Uniform Probability Density Research Articles

Inference of the cold dark matter substructure mass function at z = 0.2 using strong gravitational lenses

We present the results of a search for galaxy substructures in a sample of 11 gravitational lens galaxies from the Sloan Lens ACS Survey. We find no significant detection of mass clumps, except for a luminous satellite in the system SDSS J0956+5110. We use these non-detections, in combination with a previous detection in the system SDSS J0946+1006, to derive constraints on the substructure mass function in massive early-type host galaxies with an average redshift z ~ 0.2 and an average velocity dispersion of 270 km/s. We perform a Bayesian inference on the substructure mass function, within a median region of about 32 kpc squared around the Einstein radius (~4.2 kpc). We infer a mean projected substructure mass fraction $f = 0.0076^{+0.0208}_{-0.0052}$ at the 68 percent confidence level and a substructure mass function slope $\alpha$ < 2.93 at the 95 percent confidence level for a uniform prior probability density on alpha. For a Gaussian prior based on Cold Dark Matter (CDM) simulations, we infer $f = 0 .0064^{+0.0080}_{-0.0042}$ and a slope of $\alpha$ = 1.90$^{+0.098}_{-0.098}$ at the 68 percent confidence level. Since only one substructure was detected in the full sample, we have little information on the mass function slope, which is therefore poorly constrained (i.e. the Bayes factor shows no positive preference for any of the two models).The inferred fraction is consistent with the expectations from CDM simulations and with inference from flux ratio anomalies at the 68 percent confidence level.

Growth of multiparticle aggregates in sedimenting suspensions

AbstractThe process of multiparticle aggregation in a dilute sedimenting suspension is rigorously simulated, with precise hydrodynamical interactions. The primary particles are monodisperse non-Brownian spheres at zero Reynolds number, with short-range molecular attractions. The rigid aggregates grow, as they settle downwards, by sequential particle addition – a valid assumption for dilute suspensions during the initial stages. The growth starts from doublet–particle interaction, but the indeterminate initial doublet concentration does not affect the results for cluster geometry and settling velocity. A new particle is generated far below a cluster with uniform probability density, and many trial particle–cluster relative trajectories are computed with high accuracy until a collision is found. The new cluster is then assumed to be rigid and allowed to reach a steady sedimentation regime (which is a spiral motion around the axis of steady rotation, ASR) before another particle is added, and so on. The ASR is typically far away from the cluster centre of mass. The Stokes flow solution algorithm for particle–cluster interaction works very efficiently with high-order multipoles (to order 100) and is extended to arbitrarily small particle–cluster separations by a geometry perturbation adapted from the conductivity simulations of Zinchenko (Phil. Trans. R. Soc. Lond. A, 1998, vol. 356, pp. 2953–2998). Clusters are generated to $N=100$ spheres, with extensive averaging over many growth realizations. The fractal scaling $\sim N^{0.48}$ for the cluster settling speed is quickly attained once $N\geq 25$, and the exponent 0.48 is practically independent of the strength of molecular forces. The cluster fractal dimension is predicted to be $d_f=1.91\pm 0.02$ (in contrast to the existing views that sequential addition can only produce high-$d_f$ clusters). Several average characteristics of the cluster size are also computed. The theoretical settling speed has no adjustable parameters and agrees reasonably well with prior experiments for a moderately polydisperse system in a broad range of cluster sizes.

A production inventory model with flexible manufacturing, random machine breakdown and stochastic repair time

Article history: Received January 26 2014 Received in Revised Format July 5 2014 Accepted July 5 2014 Available online July 12 2014 This paper derives a production inventory model over infinite planning horizon with flexible but unreliable manufacturing process and the stochastic repair time. Demand is stock dependent and during the period of sale it depends on reduction on selling price. Production rate is a function of demand and reliability of the production equipment is assumed to be exponentially decreasing function of time. Repair time is estimated using uniform probability density function. The objective of the study is to determine the optimal policy for production system, which maximizes the total profit subject to some constraints under consideration. The results are discussed with a numerical example to illustrate the theory. © 2014 Growing Science Ltd. All rights reserved

