Evaluación de la susceptibilidad de las laderas a sufrir inestabilidades inducidas por terremotos: aplicación a la cuenca de drenaje del río Serpis (provincia de Alicante)

Se ha realizado un análisis para estimar la susceptibilidad de las laderas, en suelos de la cuenca de drenaje del río Serpis, a sufrir inestabilidades inducidas por terremotos. Para ello, se ha utilizado el denominado método de Newmark, que ha sido convenientemente modificado para contemplar la variabilidad que, de forma natural, se observa en las propiedades geotécnicas de los materiales. En el cálculo, se ha efectuado una simulación Monte Carlo, donde todas las propiedades geotécnicas que intervienen son tratadas como variables aleatorias. Los resultados obtenidos están expresados como probabilidad de que la aceleración crítica del talud sea menor o igual que 0.1g. Las susceptibilidades más elevadas se observan cuando los materiales están secos, pero en tal caso la extensión de territorio afectado es pequeña. En cambio, cuando el suelo está saturado se observa que gran parte del territorio presenta susceptibilidad Media o Baja, incluso con pendientes de 6 – 10º, frente a susceptibilidad Muy Baja – Nula, que los caracteriza cuando se encuentra seco. Se ha analizado también la posición de las zonas de mayor susceptibilidad con respecto a elementos constructivos existentes en el área.

Handling of Uncertainty in Life Cycle Inventory by Correlated Multivariate Lognormal Distributions: Application to the Design of Supply Chain Networks

Poster presented in the 24th European Symposium on Computer Aided Process Engineering (ESCAPE 24), Budapest, Hungary, June 15-18, 2014.

Handling of Uncertainty in Life Cycle Inventory by Correlated Multivariate Lognormal Distributions: Application to the Design of Supply Chain Networks

In this work, we analyze the effect of incorporating life cycle inventory (LCI) uncertainty on the multi-objective optimization of chemical supply chains (SC) considering simultaneously their economic and environmental performance. To this end, we present a stochastic multi-scenario mixed-integer linear programming (MILP) coupled with a two-step transformation scenario generation algorithm with the unique feature of providing scenarios where the LCI random variables are correlated and each one of them has the desired lognormal marginal distribution. The environmental performance is quantified following life cycle assessment (LCA) principles, which are represented in the model formulation through standard algebraic equations. The capabilities of our approach are illustrated through a case study of a petrochemical supply chain. We show that the stochastic solution improves the economic performance of the SC in comparison with the deterministic one at any level of the environmental impact, and moreover the correlation among environmental burdens provides more realistic scenarios for the decision making process.

A Quantile-Based Probabilistic Mean Value Theorem

For non-negative random variables with finite means we introduce an analogous of the equilibrium residual-lifetime distribution based on the quantile function. This allows us to construct new distributions with support (0, 1), and to obtain a new quantile-based version of the probabilistic generalization of Taylor's theorem. Similarly, for pairs of stochastically ordered random variables we come to a new quantile-based form of the probabilistic mean value theorem. The latter involves a distribution that generalizes the Lorenz curve. We investigate the special case of proportional quantile functions and apply the given results to various models based on classes of distributions and measures of risk theory. Motivated by some stochastic comparisons, we also introduce the “expected reversed proportional shortfall order”, and a new characterization of random lifetimes involving the reversed hazard rate function.

A four moments theorem for Gamma limits on a Poisson chaos

This paper deals with sequences of random variables belonging to a fixed chaos of order q generated by a Poisson random measure on a Polish space. The problem is investigated whether convergence of the third and fourth moment of such a suitably normalized sequence to the third and fourth moment of a centred Gamma law implies convergence in distribution of the involved random variables. A positive answer is obtained for q = 2 and q = 4. The proof of this four moments theorem is based on a number of new estimates for contraction norms. Applications concern homogeneous sums and U-statistics on the Poisson space.

