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Recently, there has been a lot of success in using the deterministic approach to provide approximate characterization of Gaussian network capacity. In this paper, we take a deterministic view and revisit the problem of wiretap channel with side information. A precise characterization of the secrecy capacity is obtained for a linear deterministic model, which naturally suggests a coding scheme which we show to achieve the secrecy capacity of the degraded Gaussian model (dubbed as “secret writing on dirty paper”) to within half a bit. [ABSTRACT FROM PUBLISHER]

This article presents a discussion on a study by Bradley Jones and Rachel T. Johnson on the use of Gaussian Process model in computer simulation research. The authors believe that the uncertainty intervals on unsampled points generated by using a plug-in approach from maximum likelihood estimates may be too short. Their own experiences confirm that computer models are widely used in many areas of science and engineering, and the need to understand the performance of such models is critical.

This article presents a discussion on a study by Bradley Jones and Rachel T. Johnson on the use of Gaussian Process model in computer simulation research. The author believes that the researchers offer a clear and helpful introduction to ideas and methods used in the design and analysis of computer experiments. He provides some additional points of importance regarding analysis, design and computing.

This article presents a discussion on a study by Bradley Jones and Rachel T. Johnson on the use of Gaussian Process model in computer simulation research. The author believes that the Gaussian process model often performs adequately apparent nonstationarity. He explores the topic of model calibration, the relationship between the design and the model used to fit the data, and design augmentation.

The proportion of spot trading and short-term contracts has gradually increased in the rapidly growing LNG market, leading to more uncertainties in LNG demand and prices that significantly challenge LNG shipping decisions. In this paper, a mathematical model is developed to minimize transportation costs from multiple exporting countries to multiple importing countries under demand and price uncertainty, both of which are results of LNG market liberalization. A Gaussian process metamodel based simulation optimization method is proposed to solve the fleet planning problem, accounting for various uncertainties. A case study is given to illustrate the effects of uncertainties on the optimal solutions. The results demonstrate that shipping companies may purchase fewer ships and charter more ships to hedge against the risk of uncertainty. LNG market liberalization can significantly reduce its transportation costs and carbon emissions. The results suggest the need for further LNG market liberalization and measures to mitigate uncertainties for shipping companies, such as removing destination clauses. • More price and demand uncertainties stemming from LNG market liberalization challenge fleet planning decisions. • Consider a fleet size and composition optimization problem with a mathematical model. • A Gaussian process based simulation optimization method solves the fleet planning problem. • Shipping companies may purchase fewer ships and charter more ships to hedge against the risk of uncertainty. • LNG market liberalization can significantly reduce transportation costs and carbon emissions. [ABSTRACT FROM AUTHOR]

For general memoryless systems, the existing information-theoretic solutions have a "single-letter" form. This reflects the fact that optimum performance can be approached by a random code (or a random binning scheme), generated using independent and identically distributed copies of some scalar distribution. Is that the form of the solution of any (information-theoretic) problem? In fact, some counter examples are known. The most famous one is the "two help one" problem: Körner and Marton showed that if we want to decode the modulo-two sum of two correlated binary sources from their independent encodings, then linear coding is better than random coding. In this paper we provide another counter example, the "doubly-dirty" multiple-access channel (MAC). Like the Körner-Marton problem, this is a multiterminal scenario where side information is distributed among several terminals; each transmitter knows part of the channel interference while the receiver only observes the channel output. We give an explicit solution for the capacity region of the binary doubly-dirty MAC, demonstrate how this region can be approached using a linear coding scheme, and prove that the "best known single-letter region" is strictly contained in it. We also state a conjecture regarding the capacity loss of single-letter characterization in the Gaussian case. [ABSTRACT FROM AUTHOR]

A relay channel with orthogonal components in which the destination is affected by an interference signal that is non-causally available only at the source is studied. The interference signal has structure in that it is produced by another transmitter communicating with its own destination. Moreover, the interferer is not willing to adjust its communication strategy to minimize the interference. Knowledge of the interferer's signal may be acquired by the source, for instance, by exploiting HARQ retransmissions on the interferer's link. The source can then utilize the relay not only for communicating its own message, but also for cooperative interference mitigation at the destination by informing the relay about the interference signal. Proposed transmission strategies are based on partial decode-and-forward (PDF) relaying and leverage the interference structure. Achievable schemes are derived for discrete memoryless models, Gaussian and Ricean fading channels. Furthermore, optimal strategies are identified in some special cases. Finally, numerical results bring insight into the advantages of utilizing the interference structure at the source, relay or destination. [ABSTRACT FROM AUTHOR]

