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

Context switching accounting mechanism

How many times a given process p preempts, either voluntarily or involuntarily, is an important threat to computer's processes throughput. Whenever running cpu-bound processes on a multi-core system without an actual system grid engine as commonly found on Grid Clusters, their performance and stability are directly related to their accurate implementation and the system reliability which is, to an extend, an important caveat most of the times so difficult to detect. Context Switching is time-consuming. Thus, if we could develop a tool capable of detecting it and gather data from every single performed Context Switch, we would beable to study this data and present some results that should pin-point at whatever their main cause could be.

Discrimination in Bankruptcy Situations

In a bankruptcy situation, not all claimants are affected in the same way. In particular, some depositors may enter into a situation of personal bankruptcy if they lose part of their investments. Events of this kind may lead to a social catastrophe. We propose discrimination among the claimants as a possible solution. A fact considered in the American bankruptcy law (among others) that establishes some discrimination on the claimants, or the Santander Bank that in the Madoff’s case reimbursed only the deposits to its particular customers. Moreover, the necessity of discriminating has already been mentioned in different contexts by Young (1988), Bossert (1995), Thomson (2003) and Pulido et al. (2002, 2007), for instance. In this paper, we take a bankruptcy solution as the reference point. Given this initial allocation, we make transfers from richer to poorer with the purpose of distributing not only the personal incurred losses as evenly as possible but also the transfers in a progressive way. The agents are divided into two groups depending on their personal monetary value (wealth, net-income, GDP or any other characteristic). Then, we impose a set of Axioms that bound the maximal transfer that each net-contributor can make and each net-receiver can obtain. Finally, we define a value discriminant solution, and we characterize it by means of the Lorenz criterion. Endogenous convex combinations between solutions are also considered. Keywords: Bankruptcy, Discrimination, Compensation, Rules JEL classification: C71, D63, D71.

A note on discrete claims problems

In this note, we consider claims problems with indivisible goods. Specifically, by applying recursively the P-rights lower bound (Jiménez-Gómez and Marco-Gil (2008)), we ensure the fulfillment of Weak Order Preservation, considered by many authors as a minimal requirement of fairness. Moreover, we retrieve the Discrete Constrained Equal Losses and the Discrete Constrained Equal Awards rules (Herrero and Martíınez (2008)). Finally, by the recursive double imposition of a lower and an upper bound, we obtain the average between them. Keywords: Claims problems, Indivisibilities, Order Preservation, Constrained Egalitarian rules, Midpoint. JEL classification: C71, D63, D71.

Fair bounds based solidarity

How should scholarships be distributed among the (public) higher education students? We raise this situation as a redistribution problem. Following the approach developed in Fleurbaey (1994) and Bossert (1995), redistribution should be based on the notion of solidarity and it re-allocates resources taking into account only agents’ relevant characteristics. We also follow Luttens (2010a), who considers that compensation of relevant characteristics must be based on a lower bound on what every individual deserves. In doing so, we use the so-called fair bound (Moulin (2002)) to define an egalitarian redistribution mechanism and characterize it in terms of non-negativity, priority in lower bound and solidarity. Finally, we apply our approach to the scholarships redistribution problem. Keywords: Redistribution mechanism, Lower bounds, Scholarship, Solidarity. JEL classification: C71, D63, D71