Probabilistic Perspective Research Articles

Probabilistic perspective of the optimal distributed generation integration on a distribution system

The effects of optimal dimensioning and integration of distributed generation (DG) on an electricity distribution system (DS) from a probabilistic viewpoint is presented in this paper, as a new contribution to earlier studies. The proposed methodology pays special attention to preventing reverse power flow at substation as a consequence of excessive integration of renewable energy based DG. As the analysis of large amounts of data typically measured on an annual basis could be exhausting from a computational perspective, a methodology based on estimating the potential of wind and solar resources is applied; from this procedure, those months of highest renewable potential are selected so that indirectly those situations with probability of reverse power flow at substation are considered. After this, time series of load demand per node and phase are generated using typical profiles and the corresponding peak-load expected. Finally, all this information is introduced on an optimization algorithm based on a genetic algorithm in order to minimize the net present cost over the project lifetime, obtaining the type and number of photovoltaic (PV) panels and wind turbines (WTs) to be installed. This approach allows integrating detailed mathematical models of DG related to PV and wind generation, including specific factors frequently reported by the manufacturers such as temperature coefficients, nominal operating cell temperature, particular WT power curves, and variable efficiency of power converter, among other characteristics. The proposed method is illustrated by studying a DS supposed to be located in Zaragoza, Spain, with 35 nodes under unbalanced conditions, with residential as well as small, medium, and large commercial electricity demands. Focusing our attention on the month of February, due to its high renewable potential, the proposed technique was applied resulting in a system mainly based on wind energy of at least 40% of the substation capacity. This model could be used to perform the renewable energy integration analysis on DS, starting from typical load profiles, hourly estimations of solar and wind resources, and data frequently provided by PV panels and WT manufacturers.

Probabilistic LCF life assessment for turbine discs with DC strategy-based wavelet neural network regression

Low cycle fatigue (LCF) seriously affects the performance and reliability of turbomachinery like aeroengine. Probabilistic LCF assessment can effectively quantify risk and improve components reliability. To improve the accuracy and efficiency of probabilistic LCF life assessment, a distributed collaborative (DC)-wavelet neural network regression (WNNR) (called as DC-WNNR) surrogate model is developed by proposing Bayesian regularization-Quasi Newton (BR-QN) error control technique. The mathematical model of DC-WNNR is structured and the corresponding probabilistic framework of LCF life assessment is introduced. The probabilistic LCF life assessment for turbine discs is regarded as one case to evaluate the proposed method with respect to various uncertainties such as material property, load fluctuation and model variability. The analysis results reveal that the reliability-based LCF life of a turbine disc under reliability 99.87% is 6 058 cycles; fatigue strength coefficient σf′ and strain range Δɛt play a leading role on the fatigue life failure since their effect probabilities of 45% and 36%, respectively. The comparison of methods (Monte Carlo method, WNNR, DC response surface method and DC-WNNR) shows that the DC-WNNR holds high efficiency and accuracy for the probabilistic LCF assessment. The present efforts offer an effective way for predicting and evaluating structural LCF failure from a probabilistic perspective.

THE FRIENDSHIP PARADOX FOR WEIGHTED AND DIRECTED NETWORKS

This paper studies the friendship paradox for weighted and directed networks, from a probabilistic perspective. We consolidate and extend recent results of Cao and Ross and Kramer, Cutler and Radcliffe, to weighted networks. Friendship paradox results for directed networks are given; connections to detailed balance are considered.

Distributed Federated Tobit Kalman Filter Fusion Over a Packet-Delaying Network: A Probabilistic Perspective

This paper investigates the distributed federated Tobit Kalman filter fusion problem for a class of discrete-time systems subject to measurement censoring and packet delays. The censored measurement is characterized by the Tobit measurement model and the packet delay obeys the Poisson distribution. At the input terminal of each local estimator, a censoring detection device and a buffer with finite length are exploited to tackle the censored/delayed measurements. The filtering fusion is carried out in two steps: in the first step, every sensor in the network collects and sends its measurements to the corresponding local estimator via an unreliable network with probabilistic packet delays and, in the second step, the estimates from local estimators are further collected by the fusion center to form a fused estimate. The local estimator runs a modified Tobit Kalman filtering algorithm, which is designed based on the modified Tobit regression model, while the fusion center performs a distributed federated modified Tobit Kalman filtering algorithm, which is devised on the basis of the federated Kalman fusion rule. Given the buffer length, the prescribed bound on the estimation error covariance and the probability distribution of the packet delay, the stability performance of the proposed filtering fusion algorithm is evaluated via a probabilistic approach. Simulation results are provided to show the feasibility of the proposed filter.