A Hybrid Stochastic-Deterministic Approach For Active Fault Diagnosis Using Scenario Optimization

Active fault diagnosis can improve the diagnosability of potential faults by injecting a suitable input into the system. This input can be designed using either a stochastic or a deterministic framework. The stochastic approach aims to maximize the probability of a correct diagnosis at a certain time, whereas the deterministic approach aims to guarantee diagnosis within a certain time interval. Recently, a hybrid stochastic-deterministic approach has been developed in which all uncertainties are described by uniform probability density functions (PDFs) with finite support on zonotopes. This method is able to provide a guaranteed diagnosis at a given time N, while approximately maximizing the probability of diagnosis at some earlier time M < N. In this article, the hybrid stochastic-deterministic method is extended to arbitrary PDFs using a sampling approach based on scenario optimization.

Stochastic frontier models with threshold efficiency

This paper proposes a tail-truncated stochastic frontier model that allows for the truncation of technical efficiency from below. The truncation bound implies the inefficiency threshold for survival. Specifically, this paper assumes a uniform distribution of technical inefficiency and derives the likelihood function. Even though this distributional assumption imposes a strong restriction that technical inefficiency has a uniform probability density over [0, θ], where θ is the threshold parameter, this model has two advantages: (1) the reduction in the number of parameters compared with more complicated tail-truncated models allows better performance in numerical optimization; and (2) it is useful for empirical studies of the distribution of efficiency or productivity, particularly the truncation of the distribution. The Monte Carlo simulation results support the argument that this model approximates the distribution of inefficiency precisely, as the data-generating process not only follows the uniform distribution but also the truncated half-normal distribution if the inefficiency threshold is small.

Conformists and Contrarians in a Kuramoto Model with Uniformly Distributed Natural Frequencies

A generalization of the Kuramoto model in which oscillators are coupled to the mean field with random signs is investigated in this work. We focus on a situation in which the natural frequencies of oscillators follow a uniform probability density. By numerically simulating the model, we find that the model supports a modulated travelling wave state except for already reported π state and travelling wave state in the one with natural frequencies following Lorenztian probability density or a delta function. The dependence of the observed dynamics on the parameters of the model is explored and we find that the onset of synchronization in the model displays a non-monotonic dependence on both positive and negative coupling strength.

Improving tool wear and surface covering in polishing via toolpath optimization

Polishing operations are commonly carried out manually, thus inducing variability on the surface quality. The aim of this paper is to automate the polishing of free-form surfaces in order to obtain high quality surfaces. Tool wear and toolpath surface covering have a great impact on surface properties. The current work proposes therefore a toolpath which optimizes both tool wear and surface covering. This toolpath is composed of an optimized elementary pattern repeated along a 5-axis carrier trajectory. Usually, trochoid patterns are used. Non uniform wear of the tool and uneven probability density function of the surface covering are the main inconvenients of such pattern. So, this paper proposes two optimized patterns: Spade and Triangular. Both of them lead to uniform tool wear. Our paper also demonstrates that the second solution provides a uniform probability density function. All presented computations are validated experimentally.

Comment on “Quantum phase for an arbitrary system with finite-dimensional Hilbert space”

A construction of covariant quantum phase observables, for Hamiltonians with a finite number of energy eigenvalues, has been recently given by D. Arsenovic et al. [Phys. Rev. A 85, 044103 (2012)]. For Hamiltonians generating periodic evolution, we show that this construction is just a simple rescaling of the known canonical 'time' or 'age' observable, with the period T rescaled to 2\pi. Further, for Hamiltonians generating quasiperiodic evolution, we note that the construction leads to a phase observable having several undesirable features, including (i) having a trivially uniform probability density for any state of the system, (ii) not reducing to the periodic case in an appropriate limit, and (iii) not having any clear generalisation to an infinite energy spectrum. In contrast, we note that a covariant time observable has been previously defined for such Hamiltonians, which avoids these features. We also show how this 'quasiperiodic' time observable can be represented as the well-defined limit of a sequence of periodic time observables.

