Fermat's treatise on quadrature: A new reading

The Treatise on Quadrature of Fermat (c. 1659), besides containing the first known proof of the computation of the area under a higher parabola, R x+m/n dx, or under a higher hyperbola, R x-m/n dx with the appropriate limits of integration in each case , has a second part which was not understood by Fermat s contemporaries. This second part of the Treatise is obscure and difficult to read and even the great Huygens described it as'published with many mistakes and it is so obscure (with proofs redolent of error) that I have been unable to make any sense of it'. Far from the confusion that Huygens attributes to it, in this paper we try to prove that Fermat, in writing the Treatise, had a very clear goal in mind and he managed to attain it by means of a simple and original method. Fermat reduced the quadrature of a great number of algebraic curves to the quadrature of known curves: the higher parabolas and hyperbolas of the first part of the paper. Others, he reduced to the quadrature of the circle. We shall see how the clever use of two procedures, quite novel at the time: the change of variables and a particular case of the formulaof integration by parts, provide Fermat with the necessary tools to square very easily curves as well-known as the folium of Descartes, the cissoid of Diocles or the witch of Agnesi.

La ración de mantenimiento, la densidad de mantenimiento y la eficiencia de crecimiento de Engraulis ringens y Sardinops sagax como una medida de su potencia ecológica

Presentamos en este estudio resultados calculados sobre la potencia ecológica de la anchoveta y sardina peruana mediante el procesamiento de datos de los gastos metabólicos, velocidad de natación.e ingestión de alimento en relación a diferentes tallas de peces, temperaturas y densidades de alimento. Como medida de la potencia ecológica hemos calculado: (1) ración de mantenimiento, (2) la eficiencia de crecimiento y (3) densidad del alimento para mantenimiento. (para larvas). Asumiendo un alimento mixto de fito y zooplancton {1 g peso húmedo = 1000 cal) y una eficiencia de asimilación de 0.7 tenemos para la ración de mantenimiento expresada en calorías por individuo por día y en porcentaje del peso húmedo por día.

Quantitative Assessment of Handwriting Evidence: The Value of the Shape of the Letter "A"

To provide a quantitative support to the handwriting evidence evaluation, a new method was developed through the computation of a likelihood ratio based on a Bayesian approach. In the present paper, the methodology is briefly described and applied to data collected within a simulated case of a threatening letter. Fourier descriptors are used to characterise the shape of loops of handwritten characters "a" of the true writer of the threatening letter, and: 1) with reference characters "a" of the true writer of the threatening letter, and then 2) with characters "a" of a writer who did not write the threatening letter. The findings support that the probabilistic methodology correctly supports either the hypothesis of authorship or the alternative hypothesis. Further developments will enable the handwriting examiner to use this methodology as a helpful assistance to assess the strength of evidence in handwriting casework.

Nutritional ecology of blowflies (Diptera, Calliphoridae): estimates of critical larval weight for pupation on two different

Under natural environmental conditions, blowflies utilize discrete and ephemeral feeding resources such as decaying carcasses. Competition for food on such feeding substrates is usually very severe, and only the individuals that are capable of attaining the critical larval weight for pupation will be able to survive. This critical weight is hitherto unknown for several blowfly species; therefore, the current work is aimed at obtaining such a critical value for four blowfly species of the genera Chrysomya and Lucilia, deploying two types of feeding substrate, namely, artificial diet and macerated bovine meat. On the whole, the critical weights ranged from 30 to 35 mg. The lowest larval weight which permitted pupation was 30.0 mg for Chrysomya megacephala reared on macerated bovine meat. This species was also the best adapted to pupation at low larval weights in relation to the maximum larval weight for males. Regarding the pupation of females, the best-adapted individual was a C. albiceps specimen exhibiting a critical weight that was equal to 39.20 % of the maximum value obtained. Concerning all the species and diet types, the female individuals exhibited the lowest critical weights that produced viable pupae, probably representing an evolutionary strategy that favoured the survival of females, responsible for the egg formation, contributing to the establishment of future generations. Regarding the loss (in percentage) of adult biomass in relation to the third instar larvae, the females of C. megacephala lost less weight than males in both feeding substrates. On the other hand, such a loss of weight occurred in males of C. albiceps and L. cuprina.

Portfolio choice beyond the traditional approach

This paper surveys asset allocation methods that extend the traditional approach. An important feature of the the traditional approach is that measures the risk and return tradeoff in terms of mean and variance of final wealth. However, there are also other important features that are not always made explicit in terms of investor s wealth, information, and horizon: The investor makes a single portfolio choice based only on the mean and variance of her final financial wealth and she knows the relevant parameters in that computation. First, the paper describes traditional portfolio choice based on four basic assumptions, while the rest of the sections extend those assumptions. Each section will describe the corresponding equilibrium implications in terms of portfolio advice and asset pricing.

Comparative phylogeography of mutualists and the effect of the host on the genetic structure of its partners.