Uncertainty quantification (UQ) is a vital step in using mathematical models and simulations to take decisions. The field of cardiac simulation has begun to explore and adopt UQ methods to characterize uncertainty in model inputs and how that propagates through to outputs or predictions; examples of this can be seen in the papers of this issue. In this review and perspective piece, we draw attention to an important and under-addressed source of uncertainty in our predictions-that of uncertainty in the model structure or the equations themselves. The difference between imperfect models and reality is termed model discrepancy, and we are often uncertain as to the size and consequences of this discrepancy. Here, we provide two examples of the consequences of discrepancy when calibrating models at the ion channel and action potential scales. Furthermore, we attempt to account for this discrepancy when calibrating and validating an ion channel model using different methods, based on modelling the discrepancy using Gaussian processes and autoregressive-movingaverage models, then highlight the advantages and shortcomings of each approach. Finally, suggestions and lines of enquiry for future work are provided. [ABSTRACT FROM AUTHOR]

In this paper we set up a method called overlap decoherence correction (ODC) to take into account the quantum decoherence effect in a surface hopping framework. While keeping the standard surface hopping approach based on independent trajectories, our method allows to account for quantum decoherence by evaluating the overlap between frozen Gaussian wavepackets, the time evolution of which is obtained in an approximate way. The ODC scheme mainly depends on the parameter σ, which is the Gaussian width of the wavepackets. The performance of the ODC method is tested versus full quantum calculations on three model systems, and by comparison with full multiple spawning (FMS) results for the S1→S0 decay in the azobenzene molecule. [ABSTRACT FROM AUTHOR]

Makarov, Keller, Plaxco, and Metiu (MKPM) (to be published) have proposed a model that assumes that the kinetics of protein folding is controlled by the formation of the native contacts. An approximate solution of this model leads to a connection between the rate constant and the number of contacts in the folded state, which agrees with the measurements. In the present article, we perform Kinetic Monte Carlo simulations to test the assumptions and the results of MKPM theory. These simulations require us to know the rate constant for contact formation and dissociation. We show that these can be calculated for the case of a Gaussian chain and then used, in a Kinetic Monte Carlo program, to simulate folding kinetics. It is likely that a Gaussian chain is not a realistic model for the folding of a specific protein. However, it is reasonable to use it to test the assumptions made by MKPM, or by other kinetic models, or to derive generic features of folding rate, such as the dependence on the number of contacts. Another valuable feature of the simulation is that it provides information about the stochastic kinetics of a single chain, which is not yet available experimentally. The simulations find that the probability that a single chain folds at a time t has a maximum, at a time t[sub m], and decays exponentially for longer times. We show that t[sub m] is shorter than the time resolution of the experiments and therefore the measurements will conclude that folding is a first-order rate process. This is what is observed experimentally. The folding rate constant produced by simulations agrees with the one obtained by the simplified MKPM theory. Moreover, the simulations were used to test directly some of the assumptions made by MKPM. For example, we show that the free energy of a chain that has made a fair number of contacts can be approximated by a linear function of the number of contacts. The paper also contains two simplified models, which do not assume that the... [ABSTRACT FROM AUTHOR]

In this paper, we extend the earlier presented real options control chart (ROCC). In the real options framework, at any given moment, we compare the cost of recalibrating the process with the cost of postponing the (optimal) decision for later. The decision is thus based on cost minimization rather than statistically significant deviations from the in‐control process. We explain the general principles of constructing ROCC for both discrete and continuous processes and the describe the numeric algorithms that allow us to apply these principles to the cases of binomial and Gaussian process. Simulation studies demonstrate that, on average, ROCC runs longer than the standard economic control chart (SECC) and outperforms it in terms of average final costs. [ABSTRACT FROM AUTHOR]

Abstract Dynamic traffic assignment models rely on a network performance module known as dynamic network loading (DNL), which expresses flow propagation, flow conservation, and travel delay at a network level. The DNL defines the so-called network delay operator , which maps a set of path departure rates to a set of path travel times (or costs). It is widely known that the delay operator is not available in closed form, and has undesirable properties that severely complicate DTA analysis and computation, such as discontinuity, non-differentiability, non-monotonicity, and computational inefficiency. This paper proposes a fresh take on this important and difficult issue, by providing a class of surrogate DNL models based on a statistical learning method known as Kriging. We present a metamodeling framework that systematically approximates DNL models and is flexible in the sense of allowing the modeler to make trade-offs among model granularity, complexity, and accuracy. It is shown that such surrogate DNL models yield highly accurate approximations (with errors below 8%) and superior computational efficiency (9 to 455 times faster than conventional DNL procedures such as those based on the link transmission model). Moreover, these approximate DNL models admit closed-form and analytical delay operators, which are Lipschitz continuous and infinitely differentiable, with closed-form Jacobians. We provide in-depth discussions on the implications of these properties to DTA research and model applications. [ABSTRACT FROM AUTHOR]

