A stopping rule while searching for optimal solution of facility-location

Solutions to combinatorial optimization, such as p-median problems of locating facilities, frequently rely on heuristics to minimize the objective function. The minimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. However, pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small branch of the literature suggests using statistical principles to estimate the minimum and use the estimate for either stopping or evaluating the quality of the solution. In this paper we use test-problems taken from Baesley's OR-library and apply Simulated Annealing on these p-median problems. We do this for the purpose of comparing suggested methods of minimum estimation and, eventually, provide a recommendation for practioners. An illustration ends the paper being a problem of locating some 70 distribution centers of the Swedish Post in a region.

A Spatial-Temporal Downscaling Approach To Construction Of Rainfall Intensity-Duration-Frequency Relations In The Context Of Climate Change

This paper proposes a spatial-temporal downscaling approach to construction of the intensity-duration-frequency (IDF) relations at a local site in the context of climate change and variability. More specifically, the proposed approach is based on a combination of a spatial downscaling method to link large-scale climate variables given by General Circulation Model (GCM) simulations with daily extreme precipitations at a site and a temporal downscaling procedure to describe the relationships between daily and sub-daily extreme precipitations based on the scaling General Extreme Value (GEV) distribution. The feasibility and accuracy of the suggested method were assessed using rainfall data available at eight stations in Quebec (Canada) for the 1961-2000 period and climate simulations under four different climate change scenarios provided by the Canadian (CGCM3) and UK (HadCM3) GCM models. Results of this application have indicated that it is feasible to link sub-daily extreme rainfalls at a local site with large-scale GCM-based daily climate predictors for the construction of the IDF relations for present (1961-1990) and future (2020s, 2050s, and 2080s) periods at a given site under different climate change scenarios. In addition, it was found that annual maximum rainfalls downscaled from the HadCM3 displayed a smaller change in the future, while those values estimated from the CGCM3 indicated a large increasing trend for future periods. This result has demonstrated the presence of high uncertainty in climate simulations provided by different GCMs. In summary, the proposed spatial-temporal downscaling method provided an essential tool for the estimation of extreme rainfalls that are required for various climate-related impact assessment studies for a given region.

An evolving possibilistic fuzzy modeling approach for value-at-risk estimation

Market risk exposure plays a key role for nancial institutions risk management. A possible measure for this exposure is to evaluate losses likely to incurwhen the price of the portfolio's assets declines using Value-at-Risk (VaR) estimates, one of the most prominent measure of nancial downside market risk. This paper suggests an evolving possibilistic fuzzy modeling approach for VaR estimation. The approach is based on an extension of the possibilistic fuzzy c-means clustering and functional fuzzy rule-based modeling, which employs memberships and typicalities to update clusters and creates new clusters based on a statistical control distance-based criteria. ePFM also uses an utility measure to evaluate the quality of the current cluster structure. Computational experiments consider data of the main global equity market indexes of United States, London, Germany, Spain and Brazil from January 2000 to December 2012 for VaR estimation using ePFM, traditional VaR benchmarks such as Historical Simulation, GARCH, EWMA, and Extreme Value Theory and state of the art evolving approaches. The results show that ePFM is a potential candidate for VaR modeling, with better performance than alternative approaches.

A Poisson mixed model with nonnormal random effect distribution

In this paper, we propose a random intercept Poisson model in which the random effect is assumed to follow a generalized log-gamma (GLG) distribution. This random effect accommodates (or captures) the overdispersion in the counts and induces within-cluster correlation. We derive the first two moments for the marginal distribution as well as the intraclass correlation. Even though numerical integration methods are, in general, required for deriving the marginal models, we obtain the multivariate negative binomial model from a particular parameter setting of the hierarchical model. An iterative process is derived for obtaining the maximum likelihood estimates for the parameters in the multivariate negative binomial model. Residual analysis is proposed and two applications with real data are given for illustration. (C) 2011 Elsevier B.V. All rights reserved.

(Table 4) Seasonal variation of sea spray sodium concentrations during 2004-2007 at Concordia Station, Antarctica