Exact Gradients Improve Parameter Estimation in Nonlinear Mixed Effects Models with Stochastic Dynamics

Nonlinear mixed effects (NLME) modeling based on stochastic differential equations (SDEs) have evolved into a promising approach for analysis of PK/PD data. SDE-NLME models go beyond the realm of standard population modeling as they consider stochastic dynamics, thereby introducing a probabilistic perspective on the state variables. This article presents a summary of the main contributions to SDE-NLME models found in the literature. The aims of this work were to develop an exact gradient version of the first-order conditional estimation (FOCE) method for SDE-NLME models and to investigate whether it enabled faster estimation and better gradient precision/accuracy compared to the use of gradients approximated by finite differences. A simulation-estimation study was set up whereby finite difference approximations of the gradients of each level were interchanged with the exact gradients. Following previous work, the uncertainty of the state variables was accounted for using the extended Kalman filter (EKF). The exact gradient FOCE method was implemented in Mathematica 11 and evaluated on SDE versions of three common PK/PD models. When finite difference gradients were replaced by exact gradients at both FOCE levels, relative runtimes improved between 6- and 32-fold, depending on model complexity. Additionally, gradient precision/accuracy was significantly better in the exact gradient case. We conclude that parameter estimation using FOCE with exact gradients can successfully be applied to SDE-NLME models.

Phylogenetic relationships and biogeography of theIpsiuracuckoo wasps (Hymenoptera: Chrysididae)

AbstractPhylogenetic studies addressing relationships among chrysidid wasps have been limited. There are no hypotheses proposed for the Neotropical lineages of Chrysidini other than the classic cladogram published in the 1990s by Kimsey and Bohart. Herein we present a cladistic analysis based on 64 morphological characters coded for 54 species of Chrysidini, 32 of them beingIpsiuraand 22 representingCaenochrysis,Chrysis,Exochrysis,Gaullea,Neochrysis, andPleurochrysis. The species ofIpsiurawere recovered as monophyletic and as the sister clade ofNeochrysisin all most parsimonious trees. We discuss the high plasticity of some morphological characters as evidenced by their high homoplasy in the phylogenetic results, and we clarify the main morphological changes inferred on the phylogenetic tree for this genus. The effects of the inferred homoplasy were evaluated under an implied weighting cladistic analysis, and from a probabilistic perspective with Bayesian inference. Those alternative strategies did not alter the general conclusions about the monophyly ofIpsiuraor the generic relationships in Chrysidini (changes were noticed in the species‐level relationships within certain parts ofIpsiura, where low branch support was common across all approaches). Among the species groups proposed by Linsenmaier (1985), only themarginalisgroup was recovered as monophyletic. We also evaluated the convoluted biogeographic history of the group. The resulting historical reconstructions indicate a complicated scenario of diversification of these wasps in the Neotropics, and a close association with forested biomes is discussed.

Sparse multi-modal probabilistic latent semantic analysis for single-image super-resolution

Abstract This paper presents a novel single-image super-resolution (SR) approach based on latent topics in order to take advantage of the semantics pervading the topic space when super-resolving images. Image semantics has shown to be useful to relieve the ill-posed nature of the SR problem, however the most accepted clustering-based approach used to define semantic concepts limits the capability of representing complex visual relationships. The proposed approach provides a new probabilistic perspective where the SR process is performed according to the semantics encapsulated by a new topic model, the Sparse Multi-modal probabilistic Latent Semantic Analysis (sMpLSA). Firstly, the sMpLSA model is formulated. Subsequently, a new SR framework based on sMpLSA is defined. Finally, an experimental comparison is conducted using seven learning-based SR methods over three different image datasets. Experiments reveal the potential of latent topics in SR by reporting that the proposed approach is able to provide a competitive performance.