Constrained Independent Component Analysis (cICA) was developed from Independent Component Analysis (ICA), and the concepts and principles of independent component analysis still apply to constrained independent component analysis. This paper introduces the mathematical basis, basic principles and algorithms of constrained independent component analysis. Firstly, the mathematical basis of cICA is introduced. It mainly includes the entropy and negative entropy of irrelevant and whitening, Statistical opposition and multivariate Gaussian density random variables. Then the mathematical model of Constrained FastICA, the identifiability and uncertainty of the model, the FastICA independence criterion, FastICA optimization and preprocessing, FastICA algorithm and simulation examples are introduced. Finally, the shortcomings of fast independent component analysis and the advantages of constrained independent component analysis are analyzed. According to the establishment and evaluation indicators of signals, the basic principles and corresponding algorithms of constrained independent component analysis are introduced. The characteristics of the corresponding simulation show that the algorithm is effective in extracting signal characteristics. [ABSTRACT FROM AUTHOR]

The exponential-dispersion (ED) process is a generalized stochastic process, including Wiener, gamma, and inverse Gaussian processes as special cases. This paper studies the reliability evaluation problem for products based on the ED process with random effects and covariates. The expectation maximization algorithm is applied to estimate the parameters of the ED processes. The probability density functions, the cumulative distribution functions of the lifetime and the remaining useful life distributions of products are derived based on Birnbaum–Saunders distribution. Finally, two illustrative examples are presented to show the effectiveness of the developed methods. [ABSTRACT FROM AUTHOR]

In this paper, a novel image quality assessment (IQA) model for the screen content images (SCIs) is proposed by using multi-scale difference of Gaussian (MDOG). Motivated by the observation that the human visual system (HVS) is sensitive to the edges while the image details can be better explored in different scales, the proposed model exploits MDOG to effectively characterize the edge information of the reference and distorted SCIs at two different scales, respectively. Then, the degree of edge similarity is measured in terms of the smaller-scale edge map. Finally, the edge strength computed based on the larger-scale edge map is used as the weighting factor to generate the final SCI quality score. Experimental results have shown that the proposed IQA model for the SCIs produces high consistency with human perception of the SCI quality and outperforms the state-of-the-art quality models. [ABSTRACT FROM AUTHOR]

Scheduling for directed acyclic graph (DAG) tasks with the objective of minimizing makespan has become an important problem in a variety of applications on heterogeneous computing platforms, which involves making decisions about the execution order of tasks and task-to-processor mapping. Recently, the chemical reaction optimization (CRO) method has proved to be very effective in many fields. In this paper, an improved hybrid version of the CRO method called HCRO (hybrid CRO) is developed for solving the DAG-based task scheduling problem. In HCRO, the CRO method is integrated with the novel heuristic approaches, and a new selection strategy is proposed. More specifically, the following contributions are made in this paper. (1) A Gaussian random walk approach is proposed to search for optimal local candidate solutions. (2) A left or right rotating shift method based on the theory of maximum Hamming distance is used to guarantee that our HCRO algorithm can escape from local optima. (3) A novel selection strategy based on the normal distribution and a pseudo-random shuffle approach are developed to keep the molecular diversity. Moreover, an exclusive-OR (XOR) operator between two strings is introduced to reduce the chance of cloning before new molecules are generated. Both simulation and real-life experiments have been conducted in this paper to verify the effectiveness of HCRO. The results show that the HCRO algorithm schedules the DAG tasks much better than the existing algorithms in terms of makespan and speed of convergence. [ABSTRACT FROM AUTHOR]

This paper proposed a hybrid intelligent process model, based on finite-element method (FEM) and Gaussian process regression (GPR), for electrical discharge machining (EDM) process. A model of single-spark EDM process has been constructed based on FEM method, considering the latent heat, variable heat distribution coefficient of cathode ( f), and plasma flushing efficiency (PFE), to predict material removal rate (MRR) and surface roughness (Ra). This model was validated using reported analytical and experimental results. Then, a GPR model was proposed to establish relationship between input process parameters (pulse current, pulse duration, and discharge voltage) and the process responses (MRR and Ra) for EDM process. The GPR model was trained, tested, and tuned using the data generated from the numerical simulations. Through the GPR model, it was found that responses of EDM process can be accurately predicted for the chosen process conditions. Therefore, for the selection of optimum parameters, the hybrid intelligent model proposed in this paper can be used in EDM process. [ABSTRACT FROM AUTHOR]

Jounce bumpers are indispensable components in vehicle suspension systems. It can attenuate impact energy and improve the ride comfort performances during transient pulse impacts from roads. However, the traditional jounce bumpers cannot achieve ideal mechanical performance and are difficult for parametric optimization due to its various shapes which are hard for parameterization. In this paper, a cylinder auxetic structure was introduced and applied as the suspension jounce bumper. Auxetic jounce bumper can be primarily defined by several variables. With tunable structure parameters, a large region of mechanical performances can be realized. In order to evaluate and optimize the performance of auxetic jounce bumpers, they were assembled into vehicle models to conduct virtual ride comfort tests under bump road. The maximum vertical acceleration of vehicle was defined as the objective function of the optimization problem of auxetic jounce bumper. On the purpose of improving optimization efficiency, Gaussian process regression method was employed to establish the metamodel of auxetic jounce bumper based on the sample set created by orthogonal design of experiments method. A series hybrid GA-SQP (Genetic algorithm-Sequential quadratic programming) algorithm, provided with both global and fast local searching abilities, was used for the optimization of auxetic jounce bumper. For comparison, GA algorithm was also applied for auxetic jounce bumper optimization alone. It is proved that the proposed optimization process is accurate and can improve optimization efficiency. Then the optimized design through hybrid algorithm was compared with original design. The maximum vertical acceleration of vehicle when travelling through bump was reduced with optimized design, and the vehicle ride comfort performance was improved. [ABSTRACT FROM AUTHOR]

