Productivity analysis and measurement

The state of the art in productivity measurement and analysis shows a gap between simple methods having little relevance in practice and sophisticated mathematical theory which is unwieldy for strategic and tactical planning purposes, -particularly at company level. An extension is made in this thesis to the method of productivity measurement and analysis based on the concept of added value, appropriate to those companies in which the materials, bought-in parts and services change substantially and a number of plants and inter-related units are involved in providing components for final assembly. Reviews and comparisons of productivity measurement dealing with alternative indices and their problems have been made and appropriate solutions put forward to productivity analysis in general and the added value method in particular. Based on this concept and method, three kinds of computerised models two of them deterministic, called sensitivity analysis and deterministic appraisal, and the third one, stochastic, called risk simulation, have been developed to cope with the planning of productivity and productivity growth with reference to the changes in their component variables, ranging from a single value 'to• a class interval of values of a productivity distribution. The models are designed to be flexible and can be adjusted according to the available computer capacity expected accuracy and 'presentation of the output. The stochastic model is based on the assumption of statistical independence between individual variables and the existence of normality in their probability distributions. The component variables have been forecasted using polynomials of degree four. This model is tested by comparisons of its behaviour with that of mathematical model using real historical data from British Leyland, and the results were satisfactory within acceptable levels of accuracy. Modifications to the model and its statistical treatment have been made as required. The results of applying these measurements and planning models to the British motor vehicle manufacturing companies are presented and discussed.

Bandwidth management of WiMAX systems and performance modeling

WiMAX has been introduced as a competitive alternative for metropolitan broadband wireless access technologies. It is connection oriented and it can provide very high data rates, large service coverage, and flexible quality of services (QoS). Due to the large number of connections and flexible QoS supported by WiMAX, the uplink access in WiMAX networks is very challenging since the medium access control (MAC) protocol must efficiently manage the bandwidth and related channel allocations. In this paper, we propose and investigate a cost-effective WiMAX bandwidth management scheme, named the WiMAX partial sharing scheme (WPSS), in order to provide good QoS while achieving better bandwidth utilization and network throughput. The proposed bandwidth management scheme is compared with a simple but inefficient scheme, named the WiMAX complete sharing scheme (WCPS). A maximum entropy (ME) based analytical model (MEAM) is proposed for the performance evaluation of the two bandwidth management schemes. The reason for using MEAM for the performance evaluation is that MEAM can efficiently model a large-scale system in which the number of stations or connections is generally very high, while the traditional simulation and analytical (e.g., Markov models) approaches cannot perform well due to the high computation complexity. We model the bandwidth management scheme as a queuing network model (QNM) that consists of interacting multiclass queues for different service classes. Closed form expressions for the state and blocking probability distributions are derived for those schemes. Simulation results verify the MEAM numerical results and show that WPSS can significantly improve the network's performance compared to WCPS.

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.

Nonlinear propagation of an optical speckle field

We provide a theoretical explanation of the results on the intensity distributions and correlation functions obtained from a random-beam speckle field in nonlinear bulk waveguides reported in the recent publication by Bromberg et al. [Nat. Photonics 4, 721 (2010) ].. We study both the focusing and defocusing cases and in the limit of small speckle size (short-correlated disordered beam) provide analytical asymptotes for the intensity probability distributions at the output facet. Additionally we provide a simple relation between the speckle sizes at the input and output of a focusing nonlinear waveguide. The results are of practical significance for nonlinear Hanbury Brown and Twiss interferometry in both optical waveguides and Bose-Einstein condensates. © 2012 American Physical Society.

Attributed graph kernels using the Jensen-Tsallis q-differences

We propose a family of attributed graph kernels based on mutual information measures, i.e., the Jensen-Tsallis (JT) q-differences (for q  ∈ [1,2]) between probability distributions over the graphs. To this end, we first assign a probability to each vertex of the graph through a continuous-time quantum walk (CTQW). We then adopt the tree-index approach [1] to strengthen the original vertex labels, and we show how the CTQW can induce a probability distribution over these strengthened labels. We show that our JT kernel (for q  = 1) overcomes the shortcoming of discarding non-isomorphic substructures arising in the R-convolution kernels. Moreover, we prove that the proposed JT kernels generalize the Jensen-Shannon graph kernel [2] (for q = 1) and the classical subtree kernel [3] (for q = 2), respectively. Experimental evaluations demonstrate the effectiveness and efficiency of the JT kernels.