From November 2004 to December 2007, size-segregated aerosol samples were collected all-year-round at Dome C (East Antarctica) by using PM10 and PM2.5 samplers, and multi-stage impactors. The data set obtained from the chemical analysis provided the longest and the most time-resolved record of sea spray aerosol (sea salt Na+) in inner Antarctica. Sea spray showed a sharp seasonal pattern. The highest values measured in winter (Apr-Nov) were about ten times larger than in summer (Dec-Mar). For the first time, a size-distribution seasonal pattern was also shown: in winter, sea spray particles are mainly submicrometric, while their summer size-mode is around 1-2 µm. Meteorological analysis on a synoptic scale allowed the definition of atmospheric conditions leading sea spray to Dome C. An extreme-value approach along with specific environmental based criteria was taken to yield stronger fingerprints linking atmospheric circulation (means and anomalies) to extreme sea spray events. Air mass back-trajectory analyses for some high sea spray events allowed the identification of two major air mass pathways, reflecting different size distributions: micrometric fractions for transport from the closer Indian-Pacific sector, and sub-micrometric particles for longer trajectories over the Antarctic Plateau. The seasonal pattern of the SO4**2- /Na+ ratio enabled the identification of few events depleted in sulphate, with respect to the seawater composition. By using methanesulphonic acid (MSA) profile to evaluate the biogenic SO4**2- contribution, a more reliable sea salt sulphate was calculated. In this way, few events (mainly in April and in September) were identified originating probably from the "frost flower" source. A comparison with daily-collected superficial snow samples revealed that there is a temporal shift between aerosol and snow sea spray trends. This feature could imply a more complex deposition processes of sea spray, involving significant contribution of wet and diamond dust deposition, but further work has to be carried out to rule out the effect of wind re-distribution and to have more statistic significance.

Empirical global value chain analysis in electronics and automobile industries :An application of Asian international input-output tables

This study aims to examine the international value distribution structure among major East Asian economies and the US. The mainstream trade theory explains the gains from trade; however, global value chain (GVC) approach emphasises uneven benefits of globalization among trading partners. The present study is mainly based on this view, examining which economy gains the most and which the least from the East Asian production networks. Two key industries, i.e., electronics and automobile, are our principle focus. Input-output method is employed to trace the creation and flows of value-added within the region. A striking fact is that some ASEAN economies increasingly reduce their shares of value-added, taken by developed countries, particularly by Japan. Policy implications are discussed in the final section.

Tropospheric scintillation with concurrent rain attenuation at 50 GHz in Madrid

Tropospheric scintillation can become a significant impairment in satellite communication systems, especially in those with low fade-margin. Moreover, fast amplitude fluctuations due to scintillation are even larger when rain is present on the propagation path. Few studies of scintillation during rain have been reported and the statistical characterization is still not totally clear. This paper presents experimental results on the relationship between scintillation and rain attenuation obtained from slant-path attenuation measurements at 50 GHz. The study is focused on the probability density function (PDF) of various scintillation parameters. It is shown that scintillation intensity, measured as the standard deviation of the amplitude fluctuations, increases with rain attenuation; in the range 1-10 dB this relationship can be expressed by power-law or linear equations. The PDFs of scintillation intensity conditioned to a given rain attenuation level are lognormal, while the overall long-term PDF is well fltted by a generalized extreme valué (GEV) distribution. The short-term PDFs of amplitude conditioned to a given intensity are normal, although skewness effects are observed for the strongest intensities. A procedure is given to derive numerically the overall PDF of scintillation amplitude using a combination of conditional PDFs and local statistics of rain attenuation.

On a Second Order Condition for Max-Semistable Laws

2000 Mathematics Subject Classification: 62G32, 62G20.

On Estimation and Testing for Pareto Tails

2010 Mathematics Subject Classification: 62F10, 62F12.

Modelos de dispersão para extremos de precipitação. Estudo de caso: o nordeste do Brasil

In this thesis used four different methods in order to diagnose the precipitation extremes on Northeastern Brazil (NEB): Generalized Linear Model s via logistic regression and Poisson, extreme value theory analysis via generalized extre me value (GEV) and generalized Pareto (GPD) distributions and Vectorial Generalized Linea r Models via GEV (MVLG GEV). The logistic regression and Poisson models were used to identify the interactions between the precipitation extremes and other variables based on the odds ratios and relative risks. It was found that the outgoing longwave radiation was the indicator variable for the occurrence of extreme precipitation on eastern, northern and semi arid NEB, and the relative humidity was verified on southern NEB. The GEV and GPD distribut ions (based on the 95th percentile) showed that the location and scale parameters were presented the maximum on the eastern and northern coast NEB, the GEV verified a maximum core on western of Pernambuco influenced by weather systems and topography. The GEV and GPD shape parameter, for most regions the data fitted by Weibull negative an d Beta distributions (ξ < 0) , respectively. The levels and return periods of GEV (GPD) on north ern Maranhão (centerrn of Bahia) may occur at least an extreme precipitation event excee ding over of 160.9 mm /day (192.3 mm / day) on next 30 years. The MVLG GEV model found tha t the zonal and meridional wind components, evaporation and Atlantic and Pacific se a surface temperature boost the precipitation extremes. The GEV parameters show the following results: a) location ( ), the highest value was 88.26 ± 6.42 mm on northern Maran hão; b) scale ( σ ), most regions showed positive values, except on southern of Maranhão; an d c) shape ( ξ ), most of the selected regions were adjusted by the Weibull negative distr ibution ( ξ < 0 ). The southern Maranhão and southern Bahia have greater accuracy. The level period, it was estimated that the centern of Bahia may occur at least an extreme precipitatio n event equal to or exceeding over 571.2 mm/day on next 30 years.

