Heat kernels and thermodynamics in Rindler space

We point out that using the heat kernel on a cone to compute the first quantum correction to the entropy of Rindler space does not yield the correct temperature dependence. In order to obtain the physics at arbitrary temperature one must compute the heat kernel in a geometry with different topology (without a conical singularity). This is done in two ways, which are shown to agree with computations performed by other methods. Also, we discuss the ambiguities in the regularization procedure and their physical consequences.

A comment on the cost of capital for investments with non-homogeneous components

In this paper, the expression for the cost of capital is derived when net and replacement investments exhibit differences in their effective prices due to a different fiscal treatment. It is shown that, contrary to previous results in the literature, the cost of capital should be constructed under an opportunity cost criterion rather than a historical one. This result has some important economic consequences, since the optimizing firm will take into account not only the effective price for the new investments but also consider the opportunity cost of replacing them.

Estimating biophysical variable dependences with kernels

This paper introduces a nonlinear measure of dependence between random variables in the context of remote sensing data analysis. The Hilbert-Schmidt Independence Criterion (HSIC) is a kernel method for evaluating statistical dependence. HSIC is based on computing the Hilbert-Schmidt norm of the cross-covariance operator of mapped samples in the corresponding Hilbert spaces. The HSIC empirical estimator is very easy to compute and has good theoretical and practical properties. We exploit the capabilities of HSIC to explain nonlinear dependences in two remote sensing problems: temperature estimation and chlorophyll concentration prediction from spectra. Results show that, when the relationship between random variables is nonlinear or when few data are available, the HSIC criterion outperforms other standard methods, such as the linear correlation or mutual information.

Stochastic generation of homogeneous isotropic turbulence with well-defined-spectra

A precise and simple computational model to generate well-behaved two-dimensional turbulent flows is presented. The whole approach rests on the use of stochastic differential equations and is general enough to reproduce a variety of energy spectra and spatiotemporal correlation functions. Analytical expressions for both the continuous and the discrete versions, together with simulation algorithms, are derived. Results for two relevant spectra, covering distinct ranges of wave numbers, are given.

Learning wind fields with multiple kernels

This paper presents multiple kernel learning (MKL) regression as an exploratory spatial data analysis and modelling tool. The MKL approach is introduced as an extension of support vector regression, where MKL uses dedicated kernels to divide a given task into sub-problems and to treat them separately in an effective way. It provides better interpretability to non-linear robust kernel regression at the cost of a more complex numerical optimization. In particular, we investigate the use of MKL as a tool that allows us to avoid using ad-hoc topographic indices as covariables in statistical models in complex terrains. Instead, MKL learns these relationships from the data in a non-parametric fashion. A study on data simulated from real terrain features confirms the ability of MKL to enhance the interpretability of data-driven models and to aid feature selection without degrading predictive performances. Here we examine the stability of the MKL algorithm with respect to the number of training data samples and to the presence of noise. The results of a real case study are also presented, where MKL is able to exploit a large set of terrain features computed at multiple spatial scales, when predicting mean wind speed in an Alpine region.

Multi-source composite kernels for urban image classification

This letter presents advanced classification methods for very high resolution images. Efficient multisource information, both spectral and spatial, is exploited through the use of composite kernels in support vector machines. Weighted summations of kernels accounting for separate sources of spectral and spatial information are analyzed and compared to classical approaches such as pure spectral classification or stacked approaches using all the features in a single vector. Model selection problems are addressed, as well as the importance of the different kernels in the weighted summation.

Mixed spectral-structural classification of very high resolution images with summation kernels

In this paper, mixed spectral-structural kernel machines are proposed for the classification of very-high resolution images. The simultaneous use of multispectral and structural features (computed using morphological filters) allows a significant increase in classification accuracy of remote sensing images. Subsequently, weighted summation kernel support vector machines are proposed and applied in order to take into account the multiscale nature of the scene considered. Such classifiers use the Mercer property of kernel matrices to compute a new kernel matrix accounting simultaneously for two scale parameters. Tests on a Zurich QuickBird image show the relevance of the proposed method : using the mixed spectral-structural features, the classification accuracy increases of about 5%, achieving a Kappa index of 0.97. The multikernel approach proposed provide an overall accuracy of 98.90% with related Kappa index of 0.985.

