Approximation of quadratic irrationals and their pierce expansions

In this article two aims are pursued: on the one hand, to present arapidly converging algorithm for the approximation of square roots; on theother hand and based on the previous algorithm, to find the Pierce expansionsof a certain class of quadratic irrationals as an alternative way to themethod presented in 1984 by J.O. Shallit; we extend the method to findalso the Pierce expansions of quadratic irrationals of the form $2 (p-1)(p - \sqrt{p^2 - 1})$ which are not covered in Shallit's work.

A generalization of Hull and White formula and applications to option pricing approximation

By means of Malliavin Calculus we see that the classical Hull and White formulafor option pricing can be extended to the case where the noise driving thevolatility process is correlated with the noise driving the stock prices. Thisextension will allow us to construct option pricing approximation formulas.Numerical examples are presented.

Improving generalized regression analysis for the spatial prediction of forest communities

Aim This study used data from temperate forest communities to assess: (1) five different stepwise selection methods with generalized additive models, (2) the effect of weighting absences to ensure a prevalence of 0.5, (3) the effect of limiting absences beyond the environmental envelope defined by presences, (4) four different methods for incorporating spatial autocorrelation, and (5) the effect of integrating an interaction factor defined by a regression tree on the residuals of an initial environmental model. Location State of Vaud, western Switzerland. Methods Generalized additive models (GAMs) were fitted using the grasp package (generalized regression analysis and spatial predictions, http://www.cscf.ch/grasp). Results Model selection based on cross-validation appeared to be the best compromise between model stability and performance (parsimony) among the five methods tested. Weighting absences returned models that perform better than models fitted with the original sample prevalence. This appeared to be mainly due to the impact of very low prevalence values on evaluation statistics. Removing zeroes beyond the range of presences on main environmental gradients changed the set of selected predictors, and potentially their response curve shape. Moreover, removing zeroes slightly improved model performance and stability when compared with the baseline model on the same data set. Incorporating a spatial trend predictor improved model performance and stability significantly. Even better models were obtained when including local spatial autocorrelation. A novel approach to include interactions proved to be an efficient way to account for interactions between all predictors at once. Main conclusions Models and spatial predictions of 18 forest communities were significantly improved by using either: (1) cross-validation as a model selection method, (2) weighted absences, (3) limited absences, (4) predictors accounting for spatial autocorrelation, or (5) a factor variable accounting for interactions between all predictors. The final choice of model strategy should depend on the nature of the available data and the specific study aims. Statistical evaluation is useful in searching for the best modelling practice. However, one should not neglect to consider the shapes and interpretability of response curves, as well as the resulting spatial predictions in the final assessment.

Adaptive approach heuristics for the generalized assignment problem

The Generalized Assignment Problem consists in assigning a setof tasks to a set of agents with minimum cost. Each agent hasa limited amount of a single resource and each task must beassigned to one and only one agent, requiring a certain amountof the resource of the agent. We present new metaheuristics forthe generalized assignment problem based on hybrid approaches.One metaheuristic is a MAX-MIN Ant System (MMAS), an improvedversion of the Ant System, which was recently proposed byStutzle and Hoos to combinatorial optimization problems, and itcan be seen has an adaptive sampling algorithm that takes inconsideration the experience gathered in earlier iterations ofthe algorithm. Moreover, the latter heuristic is combined withlocal search and tabu search heuristics to improve the search.A greedy randomized adaptive search heuristic (GRASP) is alsoproposed. Several neighborhoods are studied, including one basedon ejection chains that produces good moves withoutincreasing the computational effort. We present computationalresults of the comparative performance, followed by concludingremarks and ideas on future research in generalized assignmentrelated problems.

Generalized canonical correlation analysis of matrices with different row and column orders

A Method is offered that makes it possible to apply generalized canonicalcorrelations analysis (CANCOR) to two or more matrices of different row and column order. The new method optimizes the generalized canonical correlationanalysis objective by considering only the observed values. This is achieved byemploying selection matrices. We present and discuss fit measures to assessthe quality of the solutions. In a simulation study we assess the performance of our new method and compare it to an existing procedure called GENCOM,proposed by Green and Carroll. We find that our new method outperforms the GENCOM algorithm both with respect to model fit and recovery of the truestructure. Moreover, as our new method does not require any type of iteration itis easier to implement and requires less computation. We illustrate the methodby means of an example concerning the relative positions of the political parties inthe Netherlands based on provincial data.

