Semi-continuous Model Research Articles

Coherent indexes for shifted count and semicontinuous models

Coherent indexes for shifted count and semicontinuous models

Adult–child pairs walking down stairs: empirical analysis and optimal-step-based modeling of a complex pedestrian flow, with an exploration of flow-improvement strategies

Pedestrian egress from training schools in the after-class period (especially in China, as children walk down stairs together with their parents) raises practical concerns related to degraded flow conditions and possible safety hazards. But it also represents a challenge to mainstream modeling approaches for several reasons: they involve heterogeneous groups (adult–child pairs), which are hardly studied compared to their homogeneous counterparts, in a complex geometry, made of staircases connected by a platform where pedestrians rotate, and over a wide range of densities. In light of our field observations at a training school in China, we develop a semi-continuous model which quantitatively reproduces the collective dynamics observed empirically and enables us to assess some guidance strategies to improve egress efficiency. In this model, which extends the optimal step approach, adults and children are described as ellipses with prescribed relative positions that evolve by successive steps handled by an event-driven algorithm, along a spontaneous semi-circular path on the platform, but may deviate from it in crowded conditions by selecting their preferred next positions. In line with the observations, most pairs walk side by side overall and only a small fraction sometimes make a detour to avoid queuing. Turning to the guidance strategies, we find that promoting front-back pairing may increase the flow, while urging people to make more detours may be counterproductive. Perhaps even more relevantly, the intuitive measure consisting in desynchronizing the flows from the different floors by shifting the ends of classes succeeds in reducing the egress time by at least 10%.

A new implementation of a semi-continuous method for DNA mixture interpretation

A new calculation module within the PopStats module of the CODIS software package, based on the underlying mathematics presented in the MixKin software package, has been developed for assigning the Likelihood Ratio (LR) of DNA mixture profiles. This module uses a semi-continuous model that allows for population structure and allelic drop-out and drop-in but does not require allelic peak heights or other laboratory-specific parameters. This new implementation (named SC Mixture), like MixKin, does not specify or estimate a probability of drop-out. Instead, each contributor to a mixture has an independent drop-out rate, and the probability of the mixture profile for a specified proposition concerning the contributors is integrated over the range of possible drop-out rates. The allelic drop-in rate and the population structure parameter, theta, used by the software are specified by the user. The user can examine up to five contributors to a mixture, however, conditioning on assumed contributors and limiting the number of unknowns in both numerator and denominator hypotheses greatly improves performance. We report results from an extensive validation study performed for ten mixtures with each of one (single source), two, three, four, or five contributors, with four combinations of drop-in rate and a population structure parameter. Each mixture was run as a complete profile or with the random removal of alleles to simulate drop-out. All 1620 combinations were evaluated with PopStats, MixKin, and LRmix and considerable consistency was found among the results with all three packages.

Simultaneous modeling of detection rate and exposure concentration using semi-continuous models to identify exposure determinants when left-censored data may be a true zero.

Background:Most methods for treating left-censored data assume the analyte is present but not quantified. Biased estimates may result if the analyte is absent such that the unobserved data represents a mixed exposure distribution with an unknown proportion clustered at zero.Objective:We used semi-continuous models to identify time and industry trends in 52,457 OSHA inspection lead sample results.Method:The first component of the semi-continuous model predicted the probability of detecting concentrations ≥0.007 mg/m3 (highest estimated detection limit, 62% of measurements). The second component predicted the median concentration of measurements ≥0.007 mg/m3. Both components included a random-effect for industry and fixed-effects for year, industry group, analytical method, and other variables. We used the two components together to predict median industry- and time-specific lead concentrations.Results:The probabilities of detectable concentrations and the median detected concentrations decreased with year; both were also lower for measurements analyzed for multiple (vs. one) metals and for those analyzed by inductively-coupled plasma (vs. atomic absorption spectroscopy). The covariance was 0.30 (standard error=0.06), confirming the two components were correlated.Significance:We identified determinants of exposure in data with over 60% left-censored, while accounting for correlated relationships and without assuming a distribution for the censored data.