Some Probabilistic Results in a Bisexual Branching Process with Immigration

2000 Mathematics Subject Classification: 60J80.

On the Lp-Norm Regression Models for Estimating Value-at-Risk

Analysis of risk measures associated with price series data movements and its predictions are of strategic importance in the financial markets as well as to policy makers in particular for short- and longterm planning for setting up economic growth targets. For example, oilprice risk-management focuses primarily on when and how an organization can best prevent the costly exposure to price risk. Value-at-Risk (VaR) is the commonly practised instrument to measure risk and is evaluated by analysing the negative/positive tail of the probability distributions of the returns (profit or loss). In modelling applications, least-squares estimation (LSE)-based linear regression models are often employed for modeling and analyzing correlated data. These linear models are optimal and perform relatively well under conditions such as errors following normal or approximately normal distributions, being free of large size outliers and satisfying the Gauss-Markov assumptions. However, often in practical situations, the LSE-based linear regression models fail to provide optimal results, for instance, in non-Gaussian situations especially when the errors follow distributions with fat tails and error terms possess a finite variance. This is the situation in case of risk analysis which involves analyzing tail distributions. Thus, applications of the LSE-based regression models may be questioned for appropriateness and may have limited applicability. We have carried out the risk analysis of Iranian crude oil price data based on the Lp-norm regression models and have noted that the LSE-based models do not always perform the best. We discuss results from the L1, L2 and L∞-norm based linear regression models. ACM Computing Classification System (1998): B.1.2, F.1.3, F.2.3, G.3, J.2.

On Special Case of Multiple Hypotheses Optimal Testing for Three Differently Distributed Random Variables

2000 Mathematics Subject Classification: 62P30.

An asymptotic test for the Conditional Value-at-Risk

Conditional Value-at-Risk (equivalent to the Expected Shortfall, Tail Value-at-Risk and Tail Conditional Expectation in the case of continuous probability distributions) is an increasingly popular risk measure in the fields of actuarial science, banking and finance, and arguably a more suitable alternative to the currently widespread Value-at-Risk. In my paper, I present a brief literature survey, and propose a statistical test of the location of the CVaR, which may be applied by practising actuaries to test whether CVaR-based capital levels are in line with observed data. Finally, I conclude with numerical experiments and some questions for future research.

Não-extensividade no contexto da atividade magnética solar: o problema da assimetria hemisférica

Solar activity indicators, each as sunspot numbers, sunspot area and flares, over the Sun’s photosphere are not considered to be symmetric between the northern and southern hemispheres of the Sun. This behavior is also known as the North-South Asymmetry of the different solar indices. Among the different conclusions obtained by several authors, we can point that the N-S asymmetry is a real and systematic phenomenon and is not due to random variability. In the present work, the probability distributions from the Marshall Space Flight Centre (MSFC) database are investigated using a statistical tool arises from well-known Non-Extensive Statistical Mechanics proposed by C. Tsallis in 1988. We present our results and discuss their physical implications with the help of theoretical model and observations. We obtained that there is a strong dependence between the nonextensive entropic parameter q and long-term solar variability presents in the sunspot area data. Among the most important results, we highlight that the asymmetry index q reveals the dominance of the North against the South. This behavior has been discussed and confirmed by several authors, but in no time they have given such behavior to a statistical model property. Thus, we conclude that this parameter can be considered as an effective measure for diagnosing long-term variations of solar dynamo. Finally, our dissertation opens a new approach for investigating time series in astrophysics from the perspective of non-extensivity.

Universal critical behavior of the two-dimensional Ising spin glass

We use finite size scaling to study Ising spin glasses in two spatial dimensions. The issue of universality is addressed by comparing discrete and continuous probability distributions for the quenched random couplings. The sophisticated temperature dependency of the scaling fields is identified as the major obstacle that has impeded a complete analysis. Once temperature is relinquished in favor of the correlation length as the basic variable, we obtain a reliable estimation of the anomalous dimension and of the thermal critical exponent. Universality among binary and Gaussian couplings is confirmed to a high numerical accuracy.