A decomposition formula for option prices in the Heston model and applications to option pricing approximation

By means of classical Itô's calculus we decompose option prices asthe sum of the classical Black-Scholes formula with volatility parameterequal to the root-mean-square future average volatility plus a term dueby correlation and a term due to the volatility of the volatility. Thisdecomposition allows us to develop first and second-order approximationformulas for option prices and implied volatilities in the Heston volatilityframework, as well as to study their accuracy. Numerical examples aregiven.

Nonlinear models and small sample performance of the generalized method of moments

In this paper I explore the issue of nonlinearity (both in the datageneration process and in the functional form that establishes therelationship between the parameters and the data) regarding the poorperformance of the Generalized Method of Moments (GMM) in small samples.To this purpose I build a sequence of models starting with a simple linearmodel and enlarging it progressively until I approximate a standard (nonlinear)neoclassical growth model. I then use simulation techniques to find the smallsample distribution of the GMM estimators in each of the models.

A genetic isolation gradient of populations of the Balearic green toad (Bufo balearicus) follows rising eastward fragmentation of the rural landscapes on the island of Menorca.

We present the first approach to the genetic diversity and structure of the Balearic toad (Bufo balearicus Boettger, 1880) for the island of Menorca. Forty-one individ- uals from 21 localities were analyzed for ten microsatellite loci. We used geo-refer- enced individual multilocus genotypes and a model-based clustering method for the inference of the number of populations and of the spatial location of genetic dis- continuities between those populations.¦Only six of the microsatellites analyzed were polymorphic. We revealed a northwest- ern area inhabited by a single population with several well-connected localities and another set of populations in the southeast that includes a few unconnected small units with genetically significant differences among them as well as with the individ- uals from the northwest of the island. The observed fragmentation may be explained by shifts from agricultural to tourism practices that have been taking place on the island of Menorca since the 1960s. The abandonment of rural activities in favor of urbanization and concomitant service areas has mostly affected the southeast of the island and is currently threatening the overall geographic connectivity between the different farming areas of the island that are inhabited by the Balearic toad.

The variability of money velocity in a generalized cash-in-advance model

This paper presents a general equilibrium model of money demand wherethe velocity of money changes in response to endogenous fluctuations in the interest rate. The parameter space can be divided into two subsets: one where velocity is constant and equal to one as in cash-in-advance models, and another one where velocity fluctuates as in Baumol (1952). Despite its simplicity, in terms of paramaters to calibrate, the model performs surprisingly well. In particular, it approximates the variability of money velocity observed in the U.S. for the post-war period. The model is then used to analyze the welfare costs of inflation under uncertainty. This application calculates the errors derived from computing the costs of inflation with deterministic models. It turns out that the size of this difference is small, at least for the levels of uncertainty estimated for the U.S. economy.

Snapshot gradient-recalled echo-planar images of rat brains at long echo time at 9.4 T.

With improved B 0 homogeneity along with satisfactory gradient performance at high magnetic fields, snapshot gradient-recalled echo-planar imaging (GRE-EPI) would perform at long echo times (TEs) on the order of T2*, which intrinsically allows obtaining strongly T2*-weighted images with embedded substantial anatomical details in ultrashort time. The aim of this study was to investigate the feasibility and quality of long TE snapshot GRE-EPI images of rat brain at 9.4 T. When compensating for B 0 inhomogeneities, especially second-order shim terms, a 200 x 200 microm2 in-plane resolution image was reproducibly obtained at long TE (>25 ms). The resulting coronal images at 30 ms had diminished geometric distortions and, thus, embedded substantial anatomical details. Concurrently with the very consistent stability, such GRE-EPI images should permit to resolve functional data not only with high specificity but also with substantial anatomical details, therefore allowing coregistration of the acquired functional data on the same image data set.