Pulse signal detection in cognitive UWB system

According to the problem of cognitive ultra wide-band (UWB) spectrum sensing, a novel UWB pulse signal detection algorithm based on cumulative sum (CUSUM) test is proposed in this paper. Based on the analysis of the existing spectrum sensing schemes for cognitive UWB system, some obvious facts are obtained that it is difficult to detect UWB pulse signal with conventional spectrum sensing schemes, due to its low average signal to noise ratio (SNR), large bandwidth, and low duty ratio. In this paper the detection algorithm of signal distribution change, which is application of CUSUM test, is considered to be applied to cognitive UWB spectrum sensing. But CUSUM test request that the pre-change and the post-change distributions are i.i.d, which cannot be satisfied in the detection process of UWB pulse signal. Since there are two time domain descriptions on UWB pulse signal, namely one contains only noise and the other one contains pulse signal plus noise, the existing detection algorithm of signal distribution change cannot be directly applied to detect UWB pulse signal. Hence the uniform probability density function expression of UWB pulse signal is first deduced, then CUSUM test is applied to cognitive UWB spectrum sensing. The proposed algorithm is a time sequential detection algorithm, with low complexity and minimal detection delay, which is suitable to detect the low duty ratio signal. Its performance is evaluated through theoretical analysis and numerical simulations. It is shown that this algorithm outperforms the conventional energy detection algorithm and conquers SNR wall phenomenon.

Properties of design-based estimation under stratified spatial sampling with application to canopy coverage estimation

The estimation of the total of an attribute defined over a continuous planar domain is required in many applied settings, such as the estimation of canopy coverage in the Monterano Nature Reserve in Italy. If the design-based approach is considered, the scheme for the placement of the sample sites over the domain is fundamental in order to implement the survey. In real situations, a commonly adopted scheme is based on partitioning the domain into suitable strata, in such a way that a single sample site is uniformly placed (i.e., selected with uniform probability density) in each stratum and sample sites are independently located. Under mild conditions on the function representing the target attribute, it is shown that this scheme gives rise to an unbiased spatial total estimator which is “superefficient” with respect to the estimator based on the uniform placement of independent sample sites over the domain. In addition, the large-sample normality of the estimator is proven and variance estimation issues are discussed.

Assessment methodology for confidence in safety margin for large break loss of coolant accident sequences

Deterministic Safety Analysis and Probabilistic Safety Assessment (PSA) analyses are used to assess the Nuclear Power Plant (NPP) safety. The conventional deterministic analysis is conservative. The best estimate plus uncertainty analysis (BEPU) is increasingly being used for deterministic calculation in NPPs. The PSA methodology integrates information about the postulated accident, plant design, operating practices, component reliability and human behavior. The deterministic and probabilistic methodologies are combined by analyzing the accident sequences within design basis in the event trees of a postulated initiating event (PIE) by BEPU. The peak clad temperature (PCT) distribution provides an insight into the confidence in safety margin for an initiating event. The paper deals with calculating the safety margin with 95% confidence and 95% probability in large break loss of coolant accident (LBLOCA). In the present study, five uncertain input parameters were selected. Uniform probability density function was assigned to the uncertain parameters in the selected range and these uncertainties are propagated using Latin Hypercube Sampling (LHS) technique. The sampled data for five parameters was randomly mixed by LHS to obtain 25 input sets. An event tree for the initiating event, LBLOCA inside containment, has been used from a VVER study on Level-1 PSA and four non-core damage (NCD) accident sequences were identified for this study. In the accident analysis the success and failure of safety systems reflected in event tree was appropriately modeled in the system thermal hydraulics code runs. The PCT was obtained for each of 25 code runs for each accident sequence. A Kolmogorov – Smirnov goodness-of-fit test carried out for PCTs indicated that they followed normal distribution for each of the accident sequences. The probability distribution of safety margin (difference between acceptable value and PCT) in each accident sequence was also obtained. The values of safety margin for the 95% confidence and 95% probability are estimated. The robustness of the system can be judged based on this. This paper describes the methodology. LBLOCA in a VVER type reactor is considered as an example.

