Separate Probability Distributions Research Articles

Urban localization using robust filtering at multiple linearization points

We propose a robust Bayesian filtering framework for state and multi-modal uncertainty estimation in urban settings by fusing diverse sensor measurements. Our framework addresses multi-modal uncertainty from various error sources by tracking a separate probability distribution for linearization points corresponding to dynamics, measurements, and cost functions. Multiple parallel robust Extended Kalman filters (R-EKF) leverage these linearization points to characterize the state probability distribution. Employing Rao–Blackwellization, we combine the linearization point distribution with the state distribution, resulting in a unified, efficient, and outlier-resistant Bayesian filter that captures multi-modal uncertainty. Furthermore, we introduce a gradient descent-based optimization method to refine the filter parameters using available data. Evaluating our filter on real-world data from a multi-sensor setup comprising camera, Global Navigation Satellite System (GNSS), and Attitude and Heading Reference System (AHRS) demonstrates improved performance in bounding position errors based on uncertainty, while maintaining competitive accuracy and comparable computation to existing methods. Our results suggest that our framework is a promising direction for safe and reliable localization in urban environments.

Mesoscopic simulation and characterization of the morphological evolution in phase separating fluid mixtures

In this article, we use a mesoscopic model discretized with Smoothed Dissipative Particle Dynamics to study the formation of morphology behind a moving precipitation front in a phase separating fluid mixture. In contrast to previous models we include thermodynamically consistent thermal fluctuations of the mass fraction in a binary mixture. The model is validated by phase separation dynamics and probability distribution functions of the thermal fluctuations. Variation of the velocity of the precipitation front and initial composition in 2D and 3D leads to diverse morphology. We characterize these morphology using a time- and space-dependent mapping procedure using the variables of the model of Doi & Ohta to identify different orientations of the evolving porous structure.

The effect of disorder on spin hall conductance in the bulk states of HgTe/CdTe heterostructure

By using the Green's function method, we have investigated spin Hall conductance (SHC) in a four terminal quantum spin Hall insulator. The results show that the intrinsic spin orbit coupling in a HgTe/CdTe hetero-structure interface naturally leads to separate probability distributions for the two spins in coordinate space, which leads to the spin Hall effect in our proposed device. We also find that the SHC of bulk states exhibits an oscillatory behavior as a function of the device width and persists at a broad device width. In addition, we calculate the effects of disorder on the SHC of the bulk states of non-trivial and trivial topology. The results indicate that the spin up and spin down conductances show different degrees of suppression by disorder; thus the SHC could be significantly enhanced by the disorder. This kind of property has a great value to practical applications.

Study of the Dynamics of a Condensing Bubble Using Lattice Boltzmann Method

Mesoscopic lattice Boltzmann method (LBM) is used to discretize the governing equations for a steam bubble inside a tube filled with water. The bubbles are kept at higher temperature compared to its boiling point while the liquid is kept subcooled. Heat transfer is allowed to take place between the two phases by virtue of which the bubble will condense. Three separate probability distribution functions are used in LBM to handle continuity, momentum and energy equations separately. The interface is considered to be diffused within a narrow zone and it has been modeled using convective Cahn-Hillard equation. Combined diffused interface-LBM framework is adapted accordingly to handle complex interface separating two phases having high density ratio. Developed model is validated with respect to established correlations for instantaneous equivalent radius of a spherical condensing bubble. Numerical snapshots of the simulation depict that the bubble volume decreases faster for higher degree of superheat. The degrees of superheat are varied over a wide range to note its effect on bubble shape and size. Effect of initial volume of the bubble on the condensation rate is also studied. It has been observed that for a fixed degree of superheat, the condensation rate is not exactly proportional to its volume. Due to the variation in interfacial configuration for different sized bubbles, condensation rate changes drastically. Influence of gravity on the rate of condensation is also studied using the developed methodology.

