Probabilistic Version Research Articles

An architecture framework for enterprise IT service availability analysis

This paper presents an integrated enterprise architecture framework for qualitative and quantitative modeling and assessment of enterprise IT service availability. While most previous work has either focused on formal availability methods such as fault trees or qualitative methods such as maturity models, this framework offers a combination. First, a modeling and assessment framework is described. In addition to metamodel classes, relationships and attributes suitable for availability modeling, the framework also features a formal computational model written in a probabilistic version of the object constraint language. The model is based on 14 systemic factors impacting service availability and also accounts for the structural features of the service architecture. Second, the framework is empirically tested in nine enterprise information system case studies. Based on an initial availability baseline and the annual evolution of the 14 factors of the model, annual availability predictions are made and compared with the actual outcomes as reported in SLA reports and system logs. The practical usefulness of the method is discussed based on the outcomes of a workshop conducted with the participating enterprises, and some directions for future research are offered.

On the equivalence of PLSI and projected clustering

The problem of projected clustering was first proposed in the ACMSIGMOD Conference in 1999, and the Probabilistic Latent Semantic Indexing (PLSI) technique was independently proposed in the ACMSIGIR Conference in the same year. Since then, more than two thousand papers have been written on these problems by the database, data mining and information retrieval communities, along completely independent lines of work . In this paper, we show that these two problems are essentially equivalent, under a probabilistic interpretation to the projected clustering problem. We will show that the EM-algorithm, when applied to the probabilistic version of the projected clustering problem, can be almost identically interpreted as the PLSI technique. The implications of this equivalence are significant, in that they imply the cross-usability of many of the techniques which have been developed for these problems over the last decade. We hope that our observations about the equivalence of these problems will stimulate further research which can significantly improve the currently available solutions for either of these problems.

Injections de Sobolev probabilistes et applications

In this article, we give probabilistic versions of Sobolev embeddings on any Riemannian manifold $(M,g)$. More precisely, we prove that for natural probability measures on $L^2(M)$, almost every function belong to all spaces $L^p(M)$, $p<+\infty$. We then give applications to the study of the growth of the $L^p$ norms of spherical harmonics on spheres $\mathbb{S}^d$: we prove (again for natural probability measures) that almost every Hilbert base of $L^2( \mathbb{S}^d)$ made of spherical harmonics has all its elements uniformly bounded in all $L^p(\mathbb{S}^d), p<+\infty$ spaces. We also prove similar results on tori $\mathbb{T}^d$. We give then an application to the study of the decay rate of damped wave equations in a frame-work where the geometric control property on Bardos-Lebeau-Rauch is not satisfied. Assuming that it is violated for a measure $0$ set of trajectories, we prove that there exists almost surely a rate. Finally, we conclude with an application to the study of the $H^1$-supercritical wave equation, for which we prove that for almost all initial data, the weak solutions are strong and unique, locally in time.

Consensus Clustering Based on a New Probabilistic Rand Index with Application to Subtopic Retrieval

We introduce a probabilistic version of the well-known Rand Index (RI) for measuring the similarity between two partitions, called Probabilistic Rand Index (PRI), in which agreements and disagreements at the object-pair level are weighted according to the probability of their occurring by chance. We then cast consensus clustering as an optimization problem of the PRI value between a target partition and a set of given partitions, experimenting with a simple and very efficient stochastic optimization algorithm. Remarkable performance gains over input partitions as well as over existing related methods are demonstrated through a range of applications, including a new use of consensus clustering to improve subtopic retrieval.

