On the q=1/2 non-extensive maximum entropy distribution

A detailed mathematical analysis on the q = 1/2 non-extensive maximum entropydistribution of Tsallis' is undertaken. The analysis is based upon the splitting of such adistribution into two orthogonal components. One of the components corresponds to theminimum norm solution of the problem posed by the fulfillment of the a priori conditionson the given expectation values. The remaining component takes care of the normalizationconstraint and is the projection of a constant onto the Null space of the "expectation-values-transformation"

A non-extensive maximum entropy based regulations method for bad conditioned inverse problems

A regularization method based on the non-extensive maximum entropy principle is devised. Special emphasis is given to the q=1/2 case. We show that, when the residual principle is considered as constraint, the q=1/2 generalized distribution of Tsallis yields a regularized solution for bad-conditioned problems. The so devised regularized distribution is endowed with a component which corresponds to the well known regularized solution of Tikhonov (1977).

Frames: a maximum entropy statistical estimate of the inverse problem

A maximum entropy statistical treatment of an inverse problem concerning frame theory is presented. The problem arises from the fact that a frame is an overcomplete set of vectors that defines a mapping with no unique inverse. Although any vector in the concomitant space can be expressed as a linear combination of frame elements, the coefficients of the expansion are not unique. Frame theory guarantees the existence of a set of coefficients which is “optimal” in a minimum norm sense. We show here that these coefficients are also “optimal” from a maximum entropy viewpoint.

The maximum voltage drop in an on-chip power distribution network: analysis of square, triangular and hexagonal power pad arrangements

A mathematical model of the voltage drop which arises in on-chip power distribution networks is used to compare the maximum voltage drop in the case of different geometric arrangements of the pads supplying power to the chip. These include the square or Manhattan power pad arrangement, which currently predominates, as well as equilateral triangular and hexagonal arrangements. In agreement with the findings in the literature and with physical and SPICE models, the equilateral triangular power pad arrangement is found to minimize the maximum voltage drop. This headline finding is a consequence of relatively simple formulas for the voltage drop, with explicit error bounds, which are established using complex analysis techniques, and elliptic functions in particular.

Survival of wild adults of Ceratitis capitata (Wiedemann) under natural winter conditions in north east Spain

The overwintering of the Mediterranean fruit fly (medfly), Ceratitis capitata (Wiedemann) at the northern limits of its geographic distribution is not yet well known. With the aim of estimating the survival rate of medfly adults in northeast Spain under natural winter conditions, a two-winter-season trial was carried out. A control was carried out in a climatic chamber at 25°C. The results showed that medfly adults were unable to survive the entire winter season in the Girona area. Climatic conditions, including the daily minimum temperature, daily maximum temperature and the high rainfall, appeared to be involved in adult mortality in winter.

Rainfall is a risk factor for sporadic cases of Legionella pneumophila Pneumonia

It is not known whether rainfall increases the risk of sporadic cases of Legionella pneumonia. We sought to test this hypothesis in a prospective observational cohort study of non-immunosuppressed adults hospitalized for community-acquired pneumonia (1995-2011). Cases with Legionella pneumonia were compared with those with non-Legionella pneumonia. Using daily rainfall data obtained from the regional meteorological service we examined patterns of rainfall over the days prior to admission in each study group. Of 4168 patients, 231 (5.5%) had Legionella pneumonia. The diagnosis was based on one or more of the following: sputum (41 cases), antigenuria (206) and serology (98). Daily rainfall average was 0.556 liters/m2 in the Legionella pneumonia group vs. 0.328 liters/m2 for non-Legionella pneumonia cases (p = 0.04). A ROC curve was plotted to compare the incidence of Legionella pneumonia and the weighted median rainfall. The cut-off point was 0.42 (AUC 0.54). Patients who were admitted to hospital with a prior weighted median rainfall higher than 0.42 were more likely to have Legionella pneumonia (OR 1.35; 95% CI 1.02-1.78; p = .03). Spearman Rho correlations revealed a relationship between Legionella pneumonia and rainfall average during each two-week reporting period (0.14; p = 0.003). No relationship was found between rainfall average and non-Legionella pneumonia cases (−0.06; p = 0.24). As a conclusion, rainfall is a significant risk factor for sporadic Legionella pneumonia. Physicians should carefully consider Legionella pneumonia when selecting diagnostic tests and antimicrobial therapy for patients presenting with CAP after periods of rainfall.