Whether or not species participating in specialized and obligate interactions display similar and simultaneous demographic variations at the intraspecific level remains an open question in phylogeography. In the present study, we used the mutualistic nursery pollination occurring between the European globeflower Trollius europaeus and its specialized pollinators in the genus Chiastocheta as a case study. Explicitly, we investigated if the phylogeographies of the pollinating flies are significantly different from the expectation under a scenario of plant-insect congruence. Based on a large-scale sampling, we first used mitochondrial data to infer the phylogeographical histories of each fly species. Then, we defined phylogeographical scenarios of congruence with the plant history, and used maximum likelihood and Bayesian approaches to test for plant-insect phylogeographical congruence for the three Chiastocheta species. We show that the phylogeographical histories of the three fly species differ. Only Chiastocheta lophota and Chiastocheta dentifera display strong spatial genetic structures, which do not appear to be statistically different from those expected under scenarios of phylogeographical congruence with the plant. The results of the present study indicate that the fly species responded in independent and different ways to shared evolutionary forces, displaying varying levels of congruence with the plant genetic structure

Determination of extreme floods using a distributed hydrological model

Hydrological models developed for extreme precipitation of PMP type are difficult to calibrate because of the scarcity of available data for these events. This article presents the process and results of calibration for a distributed hydrological model at fine scale developed for the estimation of probable maximal floods in the case of a PMP. This calibration is done on two Swiss catchments for two events of summer storms. The calculation done is concentrated on the estimation of the parameters of the model, divided in two parts. The first is necessary for the computation of flow speeds while the second is required for the determination of the initial and final infiltration capacities for each terrain type. The results, validated with the Nash equation show a good correlation between the simulated and observed flows. We also apply this model on two Romanian catchments, showing the river network and estimated flow.

Model selection and error estimation

We study model selection strategies based on penalized empirical loss minimization. We point out a tight relationship between error estimation and data-based complexity penalization: any good error estimate may be converted into a data-based penalty function and the performance of the estimate is governed by the quality of the error estimate. We consider several penalty functions, involving error estimates on independent test data, empirical {\sc vc} dimension, empirical {\sc vc} entropy, andmargin-based quantities. We also consider the maximal difference between the error on the first half of the training data and the second half, and the expected maximal discrepancy, a closely related capacity estimate that can be calculated by Monte Carlo integration. Maximal discrepancy penalty functions are appealing for pattern classification problems, since their computation is equivalent to empirical risk minimization over the training data with some labels flipped.

Parallelizing remote sensing image geometric correction

Remote sensing spatial, spectral, and temporal resolutions of images, acquired over a reasonably sized image extent, result in imagery that can be processed to represent land cover over large areas with an amount of spatial detail that is very attractive for monitoring, management, and scienti c activities. With Moore's Law alive and well, more and more parallelism is introduced into all computing platforms, at all levels of integration and programming to achieve higher performance and energy e ciency. Being the geometric calibration process one of the most time consuming processes when using remote sensing images, the aim of this work is to accelerate this process by taking advantage of new computing architectures and technologies, specially focusing in exploiting computation over shared memory multi-threading hardware. A parallel implementation of the most time consuming process in the remote sensing geometric correction has been implemented using OpenMP directives. This work compares the performance of the original serial binary versus the parallelized implementation, using several multi-threaded modern CPU architectures, discussing about the approach to nd the optimum hardware for a cost-e ective execution.

One-sided tolerance interval in a two-way balanced nested model with mixed effects

In many research areas (such as public health, environmental contamination, and others) one deals with the necessity of using data to infer whether some proportion (%) of a population of interest is (or one wants it to be) below and/or over some threshold, through the computation of tolerance interval. The idea is, once a threshold is given, one computes the tolerance interval or limit (which might be one or two - sided bounded) and then to check if it satisfies the given threshold. Since in this work we deal with the computation of one - sided tolerance interval, for the two-sided case we recomend, for instance, Krishnamoorthy and Mathew [5]. Krishnamoorthy and Mathew [4] performed the computation of upper tolerance limit in balanced and unbalanced one-way random effects models, whereas Fonseca et al [3] performed it based in a similar ideas but in a tow-way nested mixed or random effects model. In case of random effects model, Fonseca et al [3] performed the computation of such interval only for the balanced data, whereas in the mixed effects case they dit it only for the unbalanced data. For the computation of twosided tolerance interval in models with mixed and/or random effects we recomend, for instance, Sharma and Mathew [7]. The purpose of this paper is the computation of upper and lower tolerance interval in a two-way nested mixed effects models in balanced data. For the case of unbalanced data, as mentioned above, Fonseca et al [3] have already computed upper tolerance interval. Hence, using the notions persented in Fonseca et al [3] and Krishnamoorthy and Mathew [4], we present some results on the construction of one-sided tolerance interval for the balanced case. Thus, in order to do so at first instance we perform the construction for the upper case, and then the construction for the lower case.

Sequencing primate genomes: what have we learned?

We summarize the progress in whole-genome sequencing and analyses of primate genomes. These emerging genome datasets have broadened our understanding of primate genome evolution revealing unexpected and complex patterns of evolutionary change. This includes the characterization of genome structural variation, episodic changes in the repeat landscape, differences in gene expression, new models regarding speciation, and the ephemeral nature of the recombination landscape. The functional characterization of genomic differences important in primate speciation and adaptation remains a significant challenge. Limited access to biological materials, the lack of detailed phenotypic data and the endangered status of many critical primate species have significantly attenuated research into the genetic basis of primate evolution. Next-generation sequencing technologies promise to greatly expand the number of available primate genome sequences; however, such draft genome sequences will likely miss critical genetic differences within complex genomic regions unless dedicated efforts are put forward to understand the full spectrum of genetic variation.