Implicit stochastic Runge-Kutta methods for stochastic differential equations

In this paper we construct implicit stochastic Runge-Kutta (SRK) methods for solving stochastic differential equations of Stratonovich type. Instead of using the increment of a Wiener process, modified random variables are used. We give convergence conditions of the SRK methods with these modified random variables. In particular, the truncated random variable is used. We present a two-stage stiffly accurate diagonal implicit SRK (SADISRK2) method with strong order 1.0 which has better numerical behaviour than extant methods. We also construct a five-stage diagonal implicit SRK method and a six-stage stiffly accurate diagonal implicit SRK method with strong order 1.5. The mean-square and asymptotic stability properties of the trapezoidal method and the SADISRK2 method are analysed and compared with an explicit method and a semi-implicit method. Numerical results are reported for confirming convergence properties and for comparing the numerical behaviour of these methods.

Binomial leap methods for simulating stochastic chemical kinetics

This paper discusses efficient simulation methods for stochastic chemical kinetics. Based on the tau-leap and midpoint tau-leap methods of Gillespie [D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001)], binomial random variables are used in these leap methods rather than Poisson random variables. The motivation for this approach is to improve the efficiency of the Poisson leap methods by using larger stepsizes. Unlike Poisson random variables whose range of sample values is from zero to infinity, binomial random variables have a finite range of sample values. This probabilistic property has been used to restrict possible reaction numbers and to avoid negative molecular numbers in stochastic simulations when larger stepsize is used. In this approach a binomial random variable is defined for a single reaction channel in order to keep the reaction number of this channel below the numbers of molecules that undergo this reaction channel. A sampling technique is also designed for the total reaction number of a reactant species that undergoes two or more reaction channels. Samples for the total reaction number are not greater than the molecular number of this species. In addition, probability properties of the binomial random variables provide stepsize conditions for restricting reaction numbers in a chosen time interval. These stepsize conditions are important properties of robust leap control strategies. Numerical results indicate that the proposed binomial leap methods can be applied to a wide range of chemical reaction systems with very good accuracy and significant improvement on efficiency over existing approaches. (C) 2004 American Institute of Physics.

An optimal sequential procedure for a buying-selling problem with independent observations

We consider a buying-selling problem when two stops of a sequence of independent random variables are required. An optimal stopping rule and the value of a game are obtained.

Stochastic models for regulatory networks of the genetic toggle switch

Bistability arises within a wide range of biological systems from the A phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. in this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.

Structural change in macroeconomic time series: A complex systems perspective

We demonstrate that the process of generating smooth transitions Call be viewed as a natural result of the filtering operations implied in the generation of discrete-time series observations from the sampling of data from an underlying continuous time process that has undergone a process of structural change. In order to focus discussion, we utilize the problem of estimating the location of abrupt shifts in some simple time series models. This approach will permit its to address salient issues relating to distortions induced by the inherent aggregation associated with discrete-time sampling of continuous time processes experiencing structural change, We also address the issue of how time irreversible structures may be generated within the smooth transition processes. (c) 2005 Elsevier Inc. All rights reserved.