Effects of Colonic Fermentation Products of Polydextrose, Lactitol and Xylitol on Intestinal Barrier Repair In Vitro

Many functional food ingredients improve intestinal barrier function through their colonic fermentation products short chain fatty acids (SCFAs). Effects of individual SCFAs have been well studied, but the effects of SCFA mixtures–colonic fermentation products have been rarely investigated. Therefore, this study used an EnteroMix semi-continuous model to simulate the colonic fermentation of three widely used food ingredients, polydextrose, lactitol and xylitol in vitro, and investigated the effects of their fermentation products on impaired colonic epithelial barrier function through a mucus-secreting human HT29-MTX-E12 cell model. Fermentation of polydextrose and lactitol produced mainly acetate, while fermentation of xylitol produced mainly butyrate and resulted in a much higher butyrate proportion. All fermentation products significantly improved intestinal barrier repairing as measured by increased transepithelial electrical resistance and decreased paracellular permeability. Among these, xylitol fermentation products exhibited better repairing effects than that of polydextrose and lactitol. Correlation analysis showed that the repairing effects were attribute to butyrate but not acetate or propionate, implying that in the fermentation products butyrate may play a major role in improving intestinal barrier function. Our results suggest that functional food ingredients that mainly produce butyrate during fermentation may be of more value for improving gut health related to chronic diseases.

Validation of a top-down DNA profile analysis for database searching using a fully continuous probabilistic genotyping model

Slooten described a method of targeting major contributors in mixed DNA profiles and comparing them to individuals on a DNA database. The method worked by taking incrementally more peak information from the profile (based on the peak contribution), and using a semi-continuous model, calculating likelihood ratios for the comparison to database individuals. We describe the performance of this “top down approach” to profile interpretation within probabilistic genotyping software employing a fully continuous model. We interpret both complex constructed profiles where ground truth is known and casework profiles from non-suspect crimes. The interpretation of constructed four- and five- person mixtures demonstrated good discrimination power between contributors and non-contributors to the mixtures. Not all known contributors linked, and this is expected, particularly for minor contributors of DNA to the profile, or when the DNA from contributors was in relatively equal contributions. This finding was also reported by Slooten for the semi-continuous application of the approach. The maximum observed LR was shown to not exceed the LR obtained after a standard interpretation approach outside of that expected due to Monte Carlo variation. The interpretation of 91 complex profiles from no-suspect casework demonstrated that approximately 75% of profiles returned a link to someone on a database of known individuals. With a yearly average of 110 no-suspect cases that fall into this too-complex category at Forensic Science SA, the top down analysis, if applied to all such profiles, would represent an increase of 83 links per year of investigative information that could be provided to investigators.

Modeling Interactions between Graphene and Heterogeneous Molecules

The Lennard–Jones potential and a continuum approach can be used to successfully model interactions between various regular shaped molecules and nanostructures. For single atomic species molecules, the interaction can be approximated by assuming a uniform distribution of atoms over surfaces or volumes, which gives rise to a constant atomic density either over or throughout the molecule. However, for heterogeneous molecules, which comprise more than one type of atoms, the situation is more complicated. Thus far, two extended modeling approaches have been considered for heterogeneous molecules, namely a multi-surface semi-continuous model and a fully continuous model with average smearing of atomic contribution. In this paper, we propose yet another modeling approach using a single continuous surface, but replacing the atomic density and attractive and repulsive constants in the Lennard–Jones potential with functions, which depend on the heterogeneity across the molecules, and the new model is applied to study the adsorption of coronene onto a graphene sheet. Comparison of results is made between the new model and two other existing approaches as well as molecular dynamics simulations performed using the LAMMPS molecular dynamics simulator. We find that the new approach is superior to the other continuum models and provides excellent agreement with molecular dynamics simulations.

Bayesian analyses of an exponential-Poisson and related zero augmented type models

We consider several alternatives to the continuous exponential-Poisson distribution in order to accommodate the occurrence of zeros. Three of these are modifications of the exponential-Poisson model. One of these remains a fully continuous model. The other models we consider are all semi-continuous models, each with a discrete point mass at zero and a continuous density on the positive values. All of the models are applied to two environmental data sets concerning precipitation, and their Bayesian analyses using MCMC are discussed. This discussion covers convergence of the MCMC simulations and model selection procedures and considerations.

A Semi-Continuous PWA Model Based Optimal Control Method for Nonlinear Systems

To alleviate the mode mismatch of multiple model methods for nonlinear systems when completely discrete dynamical equations are adopted, a semi-continuous piecewise affine (SCPWA) model based optimal control method is proposed. Firstly, a SCPWA model is constructed where modes evolve in continuous time and continuous states evolve in discrete time. Thanks to this model, a piecewise affine (PWA) system can switch at any time instant whereas mode switching only occurs at sample instants when a completely discrete PWA model is adopted, which improves the prediction accuracy of multi-models. Secondly, the switching condition is relaxed such that operating subspaces have overlaps and switching condition parameters are introduced. As a consequence, an optimal control problem with fixed mode switching sequence is established. Finally, a SCPWA model based model predictive control (MPC) policy is designed for nonlinear systems. The convergence of the MPC algorithm is proved. Compared with widely used mixed logical dynamic (MLD) model based methods, the proposed method not only alleviates mode mismatch, but also lightens the computing burden, hence improves the control performance and reduces the computation time. Some numerical examples are provided as well to show the efficiency of the method.