Extreme wind climate modeling of some locations in India for the specification of the design wind speed of structures

The wind load on a structure is proportional to the square of the wind speed. Extreme wind climate modeling should be required for specifying the design wind speed of structures. Extreme wind speeds for a storm type should be fitted in a suitable probability distribution, from which the design wind speed can be specified for a particular service life of a structure. The methodology, used in India for the specification of the design wind speed of existing structures, is fairly old and should be updated. Extreme wind climate in India is mainly influenced by thunderstorms and cyclones. Because thunderstorms and cyclones occur due to different geophysical reasons, it is necessary to fit extreme events of these two storm types in separate probability distributions, which can be subsequently combined to determine the overall non-exceedance probability. For a thunderstorm analysis, the wind speed data for three stations were considered, namely Kolkata, Lucknow and New Delhi. However, the statistical analysis greatly suffered due to the low ensemble size in Lucknow. Moreover, cyclones very rarely occur; as a result, cyclone modeling for the Bay of Bengal (total east coast) was initially considered to obtain a sufficient ensemble size. This paper provides a strategy to determine the specification of the design wind speed of structures at a particular location, which is affected by both thunderstorms and cyclones. The motivation of this work is to improve the current design methodology as well as the national code of standards to make engineering structures in India less vulnerable to damage due to strong winds.

Improving hospital bed utilisation through simulation and optimisation: With application to a 40% increase in patient volume in a Norwegian general hospital

PurposeThis paper analyses the problem of allocating beds among hospital wards in order to minimise crowding. MethodWe present a generic discrete event simulation model of patient flow through the wards of a hospital. In the generic model, each ward can have separate probability distributions for arrival times and length of stay, which may be time dependent. Output of the model is a matrix, with statistics on the utilisation of different hypothetical numbers of beds for each ward. This matrix is fed into an allocation algorithm, which distributes the available beds among the wards in an optimal way. We define bed utilisation either in terms of how often it is in use (prevalence), or in terms of how often a newly arriving patient is placed in it (incidence). For these classes of utilisation measures we develop efficient allocation algorithms, which we prove to be optimal. ApplicationThe model was applied to Akershus University Hospital in Norway. In 2011, some of the wards of this hospital experienced a high occupancy rate, while others had a lower utilisation. Our model was applied in order to reallocate the hospital beds among the wards. For each ward, acute arrivals were modelled with Poisson-distributions with time-varying intensity, while elective arrivals were programmed to arrive in specific numbers at specific times. The arrival rates were based on empirical data for 2010, scaled up by an expected increase of 40% due to a restructuring of the hospital districts in Oslo and the greater metropolitan area in 2011. Length of stay was modelled as beta-distributions, using a combination of subject matter experts’ evaluations and empirical data from 2010. The model has been verified and validated. ResultsIntuitively, both prevalence (average number of crowding beds in use) and incidence (number of patients placed in crowding beds) might seem like relevant optimisation criteria. However, our experiments show that prevalence optimisation gives more sensible solutions than incidence optimisation, as the latter tends to sacrifice entire wards where length of stay is long and patient turnover is slow. Prevalence optimisation was therefore used. The main results show that when the bed distribution is optimised, the share of crowding patient nights is reduced from 6.5% to 4.2%. ConclusionThis model provides a powerful tool for optimising hospital bed utilisation, and the application showed an important reduction in crowding bed usage. The generic model is flexible, as the level of detail in the modelling of arrivals and length of stay can vary according to the data available and accuracy required.

An improved differential evolution algorithm with fitness-based adaptation of the control parameters

Differential Evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms of current interest. DE operates through the similar computational steps as employed by a standard Evolutionary Algorithm (EA). However, unlike the traditional EAs, the DE-variants perturb the current-generation population members with the scaled differences of randomly selected and distinct population members. Therefore, no separate probability distribution has to be used, which makes the scheme self-organizing in this respect. Scale Factor ( F) and Crossover Rate ( Cr) are two very important control parameters of DE since the former regulates the step-size taken while mutating a population member in DE and the latter controls the number of search variables inherited by an offspring from its parent during recombination. This article describes a very simple yet very much effective adaptation technique for tuning both F and Cr, on the run, without any user intervention. The adaptation strategy is based on the objective function value of individuals in the DE population. Comparison with the best-known and expensive variants of DE over fourteen well-known numerical benchmarks and one real-life engineering problem reflects the superiority of proposed parameter tuning scheme in terms of accuracy, convergence speed, and robustness.