Advanced receivers for next generation wireless communication systems

Despite extensive progress on the theoretical aspects of spectral efficient communication systems, hardware impairments, such as phase noise, are the key bottlenecks in next generation wireless communication systems. The presence of non-ideal oscillators at the transceiver introduces time varying phase noise and degrades the performance of the communication system. Significant research literature focuses on joint synchronization and decoding based on joint posterior distribution, which incorporate both the channel and code graph. These joint synchronization and decoding approaches operate on well designed sum-product algorithms, which involves calculating probabilistic messages iteratively passed between the channel statistical information and decoding information. Channel statistical information, generally entails a high computational complexity because its probabilistic model may involve continuous random variables. The detailed knowledge about the channel statistics for these algorithms make them an inadequate choice for real world applications due to power and computational limitations. In this thesis, novel phase estimation strategies are proposed, in which soft decision-directed iterative receivers for a separate A Posteriori Probability (APP)-based synchronization and decoding are proposed. These algorithms do not require any a priori statistical characterization of the phase noise process. The proposed approach relies on a Maximum A Posteriori (MAP)-based algorithm to perform phase noise estimation and does not depend on the considered modulation/coding scheme as it only exploits the APPs of the transmitted symbols. Different variants of APP-based phase estimation are considered. The proposed algorithm has significantly lower computational complexity with respect to joint synchronization/decoding approaches at the cost of slight performance degradation. With the aim to improve the robustness of the iterative receiver, we derive a new system model for an oversampled (more than one sample per symbol interval) phase noise channel. We extend the separate APP-based synchronization and decoding algorithm to a multi-sample receiver, which exploits the received information from the channel by exchanging the information in an iterative fashion to achieve robust convergence. Two algorithms based on sliding block-wise processing with soft ISI cancellation and detection are proposed, based on the use of reliable information from the channel decoder. Dually polarized systems provide a cost-and spatial-effective solution to increase spectral efficiency and are competitive candidates for next generation wireless communication systems. A novel soft decision-directed iterative receiver, for separate APP-based synchronization and decoding, is proposed. This algorithm relies on an Minimum Mean Square Error (MMSE)-based cancellation of the cross polarization interference (XPI) followed by phase estimation on the polarization of interest. This iterative receiver structure is motivated from Master/Slave Phase Estimation (M/S-PE), where M-PE corresponds to the polarization of interest. The operational principle of a M/S-PE block is to improve the phase tracking performance of both polarization branches: more precisely, the M-PE block tracks the co-polar phase and the S-PE block reduces the residual phase error on the cross-polar branch. Two variants of MMSE-based phase estimation are considered; BW and PLP.

Advanced mean field methods:theory and practice

A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large. Because exact computations are infeasible in such cases and Monte Carlo sampling techniques may reach their limits, there is a need for methods that allow for efficient approximate computations. One of the simplest approximations is based on the mean field method, which has a long history in statistical physics. The method is widely used, particularly in the growing field of graphical models. Researchers from disciplines such as statistical physics, computer science, and mathematical statistics are studying ways to improve this and related methods and are exploring novel application areas. Leading approaches include the variational approach, which goes beyond factorizable distributions to achieve systematic improvements; the TAP (Thouless-Anderson-Palmer) approach, which incorporates correlations by including effective reaction terms in the mean field theory; and the more general methods of graphical models. Bringing together ideas and techniques from these diverse disciplines, this book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling.

UncertML: an XML schema for exchanging uncertainty

Authors from Burrough (1992) to Heuvelink et al. (2007) have highlighted the importance of GIS frameworks which can handle incomplete knowledge in data inputs, in decision rules and in the geometries and attributes modelled. It is particularly important for this uncertainty to be characterised and quantified when GI data is used for spatial decision making. Despite a substantial and valuable literature on means of representing and encoding uncertainty and its propagation in GI (e.g.,Hunter and Goodchild 1993; Duckham et al. 2001; Couclelis 2003), no framework yet exists to describe and communicate uncertainty in an interoperable way. This limits the usability of Internet resources of geospatial data, which are ever-increasing, based on specifications that provide frameworks for the ‘GeoWeb’ (Botts and Robin 2007; Cox 2006). In this paper we present UncertML, an XML schema which provides a framework for describing uncertainty as it propagates through many applications, including online risk management chains. This uncertainty description ranges from simple summary statistics (e.g., mean and variance) to complex representations such as parametric, multivariate distributions at each point of a regular grid. The philosophy adopted in UncertML is that all data values are inherently uncertain, (i.e., they are random variables, rather than values with defined quality metadata).

