectively, can greatly help to build intelligent systems that are able to act accordingly in different problem domains. Evolutionary algorithms is one such discipline that has employed probabilistic graphical models to improve the search for optimal solutions in complex problems. This paper shows how probabilistic graphical models have been used in evolutionary algorithms to improve their performance in solving complex problems. Specifically, we give a survey of probabilistic model building-based evolutionary algorithms, called estimation of distribution algorithms, and compare different methods for probabilistic modeling in these algorithms.

Probabilistic reasoning with an enzyme-driven DNA device

We present a biomolecular probabilistic model driven by the action of a DNA toolbox made of a set of DNA templates and enzymes that is able to perform Bayesian inference. The model will take single-stranded DNA as input data, representing the presence or absence of a specific molecular signal (the evidence). The program logic uses different DNA templates and their relative concentration ratios to encode the prior probability of a disease and the conditional probability of a signal given the disease. When the input and program molecules interact, an enzyme-driven cascade of reactions (DNA polymerase extension, nicking and degradation) is triggered, producing a different pair of single-stranded DNA species. Once the system reaches equilibrium, the ratio between the output species will represent the application of Bayes? law: the conditional probability of the disease given the signal. In other words, a qualitative diagnosis plus a quantitative degree of belief in that diagno- sis. Thanks to the inherent amplification capability of this DNA toolbox, the resulting system will be able to to scale up (with longer cascades and thus more input signals) a Bayesian biosensor that we designed previously.

Model, Metamodel and Topology

This reply to Gash’s (Found Sci 2013) commentary on Nescolarde-Selva and Usó-Doménech (Found Sci 2013) answers the three questions raised and at the same time opens up new questions.

Population-based continuous optimization, probabilistic modelling and mean shift

Evolutionary algorithms perform optimization using a population of sample solution points. An interesting development has been to view population-based optimization as the process of evolving an explicit, probabilistic model of the search space. This paper investigates a formal basis for continuous, population-based optimization in terms of a stochastic gradient descent on the Kullback-Leibler divergence between the model probability density and the objective function, represented as an unknown density of assumed form. This leads to an update rule that is related and compared with previous theoretical work, a continuous version of the population-based incremental learning algorithm, and the generalized mean shift clustering framework. Experimental results are presented that demonstrate the dynamics of the new algorithm on a set of simple test problems.

A generative model for separating illumination and reflectance from images

It is well known that even slight changes in nonuniform illumination lead to a large image variability and are crucial for many visual tasks. This paper presents a new ICA related probabilistic model where the number of sources exceeds the number of sensors to perform an image segmentation and illumination removal, simultaneously. We model illumination and reflectance in log space by a generalized autoregressive process and Hidden Gaussian Markov random field, respectively. The model ability to deal with segmentation of illuminated images is compared with a Canny edge detector and homomorphic filtering. We apply the model to two problems: synthetic image segmentation and sea surface pollution detection from intensity images.

Driving licensing renewal policy using neural network-based probabilistic decision support system

This paper investigates neural network-based probabilistic decision support system to assess drivers' knowledge for the objective of developing a renewal policy of driving licences. The probabilistic model correlates drivers' demographic data to their results in a simulated written driving exam (SWDE). The probabilistic decision support system classifies drivers' into two groups of passing and failing a SWDE. Knowledge assessment of drivers within a probabilistic framework allows quantifying and incorporating uncertainty information into the decision-making system. The results obtained in a Jordanian case study indicate that the performance of the probabilistic decision support systems is more reliable than conventional deterministic decision support systems. Implications of the proposed probabilistic decision support systems on the renewing of the driving licences decision and the possibility of including extra assessment methods are discussed.

Using observation ageing to improve Markovian model learning in QoS engineering

Markovian models are widely used to analyse quality-of-service properties of both system designs and deployed systems. Thanks to the emergence of probabilistic model checkers, this analysis can be performed with high accuracy. However, its usefulness is heavily dependent on how well the model captures the actual behaviour of the analysed system. Our work addresses this problem for a class of Markovian models termed discrete-time Markov chains (DTMCs). We propose a new Bayesian technique for learning the state transition probabilities of DTMCs based on observations of the modelled system. Unlike existing approaches, our technique weighs observations based on their age, to account for the fact that older observations are less relevant than more recent ones. A case study from the area of bioinformatics workflows demonstrates the effectiveness of the technique in scenarios where the model parameters change over time.