Differential Evolution: A Survey of the State-of-the-Art

Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms in current use. DE operates through similar computational steps as employed by a standard evolutionary algorithm (EA). However, unlike traditional EAs, the DE-variants perturb the current-generation population members with the scaled differences of randomly selected and distinct population members. Therefore, no separate probability distribution has to be used for generating the offspring. Since its inception in 1995, DE has drawn the attention of many researchers all over the world resulting in a lot of variants of the basic algorithm with improved performance. This paper presents a detailed review of the basic concepts of DE and a survey of its major variants, its application to multiobjective, constrained, large scale, and uncertain optimization problems, and the theoretical studies conducted on DE so far. Also, it provides an overview of the significant engineering applications that have benefited from the powerful nature of DE.

Influence of droplet properties on the formation of microemulsion-ABA-triblock copolymer networks

Structural equilibrium properties of transient networks formed by microemulsion droplets and ABA triblock copolymers in solution have been studied by Monte Carlo simulation. The droplets were represented by soft spheres and the polymers by junctions connected by harmonic bonds with an angular potential regulating the intrinsic chain stiffness. The interaction parameters were selected such that the end A-blocks were localized inside the droplets and the middle B-block in the continuous phase. The influence of (i) the droplet volume fraction, (ii) the droplet radius, and (iii) the contour length of the middle B-block on the formation and the structure of the microemulsion-polymer network at three-fold excess of the polymers were investigated by using polymer end-to-end separation probability distribution functions, droplet radial distribution functions, and network connectivity indicators. A universal behavior of the properties investigated was found when examining the results versus the length ratio of the polymer end-to-end separation and the surface-to-surface separation between neighboring droplets for a hypothetical homogeneous droplet distribution. At a length ratio of 0.5, few polymer bridges between droplets were established and only clusters with a small number of droplets were found. However at a length ratio of ca. 1.5 a connected network was formed and most of the polymers formed bridges between two droplets.

Probabilistic analysis of preload in the abutment screw of a dental implant complex

Screw loosening is a problem for a percentage of implants. A probabilistic analysis to determine the cumulative probability distribution of the preload, the probability of obtaining an optimal preload, and the probabilistic sensitivities identifying important variables is lacking. The purpose of this study was to examine the inherent variability of material properties, surface interactions, and applied torque in an implant system to determine the probability of obtaining desired preload values and to identify the significant variables that affect the preload. Using software programs, an abutment screw was subjected to a tightening torque and the preload was determined from finite element (FE) analysis. The FE model was integrated with probabilistic analysis software. Two probabilistic analysis methods (advanced mean value and Monte Carlo sampling) were applied to determine the cumulative distribution function (CDF) of preload. The coefficient of friction, elastic moduli, Poisson's ratios, and applied torque were modeled as random variables and defined by probability distributions. Separate probability distributions were determined for the coefficient of friction in well-lubricated and dry environments. The probabilistic analyses were performed and the cumulative distribution of preload was determined for each environment. A distinct difference was seen between the preload probability distributions generated in a dry environment (normal distribution, mean (SD): 347 (61.9) N) compared to a well-lubricated environment (normal distribution, mean (SD): 616 (92.2) N). The probability of obtaining a preload value within the target range was approximately 54% for the well-lubricated environment and only 0.02% for the dry environment. The preload is predominately affected by the applied torque and coefficient of friction between the screw threads and implant bore at lower and middle values of the preload CDF, and by the applied torque and the elastic modulus of the abutment screw at high values of the preload CDF. Lubrication at the threaded surfaces between the abutment screw and implant bore affects the preload developed in the implant complex. For the well-lubricated surfaces, only approximately 50% of implants will have preload values within the generally accepted range. This probability can be improved by applying a higher torque than normally recommended or a more closely controlled torque than typically achieved. It is also suggested that materials with higher elastic moduli be used in the manufacture of the abutment screw to achieve a higher preload.