Characteristics of 2D convective structures in Catalonia (NE Spain): an analysis using radar data and GIS

Flood simulation studies use spatial-temporal rainfall data input into distributed hydrological models. A correct description of rainfall in space and in time contributes to improvements on hydrological modelling and design. This work is focused on the analysis of 2-D convective structures (rain cells), whose contribution is especially significant in most flood events. The objective of this paper is to provide statistical descriptors and distribution functions for convective structure characteristics of precipitation systems producing floods in Catalonia (NE Spain). To achieve this purpose heavy rainfall events recorded between 1996 and 2000 have been analysed. By means of weather radar, and applying 2-D radar algorithms a distinction between convective and stratiform precipitation is made. These data are introduced and analyzed with a GIS. In a first step different groups of connected pixels with convective precipitation are identified. Only convective structures with an area greater than 32 km2 are selected. Then, geometric characteristics (area, perimeter, orientation and dimensions of the ellipse), and rainfall statistics (maximum, mean, minimum, range, standard deviation, and sum) of these structures are obtained and stored in a database. Finally, descriptive statistics for selected characteristics are calculated and statistical distributions are fitted to the observed frequency distributions. Statistical analyses reveal that the Generalized Pareto distribution for the area and the Generalized Extreme Value distribution for the perimeter, dimensions, orientation and mean areal precipitation are the statistical distributions that best fit the observed ones of these parameters. The statistical descriptors and the probability distribution functions obtained are of direct use as an input in spatial rainfall generators.

Effect of radar rainfall time resolution on the predictive capability of a distributed hydrologic model

The performance of a hydrologic model depends on the rainfall input data, both spatially and temporally. As the spatial distribution of rainfall exerts a great influence on both runoff volumes and peak flows, the use of a distributed hydrologic model can improve the results in the case of convective rainfall in a basin where the storm area is smaller than the basin area. The aim of this study was to perform a sensitivity analysis of the rainfall time resolution on the results of a distributed hydrologic model in a flash-flood prone basin. Within such a catchment, floods are produced by heavy rainfall events with a large convective component. A second objective of the current paper is the proposal of a methodology that improves the radar rainfall estimation at a higher spatial and temporal resolution. Composite radar data from a network of three C-band radars with 6-min temporal and 2 × 2 km2 spatial resolution were used to feed the RIBS distributed hydrological model. A modification of the Window Probability Matching Method (gauge-adjustment method) was applied to four cases of heavy rainfall to improve the observed rainfall sub-estimation by computing new Z/R relationships for both convective and stratiform reflectivities. An advection correction technique based on the cross-correlation between two consecutive images was introduced to obtain several time resolutions from 1 min to 30 min. The RIBS hydrologic model was calibrated using a probabilistic approach based on a multiobjective methodology for each time resolution. A sensitivity analysis of rainfall time resolution was conducted to find the resolution that best represents the hydrological basin behaviour.

Validation of and comparison between a semidistributed rainfall-runoff hydrological model (PREVAH) and a spatially distributed snow-evolution model (SnowModel) for snow cover prediction in mountain ecosystems