Perturbation-based stochastic finite element analysis of the interface defects in composites via Response Function Method

The main aim of this paper is to present a mathematical model and its numerical realization for the composite material with stochastic interface defects employing the perturbation-based stochastic finite elements. The defects are modeled as the semicircular micro-cavities (“bubbles”) lying with their diameters on the reinforcement-matrix interface inside the weaker material region (matrix). Both total number of the defects as well as their radii may be defined as the truncated Gaussian random variables with the given first two probabilistic moments. The composite micro-geometry is simulated according to these parameters and the entire structure is discretized in both scales using traditional Finite Element Method procedures. Its probabilistic version is provided thanks to the Response Function Method, where several numerical tests with random parameter values varying around its mean value enable to determine the structural response and, thanks to the Least Squares Method, its final probabilistic moments. The proposed technique has been validated on the shear test for the carbon–epoxy composite with the few interface defects and Young modulus of the matrix being Gaussian random variable, where three meshes with various density show overall convergence of the numerical procedure.

On the biological plausibility of artificial metaplasticity learning algorithm

The training algorithm studied in this paper is inspired by the biological metaplasticity property of neurons. During the training phase, the Artificial Metaplasticity Learning Algorithm could be considered a new probabilistic version of the presynaptic rule, as during this phase the algorithm assigns higher values for updating the weights in the less probable activations than in the ones with higher probability. The algorithm is proposed for Artificial Neural Networks in general, although results at the moment have only been implemented and tested for Multilayer Perceptrons. Tested on different multidisciplinary applications, experiments show a much more efficient training, improving also Multilayer Perceptron results till the performance of the best systems in the state of the art, systems that usually are much more complex.

An end-to-end stochastic network calculus with effective bandwidth and effective capacity

Network calculus is an elegant theory which uses envelopes to determine the worst-case performance bounds in a network. Statistical network calculus is the probabilistic version of network calculus, which strives to retain the simplicity of envelope approach from network calculus and use the arguments of statistical multiplexing to determine probabilistic performance bounds in a network. The tightness of the determined probabilistic bounds depends on the efficiency of modelling stochastic properties of the arrival traffic and the service available to the traffic at a network node. The notion of effective bandwidth from large deviations theory is a well known statistical descriptor of arrival traffic. Similarly, the notion of effective capacity summarizes the time varying resource availability to the arrival traffic at a network node. The main contribution of this paper is to establish an end-to-end stochastic network calculus with the notions of effective bandwidth and effective capacity which provides efficient end-to-end delay and backlog bounds that grows linearly in the number of nodes (H) traversed by the arrival traffic, under the assumption of independence.

Sharp Inequalities for Differentially Subordinate Harmonic Functions and Martingales

AbstractWe determine the best constants Cp,∞ and C1,p, 1 &lt; p &lt; ∞, for which the following holds. If u, v are orthogonal harmonic functions on a Euclidean domain such that v is differentially subordinate to u, thenIn particular, the inequalities are still sharp for the conjugate harmonic functions on the unit disc of ℝ2. Sharp probabilistic versions of these estimates are also studied. As an application, we establish a sharp version of the classical logarithmic inequality of Zygmund.

Behavioural equivalences of a probabilistic pi-calculus

Although different kinds of probabilistic π-calculus have been introduced and found their place in quantitative verification and evaluation, their behavioural equivalences still lack a deep investigation. We propose a simple probabilistic extension of the π-calculus, πp, which is inspired by Herescu and Palamidessi’s probabilistic asynchronous π-calculus. An early semantics of our πp is presented. We generalise several classic behavioural equivalences to probabilistic versions, obtaining the probabilistic (strong) barbed equivalence and probabilistic bisimulation for πp. Then we prove that the coincidence between the barbed equivalence and bisimilarity in the π-calculus is preserved in the probabilistic setting.

A probabilistic position value

In this article, we generalize the position value, defined by Meessen (1988) for the class of deterministic communication situations, to the class of generalized probabilistic communication situations (G´ omez et al. (2008)). We provide two characterizations of this new allocation rule. Following in Slikker’s (2005a) footsteps, we characterize the probabilistic position value using probabilistic versions of component e ciency and balanced link contributions. Then we generalize the notion of link potential, defined by Slikker (2005b) for the class of deterministic communication situations, to the class of generalized probabilistic communication situations, and use it to characterize our allocation rule. Finally, we show that these two characterizations are logically equivalent.