Structure of Microemulsion−ABA Triblock Copolymer Networks

Structural equilibrium properties of transient networks formed by microemulsion droplets and ABA triblock copolymers in solution have been studied by Monte Carlo simulation. The droplets were represented by soft spheres, and the polymers were represented by junctions connected by harmonic bonds with an angular potential regulating the intrinsic chain stiffness. The interaction parameters were selected such that the end A-blocks were localized inside the droplets and the middle B-block in the continuous phase. The influence of (i) the polymer concentration, (ii) the polymer stiffness, and (iii) the contour length of the middle B-block on the formation and the structure of the microemulsion-polymer network were investigated using polymer end-to-end separation probability distribution functions, droplet radial distribution functions, droplet-droplet nearest-neighbor probability distribution functions, and network connectivity indicators. An increase of the polymer-droplet number ratio had a strong impact on the network formation. Under typical conditions and at an intermediate polymer-droplet number ratio, (i) the fraction of polymers forming bridges between droplets increased from essentially zero to unity and (ii) the fraction of polymers that were forming loops decreased as the ratio of the polymer end-to-end separation and the surface-to-surface separation between neighboring droplets for a hypothetical homogeneous droplet distribution was increased from 0.5 to 2. For long and flexible polymers, a mesoscopic segregation triggered by a depletion attraction between droplets appeared, and, furthermore, for sufficiently stiff chains, only bridge conformations occurred. The percolation probability could be represented as a function of the average droplet cluster size only, across all systems.

A cirrus cloud scheme for general circulation models

AbstractA statistical cloud scheme for non‐convective cirrus formed by homogeneous freezing of supercooled aerosols is presented. As large‐scale cirrus clouds exhibit metastable thermodynamic states and have long lifetimes, a fully prognostic approach is developed. The scheme is based on separate probability distribution functions of total water representing clear‐sky and in‐cloud conditions. These distributions are based on in situ observations and have few degrees of freedom so that they can be used in forecast and climate models. Predictive equations are derived for horizontal cloud fraction and mixing ratios of grid‐mean water vapour and ice water, in‐cloud water vapour and ice crystal number. The scheme allows sub‐ and supersaturations with respect to ice to occur in cloud‐free air and inside cirrus, and produces nucleated ice crystal concentrations and sizes in good agreement with observations, an important prerequisite for an improved treatment of cirrus cloud radiative properties. Implementation in general circulation models, open issues and future research avenues are discussed. Copyright © 2008 Royal Meteorological Society

Bayesian data fusion in a spatial prediction context: a general formulation

In spite of the exponential growth in the amount of data that one may expect to provide greater modeling and predictions opportunities, the number and diversity of sources over which this information is fragmented is growing at an even faster rate. As a consequence, there is real need for methods that aim at reconciling them inside an epistemically sound theoretical framework. In a statistical spatial prediction framework, classical methods are based on a multivariate approach of the problem, at the price of strong modeling hypotheses. Though new avenues have been recently opened by focusing on the integration of uncertain data sources, to the best of our knowledges there have been no systematic attemps to explicitly account for information redundancy through a data fusion procedure. Starting from the simple concept of measurement errors, this paper proposes an approach for integrating multiple information processing as a part of the prediction process itself through a Bayesian approach. A general formulation is first proposed for deriving the prediction distribution of a continuous variable of interest at unsampled locations using on more or less uncertain (soft) information at neighboring locations. The case of multiple information is then considered, with a Bayesian solution to the problem of fusing multiple information that are provided as separate conditional probability distributions. Well-known methods and results are derived as limit cases. The convenient hypothesis of conditional independence is discussed by the light of information theory and maximum entropy principle, and a methodology is suggested for the optimal selection of the most informative subset of information, if needed. Based on a synthetic case study, an application of the methodology is presented and discussed.