Current remote sensing image classification problems have to deal with an unprecedented amount of heterogeneous and complex data sources. Upcoming missions will soon provide large data streams that will make land cover/use classification difficult. Machine-learning classifiers can help at this, and many methods are currently available. A popular kernel classifier is the Gaussian process classifier (GPC), since it approaches the classification problem with a solid probabilistic treatment, thus yielding confidence intervals for the predictions as well as very competitive results to the state-of-theart neural networks and support vector machines. However, its computational cost is prohibitive for large-scale applications, and constitutes the main obstacle precluding wide adoption. This paper tackles this problem by introducing two novel efficient methodologies for GP classification. We first include the standard random Fourier features approximation into GPC, which largely decreases its computational cost and permits large-scale remote sensing image classification. In addition, we propose a model which avoids randomly sampling a number of Fourier frequencies and alternatively learns the optimal ones within a variational Bayes approach. The performance of the proposed methods is illustrated in complex problems of cloud detection from multispectral imagery and infrared sounding data. Excellent empirical results support the proposal in both computational cost and accuracy. [ABSTRACT FROM AUTHOR]

We consider a class of effective models on ℤd called Gaussian membrane models with square-well pinning or δ-pinning. It is known that when d = 1 this model exhibits a localization/delocalization transition that depends on the strength of the pinning. In this paper, we show that when d ≥ 2, once we impose weak pinning potentials the field is always localized in the sense that the corresponding free energy is always positive. We also discuss the case that both square-well potentials and repulsive potentials are acting in high dimensions. [ABSTRACT FROM AUTHOR]

The aim of this paper is to extend the domain of the Gauss–Lucas theorem from the set of complex numbers to the set of bicomplex numbers. We also discuss a bicomplex version of another compact generalization of the Gauss–Lucas theorem. [ABSTRACT FROM AUTHOR]

In order to gain new insights into multiple-input–multiple-output (MIMO) interference networks, the optimality of \sum k=1^{K} Mk/2 (half the cake per user) degrees of freedom is explored for a K -user MIMO interference channel where the cross-channels have arbitrary rank constraints, and the k th transmitter and receiver are equipped with Mk antennas each. The result consolidates and significantly generalizes results from prior studies by Krishnamurthy et al., of rank-deficient interference channels where all users have M antennas; and by Tang et al., of full rank interference channels where the $k$ th user pair has M_{k} antennas. The broader outcome of this paper is a novel class of replication-based outer bounds for arbitrary rank-constrained MIMO interference networks where replicas of existing users are added as auxiliary users and the network connectivity is chosen to ensure that any achievable scheme for the original network also works in the new network. The replicated network creates a new perspective of the problem, so that even simple arguments such as user cooperation become quite powerful when applied in the replicated network, giving rise to stronger outer bounds, than when applied directly in the original network. Remarkably, the replication-based bounds are broadly applicable not only to MIMO interference channels with arbitrary rank-constraints, but much more broadly, even beyond Gaussian settings. [ABSTRACT FROM PUBLISHER]

In this paper we obtain expressions for truncated moment-generating functions of the normal-inverse Gaussian (NIG) process in closed forms. The result is derived without any additional martingale-type restriction on the initial probability measure. Applications to option pricing and risk measuring in the NIG model are given. The established formulas depend on values of the Humbert series. [ABSTRACT FROM AUTHOR]

In this paper, we engineered a Circular PCF having a very low confinement loss and high nonlinear coefficient, from five Circular PCFs of same ring separation value. From the analysis, it is derived that the zero dispersion wavelengths can be shifted by increasing the d/R ratio. Analysis of light propagation fiber characteristics such as confinement loss, effective mode area, non linear coefficient, numerical aperture and chromatic dispersion of silica core circular photonic crystal fibers have been investigated by full vector finite element method. Simulation results show that, the magnitude of confinement loss can be reduced to a value of 5.5012 × 10 −6 dB/km at the operating wavelength 1550 nm for the structure with d/R = 0.8 and the corresponding effective mode area is 3.78046 μm 2 and nonlinear coefficient is 0.03313 km −1 W −1 . C-PCFs with small air hole diameter show flat chromatic dispersion response over the wavelength region 1400 nm to 1800 nm. In addition to tight light confinement and Gaussian output over the entire operating wavelengths, we have simulated the Supercontinuum generation in the d/R = 0.8 fiber for different coupled power. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a novel peak to average power ratio (PAPR) reduction scheme for the DC-biased optical orthogonal frequency division multiplexing visible light communications (DCO-OFDM) systems. We implement the Gaussian matrix multiplication method to reduce the high PAPR of the DCO-OFDM system at the transmitter and use the back propagation (BP) algorithm to recover the original OFDM frame at the receiver. The simulation results show that the proposed scheme can achieve a PAPR 0 reduction by about 3 dB for 128-subcarrier DCO-OFDM systems, and a nearly identical bit error rate (BER) performance to the ideal OFDM system with no distortion. [ABSTRACT FROM AUTHOR]