On the Relationship Between Probabilistic and Deterministic Skills in Dynamical Seasonal Climate Prediction

AbstractDespite the gradually increasing emphasis on assessing the skill of dynamical seasonal climate predictions from the probabilistic perspective, there is a lack of in‐depth understanding that an inherent relationship may exist between the probabilistic and deterministic seasonal forecast skills. In this study, we focus on investigating this relationship, through theoretical consideration based on an analytical approach and diagnostic analysis of the historical forecasts produced by multiple dynamical models. The probabilistic forecast skill is gauged in terms of its two different attributes: resolution and reliability, while the deterministic forecast skill is measured in terms of anomaly correlation (AC). Through the theoretical consideration under certain simplified assumptions, a nonlinear, monotonic relationship is analytically derived between the resolution and the AC. Subsequent diagnostic analysis shows that the resolution and AC skills of both the multimodel ensemble and its member single models indeed appear to be approximately monotonically and nonlinearly related, specifically when they are calculated in a zonally aggregated manner by which the impact of finite sample size is reduced. This observed relationship has a specific form that is consistent with what the theory predicts. In short, the theoretical result is well verified by the dynamical model forecasts. Diagnostic analysis also shows that no good relationship exists between the reliability and the AC, signifying the difference of reliability and resolution in nature. A specific application of the proven resolution‐AC coherence is also demonstrated. The proved resolution‐AC relationship can facilitate comparisons among various assessments of seasonal climate prediction skill from the deterministic or probabilistic perspective alone.

Visual Classification With Multikernel Shared Gaussian Process Latent Variable Model.

Multiview learning methods often achieve improvement compared with single-view-based approaches in many applications. Due to the powerful nonlinear ability and probabilistic perspective of Gaussian process (GP), some GP-based multiview efforts were presented. However, most of these methods make a strong assumption on the kernel function (e.g., radial basis function), which limits the capacity of the real data modeling. In order to address this issue, in this paper, we propose a novel multiview approach by combining a multikernel and GP latent variable model. Instead of designing a deterministic kernel function, multiple kernel functions are established to automatically adapt various types of data. Considering a simple way of obtaining latent variables at the testing stage, a projection from the observed space to the latent space as a back constraint has also been simultaneously introduced into the proposed method. Additionally, different from some existing methods which apply the classifiers off-line, a hinge loss is embedded into the model to jointly learn the classification hyperplane, encouraging the latent variables belonging to the different classes to be separated. An efficient algorithm based on the gradient decent technique is constructed to optimize our method. Finally, we apply the proposed approach to three real-world datasets and the associated results demonstrate the effectiveness and superiority of our model compared with other state-of-the-art methods.

Exploring temporal community structure and constant evolutionary pattern hiding in dynamic networks

Abstract Detecting the temporal communities and analyzing their evolution in dynamic networks is an important question for understanding the structure and function of complex networks. Most existing methods deal the temporal community detection and evolution as a two-step processes and only apply to unweighted and undirected dynamic networks. In this paper, we proposed a new clustering method based on non-negative matrix factorization from a fully probabilistic perspective, to explore temporal and constant community structure as well as the importance of nodes in any type dynamic networks synchronously. In detailed, we first denote the important matrix of node in dynamic networks, the community membership matrix, the similarity matrix at each snapshot and the probability transition matrix of community between the two consecutive snapshots. Second, we constitute the temporal community detection method from the view of generating networks. Third, we introduce a gradient descent algorithm to optimize the objection function of the proposed model. The experimental results on both artificial and real dynamic networks demonstrate that the superior performance of our proposed method is over some widely-used methods.

A Stochastic Model of Cascading Failure Dynamics in Communication Networks

In this brief, we propose a stochastic model based on state transition theory to investigate the dynamics of cascading failures in communication networks. We describe the failure events of the nodes in the network as node state transitions. Taking a probabilistic perspective, we focus on two uncertain conditions in the failure propagation process: which node in the network will fail next and how long it will last before the next node state transition takes place. The stochastic model gives each overloaded element a probability of failing, and the failure rate is relevant to the degree of overloading. Moreover, the time dimension is considered in the stochastic process, by removing a node after a time delay when its traffic load exceeds its capacity. We employ this proposed model to study the dynamics of cascading failure evolution in a Barabasi–Albert scale-free network and an Internet AS-level network. Simulation results reveal the effects of the initial failure pattern, community structure and network design parameters on the dynamic propagation of cascading failures.

