Non-commutative symbolic coding

We give a non-commutative generalization of classical symbolic coding in the presence of a synchronizing word. This is done by a scattering theoretical approach. Classically, the existence of a synchronizing word turns out to be equivalent to asymptotic completeness of the corresponding Markov process. A criterion for asymptotic completeness in general is provided by the regularity of an associated extended transition operator. Commutative and non-commutative examples are analysed.

A Wiener-Hopf type factorization for the exponential functional of Levy processes

For a Lévy process ξ=(ξt)t≥0 drifting to −∞, we define the so-called exponential functional as follows: Formula Under mild conditions on ξ, we show that the following factorization of exponential functionals: Formula holds, where × stands for the product of independent random variables, H− is the descending ladder height process of ξ and Y is a spectrally positive Lévy process with a negative mean constructed from its ascending ladder height process. As a by-product, we generate an integral or power series representation for the law of Iξ for a large class of Lévy processes with two-sided jumps and also derive some new distributional properties. The proof of our main result relies on a fine Markovian study of a class of generalized Ornstein–Uhlenbeck processes, which is itself of independent interest. We use and refine an alternative approach of studying the stationary measure of a Markov process which avoids some technicalities and difficulties that appear in the classical method of employing the generator of the dual Markov process.

Linkage disequilibrium assessment via log-linear modeling of SNP haplotype frequencies

Analyses of high-density single-nucleotide polymorphism (SNP) data, such as genetic mapping and linkage disequilibrium (LD) studies, require phase-known haplotypes to allow for the correlation between tightly linked loci. However, current SNP genotyping technology cannot determine phase, which must be inferred statistically. In this paper, we present a new Bayesian Markov chain Monte Carlo (MCMC) algorithm for population haplotype frequency estimation, particulary in the context of LD assessment. The novel feature of the method is the incorporation of a log-linear prior model for population haplotype frequencies. We present simulations to suggest that 1) the log-linear prior model is more appropriate than the standard coalescent process in the presence of recombination (>0.02cM between adjacent loci), and 2) there is substantial inflation in measures of LD obtained by a "two-stage" approach to the analysis by treating the "best" haplotype configuration as correct, without regard to uncertainty in the recombination process. Genet Epidemiol 25:106-114, 2003. (C) 2003 Wiley-Liss, Inc.

(Non-)ergodicity of a degenerate diffusion modeling the fiber lay down process

We analyze the large time behavior of a stochastic model for the lay down of fibers on a moving conveyor belt in the production process of nonwovens. It is shown that under weak conditions this degenerate diffusion process has a unique invariant distribution and is even geometrically ergodic. This generalizes results from previous works [M. Grothaus and A. Klar, SIAM J. Math. Anal., 40 (2008), pp. 968–983; J. Dolbeault et al., arXiv:1201.2156] concerning the case of a stationary conveyor belt, in which the situation of a moving conveyor belt has been left open.

Can the frequency of blocking be described by a red noise process?

The frequency of persistent atmospheric blocking events in the 40-yr ECMWF Re-Analysis (ERA-40) is compared with the blocking frequency produced by a simple first-order Markov model designed to predict the time evolution of a blocking index [defined by the meridional contrast of potential temperature on the 2-PVU surface (1 PVU ≡ 1 × 10−6 K m2 kg−1 s−1)]. With the observed spatial coherence built into the model, it is able to reproduce the main regions of blocking occurrence and the frequencies of sector blocking very well. This underlines the importance of the climatological background flow in determining the locations of high blocking occurrence as being the regions where the mean midlatitude meridional potential vorticity (PV) gradient is weak. However, when only persistent blocking episodes are considered, the model is unable to simulate the observed frequencies. It is proposed that this persistence beyond that given by a red noise model is due to the self-sustaining nature of the blocking phenomenon.