Motion detection is one of the key issues in intelligent video surveillance, traffic monitoring and video-based human computer interaction. In this paper, we have efficiently detected the moving objects by computing the optical flow between three consecutive frames. The proposed method first filters out noise in individual frames using Gaussian filter. Next, it computes the optical flow between (a) the current frame and the previous frame and (b) the current frame and the next frame separately. Subsequently, it combines both the optical flow components to compute the gross optical flow. An adaptive thresholding post-processing step is executed so as to remove the spurious foreground objects. Moving objects are then detected using morphological operation on the equalized output. The method has been conceived, implemented and tested on a set of real video data sets. The experimental results exhibit satisfactory performance when compared with other existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of retrieving soil moisture over a grassland alpine area from Synthetic Aperture Radar (SAR) data using a statistical algorithm trained by simulations of a physical model. A time series of C-band VV-polarized Wide Swath images acquired by Envisat Advanced SAR (ASAR) in the snow-free periods of 2010 and 2011 was simulated using a discrete radiative transfer model (RTM). The test area was located in the Mazia valley, South Tyrol (Italy), where the main land types are meadows and pastures. Soil moisture was collected from five meteorological stations, two of which situated in meadows and the rest in pastures. The smallest and the highest RMSEs of the RTM simulations were 0.78 dB and 1.91 dB, respectively. After backscattering simulation, the top soil moisture was estimated using Gaussian Process Regression (GPR). GPR was trained with the backscatter model simulations (including terrain features) for 2010, and then used to predict moisture from radar observations acquired in 2011. The relative importance of different input features was also assessed. The RMSE of the predicted soil moisture for the largest training data set (including aspect as a terrain feature) was 5.6% Vol. and the corresponding correlation coefficient was 0.84. [ABSTRACT FROM PUBLISHER]

Prior distributions for Bayesian inference that rely on the l1-norm of the parameters are of considerable interest, in part because they promote parameter fields with less regularity than Gaussian priors (e.g., discontinuities and blockiness). These l1-type priors include the total variation (TV) prior and the Besov space B1,1s prior, and in general yield non-Gaussian posterior distributions. Sampling from these posteriors is challenging, particularly in the inverse problem setting where the parameter space is high-dimensional and the forward problem may be nonlinear. This paper extends the randomize-then-optimize (RTO) method, an optimization-based sampling algorithm developed for Bayesian inverse problems with Gaussian priors, to inverse problems with l1-type priors. We use a variable transformation to convert an l1-type prior to a standard Gaussian prior, such that the posterior distribution of the transformed parameters is amenable to Metropolized sampling via RTO. We demonstrate this approach on several deconvolution problems and an elliptic PDE inverse problem, using TV or Besov space B1,1s priors. Our results show that the transformed RTO algorithm characterizes the correct posterior distribution and can be more efficient than other sampling algorithms. The variable transformation can also be extended to other non-Gaussian priors. [ABSTRACT FROM AUTHOR]

Battery health degradation detection and monitoring are crucial to realize equipment's near-zero downtime and maximum productivity. A big challenge is how to construct an effective monitoring system that can consistently exemplify the degradation propagation of battery health over its whole life. This paper proposes an on-line method based on adaptive learning scheme for monitoring of state-of-health (SOH) of battery. An adaptive Gaussian mixture model (AGMM) is developed for online learning dynamic changes of battery health in its full life. A Bayesian-inference-based probability indication is developed for detection of new health states that are online modeled by deleting and adding of components in AGMM. Furthermore, health changes are quantified by an AGMM-based health index that measures the overlap between two density distributions approximated by the adapted GMM and the historic GMM, respectively. Research results of its application in a lithium-ion battery life test illustrate that AGMM-based SOH monitoring system is effective for detection and adaptive assessment of battery health degradation. This paper provides a guidance for the development of battery SOH monitoring model based on adaptive learning scheme without too much human intervention. [ABSTRACT FROM PUBLISHER]