Nonlinear Bayesian estimation: from Kalman filtering to a broader horizon

This article presents an up-to-date tutorial review of nonlinear Bayesian estimation. State estimation for nonlinear systems has been a challenge encountered in a wide range of engineering fields, attracting decades of research effort. To date, one of the most promising and popular approaches is to view and address the problem from a Bayesian probabilistic perspective, which enables estimation of the unknown state variables by tracking their probabilistic distribution or statistics U+0028 e.g., mean and covariance U+0029 conditioned on a system U+02BC s measurement data. This article offers a systematic introduction to the Bayesian state estimation framework and reviews various Kalman filtering U+0028 KF U+0029 techniques, progressively from the standard KF for linear systems to extended KF, unscented KF and ensemble KF for nonlinear systems. It also overviews other prominent or emerging Bayesian estimation methods including Gaussian filtering, Gaussian-sum filtering, particle filtering and moving horizon estimation and extends the discussion of state estimation to more complicated problems such as simultaneous state and parameter U+002F input estimation.

Attribute CNNs for word spotting in handwritten documents

Word spotting has become a field of strong research interest in document image analysis over the last years. Recently, AttributeSVMs were proposed which predict a binary attribute representation (Almazan et al. in IEEE Trans Pattern Anal Mach Intell 36(12):2552---2566, 2014). At their time, this influential method defined the state of the art in segmentation-based word spotting. In this work, we present an approach for learning attribute representations with convolutional neural networks(CNNs). By taking a probabilistic perspective on training CNNs, we derive two different loss functions for binary and real-valued word string embeddings. In addition, we propose two different CNN architectures, specifically designed for word spotting. These architectures are able to be trained in an end-to-end fashion. In a number of experiments, we investigate the influence of different word string embeddings and optimization strategies. We show our attribute CNNs to achieve state-of-the-art results for segmentation-based word spotting on a large variety of data sets.

Comparison of mutation strategies in Differential Evolution – A probabilistic perspective

Abstract Differential Evolution (DE) is a state-of-the art evolutionary algorithm that solves global optimization problems in a real domain. The algorithm adapts the mutation range and direction by basing these on the differences between individuals in the current population. In this paper, we provide formulas for the expectation vectors and covariance matrices of the mutants' distribution for several operators of differential mutation. The covariance matrices are proportional to each other, which means that the main difference between the analyzed DE operators is the mutation range. This can be conveniently described using a generalized scaling factor g ( F ) , introduced in this paper. Next, we propose transformations of the scaling factors that make the expectation vectors and covariance matrices of the expected mutants' distributions equal to the respective statistics of DE/best/1 or DE/rand/1. These transformations establish a framework for a synthetic investigation of various differential mutation operators and for generalizing the results of parameter tuning. A simulation study based on the CEC′13 benchmark in 10, 30 and 50 dimensions confirms that the transformations do not influence the performance much, especially in the case of DE operators with two difference vectors.

Multipactor susceptibility chart of coaxial transmission lines with stationary statistical modeling

Multipactor breakdown is a detrimental electromagnetic phenomenon caused by resonant secondary electron emissions synchronizing with field oscillation, which frequently takes place in powerful microwave devices and accelerating structures. Regarded as the principal failure mode of space microwave systems, multipactor may cause the performance to degenerate or even hardware operation to deteriorate catastrophically, thus multipactor becomes a major limitation in promoting the further development of space communication technology. Meanwhile, higher power capacity and volume integration accordingly lead to continuously growing multipactor hazard. In order to prevent multipactor from occurring, the accurate predictive technique to determine multipactor susceptibility has become a key issue for the mechanical design and performance optimization of microwave devices in the ground stage. Compared with the existing approaches to investigating the multipactor, statistical theories are able to conduct multipactor threshold calculation and mechanism analysis, with the stochastic nature of secondary emission fully considered from the probabilistic perspective. Currently, stationary statistical theory of multipactor has been developed for efficient multipactor threshold analysis of the parallel-plate geometry. However, it has not been further extended to the coaxial geometry which is commonly involved in radio frequency (RF) systems. For this reason, the stationary statistical modeling of the coaxial multipactor with all influencing factors considered is detailed in this paper. Due to the field nonuniformity and the secondary emission randomness, analytic equation of electron trajectories in the coaxial geometry is approximately derived by using the perturbation approach. Based on the implicit correlation between electron emission velocity and transit time, the joint probability density function is constructed for the calculation of the probability density distribution of electron transit time. Afterwards, a system of integral equations for depicting electron multiplication process in the coaxial geometry is formulated and solved with a novel and general iteration method. Finally, this stationary statistical theory is applied to the full multipactor susceptibility chart of coaxial transmission lines with typical coating materials in space engineering, such as silver, copper, alumina and alodine. A comparison shows that the calculation results are in reasonable agreement with the experimental measurements provided by the Europe Space Agent. What is more, there exists significant difference between multipactor susceptibility curves of the parallel-plate geometry and the coaxial geometry. This research is of great significance for optimizing the mechanism design and material selection of multipactor-free microwave devices.