Coastal Shuttle Tanker Scheduling Model Considering Inventory Cost and System Reliability

The near-sea off-shore oil extraction and transportation system use heterogeneous fleets to transfer crude oil from the floating production storage and offloading to the land-based oil storage port. Based on the characteristics of this system, the short sea inventory routing problem is investigated considering the shuttle tanker fleet and inventory management. In order to minimize the total operation cost and maximize the system reliability, a semi-continuous model for the shuttle tanker scheduling problem is established. The model optimizes the tanker scheduling plan and the design of the tanker fleet. To solve the complex model, this article proposes an improved non-dominated sorting genetic algorithm with differential evolution operator to solve the optimization of the multi-objective model. This research also uses public vessel operation data to test the modeling and optimizing efficiency. The Pareto Fronts associated with the total operation cost and the system reliability from the optimization outcome is analyzed to provide scheduling priority advice. The results indicate that proposed optimization algorithms are effective, and the operation could be optimized with the proposed model and algorithm.

An assessment of the performance of the probabilistic genotyping software EuroForMix: Trends in likelihood ratios and analysis of Type I & II errors

Continuous probabilistic genotyping software enables the interpretation of highly complex DNA profiles that are prone to stochastic effects and/or consist of multiple contributions. The process of introducing probabilistic genotyping into an accredited forensic laboratory requires testing, validation, documentation and training. Documents that include guidelines and/or requirements have been published in order to guide forensic laboratories through this extensive process and there has been encouragements to share the results obtained from internal laboratory studies. To this end, we present the results obtained from the quantitative probabilistic genotyping system EuroForMix applied to mixed DNA profiles with known contributions mixed in known proportions, levels of allele sharing and levels of allelic drop-out. The mixtures were profiled using the PowerPlex® Fusion 6C (PPF6C) kit. Using these mixtures, 427 Hp-true tests and 408 Hd-true tests were performed. In the Hd-true tests, non-contributors were selected deliberately to a have large overlap with the alleles within the mixture and worst-case scenarios were examined in which a simulated relative of one of the true donors was considered as the person of interest under the prosecution hypothesis. The effects of selecting different EuroForMix modelling options, the use of PCR replicates, allelic drop-out, and varying the assigned number of contributors were examined. Instances of Type I and Type II errors are discussed. In addition 330 likelihood ratio results from EuroForMix are compared to the semi-continuous model LRmix Studio. Results demonstrate the performance and trends of EuroForMix when applied to PPF6C profiles.

Processing of Superfine and Ultrafine Phosphate of a Phosphomud (Part Two)

Mineral industries in common generate a lot of rejects in the form of fines and slimes, which ultimately create environmental and social problems besides causing losses of mineral values. In view of the recent stringent policy imposed on the environment, there is an urgent need to attempt possible simple and cheap solutions to such problems. These slimes have long been considered in the industry to be unrecoverable. It has been standard practice over many years in the phosphate industry to separate and discard the fines and ultrafine particles. 
 
 In this respect, the present study shed light on the recovery of super and ultrafine phosphate of a phosphomud produced after the processing of an East Mediterranean phosphate ore. Falcon Concentrator model SB40-VFD (semi-continuous with variable frequency drive) was used in this study to recover the -32 micron phosphate fines of D50=11 micron. The effect of the main variables of the semi-continuous Falcon concentrator model SB40-VFD, including the bowl rotation frequency Hz, the fluidizing water pressure psi, and feeding rate g/min on the separation efficiency were followed up. In addition, two feeding modes based on a particle size-by-size were tried in this study: The sample was fed as a global -32 micron sample or as two fractions, -32+11 micron, and -11 micron samples. Central Composite Rotatable Design (CCRD) was applied on the Falcon separation of the -11 micron fraction with D50 < 3 micron alone to model and optimize the separation process for the two responses: the recovered phosphate grade and recovery.
 
 Results showed that the phosphate fines containing 14.73% P2O5, 15.03% acid insoluble, and 19.07% loss in ignition was recovered with grade and P2O5 recovery reaching 28.29%, and 95.97% in case of separating the overall -32 micron sample as one feed. In case of the fractionated feeding samples, the total grade and recovery reached 29.21%, and 88.42%, respectively. The application of the CCRD results showed that the bowl rotation frequency showed to have the main irreversible effect on the product grade, where the fluidizing water pressure had the main reversible effect on the recovery. On the other hand, feeding rate showed some effect on the product grade with almost no effect on its P2O5 recovery%.