Size distribution and waiting times for the avalanches of the Cell Network Model of Fracture

The Cell Network Model is a fracture model recently introduced that resembles the microscopical structure and drying process of the parenchymatous tissue of the Bamboo Guadua angustifolia. The model exhibits a power-law distribution of avalanche sizes, with exponent −3.0 when the breaking thresholds are randomly distributed with uniform probability density. Hereby we show that the same exponent also holds when the breaking thresholds obey a broad set of Weibull distributions, and that the humidity decrements between successive avalanches (the equivalent to waiting times for this model) follow in all cases an exponential distribution. Moreover, the fraction of remaining junctures shows an exponential decay in time. In addition, introducing partial breakings and cumulative damages induces a crossover behavior between two power-laws in the histogram of avalanche sizes. This results support the idea that the Cell Network Model may be in the same universality class as the Random Fuse Model.

Reliability simulation for assemblies of airplane functional systems

The possibility of using an exponential distribution in calculations of assembly reliability is considered. It is shown that the failure probability determined by an exponential distribution estimates the probability of one or more failures. The justification of using a distribution with a uniform probability density for reliability calculations is proved.

Pavement Rehabilitation Project Ranking Approach Using Probabilistic Long-Term Performance Indicators

A probabilistic performance-based approach for generating a priority ranking of pavement rehabilitation project candidates is presented. The deployed probabilistic approach uses a discrete-time Markovian model to predict pavement conditions at the network level. The expected future distress rating associated with a particular pavement project is determined as the mean of a compound uniform probability density function derived from the corresponding future state probabilities. The expected future distress ratings for a particular pavement project are then used to construct the corresponding performance curve. The generated performance curves form the basis for developing an effective mechanism for prioritizing potential rehabilitation projects. A priority ranking system is presented with two alternatives. The first priority ranking alternative requires a fixed analysis period wherein project candidates are evaluated by using three different long-term performance indicators derived from the corresponding performance curves. The deployed performance indicators include the area under the performance curve, the average distress rating, and the terminal distress rating. The second priority ranking alternative requires a fixed terminal distress rating for the pavement network under consideration. The time required for each project to reach the terminal distress rating is determined as the rehabilitation scheduling time, which is used to establish project priority ranking. Pavement rehabilitation project candidates are then scheduled according to their priority rankings and available budget. The developed probabilistic approach is demonstrated by considering a project sample from the two-lane highway system in Ohio.

Bayesian Threshold Estimation

Bayesian estimation of a threshold time (hereafter simply threshold) for the receipt of impulse signals is accomplished given the following: 1) data, consisting of the number of impulses received in a time interval from zero to one and the time of the largest time impulse; 2) a model, consisting of a uniform probability density of impulse time from zero to the threshold, and constituting the probability density from which the data impulses are drawn randomly and independently; and 3) a prior probability density of threshold which is linear from a positive initial threshold to one and that is zero otherwise, or which is uniform from zero to one. The posterior probability density of threshold is found with the number of impulses, the time of the largest time impulse, and the initial threshold as parameters, and with the first two parameters fixed, the initial threshold is found that maximizes the entropy of the posterior probability density. It is shown that for some values of initial threshold, including the value that maximizes entropy, the following three estimates of threshold from the posterior probability density are all different: the maximum (maximum a posteriori or MAP estimate), the mean (mean squared error or MMSE estimate), and the maximum for a uniform prior probability density (maximum likelihood or ML estimate). This easily understood and practical Bayesian threshold estimation problem has two aspects of pedagogical interest: 1) the problem is unusual in that the MAP, MMSE, and ML estimates are generally different-in typical problems with Gaussian or uniform models and prior probability densities, at least two of these three estimates are equal; 2) the problem constitutes a clear illustration of how an unknown parameter in the prior probability density (here, initial threshold) may be specified so as to achieve a desired property for the posterior probability density (here, maximum entropy).