Detection of sparse signals arises in a wide range of modern scientific studies. The focus so far has been mainly on Gaussian mixture models. In this paper, we consider the detection problem under a general sparse mixture model and obtain explicit expressions for the detection boundary under mild regularity conditions. In addition, for Gaussian null hypothesis, we establish the adaptive optimality of the higher criticism procedure for all sparse mixtures satisfying the same conditions. In particular, the general results obtained in this paper recover and extend in a unified manner the previously known results on sparse detection far beyond the conventional Gaussian model and other exponential families. [ABSTRACT FROM PUBLISHER]

The paper presents a mathematical model of stock prices using a fractional Brownian motion model with adaptive parameters (FBMAP). The accuracy index of the proposed model is compared with the Brownian motion model with adaptive parameters (BMAP). The parameters in both models are adapted at anytime. The ADVANC Info Service Public Company Limited (ADVANC) and Land and Houses Public Company Limited (LH) closed prices are concerned in the paper. The Brownian motion model with adaptive parameters (BMAP) and fractional Brownian motion model with adaptive parameters (FBMAP) are applied to identify ADVANC and LH closed prices. The simulation results show that the FBMAP is more suitable for forecasting the ADVANC and LH closed price than the BMAP. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents the development of a surrogate modeling technique for efficient non-planar fatigue crack growth analysis in mechanical components under multi-axial loading. Non-planar crack fronts are freely deformable space curves and require a high-dimensional representation. The large number of Cartesian co-ordinate variables involved in crack front representation makes it prohibitively expensive to train surrogate models for crack growth. Therefore, in our previous work, the crack shape was approximated using a planar parametrized representation. However, the parametrized representation limits the choice of crack shapes that can be considered. This paper presents the development of a non-parametric crack shape representation that allows for construction of a surrogate model for non-planar crack growth with complex crack shapes. The surrogate model is trained using a few runs of high-fidelity 3D simulations and predicts the evolution of a non-planar crack front under a given multi-axial, variable amplitude load history. We first parametrize the crack fronts as 3D spline curves with a fixed number of nodes. Instead of modeling the crack growth in this high dimensional data space, we project the data to a lower dimensional space using Principal Component Analysis (PCA) and then model the crack growth in this lower dimensional space. Finally, the predicted crack fronts are recovered using PCA back to the original data space. The proposed crack representation, growth modeling and recovery are illustrated using training points gathered from high-fidelity 3-D finite element simulations of non-planar crack growth in a cylindrical component similar to a rotorcraft mast, and the ability of the surrogate model to accurately predict the evolution of the crack growth over entire load histories is demonstrated. [Copyright &y& Elsevier]

A plethora of networks is being collected in a growing number of fields, including disease transmission, international relations, social interactions, and others. As data streams continue to grow, the complexity associated with these highly multidimensional connectivity data presents novel challenges. In this paper, we focus on the time-varying interconnections among a set of actors in multiple contexts, called layers. Current literature lacks exible statistical models for dynamic multilayer networks, which can enhance quality in inference and prediction by efficiently borrowing information within each network, across time, and between layers. Motivated by this gap, we develop a Bayesian nonparametric model leveraging latent space representations. Our formulation characterizes the edge probabilities as a function of shared and layer-specific actors positions in a latent space, with these positions changing in time via Gaussian processes. This representation facilitates dimensionality reduction and incorporates different sources of information in the observed data. In addition, we obtain tractable procedures for posterior computation, inference, and prediction. We provide theoretical results on the exibility of our model. Our methods are tested on simulations and infection studies monitoring dynamic face-to-face contacts among individuals in multiple days, where we perform better than current methods in inference and prediction. [ABSTRACT FROM AUTHOR]

Gaussian process regression (GPR) has been shown to be a powerful and effective nonparametric method for regression, classification and interpolation, due to many of its desirable properties. However, most GPR models consider univariate or multivariate covariates only. In this paper we extend the GPR models to cases where the covariates include both functional and multivariate variables and the response is multidimensional. The model naturally incorporates two different types of covariates: multivariate and functional, and the principal component analysis is used to de-correlate the multivariate response which avoids the widely recognised difficulty in the multi-output GPR models of formulating covariance functions which have to describe the correlations not only between data points but also between responses. The usefulness of the proposed method is demonstrated through a simulated example and two real data sets in chemometrics. [ABSTRACT FROM AUTHOR]

This paper presents a novel image descriptor to effectively characterize the local, high-order image statistics. Our work is inspired by the Diffusion Tensor Imaging and the structure tensor method (or covariance descriptor), and motivated by popular distribution-based descriptors such as SIFT and HoG. Our idea is to associate one pixel with a multivariate Gaussian distribution estimated in the neighborhood. The challenge lies in that the space of Gaussians is not a linear space but a Riemannian manifold. We show, for the first time to our knowledge, that the space of Gaussians can be equipped with a Lie group structure by defining a multiplication operation on this manifold, and that it is isomorphic to a subgroup of the upper triangular matrix group. Furthermore, we propose methods to embed this matrix group in the linear space, which enables us to handle Gaussians with Euclidean operations rather than complicated Riemannian operations. The resulting descriptor, called Local Log-Euclidean Multivariate Gaussian (L $^2$ EMG) descriptor, works well with low-dimensional and high-dimensional raw features. Moreover, our descriptor is a continuous function of features without quantization, which can model the first- and second-order statistics. Extensive experiments were conducted to evaluate thoroughly L$^2$ EMG, and the results showed that L $^2$ EMG is very competitive with state-of-the-art descriptors in image classification. [ABSTRACT FROM PUBLISHER]