Can mean shift trackers perform better?

Many tracking algorithms have difficulties dealing with occlusions and background clutters, and consequently don't converge to an appropriate solution. Tracking based on the mean shift algorithm has shown robust performance in many circumstances but still fails e.g. when encountering dramatic intensity or colour changes in a pre-defined neighbourhood. In this paper, we present a robust tracking algorithm that integrates the advantages of mean shift tracking with those of tracking local invariant features. These features are integrated into the mean shift formulation so that tracking is performed based both on mean shift and feature probability distributions, coupled with an expectation maximisation scheme. Experimental results show robust tracking performance on a series of complicated real image sequences. © 2010 IEEE.

An Empirically Based Stochastic Turbulence Simulator with Temporal Coherence for Wind Energy Applications

In this dissertation, we develop a novel methodology for characterizing and simulating nonstationary, full-field, stochastic turbulent wind fields.

In this new method, nonstationarity is characterized and modeled via temporal coherence, which is quantified in the discrete frequency domain by probability distributions of the differences in phase between adjacent Fourier components.

The empirical distributions of the phase differences can also be extracted from measured data, and the resulting temporal coherence parameters can quantify the occurrence of nonstationarity in empirical wind data.

This dissertation (1) implements temporal coherence in a desktop turbulence simulator, (2) calibrates empirical temporal coherence models for four wind datasets, and (3) quantifies the increase in lifetime wind turbine loads caused by temporal coherence.

The four wind datasets were intentionally chosen from locations around the world so that they had significantly different ambient atmospheric conditions.

The prevalence of temporal coherence and its relationship to other standard wind parameters was modeled through empirical joint distributions (EJDs), which involved fitting marginal distributions and calculating correlations.

EJDs have the added benefit of being able to generate samples of wind parameters that reflect the characteristics of a particular site.

Lastly, to characterize the effect of temporal coherence on design loads, we created four models in the open-source wind turbine simulator FAST based on the \windpact turbines, fit response surfaces to them, and used the response surfaces to calculate lifetime turbine responses to wind fields simulated with and without temporal coherence.

The training data for the response surfaces was generated from exhaustive FAST simulations that were run on the high-performance computing (HPC) facilities at the National Renewable Energy Laboratory.

This process was repeated for wind field parameters drawn from the empirical distributions and for wind samples drawn using the recommended procedure in the wind turbine design standard \iec.

The effect of temporal coherence was calculated as a percent increase in the lifetime load over the base value with no temporal coherence.

Irreducibility of Random Hilbert Schemes

We prove that a random Hilbert scheme that parametrizes the closed subschemes with a fixed Hilbert polynomial in some projective space is irreducible and nonsingular with probability greater than $0.5$. To consider the set of nonempty Hilbert schemes as a probability space, we transform this set into a disjoint union of infinite binary trees, reinterpreting Macaulay's classification of admissible Hilbert polynomials. Choosing discrete probability distributions with infinite support on the trees establishes our notion of random Hilbert schemes. To bound the probability that random Hilbert schemes are irreducible and nonsingular, we show that at least half of the vertices in the binary trees correspond to Hilbert schemes with unique Borel-fixed points.

GIS technologies and spatial organization patterns among hunter-gatherers: an archaeological case study from Southern Patagonia (southern South America)

This paper discusses some aspects of hunter-gatherer spatial organization in southern South Patagonia, in later times to 10,000 cal yr BP. Various methods of spatial analysis, elaborated with a Geographic Information System (GIS) were applied to the distributional pattern of archaeological sites with radiocarbon dates. The shift in the distributional pattern of chronological information was assessed in conjunction with other lines of evidence within a biogeographic framework. Accordingly, the varying degrees of occupation and integration of coastal and interior spaces in human spatial organization are explained in association with the adaptive strategies hunter-gatherers have used over time. Both are part of the same human response to changes in risk and uncertainty variability in the region in terms of resource availability and environmental dynamics.