Deficit of Wide Binaries in the η Chamaeleontis Young Cluster

We have carried out a sensitive high-resolution imaging survey of stars in the young (6-8 Myr), nearby (97 pc) compact cluster around η Chamaeleontis to search for stellar and substellar companions. Our data were obtained using the NACO adaptive optics system on the ESO Very Large Telescope (VLT). Given its youth and proximity, any substellar companions are expected to be luminous, especially in the near-infrared, and thus easier to detect next to their parent stars. Here, we present VLT NACO adaptive optics imaging with companion detection limits for 17 η Cha cluster members, and follow-up VLT ISAAC near-infrared spectroscopy for companion candidates. The widest binary detected is ~02, corresponding to the projected separation 20 AU, despite our survey being sensitive down to substellar companions outside 03, and planetary-mass objects outside 05. This implies that the stellar companion probability outside 03 and the brown dwarf companion probability outside 05 are less than 0.16 with 95% confidence. We compare the wide binary frequency of η Cha to that of the similarly aged TW Hydrae association and estimate the statistical likelihood that the wide binary probability is equal in both groups to be less than 2 × 10-4. Even though the η Cha cluster is relatively dense, stellar encounters in its present configuration cannot account for the relative deficit of wide binaries. We thus conclude that the difference in wide binary probability in these two groups provides strong evidence for multiplicity properties being dependent on environment. In two appendices we derive the projected separation probability distribution for binaries, used to constrain physical separations from observed projected separations, and summarize statistical tools useful for multiplicity studies.

Multi-modal sensor fusion using a probabilistic aggregation scheme for people detection and tracking

Efficient and robust techniques for people detection and tracking are basic prerequisites when dealing with Human–Robot Interaction (HRI) in real-world scenarios. In this paper, we introduce a new approach for the integration of several sensor modalities and present a multi-modal, probability-based people detection and tracking system and its application using the different sensory systems of our mobile interaction robot Horos. These include a laser range-finder, a sonar system, and a fisheye-based omni-directional camera. For each of these sensory systems, separate and specific Gaussian probability distributions are generated to model the belief in observing one or several persons. These probability distributions are further merged into a robot-centered map by means of a flexible probabilistic aggregation scheme based on Covariance Intersection (CI). The main advantages of this approach are the simple extensibility by the integration of further sensory channels, even with different update frequencies, and the usability in real-world HRI tasks. Finally, the first promising experimental results achieved for people detection and tracking in a real-world environment (our institute building) are presented.

10,000 Standard Solar Models: A Monte Carlo Simulation

We have evolved 10,000 solar models using 21 input parameters that are randomly drawn for each model from separate probability distributions for every parameter. We use the results of these models to determine the theoretical uncertainties in the predicted surface helium abundance, the profile of the sound speed versus radius, the profile of the density versus radius, the depth of the solar convective zone, the eight principal solar neutrino fluxes, and the fractions of nuclear reactions that occur in the CNO cycle or in the three branches of the p-p chains. We also determine the correlation coefficients of the neutrino fluxes for use in analysis of solar neutrino oscillations. Our calculations include the most accurate available input parameters, including radiative opacity, equation of state, and nuclear cross sections. We incorporate both the recently determined heavy element abundances recommended by Asplund et al. and the older (higher) heavy element abundances recommended by Grevesse & Sauval. We present best estimates of many characteristics of the standard solar model for both sets of recommended heavy element compositions.

