An Analysis of black-box optimization problems in reinsurance: evolutionary-based approaches

Black-box optimization problems (BBOP) are de ned as those optimization problems in which the objective function does not have an algebraic expression, but it is the output of a system (usually a computer program). This paper is focussed on BBOPs that arise in the eld of insurance, and more speci cally in reinsurance problems. In this area, the complexity of the models and assumptions considered to de ne the reinsurance rules and conditions produces hard black-box optimization problems, that must be solved in order to obtain the optimal output of the reinsurance. The application of traditional optimization approaches is not possible in BBOP, so new computational paradigms must be applied to solve these problems. In this paper we show the performance of two evolutionary-based techniques (Evolutionary Programming and Particle Swarm Optimization). We provide an analysis in three BBOP in reinsurance, where the evolutionary-based approaches exhibit an excellent behaviour, nding the optimal solution within a fraction of the computational cost used by inspection or enumeration methods.

Negative Fukui functions: new insights based on electronegativity equalization

The occurrence of negative values for Fukui functions was studied through the electronegativity equalization method. Using algebraic relations between Fukui functions and different other conceptual DFT quantities on the one hand and the hardness matrix on the other hand, expressions were obtained for Fukui functions for several archetypical small molecules. Based on EEM calculations for large molecular sets, no negative Fukui functions were found

A comparative analysis of two methods for the calculation of electric-field-induced perturbations to molecular vibration

Two common methods of accounting for electric-field-induced perturbations to molecular vibration are analyzed and compared. The first method is based on a perturbation-theoretic treatment and the second on a finite-field treatment. The relationship between the two, which is not immediately apparent, is made by developing an algebraic formalism for the latter. Some of the higher-order terms in this development are documented here for the first time. As well as considering vibrational dipole polarizabilities and hyperpolarizabilities, we also make mention of the vibrational Stark effec

Schooling supply and the structure of production: Evidence from US States 1950-1990

We find that over the period 1950-1990, US states absorbed increases in the supplyof schooling due to tighter compulsory schooling and child labor laws mostly throughwithin-industry increases in the schooling intensity of production. Shifts in the industrycomposition towards more schooling-intensive industries played a less important role.To try and understand this finding theoretically, we consider a free trade model withtwo goods/industries, two skill types, and many regions that produce a fixed rangeof differentiated varieties of the same goods. We find that a calibrated version ofthe model can account for shifts in schooling supply being mostly absorbed throughwithin-industry increases in the schooling intensity of production even if the elasticityof substitution between varieties is substantially higher than estimates in the literature.

A total order in [0,1] defined through a 'next' operator

A `next' operator, s, is built on the set R1=(0,1]-{ 1-1/e} defining a partial order that, with the help of the axiom of choice, can be extended to a total order in R1. Besides, the orbits {sn(a)}nare all dense in R1 and are constituted by elements of the samearithmetical character: if a is an algebraic irrational of degreek all the elements in a's orbit are algebraic of degree k; if a istranscendental, all are transcendental. Moreover, the asymptoticdistribution function of the sequence formed by the elements in anyof the half-orbits is a continuous, strictly increasing, singularfunction very similar to the well-known Minkowski's ?(×) function.

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.

Timing of seasonal sales

We present a model of timing of seasonal sales where stores chooseseveral designs at the beginning of the season without knowingwich one, if any, will be fashionable. Fashionable designs have achance to fetch high prices in fashion markets while non-fashionableones must be sold in a discount market. In the beginning of theseason, stores charge high prices in the hope of capturing theirfashion market. As the end of the season approaches with goods stillon the shelves, stores adjust downward their expectations that theyare carrying a fashionable design, and may have sales to capture thediscount market. Having a greater number of designs induces a storeto put one of them on sales earlier to test the market. Moreover,price competition in the discount market induces stores to startsales earlier because of a greater perceived first-mover advantage incapturing the discount market. More competition, perhaps due todecreases in the cost of product innovation, makes sales occur evenearlier. These results are consistent with the observation that thetrend toward earlier sales since mid-1970's coincides with increasingproduct varieties in fashion good markets and increasing storecompetition.