Modeling the mechanisms that control in-stream dissolved organic carbon dynamics in upland and forested catchments

[1] We present a new, process-based model of soil and stream water dissolved organic carbon (DOC): the Integrated Catchments Model for Carbon (INCA-C). INCA-C is the first model of DOC cycling to explicitly include effects of different land cover types, hydrological flow paths, in-soil carbon biogeochemistry, and surface water processes on in-stream DOC concentrations. It can be calibrated using only routinely available monitoring data. INCA-C simulates daily DOC concentrations over a period of years to decades. Sources, sinks, and transformation of solid and dissolved organic carbon in peat and forest soils, wetlands, and streams as well as organic carbon mineralization in stream waters are modeled. INCA-C is designed to be applied to natural and seminatural forested and peat-dominated catchments in boreal and temperate regions. Simulations at two forested catchments showed that seasonal and interannual patterns of DOC concentration could be modeled using climate-related parameters alone. A sensitivity analysis showed that model predictions were dependent on the mass of organic carbon in the soil and that in-soil process rates were dependent on soil moisture status. Sensitive rate coefficients in the model included those for organic carbon sorption and desorption and DOC mineralization in the soil. The model was also sensitive to the amount of litter fall. Our results show the importance of climate variability in controlling surface water DOC concentrations and suggest the need for further research on the mechanisms controlling production and consumption of DOC in soils.

Modeling the user knowledge by belief networks

This paper describes the user modeling component of EPIAIM, a consultation system for data analysis in epidemiology. The component is aimed at representing knowledge of concepts in the domain, so that their explanations can be adapted to user needs. The first part of the paper describes two studies aimed at analysing user requirements. The first one is a questionnaire study which examines the respondents' familiarity with concepts. The second one is an analysis of concept descriptions in textbooks and from expert epidemiologists, which examines how discourse strategies are tailored to the level of experience of the expected audience. The second part of the paper describes how the results of these studies have been used to design the user modeling component of EPIAIM. This module works in a two-step approach. In the first step, a few trigger questions allow the activation of a stereotype that includes a "body" and an "inference component". The body is the representation of the body of knowledge that a class of users is expected to know, along with the probability that the knowledge is known. In the inference component, the learning process of concepts is represented as a belief network. Hence, in the second step the belief network is used to refine the initial default information in the stereotype's body. This is done by asking a few questions on those concepts where it is uncertain whether or not they are known to the user, and propagating this new evidence to revise the whole situation. The system has been implemented on a workstation under UNIX. An example of functioning is presented, and advantages and limitations of the approach are discussed.

Requirements for building information modeling based lean production management systems for construction

Smooth flow of production in construction is hampered by disparity between individual trade teams' goals and the goals of stable production flow for the project as a whole. This is exacerbated by the difficulty of visualizing the flow of work in a construction project. While the addresses some of the issues in Building information modeling provides a powerful platform for visualizing work flow in control systems that also enable pull flow and deeper collaboration between teams on and off site. The requirements for implementation of a BIM-enabled pull flow construction management software system based on the Last Planner System™, called ‘KanBIM’, have been specified, and a set of functional mock-ups of the proposed system has been implemented and evaluated in a series of three focus group workshops. The requirements cover the areas of maintenance of work flow stability, enabling negotiation and commitment between teams, lean production planning with sophisticated pull flow control, and effective communication and visualization of flow. The evaluation results show that the system holds the potential to improve work flow and reduce waste by providing both process and product visualization at the work face.

New mathematical modeling approach for predicting microbial inactivation by high hydrostatic pressure

A new primary model based on a thermodynamically consistent first-order kinetic approach was constructed to describe non-log-linear inactivation kinetics of pressure-treated bacteria. The model assumes a first-order process in which the specific inactivation rate changes inversely with the square root of time. The model gave reasonable fits to experimental data over six to seven orders of magnitude. It was also tested on 138 published data sets and provided good fits in about 70% of cases in which the shape of the curve followed the typical convex upward form. In the remainder of published examples, curves contained additional shoulder regions or extended tail regions. Curves with shoulders could be accommodated by including an additional time delay parameter and curves with tails shoulders could be accommodated by omitting points in the tail beyond the point at which survival levels remained more or less constant. The model parameters varied regularly with pressure, which may reflect a genuine mechanistic basis for the model. This property also allowed the calculation of (a) parameters analogous to the decimal reduction time D and z, the temperature increase needed to change the D value by a factor of 10, in thermal processing, and hence the processing conditions needed to attain a desired level of inactivation; and (b) the apparent thermodynamic volumes of activation associated with the lethal events. The hypothesis that inactivation rates changed as a function of the square root of time would be consistent with a diffusion-limited process.