Grain yield, carbon isotope discrimination and mineral content in mature kernels of barley under irrigated and rainfed conditions

The relationship between yield, carbon isotope discrimination and ash content in mature kernels was examined for a set of 13 barley (Hordeum vulgare) cultivars. Plants were grown under rainfed and well-irrigated conditions in a Mediterranean area. Water deficit caused a decrease in both grain yield and carbon isotope discrimination (Δ). The yield was positively related to Δ and negatively related to ash content, across genotypes within each treatment. However, whereas the correlation between yield and Δ was higher for the set of genotypes under well-irrigated (r=0.70, P<0.01) than under rainfed (r=0.42) conditions, the opposite occurred when yield and ash content were related, ie r=-0.38 under well-irrigated and r=-0.73, (P<0.01) under rainfed conditions. Carbon isotope discrimination and ash content together account for almost 60% of the variation in yield, in both conditions. There was no significant relationship (r=-0.15) between carbon isotope discrimination and ash content in well-irrigated plants, whereas in rainfed plants, this relationship, although significant (r=-0.54, P< 0.05), was weakly negative. The concentration of several mineral elements was measured in the same kernels. The mineral that correlated best with ash content, yield and A, was K. For yield and Δ, although the relationship with K followed the same pattern as the relationhip with ash content, the correlation coefficients were lower. Thus, mineral accumulation in mature kernels seems to be independent of transpiration efficiency. In fact, filling of grains takes place through the phloem pathway. The ash content in kernels is proposed as a complementary criterion, in addition to kernel Δ, to assess genotype differences in barley grain yield under rainfed conditions.

Development of a shelling method to recover whole kernels of the Cutia nut (Couepia edulis)

The kernel of the cutia nut (castanha-de-cutia, Couepia edulis (Prance) Prance) of the western Amazon, which is consumed by the local population, has traditionally been extracted from the nut with a machete, a dangerous procedure that only produces kernels cut in half. A shelling off machine prototype, which produces whole kernels without serious risks to its operator, is described and tested. The machine makes a circular cut in the central part of the fruit shell, perpendicular to its main axis. Three ways of conditioning the fruits before cutting were compared: (1) control; (2) oven drying immediately prior to cutting; (3) oven drying, followed by a 24-hour interval before cutting. The time needed to extract and separate the kernel from the endocarp and testa was measured. Treatment 3 produced the highest output: 63 kernels per hour, the highest percentage of whole kernels (90%), and the best kernel taste. Kernel extraction with treatment 3 required 50% less time than treatment 1, while treatment 2 needed 38% less time than treatment 1. The proportion of kernels attached to the testa was 93%, 47%, and 8% for treatments 1, 2, and 3, respectively, and was the main reason for extraction time differences.

Integrability of a linear center perturbed by a fourth degree homogeneous polynomial

In this work we study the integrability of a two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fourth degree. We give sufficient conditions for integrability in polar coordinates. Finally we establish a conjecture about the independence of the two classes of parameters which appear in the system; if this conjecture is true the integrable cases found will be the only possible ones.

Integrability of a linear center perturbed by a fifth degree homogeneous polynomial

In this work we study the integrability of two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fifth degree. We give a simple characterisation for the integrable cases in polar coordinates. Finally we formulate a conjecture about the independence of the two classes of parameters which appear on the system; if this conjecture is true the integrable cases found will be the only possible ones.

The Bonenblust-Hille inequality for homogeneous polynomials is hypercontractive

The Bohnenblust-Hille inequality says that the $\ell^{\frac{2m}{m+1}}$ -norm of the coefficients of an $m$-homogeneous polynomial $P$ on $\Bbb{C}^n$ is bounded by $\| P \|_\infty$ times a constant independent of $n$, where $\|\cdot \|_\infty$ denotes the supremum norm on the polydisc $\mathbb{D}^n$. The main result of this paper is that this inequality is hypercontractive, i.e., the constant can be taken to be $C^m$ for some $C>1$. Combining this improved version of the Bohnenblust-Hille inequality with other results, we obtain the following: The Bohr radius for the polydisc $\mathbb{D}^n$ behaves asymptotically as $\sqrt{(\log n)/n}$ modulo a factor bounded away from 0 and infinity, and the Sidon constant for the set of frequencies $\bigl\{ \log n: n \text{a positive integer} \le N\bigr\}$ is $\sqrt{N}\exp\{(-1/\sqrt{2}+o(1))\sqrt{\log N\log\log N}\}$.