In this paper, we study linear backward stochastic differential equations driven by a class of centered Gaussian non-martingales, including fractional Brownian motion with Hurst parameter H ∈ ( 0 , 1 ) ∖ { 1 2 } . We show that, for every choice of deterministic coefficient functions, there is a square integrable terminal condition such that the equation has no solution. [ABSTRACT FROM AUTHOR]

In many engineering problems, including those related to robotics, optimization of the control policy for multiple conflicting criteria is required. However, this can be very challenging because of the existence of noise, which may be input dependent or heteroscedastic, and restrictions regarding the number of evaluations owing to the costliness of the experiments in terms of time and/or money. This paper presents a multiobjective optimization algorithm for expensive-to-evaluate noisy functions for robotics. We present a method for model selection between heteroscedastic and standard homoscedastic Gaussian process regression techniques to create suitable surrogate functions from noisy samples, and to find the point to be observed at the next step. This algorithm is compared against an existing multiobjective optimization algorithm, and then used to optimize the speed and head stability of the sidewinding gait of a snake robot. [ABSTRACT FROM PUBLISHER]

This paper analyzes the reasons why the one-dimensional Gaussian model is inapplicable for the analysis and synthesis of the measurements of parameters of complex signals. It also describes the bi-Gaussian mathematical model of signals of radio-frequency radiation sources. [ABSTRACT FROM AUTHOR]

This paper presents tractable information value functions for Dirichlet-process Gaussian-process (DPGP) mixture models obtained via collocation methods and Monte Carlo integration. Quantifying information value in tractable closed form is key to solving control and estimation problems for autonomous information-gathering systems. The properties of the proposed value functions are analyzed and then demonstrated by planning sensor measurements so as to minimize the uncertainty in DPGP target models that are learned incrementally over time. Simulation results show that sensor planning based on expected KL divergence outperforms algorithms based on mutual information, particle filters, and randomized methods. [ABSTRACT FROM AUTHOR]

Let X, X1, . . ., Xn be i.i.d. Gaussian random variables with zero mean and covariance operator Σ = E(X X) taking values in a separable Hilbert space H. Let ... be the sample (empirical) covariance operator based on (X1, . . ., Xn). The paper deals with a problem of estimation of spectral projectors of the covariance operator Σ by their empirical counterparts, the spectral projectors of Σn (empirical spectral projectors). The focus is on the problems where both the sample size n and the effective rank r(Σ) are large. This framework includes and generalizes well known high-dimensional spiked covariance models. Given a spectral projector Pr corresponding to an eigenvalue µr of covariance operator Σ and its empirical counterpart Pr, we derive sharp concentration bounds for bilinear forms of empirical spectral projector Pr in terms of sample size n and effective dimension r(Σ). Building upon these concentration bounds, we prove the asymptotic normality of bilinear forms of random operators Pr -E Pr under the assumptions that n?8and r(Σ) = o(n). In a special case of eigenvalues of multiplicity one, these results are rephrased as concentration bounds and asymptotic normality for linear forms of empirical eigenvectors. Other results include bounds on the bias E Pr - Pr and a method of bias reduction as well as a discussion of possible applications to statistical inference in high-dimensional Principal Component Analysis. [ABSTRACT FROM AUTHOR]

This paper considers novel Bayesian non-parametric methods for stochastic epidemic models. Many standard modeling and data analysis methods use underlying assumptions (e.g. concerning the rate at which new cases of disease will occur) which are rarely challenged or tested in practice. To relax these assumptions, we develop a Bayesian non-parametric approach using Gaussian Processes, specifically to estimate the infection process. The methods are illustrated with both simulated and real data sets, the former illustrating that the methods can recover the true infection process quite well in practice, and the latter illustrating that the methods can be successfully applied in different settings. [ABSTRACT FROM AUTHOR]

This special issue is concerned with model selection and shrinkage estimators. This Introduction gives an overview of the papers published in this special issue. [ABSTRACT FROM AUTHOR]