Sparse modeling using orthogonal forward regression with PRESS statistic and regularization

The paper introduces an efficient construction algorithm for obtaining sparse linear-in-the-weights regression models based on an approach of directly optimizing model generalization capability. This is achieved by utilizing the delete-1 cross validation concept and the associated leave-one-out test error also known as the predicted residual sums of squares (PRESS) statistic, without resorting to any other validation data set for model evaluation in the model construction process. Computational efficiency is ensured using an orthogonal forward regression, but the algorithm incrementally minimizes the PRESS statistic instead of the usual sum of the squared training errors. A local regularization method can naturally be incorporated into the model selection procedure to further enforce model sparsity. The proposed algorithm is fully automatic, and the user is not required to specify any criterion to terminate the model construction procedure. Comparisons with some of the existing state-of-art modeling methods are given, and several examples are included to demonstrate the ability of the proposed algorithm to effectively construct sparse models that generalize well.

Particle swarm optimization aided orthogonal forward regression for unified data modeling

We propose a unified data modeling approach that is equally applicable to supervised regression and classification applications, as well as to unsupervised probability density function estimation. A particle swarm optimization (PSO) aided orthogonal forward regression (OFR) algorithm based on leave-one-out (LOO) criteria is developed to construct parsimonious radial basis function (RBF) networks with tunable nodes. Each stage of the construction process determines the center vector and diagonal covariance matrix of one RBF node by minimizing the LOO statistics. For regression applications, the LOO criterion is chosen to be the LOO mean square error, while the LOO misclassification rate is adopted in two-class classification applications. By adopting the Parzen window estimate as the desired response, the unsupervised density estimation problem is transformed into a constrained regression problem. This PSO aided OFR algorithm for tunable-node RBF networks is capable of constructing very parsimonious RBF models that generalize well, and our analysis and experimental results demonstrate that the algorithm is computationally even simpler than the efficient regularization assisted orthogonal least square algorithm based on LOO criteria for selecting fixed-node RBF models. Another significant advantage of the proposed learning procedure is that it does not have learning hyperparameters that have to be tuned using costly cross validation. The effectiveness of the proposed PSO aided OFR construction procedure is illustrated using several examples taken from regression and classification, as well as density estimation applications.

Adding value to ecological risk assessment with population modeling

Current measures used to estimate the risks of toxic chemicals are not relevant to the goals of the environmental protection process, and thus ecological risk assessment (ERA) is not used as extensively as it should be as a basis for cost-effective management of environmental resources. Appropriate population models can provide a powerful basis for expressing ecological risks that better inform the environmental management process and thus that are more likely to be used by managers. Here we provide at least five reasons why population modeling should play an important role in bridging the gap between what we measure and what we want to protect. We then describe six actions needed for its implementation into management-relevant ERA.

Skilloscopy: Bayesian modeling of decision makers' skill

This paper proposes and demonstrates an approach, Skilloscopy, to the assessment of decision makers. In an increasingly sophisticated, connected and information-rich world, decision making is becoming both more important and more difficult. At the same time, modelling decision-making on computers is becoming more feasible and of interest, partly because the information-input to those decisions is increasingly on record. The aims of Skilloscopy are to rate and rank decision makers in a domain relative to each other: the aims do not include an analysis of why a decision is wrong or suboptimal, nor the modelling of the underlying cognitive process of making the decisions. In the proposed method a decision-maker is characterised by a probability distribution of their competence in choosing among quantifiable alternatives. This probability distribution is derived by classic Bayesian inference from a combination of prior belief and the evidence of the decisions. Thus, decision-makers’ skills may be better compared, rated and ranked. The proposed method is applied and evaluated in the gamedomain of Chess. A large set of games by players across a broad range of the World Chess Federation (FIDE) Elo ratings has been used to infer the distribution of players’ rating directly from the moves they play rather than from game outcomes. Demonstration applications address questions frequently asked by the Chess community regarding the stability of the Elo rating scale, the comparison of players of different eras and/or leagues, and controversial incidents possibly involving fraud. The method of Skilloscopy may be applied in any decision domain where the value of the decision-options can be quantified.

Analysis and modeling of ants’ behavior from single to multi-body

In order to shed light on the collective behavior of social insects, we analyzed the behavior of ants from single to multi-body. In an experimental set-up, ants are placed in hemisphere without a nest and food. Trajectory of ants is recorded. From this bottom-up approach, we found that collective behavior of ants as follows: 1. Activity of single ant increases and decreases periodically. 2. Spontaneous meeting process is observed between two ants and meeting spot of two ants is localized in hemisphere. 3. Result on division of labor is obtained between two ants.