Water Quality Indices from Unbalanced Spatio-Temporal Monitoring Designs

This chapter investigates a variety of water quality assessment tools for reservoirs with balanced/unbalanced monitoring designs and focuses on providing informative water quality assessments to ensure decision-makers are able to make risk-informed management decisions about reservoir health. In particular, two water quality assessment methods are described: non-compliance (probability of the number of times the indicator exceeds the recommended guideline) and amplitude (degree of departure from the guideline). Strengths and weaknesses of current and alternative water quality methods will be discussed. The proposed methodology is particularly applicable to unbalanced designs with/without missing values and reflects the general conditions and is not swayed too heavily by the occasional extreme value (very high or very low quality). To investigate the issues in greater detail, we use as a case study, a reservoir within South-East Queensland (SEQ), Australia. The purpose here is to obtain an annual score that reflected the overall water quality, temporally, spatially and across water quality indicators for each reservoir.

Idealised simulation of downburst winds

Convectively driven downburst winds pose a threat to structures and communities in many regions of Australia not subject to tropical cyclones. Extreme value analysis shows that for return periods of interest to engineering design these events produce higher gust wind speeds than synoptic scale windstorms. Despite this, comparatively little is known of the near ground wind structure of these potentially hazardous windstorms. With this in mind, a series of idealised three-dimensional numerical simulations were undertaken to investigate convective storm wind fields. A dry, non-hydrostatic, sub-cloud model with parameterisation of the microphysics was used. Simulations were run with a uniform 20 m horizontal grid resolution and a variable vertical resolution increasing from 1 m. A systematic grid resolution study showed further refinement did not alter the morphological structure of the outflow. Simulations were performed for stationary downbursts in a quiescent air field, stationary downbursts embedded within environmental boundary layer winds, and also translating downbursts embedded within environmental boundary layer winds.

Lower-bound collapse load Of square footing

Based on a radial moment field and the square yield criterion, a lower-bound collapse load is developed for a square footing subjected to a generalized contact pressure distribution. The current lower-bound collapse load compares well with the available upper-bound solutions.

The Role of Abduction in Self-Similarity

Based on the Aristotelian criterion referred to as 'abductio', Peirce suggests a method of hypothetical inference, which operates in a different way than the deductive and inductive methods. “Abduction is nothing but guessing” (Peirce, 7.219). This principle is of extreme value for the study of our understanding of mathematical self-similarity in both of its typical presentations: relative or absolute. For the first case, abduction incarnates the quantitative/qualitative relationships of a self-similar object or process; for the second case, abduction makes understandable the statistical treatment of self-similarity, 'guessing' the continuity of geometric features to the infinity through the use of a systematic stereotype (for instance, the assumption that the general shape of the Sierpiński triangle continuates identically into its particular shapes). The metaphor coined by Peirce, of an exact map containig itself the same exact map (a map of itself), is not only the most important precedent of Mandelbrot’s problem of measuring the boundaries of a continuous irregular surface with a logarithmic ruler, but also still being a useful abstraction for the conceptualisation of relative and absolute self-similarity, and its mechanisms of implementation. It is useful, also, for explaining some of the most basic geometric ontologies as mental constructions: in the notion of infinite convergence of points in the corners of a triangle, or the intuition for defining two parallel straight lines as two lines in a plane that 'never' intersect.

Direction dependence in supernova data: constraining isotropy

We revise and extend the extreme value statistic, introduced in Gupta et al., to study direction dependence in the high-redshift supernova data, arising either from departures, from the cosmological principle or due to direction-dependent statistical systematics in the data. We introduce a likelihood function that analytically marginalizes over the,Hubble constant and use it to extend our previous statistic. We also introduce a new statistic that is sensitive to direction dependence arising from living off-centre inside a large void as well as from previously mentioned reasons for anisotropy. We show that for large data sets, this statistic has a limiting form that can be computed analytically. We apply our statistics to the gold data sets from Riess et al., as in our previous work. Our revision and extension of the previous statistic show that the effect of marginalizing over the Hubble constant instead of using its best-fitting value on our results is only marginal. However, correction of errors in our previous work reduces the level of non-Gaussianity in the 2004 gold data that were found in our earlier work. The revised results for the 2007 gold data show that the data are consistent with isotropy and Gaussianity. Our second statistic confirms these results.