Web based expert elicitation of uncertainties in environmental model inputs

When constructing and using environmental models, it is typical that many of the inputs to the models will not be known perfectly. In some cases, it will be possible to make observations, or occasionally physics-based uncertainty propagation, to ascertain the uncertainty on these inputs. However, such observations are often either not available or even possible, and another approach to characterising the uncertainty on the inputs must be sought. Even when observations are available, if the analysis is being carried out within a Bayesian framework then prior distributions will have to be specified. One option for gathering or at least estimating this information is to employ expert elicitation. Expert elicitation is well studied within statistics and psychology and involves the assessment of the beliefs of a group of experts about an uncertain quantity, (for example an input / parameter within a model), typically in terms of obtaining a probability distribution. One of the challenges in expert elicitation is to minimise the biases that might enter into the judgements made by the individual experts, and then to come to a consensus decision within the group of experts. Effort is made in the elicitation exercise to prevent biases clouding the judgements through well-devised questioning schemes. It is also important that, when reaching a consensus, the experts are exposed to the knowledge of the others in the group. Within the FP7 UncertWeb project (http://www.uncertweb.org/), there is a requirement to build a Webbased tool for expert elicitation. In this paper, we discuss some of the issues of building a Web-based elicitation system - both the technological aspects and the statistical and scientific issues. In particular, we demonstrate two tools: a Web-based system for the elicitation of continuous random variables and a system designed to elicit uncertainty about categorical random variables in the setting of landcover classification uncertainty. The first of these examples is a generic tool developed to elicit uncertainty about univariate continuous random variables. It is designed to be used within an application context and extends the existing SHELF method, adding a web interface and access to metadata. The tool is developed so that it can be readily integrated with environmental models exposed as web services. The second example was developed for the TREES-3 initiative which monitors tropical landcover change through ground-truthing at confluence points. It allows experts to validate the accuracy of automated landcover classifications using site-specific imagery and local knowledge. Experts may provide uncertainty information at various levels: from a general rating of their confidence in a site validation to a numerical ranking of the possible landcover types within a segment. A key challenge in the web based setting is the design of the user interface and the method of interacting between the problem owner and the problem experts. We show the workflow of the elicitation tool, and show how we can represent the final elicited distributions and confusion matrices using UncertML, ready for integration into uncertainty enabled workflows.We also show how the metadata associated with the elicitation exercise is captured and can be referenced from the elicited result, providing crucial lineage information and thus traceability in the decision making process.

Describing and communicating uncertainty within the semantic web

The Semantic Web relies on carefully structured, well defined, data to allow machines to communicate and understand one another. In many domains (e.g. geospatial) the data being described contains some uncertainty, often due to incomplete knowledge; meaningful processing of this data requires these uncertainties to be carefully analysed and integrated into the process chain. Currently, within the SemanticWeb there is no standard mechanism for interoperable description and exchange of uncertain information, which renders the automated processing of such information implausible, particularly where error must be considered and captured as it propagates through a processing sequence. In particular we adopt a Bayesian perspective and focus on the case where the inputs / outputs are naturally treated as random variables. This paper discusses a solution to the problem in the form of the Uncertainty Markup Language (UncertML). UncertML is a conceptual model, realised as an XML schema, that allows uncertainty to be quantified in a variety of ways i.e. realisations, statistics and probability distributions. UncertML is based upon a soft-typed XML schema design that provides a generic framework from which any statistic or distribution may be created. Making extensive use of Geography Markup Language (GML) dictionaries, UncertML provides a collection of definitions for common uncertainty types. Containing both written descriptions and mathematical functions, encoded as MathML, the definitions within these dictionaries provide a robust mechanism for defining any statistic or distribution and can be easily extended. Universal Resource Identifiers (URIs) are used to introduce semantics to the soft-typed elements by linking to these dictionary definitions. The INTAMAP (INTeroperability and Automated MAPping) project provides a use case for UncertML. This paper demonstrates how observation errors can be quantified using UncertML and wrapped within an Observations & Measurements (O&M) Observation. The interpolation service uses the information within these observations to influence the prediction outcome. The output uncertainties may be encoded in a variety of UncertML types, e.g. a series of marginal Gaussian distributions, a set of statistics, such as the first three marginal moments, or a set of realisations from a Monte Carlo treatment. Quantifying and propagating uncertainty in this way allows such interpolation results to be consumed by other services. This could form part of a risk management chain or a decision support system, and ultimately paves the way for complex data processing chains in the Semantic Web.