Probabilistic approaches to interpreting two-person DNA mixtures from post-coital specimens

Biological samples submitted for sexual assault investigation typically involve mixtures of DNA from the victim and the assailant/s. Providing a statistical weight to such evidence may be mathematically complex and may be affected by subjective judgment of a human analyst. Software tools have been developed to address these issues. To contribute towards improving the system for routine DNA testing of sexual assault cases, we evaluated two likelihood ratio (LR) approaches: a semi-continuous model using LRmix Studio and a fully continuous approach employed in STRmix™ for interpreting two-person DNA mixtures. LRs conditioned on the presence of the receptive partner’s DNA were calculated for a total of 102 two-person DNA samples from simulated mixtures and various post-coital samples. Our results highlight the importance of maximising information provided into the LR calculation to generate strong support for the true hypothesis. This can be achieved by recovering sufficient DNA from a sample to minimise risk of drop-out and increase peak intensities and by implementing a statistical model that utilises as much of the electropherogram information as possible. LRmix is open-source and can handle profiles with allelic drop-out and drop-ins, however stuttering is not modelled and requires manual removal by a DNA analyst especially for mixtures with low template components. STRmix™ makes effective use of all available information by incorporating into its biological model complicating aspects of a DNA profile such as degradation, allele drop-out and drop-in, stutters, and peak height variability.

An optimization framework for scheduling of converter aisle operation in a nickel smelting plant

The scheduling of converter aisle operation in a nickel smelting plant is a complex task with significant ramifications to plant profitability and production. An optimization-based scheduling formulation is developed using a continuous-time paradigm to accurately represent event timings. The formulation accounts for environmental restrictions on sulfur dioxide emissions, using event timing constraints. Flash furnaces are characterized by a continuous inlet flow and intermittent, discrete material removal, which is captured via novel semi-continuous modeling. An innovative sequencing and symmetry-breaking scheme is introduced to exploit identical units operating in parallel. A rolling horizon feature is included to accommodate real-time optimization. Tightening constraints are developed to improve the computational performance. A unique, multi-tiered procedure enhances the practicality of the solution and supports additional operability objectives, without compromising the optimality of the primary objective. The success of the approach is demonstrated via case studies arising from industrial production scenarios.

Modeling of x-ray fluorescence full field imaging using planar square pore micro-channel plate optics.

X-ray fluorescence imaging using perfect planar square pore micro-channel plate x-ray optics (MPO) is investigated through the modeling of the MPO point spread function (PSF). A semi-continuous model based on the use of a simplified two parameters reflectivity curve is developed including, in particular, three kinds of contributions. A validation of this model is carried out by calculating variations of several PSF characteristics with the MPO and fluorescence imaging parameters and comparing the results with ray-tracing simulations. A good agreement is found in a large range of x-ray energies; however, it is shown that for the lower values of the working distance a discrete model should be used to take into account the periodic nature of the PSF. Ray-tracing simulated images of extended monochromatic sources are interpreted in light of both the semi-continuous and discrete models. Finally, solutions are proposed to improve the imaging properties of the MPOs.

In silico study of multicellular automaticity of heterogeneous cardiac cell monolayers: Effects of automaticity strength and structural linear anisotropy.

The biological pacemaker approach is an alternative to cardiac electronic pacemakers. Its main objective is to create pacemaking activity from added or modified distribution of spontaneous cells in the myocardium. This paper aims to assess how automaticity strength of pacemaker cells (i.e. their ability to maintain robust spontaneous activity with fast rate and to drive neighboring quiescent cells) and structural linear anisotropy, combined with density and spatial distribution of pacemaker cells, may affect the macroscopic behavior of the biological pacemaker. A stochastic algorithm was used to randomly distribute pacemaker cells, with various densities and spatial distributions, in a semi-continuous mathematical model. Simulations of the model showed that stronger automaticity allows onset of spontaneous activity for lower densities and more homogeneous spatial distributions, displayed more central foci, less variability in cycle lengths and synchronization of electrical activation for similar spatial patterns, but more variability in those same variables for dissimilar spatial patterns. Compared to their isotropic counterparts, in silico anisotropic monolayers had less central foci and displayed more variability in cycle lengths and synchronization of electrical activation for both similar and dissimilar spatial patterns. The present study established a link between microscopic structure and macroscopic behavior of the biological pacemaker, and may provide crucial information for optimized biological pacemaker therapies.