Deep Learning: A Bayesian Perspective

Deep learning is a form of machine learning for nonlinear high dimensional pattern matching and prediction. By taking a Bayesian probabilistic perspective, we provide a number of insights into more efficient algorithms for optimisation and hyper-parameter tuning. Traditional high-dimensional data reduction techniques, such as principal component analysis (PCA), partial least squares (PLS), reduced rank regression (RRR), projection pursuit regression (PPR) are all shown to be shallow learners. Their deep learning counterparts exploit multiple deep layers of data reduction which provide predictive performance gains. Stochastic gradient descent (SGD) training optimisation and Dropout (DO) regularization provide estimation and variable selection. Bayesian regularization is central to finding weights and connections in networks to optimize the predictive bias-variance trade-off. To illustrate our methodology, we provide an analysis of international bookings on Airbnb. Finally, we conclude with directions for future research.

Discrete kinetic theory for 2D modeling of a moving crowd: Application to the evacuation of a non-connected bounded domain

This paper concerns the mathematical modeling of the motion of a crowd in a non connected bounded domain, based on kinetic and stochastic game theories. The proposed model is a mesoscopic probabilistic approach that retains features obtained from both micro- and macro-scale representations; pedestrian interactions with various obstacles being managed from a probabilistic perspective. A proof of the existence and uniqueness of the proposed mathematical model’s solution is given for large times. A numerical resolution scheme based on the splitting method is implemented and then applied to crowd evacuation in a non connected bounded domain with one rectangular obstacle. The evacuation time of the room is then calculated by our technique, according to the dimensions and position of a square-shaped obstacle, and finally compared to the time obtained by a deterministic approach by means of randomly varying some of its parameters.

Predicting Definite Article Usages in New Englishes: Variety Outweighs Genre and Syntactic Function in Nigerian English

Variability in the use of the definite article in New Englishes, and in particular, Nigerian English has received the least attention from a quantitative, probabilistic and predictive perspective. The present study narrows this gap by not only assessing the extent to which article use in Nigerian English varies, but by also simultaneously testing out previous claims found in similar varieties, using similar corpus data from the Nigerian component of the International Corpus of English (ICE). Following theoretic framework for article use by Hawkins (1978) and Prince (1981), Wahid (2013) found that variability in definite article usage in New Englishes is more predictable on the basis of genre than on the basis of variety. Revising Wahid’s method and reconceptualising same theoretic frameworks of Hawkins and Prince, together with a comparable corpus sample of 8674 definite article the from ICE-Nigeria, the extent of article usage variability in the Nigerian variety is not only shown but also that variety outweighs genre and syntactic function predicting article usage in New Englishes.

Graph Learning From Data Under Laplacian and Structural Constraints

Graphs are fundamental mathematical structures used in various fields to represent data, signals, and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i) formulation of various graph learning problems, (ii) their probabilistic interpretations, and (iii) associated algorithms. Specifically, graph learning problems are posed as the estimation of graph Laplacian matrices from some observed data under given structural constraints (e.g., graph connectivity and sparsity level). From a probabilistic perspective, the problems of interest correspond to maximum a posteriori parameter estimation of Gaussian–Markov random field models, whose precision (inverse covariance) is a graph Laplacian matrix. For the proposed graph learning problems, specialized algorithms are developed by incorporating the graph Laplacian and structural constraints. The experimental results demonstrate that the proposed algorithms outperform the current state-of-the-art methods in terms of accuracy and computational efficiency.

Two Perspectives of the 2D Unit Area Quantum Sphere and Their Equivalence

2D Liouville quantum gravity (LQG) is used as a toy model for 4D quantum gravity and is the theory of world-sheet in string theory. Recently there has been growing interest in studying LQG in the realm of probability theory: David, Kupiainen, Rhodes, Vargas (2014) and Duplantier, Miller, Sheffield (2014) both provide a probabilistic perspective of the LQG on the 2D sphere. In particular, in each of them one may find a definition of the so-called unit area quantum sphere. We examine these two perspectives and prove their equivalence by showing that the respective unit area quantum spheres are the same. This is done by considering a unified limiting procedure for defining both objects.