Teoremas de isomorfía en grupos diedros

En este art\'\ı culo discutimos los resultados principalesalcanzados en mi trabajo de grado, el cual fue dirigido por elprofesor Jairo Charris Casta\~neda. La discusi\'on la limitaremos alos llamados $(p, q)$ grupos, en particular a los grupos diedros.

Unified formalism for non-autonomous mechanical systems

We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical equations of motion and their compatibility and consistency are carefully studied, making clear that all the characteristics of the Lagrangian and the Hamiltonian formalisms are recovered in this formulation. As an example, it is studied a semidiscretization of the nonlinear wave equation proving the applicability of the proposed formalism.

Homotopy Batalin-Vilkovisky algebras

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defind by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincare-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.

Projecte de legalització d'una activitat dedicada a l'explotació ramadera i a la formatgeria artesanal

La integració en una mateixa activitat d'una explotació ramadera ecològica basada en el bestiar cabrú de llet i d'una formatgeria artesanal basada en varietats autòctones de formatge de cabra, permet ocupar un nínxol de mercat encara poc explotat actualment a Catalunya. D'igual manera, la dificultat que tenen actualment molts dels formatgers artesans del país per trobar llet de cabra en quantitats suficients i amb unes mínimes garanties higiènico-sanitàries dificulten l'avanç d'un sector amb molt bones perspectives de futur com és el de la formatgeria artesanal i justifica la necessitat de crear noves explotacions (o reconvertir-ne de ja existents) orientant-les de ple vers l'aprofitament lleter del bestiar cabrú, que és actualment molt reduït en l'àmbit Català. A més d'això, les actuals exigències en el camp del benestar animal així com en el camp de la qualitat i de la seguretat alimentaria, exigeixen a les explotacions ramaderes i a les indústries alimentàries el compliment d'una sèrie de requisits, tan de disseny dels locals i de les instal•lacions, com de control de les activitats i dels productes elaborats, que garanteixin en tot moment la seva correcte gestió i funcionament en aquestes matèries. L'objectiu d'aquest projecte, doncs, és la legalització d'una activitat, que anomenarem “Mas Peirot, S.L.”, dedicada a l'explotació ramadera ecològica de bestiar cabrú de llet i a la formatgeria artesanal de formatge de cabra. És important mencionar que tot i tractar-se d'un projecte de legalització d'una activitat,, també s'hi han contemplat aspectes i detalls relacionats amb l'execució de la mateixa, al tractar-se d'unes obres d'una certa complexitat i considerant que així es tracten amb més detall i rigorositat les actuacions projectades. En concret, en aquest projecte es planifiquen les operacions de rehabilitació de dues naus ramaderes actualment en desús, per tal que puguin destinar-se a l'explotació ramadera de bestiar cabrú i a la formatgeria artesanal, projectant-se així mateix totes les instal•lacions necessàries per tal que a les mencionades naus s'hi puguin desenvolupar les activitats citades. Com a conclusions més importants d'aquest projecte podem dir que amb un cens de 100 caps de bestiar cabrú és possible obtenir una producció mitjana de llet de 32.500 litres anuals, que es corresponen a un volum total de 3.823 quilograms de formatge a l'any (de les tipologies Formatge Garrotxa i Formatge de cabra amb oli, ambdues varietats tradicionals catalanes) obtenint un benefici de 21.389,47 Euros/any durant els primers 15 anys i un benefici de 33.386,39 Euros/any a partir del 16è any, cosa que permetrà recuperar la inversió inicial de 172.716,76 Euros que valen les naus i instal•lacions projectades, en un termini de 8 anys i permetrà, com s'ha dit, ocupar un nínxol de mercat encara poc explotat per la indústria agroalimentària a Catalunya.

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.

Generating functions for the numbers of Abelian extensions of a local field

The aim of this paper is to give an explicit formula for the num- bers of abelian extensions of a p-adic number field and to study the generating function of these numbers. More precisely, we give the number of abelian ex- tensions with given degree and ramification index, and the number of abelian extensions with given degree of any local field of characteristic zero. Moreover, we give a concrete expression of a generating function for these last numbers