Application of Relevance Vector Machine for Prediction of Ultimate Capacity of Driven Piles in Cohesionless Soils

This paper examines the potential of relevance vector machine (RVM) in prediction of ultimate capacity of driven piles in cohesionless soils. RVM is a Bayesian framework for regression and classification with analogous sparsity properties to the support vector machine (SVM). In this study, RVM has been used as a regression tool. It can be seen as a probabilistic version of SVM. In this study, RVM model outperforms the artificial neural network (ANN) model based on root-mean-square-error (RMSE) and mean-absolute-error (MAE) performance criteria. It also estimates the prediction variance. An equation has been developed for the prediction of ultimate capacity of driven piles in cohesionless soils based on the RVM model. The results show that the RVM model has the potential to be a practical tool for the prediction of ultimate capacity of driven piles in cohesionless soils.

Absolute uniqueness of phase retrieval with random illumination

Random illumination is proposed to enforce absolute uniqueness and resolve all types of ambiguity, trivial or nontrivial, in phase retrieval. Almost sure irreducibility is proved for any complex-valued object whose support set has rank ⩾ 2. While the new irreducibility result can be viewed as a probabilistic version of the classical result by Bruck, Sodin and Hayes, it provides a novel perspective and an effective method for phase retrieval. In particular, almost sure uniqueness, up to a global phase, is proved for complex-valued objects under general two-point conditions. Under a tight sector constraint absolute uniqueness is proved to hold with probability exponentially close to unity as the object sparsity increases. Under a magnitude constraint with random amplitude illumination, uniqueness modulo global phase is proved to hold with probability exponentially close to unity as object sparsity increases. For general complex-valued objects without any constraint, almost sure uniqueness up to global phase is established with two sets of Fourier magnitude data under two independent illuminations. Numerical experiments suggest that random illumination essentially alleviates most, if not all, numerical problems commonly associated with the standard phasing algorithms.

Approximating Markov processes through filtration

In this paper, we define a probabilistic version of filtration and use it to provide a finite approximation of Markov processes. In order to measure the approximation, we employ probability logic to construct the final Markov process and define a metric on the set of Markov processes through this logic. Moreover, we show that the set endowed with this metric is a Polish space. Finally we point to some questions connecting approximation to uniformity and approximate bisimilarity as topics for future research.

Quantum Decision Making by Social Agents

The influence of additional information on the decision making of agents, who are interacting members of a society, is analyzed within the mathematical framework based on the use of quantum probabilities. The introduction of social interactions, which influence the decisions of individual agents, leads to a generalization of the quantum decision theory developed earlier by the authors for separate individuals. The generalized approach is free of the standard paradoxes of classical decision theory. This approach also explains the error attenuation effects observed for the paradoxes occurring when decision makers, who are members of a society, consult with each other, increasing in this way the available mutual information. A precise correspondence between quantum decision theory and classical utility theory is formulated via the introduction of an intermediate probabilistic version of utility theory of a novel form, which obeys the requirement that zero-utility prospects should have zero probability weights.

Which Fine-Tuning Arguments Are Fine?

The argument from naturalness is widely employed in contemporary quantum field theory. Essentially a formalized aesthetic criterion, it received a meaning in the debate on the Higgs mechanism, which goes beyond aesthetics. We follow the history of technical definitions of fine tuning at the scale of electroweak symmetry breaking. It is argued that they give rise to a special interpretation of probability, which we call Gedankenfrequency. By extension of its original meaning, the argument from naturalness is used to compare different models beyond the Standard Model. We show that in this case naturalness cannot be defined objectively. Rather, it functions as socio-historical heuristics in particle physics and it contributes to the advent of a probabilistic version of Popper's falsificationism.