Accurate assessment of the weight of evidence for DNA mixtures by integrating the likelihood ratio

Several methods exist for weight of evidence calculations on DNA mixtures. Especially if dropout is a possibility, it may be difficult to estimate mixture specific parameters needed for the evaluation. For semi-continuous models, the LR for a person to have contributed to a mixture depends on the specified number of contributors and the probability of dropout for each. We show here that, for the semi-continuous model that we consider, the weight of evidence can be accurately obtained by applying the standard statistical technique of integrating the likelihood ratio against the parameter likelihoods obtained from the mixture data. This method takes into account all likelihood ratios belonging to every choice of parameters, but LR's belonging to parameters that provide a better explanation to the mixture data put in more weight into the final result. We therefore avoid having to estimate the number of contributors or their probabilities of dropout, and let the whole evaluation depend on the mixture data and the allele frequencies, which is a practical advantage as well as a gain in objectivity. Using simulated mixtures, we compare the LR obtained in this way with the best informed LR, i.e., the LR using the parameters that were used to generate the data, and show that results obtained by integration of the LR approximate closely these ideal values. We investigate both contributors and non-contributors for mixtures with various numbers of contributors. For contributors we always obtain a result close to the best informed LR whereas non-contributors are excluded more strongly if a smaller dropout probability is imposed for them. The results therefore naturally lead us to reconsider what we mean by a contributor, or by the number of contributors.

Modeling zero-modified count and semicontinuous data in health services research Part 1: background and overview.

Health services data often contain a high proportion of zeros. In studies examining patient hospitalization rates, for instance, many patients will have no hospitalizations, resulting in a count of zero. When the number of zeros is greater or less than expected under a standard count model, the data are said to be zero modified relative to the standard model. A similar phenomenon arises with semicontinuous data, which are characterized by a spike at zero followed by a continuous distribution with positive support. When analyzing zero-modified count and semicontinuous data, flexible mixture distributions are often needed to accommodate both the excess zeros and the typically skewed distribution of nonzero values. Various models have been introduced over the past three decades to accommodate such data, including hurdle models, zero-inflated models, and two-part semicontinuous models. This tutorial describes recent modeling strategies for zero-modified count and semicontinuous data and highlights their role in health services research studies. Part 1 of the tutorial, presented here, provides a general overview of the topic. Part 2, appearing as a companion piece in this issue of Statistics in Medicine, discusses three case studies illustrating applications of the methods to health services research. Copyright © 2016 John Wiley & Sons, Ltd.

SCHMM-based compensation for the random delays in networked control systems

In order to compensate the network-induced random delays in networked control systems (NCSs), the semi-continuous hidden Markov model (SCHMM) is introduced in this paper to model the controller-to-actuator (CA) delay in the forward network channel. The expectation maximization algorithm is used to obtain the optimal estimation of the model's parameters, and the Viterbi algorithm is used to predict the CA delay in the current sampling period. Thus, the predicted CA delay and the measured sensor-tocontroller (SC) delay in the current sampling period are used to design an optimal controller. Under this controller, the exponentially mean square stability of the NCS is guaranteed, and the SC and CA delays are compensated. Finally, the effectiveness of the method proposed in this paper is demonstrated by a simulation example. Moreover, a comparative example is also given to illustrate the superiority of the SCHMM-based optimal controller over the discrete hidden Markov model (DHMM)-based optimal controller.

Familial searching on DNA mixtures with dropout

Familial searching, the act of searching a database for a relative of an unknown individual whose DNA profile has been obtained, is usually restricted to cases where the DNA profile of that person has been unambiguously determined. Therefore, it is normally applied only with a good quality single source profile as starting point. In this article we investigate the performance of the method if applied to mixtures with and without allelic dropout, when likelihood ratios are computed with a semi-continuous (binary) model. We show that mixtures with dropout do not necessarily perform worse than mixtures without, especially if some separation between the donors is possible due to their different dropout probabilities. The familial searching true and false positive rates of mixed profiles on 15 loci are in some cases better than those of single source profiles on 10 loci. Thus, the information loss due to the fact that the person of interest's DNA has been mixed with that of other, and is affected by dropout, can be less than the loss of information corresponding to having 5 fewer loci available for a single source trace. Profiles typed on 10 autosomal loci are often involved in familial searching casework since many databases, including the Dutch one, in part consist of such profiles. Therefore, from this point of view, there seems to be no objection to extend familial searching to mixed or degraded profiles.