Snow cover is an important control in mountain environments and a shift of the snow-free period triggered by climate warming can strongly impact ecosystem dynamics. Changing snow patterns can have severe effects on alpine plant distribution and diversity. It thus becomes urgent to provide spatially explicit assessments of snow cover changes that can be incorporated into correlative or empirical species distribution models (SDMs). Here, we provide for the first time a with a lower overestimation comparison of two physically based snow distribution models (PREVAH and SnowModel) to produce snow cover maps (SCMs) at a fine spatial resolution in a mountain landscape in Austria. SCMs have been evaluated with SPOT-HRVIR images and predictions of snow water equivalent from the two models with ground measurements. Finally, SCMs of the two models have been compared under a climate warming scenario for the end of the century. The predictive performances of PREVAH and SnowModel were similar when validated with the SPOT images. However, the tendency to overestimate snow cover was slightly lower with SnowModel during the accumulation period, whereas it was lower with PREVAH during the melting period. The rate of true positives during the melting period was two times higher on average with SnowModel with a lower overestimation of snow water equivalent. Our results allow for recommending the use of SnowModel in SDMs because it better captures persisting snow patches at the end of the snow season, which is important when modelling the response of species to long-lasting snow cover and evaluating whether they might survive under climate change.

Hydrological evidence for a North Atlantic oscillation during the Little Ice Age outside its range observed since 1850.

An annual-resolved precipitation reconstruction for the last 800 yr in Southern Spain has been performed using stable carbon isotope (δ13C) of Pinus nigra tree rings. The reconstruction exhibits high- to low-frequency variability and distinguishes a Little Ice Age (LIA, AD 13501850) characterized by lower averaged rainfall than both in the transition from the Medieval Climate Anomaly to the LIA and in the 20th century. The driest conditions are recorded during the Maunder solar Minimum (mid 17thearly 18th centuries), in good agreement with the Spanish documentary archive. Similar linkage between solar activity (maximum/minimum) and precipitation (increase/decrease) is observed throughout the entire LIA. Additionally, the relationship between the hydrological pattern in the Iberian Peninsula and Morocco during the LIA suggests different spatial distribution of precipitation in the south-eastern sector of the North Atlantic region such as it is known currently. Whereas in the instrumental record the precipitation evolves similarly in both regions and opposite to the North Atlantic oscillation (NAO) index, the coldest periods of the LIA shows a contrasting pattern with drier conditions in the South of Spain and wetter in Northern Africa. We suggest an extreme negative NAO conditions, accompanied by a southward excursion of the winter rainfall band beyond that observed in the last century, can explain this contrast. The sustained NAO conditions could have been triggered by solar minima and higher volcanic activity during the LIA.

El clima i la producció d'olives a la Catalunya seca: el cas de Cabacés (el Priorat)

[cat] En un context de canvi climàtic cal estudiar les vulnerabilitats del territori a escala local. En aquest treball s'analitza la producció d'oli de qualitat en un indret de la Catalunya seca, Cabacés (el Priorat), i es posa en relació amb la variabilitat climàtica. Els resultats mostren que el clima té una influència important en la producció d'olives, sobretot les temperatures màximes del mes d'abril i les precipitacions del mes més sec, juliol. S'obté un model de regressió múltiple a partir d'aquestes dues variables climàtiques més influents en la producció. No obstant això, els valors del model s'allunyen dels reals a partir de l'any 2003 a causa d'un creixement molt elevat de la producció per l'extensió del reg de suport. Les futures vulnerabilitats no només depenen del canvi climàtic, sinó dels efectes del canvi global, fenomen que també engloba tots aquells canvis en els usos, hàbits i consums del territori.

Forecasting the maximum compensation offer in the automobile BI claims negotiation process

Most motor bodily injury (BI) claims are settled by negotiation, with fewer than 5% of cases going to court. A well-defined negotiation strategy is thus very useful for insurance companies. In this paper we assume that the monetary compensation awarded in court is the upper amount to be offered by the insurer in the negotiation process. Using a real database, a log-linear model is implemented to estimate the maximal offer. Non-spherical disturbances are detected. Correlation occurs when various claims are settled in the same judicial verdict. Group wise heteroscedasticity is due to the influence of the forensic valuation on the final compensation amount. An alternative approximation based on generalized inference theory is applied to estimate confidence intervals on variance components, since classical interval estimates may be unreliable for datasets with unbalanced structures.