RADIATION EFFECTIVENESS FACTORS FOR USE IN CALCULATING PROBABILITY OF CAUSATION OF RADIOGENIC CANCERS

This paper presents so-called radiation effectiveness factors that are intended to represent the biological effectiveness of different radiation types, relative to high-energy Co gamma rays, for the purpose of estimating cancer risks and probability of causation of radiogenic cancers in identified individuals. Radiation effectiveness factors are expressed as subjective probability distributions to represent uncertainty that arises from uncertainties in estimates of relative biological effectiveness obtained from radiobiological studies of stochastic endpoints, limited data on biological effectiveness obtained from human epidemiological studies, and other judgments involved in evaluating the applicability of available information to induction of cancers in humans. Primarily on the basis of reviews and evaluations of available data by experts, probability distributions of radiation effectiveness factors are developed for the following radiation types: neutrons of energy less than 10 keV, 10-100 keV, 0.1-2 MeV (including fission neutrons), 2-20 MeV, and greater than 20 MeV; alpha particles of any energy emitted by radionuclides; photons of energy 30-250 keV and less than 30 keV; and electrons of energy less than 15 keV. Photons of energy greater than 250 keV and electrons of energy greater than 15 keV are assumed to have the same biological effectiveness as reference Co gamma rays and are assigned a radiation effectiveness factor of unity, without uncertainty. For neutrons and alpha particles, separate probability distributions of radiation effectiveness factors are developed for solid tumors and leukemias, and small corrections to represent an inverse dose-rate effect are applied to those distributions in cases of chronic exposure. A radiation effectiveness factor different from unity for 15-60 keV electrons is discussed but is not adopted due to a lack of relevant radiobiological data. Radiation effectiveness factors presented in this paper are incorporated in the Interactive RadioEpidemiological Program and were developed for use by The National Institute for Occupational Safety and Health and U.S. Department of Labor in evaluating claims for compensation for radiogenic cancers by workers at U.S. Department of Energy facilities.

Frame-correlated hidden Markov model based on extended logarithmic pool

We present a novel method to incorporate temporal correlations into a speech recognition system based on conventional hidden Markov models (HMMs). The temporal correlations are considered to be useful for recognition because of the fact that the speech features of the present frame are highly informative about the feature characteristics of neighboring frames. In this paper, by treating these correlations in the form of conditional probability distributions (PDs), we propose a new technique for incorporating frame correlations. With the proposed method called the extended logarithmic pool (ELP), we approximate a joint conditional PD by separate conditional PDs associated with respective conditions. We provide a constrained optimization algorithm with which we can find the optimal value for the pooling weights. For practical purposes, we also suggest methods to get robust PD estimates for characterizing frame correlation. In addition, to improve model discriminability, a technique to combine two kinds of PDs through the exponents is introduced. The results in the experiments of speaker-independent continuous speech recognition with the proposed approaches show error reduction up to 20.5% as compared to that with the conventional bigram-constrained (BC) HMM method.

The separation of particle pairs in the eddy-damped quasinormal Markovian approximation

The implications of the eddy-damped quasinormal Markovian (EDQNM) approximation for the separation of particle pairs in (three-dimensional) inertial subrange turbulence are explored. In particular the EDQNM equations are solved for the particle separation probability distribution, without making the usual approximation of replacing the damping time scales by their large time asymptotic form. A number of properties of the separation probability distribution that are of significance for the prediction of concentration fluctuations are calculated. The values show quite large departures from the values obtained with the large time form of the damping time scales.

Mixture Probabilistic Context-Free Grammar

This paper proposes an improved probabilistic CFG (Context-Free Grammar), called the mixture probabilistic CFG, based on an idea of cluster-based language modeling. This model assumes that the language model parameters have different probability distributions in different topics or domains. In order to performs topic-or domaindependent language modeling, we first divide the training corpus into a number of subcorpora according to their topics or domains, and then estimate separate probability distribution from each subcorpus. Therefore, a mixture probabilistic CFG has several different probability distributions for CFG productuions. The language model probability of a sentence is calculated as the mixture of these probability distributions. The mixture probabilistic CFG enables us to make a context-or topic-dependent language model, and thus accurate language modeling would be possible. The proposed model was evaluated by calculating test-set perplexity using the ADD (ATR Dialogue Database) corpus and a Japanese intra-phrase grammar. The mixture probabilistic CFG had a test-set perplexity of 2.47/phone, while simple probabilistic CFG had a test-set perplexity of 2.77/phone. We also conducted speech recognition experiments using three language models, including pure CFG (without probabilities), simple probabilistic CFG, and the mixture probabilistic CFG. In our experiments, the mixture probabilistic CFG attained the best performance. The proposed model was also evaluated using sentence-level clustering. This evaluation used the dialogue corpus in which each utterance is annotated with an utterance type called IFT (Illocutionary Force Type). Using these IFTs, we divided the corpus into 9 clusters, and then estimated production probabilities from these clusters. Without IFT clustering, the perplexity was 2.18 per phone, but using IFT clustering, the perplexity was reduced to 1.82 per phone.