Latitudinal gradient effect on the wing geometry of Auca coctei (Guérin)(Lepidoptera, Nymphalidae)

Latitudinal gradient effect on the wing geometry of Auca coctei (Guérin) (Lepidoptera, Nymphalidae). When the environmental conditions change locally, the organisms and populations may also change in response to the selection pressure, so that the development of individuals may become affected in different degrees. There have been only a few studies in which the patterns of wing morphology variation have been looked into along a latitudinal gradient by means of geometric morphometrics. The aim of this work was to assess the morphologic differentiation of wing among butterfly populations of the species Auca coctei. For this purpose, 9 sampling locations were used which are representative of the distribution range of the butterfly and cover a wide latitudinal range in Chile. The wing morphology was studied in a total of 202 specimens of A. coctei (150 males and 52 females), based on digitization of 17 morphologic landmarks. The results show variation of wing shape in both sexes; however, for the centroid size there was significant variation only in females. Females show smaller centroid size at higher latitudes, therefore in this study the Bergmann reverse rule is confirmed for females of A. coctei. Our study extends morphologic projections with latitude, suggesting that wing variation is an environmental response from diverse origins and may influence different characteristics of the life history of a butterfly.

Generalized Multiobjective Multitree model solution using MOEA

In a previous paper a novel Generalized Multiobjective Multitree model (GMM-model) was proposed. This model considers for the first time multitree-multicast load balancing with splitting in a multiobjective context, whose mathematical solution is a whole Pareto optimal set that can include several results than it has been possible to find in the publications surveyed. To solve the GMM-model, in this paper a multi-objective evolutionary algorithm (MOEA) inspired by the Strength Pareto Evolutionary Algorithm (SPEA) is proposed. Experimental results considering up to 11 different objectives are presented for the well-known NSF network, with two simultaneous data flows

Incremental neural networks for function approximation

A new strategy for incremental building of multilayer feedforward neural networks is proposed in the context of approximation of functions from R-p to R-q using noisy data. A stopping criterion based on the properties of the noise is also proposed. Experimental results for both artificial and real data are performed and two alternatives of the proposed construction strategy are compared.

Comparison of the glomerular filtration rate in children by the new revised Schwartz formula and a new generalized formula.

The most widely used formula for estimating glomerular filtration rate (eGFR) in children is the Schwartz formula. It was revised in 2009 using iohexol clearances with measured GFR (mGFR) ranging between 15 and 75 ml/min × 1.73 m(2). Here we assessed the accuracy of the Schwartz formula using the inulin clearance (iGFR) method to evaluate its accuracy for children with less renal impairment comparing 551 iGFRs of 392 children with their Schwartz eGFRs. Serum creatinine was measured using the compensated Jaffe method. In order to find the best relationship between iGFR and eGFR, a linear quadratic regression model was fitted and a more accurate formula was derived. This quadratic formula was: 0.68 × (Height (cm)/serum creatinine (mg/dl))-0.0008 × (height (cm)/serum creatinine (mg/dl))(2)+0.48 × age (years)-(21.53 in males or 25.68 in females). This formula was validated using a split-half cross-validation technique and also externally validated with a new cohort of 127 children. Results show that the Schwartz formula is accurate until a height (Ht)/serum creatinine value of 251, corresponding to an iGFR of 103 ml/min × 1.73 m(2), but significantly unreliable for higher values. For an accuracy of 20 percent, the quadratic formula was significantly better than the Schwartz formula for all patients and for patients with a Ht/serum creatinine of 251 or greater. Thus, the new quadratic formula could replace the revised Schwartz formula, which is accurate for children with moderate renal failure but not for those with less renal impairment or hyperfiltration.

Bounds for the Betti numbers of generalized Cohen-Macaulay ideals

Upper bounds for the Betti numbers of generalized Cohen-Macaulay ideals are given. In particular, for the case of non-degenerate, reduced and ir- reducible projective curves we get an upper bound which only depends on their degree.