Probabilistic verification of satellite systems for mission critical applications

In this thesis, we present a quantitative approach using probabilistic verification techniques for the analysis of reliability, availability, maintainability, and safety (RAMS) properties of satellite systems. The subject of our research is satellites used in mission critical industrial applications. A strong case for using probabilistic model checking to support RAMS analysis of satellite systems is made by our verification results. This study is intended to build a foundation to help reliability engineers with a basic background in model checking to apply probabilistic model checking to small satellite systems. We make two major contributions. One of these is the approach of RAMS analysis to satellite systems. In the past, RAMS analysis has been extensively applied to the field of electrical and electronics engineering. It allows system designers and reliability engineers to predict the likelihood of failures from the indication of historical or current operational data. There is a high potential for the application of RAMS analysis in the field of space science and engineering. However, there is a lack of standardisation and suitable procedures for the correct study of RAMS characteristics for satellite systems. This thesis considers the promising application of RAMS analysis to the case of satellite design, use, and maintenance, focusing on its system segments. Data collection and verification procedures are discussed, and a number of considerations are also presented on how to predict the probability of failure. Our second contribution is leveraging the power of probabilistic model checking to analyse satellite systems. We present techniques for analysing satellite systems that differ from the more common quantitative approaches based on traditional simulation and testing. These techniques have not been applied in this context before. We present the use of probabilistic techniques via a suite of detailed examples, together with their analysis. Our presentation is done in an incremental manner: in terms of complexity of application domains and system models, and a detailed PRISM model of each scenario. We also provide results from practical work together with a discussion about future improvements.

LATENT RANK CHANGE DETECTION FOR ANALYSIS OF SPLICE-JUNCTION MICROARRAYS WITH NONLINEAR EFFECTS

Alternative splicing of gene transcripts greatly expands the functional capacity of the genome, and certain splice isoforms may indicate specific disease states such as cancer. Splice junction microarrays interrogate thousands of splice junctions, but data analysis is difficult and error prone because of the increased complexity compared to differential gene expression analysis. We present Rank Change Detection (RCD) as a method to identify differential splicing events based upon a straightforward probabilistic model comparing the over-or underrepresentation of two or more competing isoforms. RCD has advantages over commonly used methods because it is robust to false positive errors due to nonlinear trends in microarray measurements. Further, RCD does not depend on prior knowledge of splice isoforms, yet it takes advantage of the inherent structure of mutually exclusive junctions, and it is conceptually generalizable to other types of splicing arrays or RNA-Seq. RCD specifically identifies the biologically important cases when a splice junction becomes more or less prevalent compared to other mutually exclusive junctions. The example data is from different cell lines of glioblastoma tumors assayed with Agilent microarrays.

Diagnostic errors and repetitive sequential classifications in on-line process control by attributes

The procedure of on-line process control by attributes, known as Taguchi`s on-line process control, consists of inspecting the mth item (a single item) at every m produced items and deciding, at each inspection, whether the fraction of conforming items was reduced or not. If the inspected item is nonconforming, the production is stopped for adjustment. As the inspection system can be subject to diagnosis errors, one develops a probabilistic model that classifies repeatedly the examined item until a conforming or b non-conforming classification is observed. The first event that occurs (a conforming classifications or b non-conforming classifications) determines the final classification of the examined item. Proprieties of an ergodic Markov chain were used to get the expression of average cost of the system of control, which can be optimized by three parameters: the sampling interval of the inspections (m); the number of repeated conforming classifications (a); and the number of repeated non-conforming classifications (b). The optimum design is compared with two alternative approaches: the first one consists of a simple preventive policy. The production system is adjusted at every n produced items (no inspection is performed). The second classifies the examined item repeatedly r (fixed) times and considers it conforming if most classification results are conforming. Results indicate that the current proposal performs better than the procedure that fixes the number of repeated classifications and classifies the examined item as conforming if most classifications were conforming. On the other hand, the preventive policy can be averagely the most economical alternative rather than those ones that require inspection depending on the degree of errors and costs. A numerical example illustrates the proposed procedure. (C) 2009 Elsevier B. V. All rights reserved.

