Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible considerationof densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended theEuclidean structure of the simplex to a Hilbert space structure of the set of densitieswithin a bounded interval, and van den Boogaart (2005) generalized this to the setof densities bounded by an arbitrary reference density. From the many variations ofthe Hilbert structures available, we work with three cases. For bounded variables, abasis derived from Legendre polynomials is used. For variables with a lower bound, westandardize them with respect to an exponential distribution and express their densitiesas coordinates in a basis derived from Laguerre polynomials. Finally, for unboundedvariables, a normal distribution is used as reference, and coordinates are obtained withrespect to a Hermite-polynomials-based basis.To get the coordinates, several approaches can be considered. A numerical accuracyproblem occurs if one estimates the coordinates directly by using discretized scalarproducts. Thus we propose to use a weighted linear regression approach, where all k-order polynomials are used as predictand variables and weights are proportional to thereference density. Finally, for the case of 2-order Hermite polinomials (normal reference)and 1-order Laguerre polinomials (exponential), one can also derive the coordinatesfrom their relationships to the classical mean and variance.Apart of these theoretical issues, this contribution focuses on the application of thistheory to two main problems in sedimentary geology: the comparison of several grainsize distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock orsediment, like their composition

Asymptotics of orthogonal polynomials via the Koosis theorem

The main aim of this short paper is to advertize the Koosis theorem in the mathematical community, especially among those who study orthogonal polynomials. We (try to) do this by proving a new theorem about asymptotics of orthogonal polynomi- als for which the Koosis theorem seems to be the most natural tool. Namely, we consider the case when a SzegÄo measure on the unit circumference is perturbed by an arbitrary measure inside the unit disk and an arbitrary Blaschke sequence of point masses outside the unit disk.

On the zeroes of Goss polynomials

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A sharp Remez inequality for trigonometric polynomials

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Integral inequalities for algebraic and trigonometric polynomials

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Sobolev orthogonal polynomials on a simplex

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Optimal strategies for sending information through a quantum channel

Quantum states can be used to encode the information contained in a direction, i.e., in a unit vector. We present the best encoding procedure when the quantum state is made up of N spins (qubits). We find that the quality of this optimal procedure, which we quantify in terms of the fidelity, depends solely on the dimension of the encoding space. We also investigate the use of spatial rotations on a quantum state, which provide a natural and less demanding encoding. In this case we prove that the fidelity is directly related to the largest zeros of the Legendre and Jacobi polynomials. We also discuss our results in terms of the information gain.

Shifted loops and coercivity from field imprinted high energy barriers in ferritin and ferrihydrite nanoparticles

We show that the coercive field in ferritin and ferrihydrite depends on the maximum magnetic field in a hysteresis loop and that coercivity and loop shifts depend both on the maximum and cooling fields. In the case of ferritin, we show that the time dependence of the magnetization also depends on the maximum and previous cooling fields. This behavior is associated to changes in the intraparticle energy barriers imprinted by these fields. Accordingly, the dependence of the coercive and loop-shift fields with the maximum field in ferritin and ferrihydrite can be described within the frame of a uniform-rotation model considering a dependence of the energy barrier with the maximum and the cooling fields.

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 $\sqrt{N}\exp\{(-1/\sqrt{2}+o(1))\sqrt{\log N\log\log N}\}$.

Pareto-improving optimal capital and labor taxes

We show a standard model where the optimal tax reform is to cut labor taxes and leave capital taxes very high in the short and medium run. Only in the very long run would capital taxes be zero. Our model is a version of Chamley??s, with heterogeneous agents, without lump sum transfers, an upper bound on capital taxes, and a focus on Pareto improving plans. For our calibration labor taxes should be low for the first ten to twenty years, while capital taxes should be at their maximum. This policy ensures that all agents benefit from the tax reform and that capital grows quickly after when the reform begins. Therefore, the long run optimal tax mix is the opposite from the short and medium run tax mix. The initial labor tax cut is financed by deficits that lead to a positive long run level of government debt, reversing the standard prediction that government accumulates savings in models with optimal capital taxes. If labor supply is somewhat elastic benefits from tax reform are high and they can be shifted entirely to capitalists or workers by varying the length of the transition. With inelastic labor supply there is an increasing part of the equilibrium frontier, this means that the scope for benefitting the workers is limited and the total benefits from reforming taxes are much lower.

Changes in the demand for private medical insurance following a shift in tax incentives

The 1998 Spanish reform of the Personal Income Tax eliminated the 15% deduction for private medical expenditures including payments on private health insurance (PHI) policies. To avoid an undesirable increase in the demand for publicly funded health care, tax incentives to buy PHI were not completely removed but basically shifted from individual to group employer-paid policies. In a unique fiscal experiment, at the same time that the tax relief for individually purchased policies was abolished, the government provided for tax allowances on policies taken out through employment. Using a bivariate probit model on data from National Health Surveys, we estimate the impact of said reform on the demand for PHI and the changes occurred within it. Our findings suggest that the total probability of buying PHI was not significantly affected. Indeed, the fall in the demand for individual policies (by 10% between 1997 and 2001) was offset by an increase in the demand for group employer-paid ones, so that the overall size of the market remained virtually unchanged. We also briefly discuss the welfare effects on the state budget, the industry and society at large.

Diseño cooperativo de un sistema de comunicaciones por satélite basado en diversidad espacial

En este proyecto se han presentado los modelos de distribución de canal más comunes que se puede encontrar una señal en una transmisión. Seguidamente se ha presentado el concepto de diversidad en comunicaciones inalámbricas terrestres y se ha trasladado el escenario a comunicaciones por satélite. Para analizar la calidad de los enlaces con diversidad se ha realizado un simulador, con Matlab, que modele la estructura básica de un sistema de comunicaciones (emisor, canal y receptor). Simulando las comunicaciones entre los diferentes sistemas de diversidad se ha podido comparar la calidad de cada enlace. El modelo Alamouti ha presentado una robustez y una baja probabilidad de error que hacen que sea la mejor elección a la hora de diseñar un sistema de diversidad para comunicaciones por satélite. Utiliza la diversidad de canal para aprovechar cada pizca de señal que recibe y así poder descifrar el mensaje enviado.

Composición en ácidos grasos de huevos y larvas de dentón (Dentex dentex L.) de hasta 40 días en condiciones de cultivo

Total lipid content and fatty acid (FA) composition of common dentex eggs spawned at different times and larvae reared under different culture conditions until 40 days post hatch (dph) were analysed in order to get a general pattern of lipid composition during larval development. Results were grouped according to the developmental stage of the larvae instead of age in dph. Saturated and monounsaturated fatty acids decreased along larval development, while polyunsaturated fatty acid (PUFA) content increased. The ratio of docosahexaenoic acid (DHA) / eicosapentaenoic acid (EPA) shifted from 4 – 5 in early developmental stages to lower than 1 after metamorphosis. Results suggest a subdivision of the larval development into two stages of opposite FA requirements.