Three-dimensional speckle-noise reduction by using coherent integral imaging

We present a 3D imaging method to reduce speckle noise that exists in coherent imaging systems. This approach is based on integral imaging (II). The elemental images set having speckle-noise patterns of a 3D object is obtained by II technique under coherent illumination. The computational geometrical ray-propagation algorithm is applied to the elemental images in order to reconstruct the original 3D object. A uniform probability-density function is assumed for modeling the phase distribution of the speckle patterns. The statistical point estimator is used for 3D speckle removal. Speckle index is calculated to compare the computational reconstruction using the proposed method with that of conventional coherent image degraded by speckle patterns for 3D object reconstruction and by object recognition. Experimental results are presented. The speckle index, mean square error, and signal-to-noise ratio are used as performance metrics and are shown to have been significantly improved by the proposed method to reduce speckle noise in the 3D object reconstruction. 3D reconstruction experiments of objects with reduced speckle noise are presented. To the best of our knowledge, this is the first report on 3D speckle removal using II and statistical estimation algorithms.

An Algorithm for Determining Mobile Station Location Based on Space Segmentation

An algorithm to determine mobile station location using segmentation of space, taking the set of nearest base stations as the segmentation criterion, is proposed. According to the set of nearest base stations observed by the mobile station, the algorithm selects a precalculated segment where the mobile station is located. By assuming uniform probability density for the mobile station location within the segment, the expectation for the mobile station coordinates is computed. Application of the algorithm is illustrated by simulation of a real GSM network. The algorithm is characterized by low computational cost and traffic burden.

Automatic Facial Skin Segmentation Based on EM Algorithm under Varying Illumination

Facial skin detection is an important step in facial surgical planning like as many other applications. There are many problems in facial skin detection. One of them is that the image features can be severely corrupted due to illumination, noise, and occlusion, where, shadows can cause numerous strong edges. Hence, in this paper, we present an automatic Expectation-Maximization (EM) algorithm for facial skin color segmentation that uses knowledge of chromatic space and varying illumination conditions to correct and segment frontal and lateral facial color images, simultaneously. The proposed EM algorithm leads to a method that allows for more robust and accurate segmentation of facial images. The initialization of the model parameters is very important in convergence of algorithm. For this purpose, we use a method for robust parameter estimation of Gaussian mixture components. Also, we use an additional class, which includes all pixels not modeled explicitly by Gaussian with small variance, by a uniform probability density, and amending the EM algorithm appropriately, in order to obtain significantly better results. Experimental results on facial color images show that accurate estimates of the Gaussian mixture parameters are computed. Also, other results on images presenting a wide range of variations in lighting conditions, demonstrate the efficiency of the proposed color skin segmentation algorithm compared to conventional EM algorithm.

Robust Kalman filtering for uncertain discrete-time systems with probabilistic parameters bounded within a polytope

We consider the problem of finite horizon discrete-time Kalman filtering for systems with parametric uncertainties. Specifically, we consider unknown but deterministic uncertainties where the uncertain parameters are assumed to lie in a convex polyhedron with uniform probability density. The condition and a procedure for the construction of a suboptimal filter that minimizes an expected error covariance over-bound are derived.

How and how not to make predictions with temporal Copernicanism

Gott (Nature 363:315–319, 1993) considers the problem of obtaining a probabilistic prediction for the duration of a process, given the observation that the process is currently underway and began a time t ago. He uses a temporal Copernican principle according to which the observation time can be treated as a random variable with uniform probability density. A simple rule follows: with a 95% probability, $$39t > T - t > \frac{1}{39}t$$ where T is the unknown total duration of the process and hence T − t is its unknown future duration. Gott claims that this rule is of very general application. In response, I argue that we are usually only entitled to assume approximate temporal Copernicanism. That amounts to taking a probability distribution for the observation time that is, while not necessarily uniform, at least a smooth function. I work from that assumption to carry out Bayesian updating of the probability for process duration, as expressed by my Eq. 11. I find that for a wide range of conditions, processes that have already been underway a long time are likely to last a long time into the future—a qualitative conclusion that is intuitively plausible. Otherwise, however, too much depends on the specifics of various circumstances to permit any simple general rule. In particular, the simple rule proposed by Gott holds only under a very restricted set of conditions.