Economic design of an X chart for short-run production

The aim of this paper is to present an economical design of an X chart for a short-run production. The process mean starts equal to mu(0) (in-control, State I) and in a random time it shifts to mu(1) > mu(0) (out-of-control, State II). The monitoring procedure consists of inspecting a single item at every m produced ones. If the measurement of the quality characteristic does not meet the control limits, the process is stopped, adjusted, and additional (r - 1) items are inspected retrospectively. The probabilistic model was developed considering only shifts in the process mean. A direct search technique is applied to find the optimum parameters which minimizes the expected cost function. Numerical examples illustrate the proposed procedure. (C) 2009 Elsevier B.V. All rights reserved.

Numerical simulation of dendrite growth during solidification

A comprehensive probabilistic model for simulating dendrite morphology and investigating dendritic growth kinetics during solidification has been developed, based on a modified Cellular Automaton (mCA) for microscopic modeling of nucleation, growth of crystals and solute diffusion. The mCA model numerically calculated solute redistribution both in the solid and liquid phases, the curvature of dendrite tips and the growth anisotropy. This modeling takes account of thermal, curvature and solute diffusion effects. Therefore, it can simulate microstructure formation both on the scale of the dendrite tip length. This model was then applied for simulating dendritic solidification of an Al-7%Si alloy. Both directional and equiaxed dendritic growth has been performed to investigate the growth anisotropy and cooling rate on dendrite morphology. Furthermore, the competitive growth and selection of dendritic crystals have also investigated.

A practical approach to assess depression risk and to guide risk reduction strategies in later life

Background: Many factors have been associated with the onset and maintenance of depressive symptoms in later life, although this knowledge is yet to be translated into significant health gains for the population. This study gathered information about common modifiable and non-modifiable risk factors for depression with the aim of developing a practical probabilistic model of depression that can be used to guide risk reduction strategies. \Methods: A cross-sectional study was undertaken of 20,677 community-dwelling Australians aged 60 years or over in contact with their general practitioner during the preceding 12 months. Prevalent depression (minor or major) according to the Patient Health Questionnaire (PHQ-9) assessment was the main outcome of interest. Other measured exposures included self-reported age, gender, education, loss of mother or father before age 15 years, physical or sexual abuse before age 15 years, marital status, financial stress, social support, smoking and alcohol use, physical activity, obesity, diabetes, hypertension, and prevalent cardiovascular diseases, chronic respiratory diseases and cancer. Results: The mean age of participants was 71.7 +/- 7.6 years and 57.9% were women. Depression was present in 1665 (8.0%) of our subjects. Multivariate logistic regression showed depression was independently associated with age older than 75 years, childhood adverse experiences, adverse lifestyle practices (smoking, risk alcohol use, physical inactivity), intermediate health hazards (obesity, diabetes and hypertension), comorbid medical conditions (clinical history of coronary heart disease, stroke, asthma, chronic obstructive pulmonary disease, emphysema or cancers), and social or financial strain. We stratified the exposures to build a matrix that showed that the probability of depression increased progressively with the accumulation of risk factors, from less than 3% for those with no adverse factors to more than 80% for people reporting the maximum number of risk factors. Conclusions: Our probabilistic matrix can be used to estimate depression risk and to guide the introduction of risk reduction strategies. Future studies should now aim to clarify whether interventions designed to mitigate the impact of risk factors can change the prevalence and incidence of depression in later life.

Modelling of microstructure formation and evolution during solidification

A comprehensive probabilistic model for simulating microstructure formation and evolution during solidification has been developed, based on coupling a Finite Differential Method (FDM) for macroscopic modelling of heat diffusion to a modified Cellular Automaton (mCA) for microscopic modelling of nucleation, growth of microstructures and solute diffusion. The mCA model is similar to Nastac's model for handling solute redistribution in the liquid and solid phases, curvature and growth anisotropy, but differs in the treatment of nucleation and growth. The aim is to improve understanding of the relationship between the solidification conditions and microstructure formation and evolution. A numerical algorithm used for FDM and mCA was developed. At each coarse scale, temperatures at FDM nodes were calculated while nucleation-growth simulation was done at a finer scale, with the temperature at the cell locations being interpolated from those at the coarser volumes. This model takes account of thermal, curvature and solute diffusion effects. Therefore, it can not only simulate microstructures of alloys both on the scale of grain size (macroscopic level) and the dendrite tip length (mesoscopic level), but also investigate nucleation mechanisms and growth kinetics of alloys solidified with various solute concentrations and solidification morphologies. The calculated results are compared with values of grain sizes and solidification morphologies of microstructures obtained from a set of casting experiments of Al-Si alloys in graphite crucibles.