A behavioral ecology of shermen: hidden stories from trajectory data in the Northern Humboldt Current System

This work proposes an original contribution to the understanding of shermen spatial behavior, based on the behavioral ecology and movement ecology paradigms. Through the analysis of Vessel Monitoring System (VMS) data, we characterized the spatial behavior of Peruvian anchovy shermen at di erent scales: (1) the behavioral modes within shing trips (i.e., searching, shing and cruising); (2) the behavioral patterns among shing trips; (3) the behavioral patterns by shing season conditioned by ecosystem scenarios; and (4) the computation of maps of anchovy presence proxy from the spatial patterns of behavioral mode positions. At the rst scale considered, we compared several Markovian (hidden Markov and semi-Markov models) and discriminative models (random forests, support vector machines and arti cial neural networks) for inferring the behavioral modes associated with VMS tracks. The models were trained under a supervised setting and validated using tracks for which behavioral modes were known (from on-board observers records). Hidden semi-Markov models performed better, and were retained for inferring the behavioral modes on the entire VMS dataset. At the second scale considered, each shing trip was characterized by several features, including the time spent within each behavioral mode. Using a clustering analysis, shing trip patterns were classi ed into groups associated to management zones, eet segments and skippers' personalities. At the third scale considered, we analyzed how ecological conditions shaped shermen behavior. By means of co-inertia analyses, we found signi cant associations between shermen, anchovy and environmental spatial dynamics, and shermen behavioral responses were characterized according to contrasted environmental scenarios. At the fourth scale considered, we investigated whether the spatial behavior of shermen re ected to some extent the spatial distribution of anchovy. Finally, this work provides a wider view of shermen behavior: shermen are not only economic agents, but they are also foragers, constrained by ecosystem variability. To conclude, we discuss how these ndings may be of importance for sheries management, collective behavior analyses and end-to-end models.

Macaulay style formulas for sparse resultants

We present formulas for computing the resultant of sparse polyno- mials as a quotient of two determinants, the denominator being a minor of the numerator. These formulas extend the original formulation given by Macaulay for homogeneous polynomials.

Heel and toe clearance estimation for gait analysis using wireless inertial sensors.

Tripping is considered a major cause of fall in older people. Therefore, foot clearance (i.e., height of the foot above ground during swing phase) could be a key factor to better understand the complex relationship between gait and falls. This paper presents a new method to estimate clearance using a foot-worn and wireless inertial sensor system. The method relies on the computation of foot orientation and trajectory from sensors signal data fusion, combined with the temporal detection of toe-off and heel-strike events. Based on a kinematic model that automatically estimates sensor position relative to the foot, heel and toe trajectories are estimated. 2-D and 3-D models are presented with different solving approaches, and validated against an optical motion capture system on 12 healthy adults performing short walking trials at self-selected, slow, and fast speed. Parameters corresponding to local minimum and maximum of heel and toe clearance were extracted and showed accuracy ± precision of 4.1 ± 2.3 cm for maximal heel clearance and 1.3 ± 0.9 cm for minimal toe clearance compared to the reference. The system is lightweight, wireless, easy to wear and to use, and provide a new and useful tool for routine clinical assessment of gait outside a dedicated laboratory.

Enhanced radar precipitation estimates using a combined clutter and beam blockage correction technique

Weather radar observations are currently the most reliable method for remote sensing of precipitation. However, a number of factors affect the quality of radar observations and may limit seriously automated quantitative applications of radar precipitation estimates such as those required in Numerical Weather Prediction (NWP) data assimilation or in hydrological models. In this paper, a technique to correct two different problems typically present in radar data is presented and evaluated. The aspects dealt with are non-precipitating echoes - caused either by permanent ground clutter or by anomalous propagation of the radar beam (anaprop echoes) - and also topographical beam blockage. The correction technique is based in the computation of realistic beam propagation trajectories based upon recent radiosonde observations instead of assuming standard radio propagation conditions. The correction consists of three different steps: 1) calculation of a Dynamic Elevation Map which provides the minimum clutter-free antenna elevation for each pixel within the radar coverage; 2) correction for residual anaprop, checking the vertical reflectivity gradients within the radar volume; and 3) topographical beam blockage estimation and correction using a geometric optics approach. The technique is evaluated with four case studies in the region of the Po Valley (N Italy) using a C-band Doppler radar and a network of raingauges providing hourly precipitation measurements. The case studies cover different seasons, different radio propagation conditions and also stratiform and convective precipitation type events. After applying the proposed correction, a comparison of the radar precipitation estimates with raingauges indicates a general reduction in both the root mean squared error and the fractional error variance indicating the efficiency and robustness of the procedure. Moreover, the technique presented is not computationally expensive so it seems well suited to be implemented in an operational environment.