Noise is a persistent feature in seismic data and so poses challenges in extracting increased accuracy in seismic images and physical interpretation of the subsurface. In this paper, we analyse passive seismic data from the Aquistore carbon capture and storage pilot project permanent seismic array to characterise, classify and model seismic noise. We perform noise analysis for a three-month subset of passive seismic data from the array and provide conclusive evidence that the noise field is not white, stationary, or Gaussian; characteristics commonly yet erroneously assumed in most conventional noise models. We introduce a novel noise modelling method that provides a significantly more accurate characterisation of real seismic noise compared to conventional methods, which is quantified using the Mann-Whitney- White statistical test. This method is based on a statistical covariance modelling approach created through the modelling of individual noise signals. The identification of individual noise signals, broadly classified as stationary, pseudo-stationary and non-stationary, provides a basis on which to build an appropriate spatial and temporal noise field model. Furthermore, we have developed a workflow to incorporate realistic noise models within synthetic seismic data sets providing an opportunity to test and analyse detection and imaging algorithms under realistic noise conditions. [ABSTRACT FROM AUTHOR]

This paper deals with the kinetic theory framework for the modeling of the complex dynamics of crowds constituted by a large number of individuals (pedestrians) that interact in a non-linear fashion in a domain with and without obstacles. The kinetic frameworks are coupled with the stochastic games theory and Gaussian thermostats in order to model the interactions which occur at microscopic scale. After introducing the mathematical structures for continuous and granular flows, the paper outlines suitable applications and research perspectives. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a robust voice activity detection (VAD) method that operates in the presence of noise. For noise robust VAD, we have already proposed statistical models and a switching Kalman filter (SKF)-based technique. In this paper, we focus on a model re-estimation method using Gaussian pruning with weight normalization. The statistical model for SKF-based VAD is constructed using Gaussian mixture models (GMMs), and consists of pre-trained silence and clean speech GMMs and a sequentially estimated noise GMM. However, the composed model is not optimal in that it does not fully reflect the characteristics of the observed signal. Thus, to ensure the optimality of the composed model, we investigate a method for its re-estimation that reflects the characteristics of the observed signal sequence. Since our VAD method works through the use of frame-wise sequential processing, processing with the smallest latency is very important. In this case, there are insufficient re-training data for a re-estimation of all the Gaussian parameters. To solve this problem, we propose a model re-estimation method that involves the extraction of reliable characteristics using Gaussian pruning with weight normalization. Namely, the proposed method re-estimates the model by pruning non-dominant Gaussian distributions that express the local characteristics of each frame and by normalizing the Gaussian weights of the remaining distributions. In an experiment using a speech corpus for VAD evaluation, CENSREC-1-C, the proposed method significantly improved the VAD performance with compared that of the original SKF-based VAD. This result confirmed that the proposed Gaussian pruning contributes to an improvement in VAD accuracy. [Copyright &y& Elsevier]

Abstract: There is significant interest in long-range dependent processes since they occur in a wide range of phenomena across different areas of study. Based on the available models capable of describing long-range dependence, various parameter estimation methods have been developed. In this paper we revisit the maximum likelihood estimator and its computationally efficient approximations: Whittle’s Estimator and the Circulant Embedding Estimator. In particular, this paper proves the asymptotic properties of the Circulant Embedding estimator and establishes the asymptotic equivalence between the three estimators. Furthermore, it is shown that the three methods are ill-conditioned and thus highly sensitive to the presence of measurement errors. Finally, we introduce a regularisation method that improves the performance of the maximum likelihood methods when the datasets have been largely contaminated with errors. [Copyright &y& Elsevier]

In this paper, we present a novel method for shadow removal using Markov random fields (MRF). In our method, we first construct the shadow model in a hierarchical manner. At the pixel level, we use the Gaussian mixture model to model the behavior of cast shadows for every pixel in the HSV color space. The samples which are used to update the shadow model should satisfy a pre-classifier. This pre-classifier indicates the color feature of shadow in current frame. At the global level, we exploit the statistical features of shadow in the whole scene over several consecutive frames to make this pre-classifier accurate and adaptive to the change of shadow. Then, based on the shadow model, an MRF model is constructed for shadow removal. The main contribution of this paper is twofold. First, although our method is a chroma-based method, we make the pre-classifier accurate and adaptive to the change of shadow by using the statistical features of shadow at the global level. Moreover, tracking information can make this global-level statistical information more robust. Second, we construct an MRF model to represent the dependencies between the label of a pixel and the shadow models of its neighbors. Experimental results show that the proposed method is efficient and robust. [ABSTRACT FROM PUBLISHER]

Abstract: Classifying human hand gestures in the context of a Sign Language has been historically dominated by Artificial Neural Networks and Hidden Markov Model with varying degrees of success. The main objective of this paper is to introduce Gaussian Process Dynamical Model as an alternative machine learning method for hand gesture interpretation in Sign Language. In support of this proposition, the paper presents the experimental results for Gaussian Process Dynamical Model against a database of 66 hand gestures from the Malaysian Sign Language. Furthermore, the Gaussian Process Dynamical Model is tested against established Hidden Markov Model for a comparative evaluation. A discussion on why Gaussian Process Dynamical Model is superior over existing methods in Sign Language interpretation task is then presented. [Copyright &y& Elsevier]