Probabilistic Standard Penetration Test–Based Liquefaction–Triggering Procedure

AbstractA probabilistic version of the Idriss and Boulanger standard penetration test (SPT)–based liquefaction triggering correlation is derived using a maximum likelihood approach and an updated case history database. Measurement and estimation uncertainties in the cyclic stress ratio (CSR) and SPT (N1)60cs values and the effects of the choice-based sampling bias in the case history database are taken into account. The results of sensitivity analyses show that the position of the most likely triggering curve is well constrained by the case history data and that the magnitude of the total error term is also reasonably constrained. The most likely value for the SD of the error term in the triggering correlation is, however, found to be dependent on the uncertainties assigned to the CSR and (N1)60cs. The results of the sensitivity study appear to provide reasonable bounds on the effects of different interpretations on the positions of the triggering curves for various probabilities of liquefaction. Methods ...

Stochastic portfolio optimization with proportional transaction costs: Convex reformulations and computational experiments

We propose a probabilistic version of the Markowitz portfolio problem with proportional transaction costs. We derive equivalent convex reformulations, and analyze their computational efficiency for solving large (up to 2000 securities) portfolio problems. There is a great disparity in the solution times. The time differential between formulations can reach several orders of magnitude for the largest instances. The second-order cone formulation in which the number of quadratic terms is invariant to the number of assets is the most efficient.

Effectiveness of Partition and Graph Theoretic Clustering Algorithms for Multiple Source Partial Discharge Pattern Classification Using Probabilistic Neural Network and Its Adaptive Version: A Critique Based on Experimental Studies

Partial discharge (PD) is a major cause of failure of power apparatus and hence its measurement and analysis have emerged as a vital field in assessing the condition of the insulation system. Several efforts have been undertaken by researchers to classify PD pulses utilizing artificial intelligence techniques. Recently, the focus has shifted to the identification of multiple sources of PD since it is often encountered in real‐time measurements. Studies have indicated that classification of multi‐source PD becomes difficult with the degree of overlap and that several techniques such as mixed Weibull functions, neural networks, and wavelet transformation have been attempted with limited success. Since digital PD acquisition systems record data for a substantial period, the database becomes large, posing considerable difficulties during classification. This research work aims firstly at analyzing aspects concerning classification capability during the discrimination of multisource PD patterns. Secondly, it attempts at extending the previous work of the authors in utilizing the novel approach of probabilistic neural network versions for classifying moderate sets of PD sources to that of large sets. The third focus is on comparing the ability of partition‐based algorithms, namely, the labelled (learning vector quantization) and unlabelled (K‐means) versions, with that of a novel hypergraph‐based clustering method in providing parsimonious sets of centers during classification.

Probabilistic (Quasi)metric Versions for a Stability Result of Baker

By using the fixed point method, we obtain a version of a stability result of Baker in probabilistic metric and quasimetric spaces under triangular norms of Hadžić type. As an application, we prove a theorem regarding the stability of the additive Cauchy functional equation in random normed spaces.

Probabilistic version of the Robertson and Wride method for liquefaction evaluation: development and application

The Robertson and Wride method is the most widely used cone penetration test (CPT)-based method for soil liquefaction evaluation. This method is a deterministic model, which expresses liquefaction potential in terms of factor of safety. On many occasions, there is a need to express the liquefaction potential in terms of liquefaction probability. Although several probabilistic models are available in the literature, there is an advantage having a probabilistic version of the Robertson and Wride method so that the engineer who prefers to use this method can obtain additional information of liquefaction probability with minimal extra effort. In this paper, a simple model is developed, which links the factor of safety determined by the Robertson and Wride method to the liquefaction probability. The model, referred to as the probabilistic RW model, is developed, and verified, in a mathematically rigorous manner. Simplified equations for assessing the variation of liquefaction probability caused by the uncertainty in input parameters are also developed. Example applications are presented to demonstrate the developed models.