Statistical modeling on coordinates

This paper is a first draft of the principle of statistical modelling on coordinates. Several causes —which would be long to detail—have led to this situation close to the deadline for submitting papers to CODAWORK’03. The main of them is the fast development of the approach along thelast months, which let appear previous drafts as obsolete. The present paper contains the essential parts of the state of the art of this approach from my point of view. I would like to acknowledge many clarifying discussions with the group of people working in this field in Girona, Barcelona, Carrick Castle, Firenze, Berlin, G¨ottingen, and Freiberg. They have given a lot of suggestions and ideas. Nevertheless, there might be still errors or unclear aspects which are exclusively my fault. I hope this contribution serves as a basis for further discussions and new developments

Kriging coordinates: what does that mean?

Kriging is an interpolation technique whose optimality criteria are based on normality assumptions either for observed or for transformed data. This is the case of normal, lognormal and multigaussian kriging.When kriging is applied to transformed scores, optimality of obtained estimators becomes a cumbersome concept: back-transformed optimal interpolations in transformed scores are not optimal in the original sample space, and vice-versa. This lack of compatible criteria of optimality induces a variety of problems in both point and block estimates. For instance, lognormal kriging, widely used to interpolate positivevariables, has no straightforward way to build consistent and optimal confidence intervals for estimates.These problems are ultimately linked to the assumed space structure of the data support: for instance, positive values, when modelled with lognormal distributions, are assumed to be embedded in the whole real space, with the usual real space structure and Lebesgue measure

Automatic generation of active coordinates for quantum dynamics calculations: application to the dynamics of benzene photochemistry

A new practical method to generate a subspace of active coordinates for quantum dynamics calculations is presented. These reduced coordinates are obtained as the normal modes of an analytical quadratic representation of the energy difference between excited and ground states within the complete active space self-consistent field method. At the Franck-Condon point, the largest negative eigenvalues of this Hessian correspond to the photoactive modes: those that reduce the energy difference and lead to the conical intersection; eigenvalues close to 0 correspond to bath modes, while modes with large positive eigenvalues are photoinactive vibrations, which increase the energy difference. The efficacy of quantum dynamics run in the subspace of the photoactive modes is illustrated with the photochemistry of benzene, where theoretical simulations are designed to assist optimal control experiments

Determination of vibrational polarizabilities and hyperpolarizabilities using field-induced coordinates

An analytical set of field-induced coordinates is defined and is used to show that the vibrational degrees of freedom required to completely describe nuclear relaxation polarizabilities and hyperpolarizabilities is reduced from 3N-6 to a relatively small number. As this number does not depend upon the size of the molecule, the process provides computational advantages. A method is provided to separate anharmonic contributions from harmonic contributions as well as effective mechanical from electrical anharmonicity. The procedures are illustrated by Hartree-Fock calculations, indicating that anharmonicity can be very important

Field-induced coordinates for the determination of dynamic vibrational nonlinear optical properties

Three conjugated organic molecules that span a range of polarity and valence-bond/charge transfer characteristics were studied. It was found that dispersion can be insignificant, and that adequate treatment can be achieved with frequency-dependent field-induced vibrational coordinates (FD-FICs)

p38/MKP-1-regulated AKT coordinates macrophage transitions and resolution of inflammation during tissue repair

Repair of damaged tissue requires the coordinated action of inflammatory and tissue-specific cells to restore homeostasis, but the underlying regulatory mechanisms are poorly understood. In this paper, we report new roles for MKP-1 (mitogen-activated protein kinase [MAPK] phosphatase-1) in controlling macrophage phenotypic transitions necessary for appropriate muscle stem cell¿dependent tissue repair. By restricting p38 MAPK activation, MKP-1 allows the early pro- to antiinflammatory macrophage transition and the later progression into a macrophage exhaustion-like state characterized by cytokine silencing, thereby permitting resolution of inflammation as tissue fully recovers. p38 hyperactivation in macrophages lacking MKP-1 induced the expression of microRNA-21 (miR-21), which in turn reduced PTEN (phosphatase and tensin homologue) levels, thereby extending AKT activation. In the absence of MKP-1, p38-induced AKT activity anticipated the acquisition of the antiinflammatory gene program and final cytokine silencing in macrophages, resulting in impaired tissue healing. Such defects were reversed by temporally controlled p38 inhibition. Conversely, miR-21¿AKT interference altered homeostasis during tissue repair. This novel regulatory mechanism involving the appropriate balance of p38, MKP-1, miR-21, and AKT activities may have implications in chronic inflammatory degenerative diseases.

The problem of physical coordinates in predictive Hamiltonian systems

In the Hamiltonian formulation of predictive relativistic systems, the canonical coordinates cannot be the physical positions. The relation between them is given by the individuality differential equations. However, due to the arbitrariness in the choice of Cauchy data, there is a wide family of solutions for these equations. In general, those solutions do not satisfy the condition of constancy of velocities moduli, and therefore we have to reparametrize the world lines into the proper time. We derive here a condition on the Cauchy data for the individuality equations which ensures the constancy of the velocities moduli and makes the reparametrization unnecessary.

Bifurcations of homoclinic tangency in two-dimensional area-preserving and reversible maps

Report for the scientific sojourn at the Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia, from July to September 2006. Within the project, bifurcations of orbit behavior in area-preserving and reversible maps with a homoclinic tangency were studied. Finitely smooth normal forms for such maps near saddle fixed points were constructed and it was shown that they coincide in the main order with the analytical Birkhoff-Moser normal form. Bifurcations of single-round periodic orbits for two-dimensional symplectic maps close to a map with a quadratic homoclinic tangency were studied. The existence of one- and two-parameter cascades of elliptic periodic orbits was proved.

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 defined 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 Poincaré-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.

Some Considerations Concerning Regulation and Competition in the Port Sector

The aim of this paper is to discuss the circumstances in which the process of competition between ports takes place in Spain − circumstances arising from the way the port system is currently set up and from the regulations governing it. The importance of this matter lies both in the fact that intensified competition between ports is the way to set about boosting the efficiency of the Spanish port sector and in the relevance of this business to the economies of the regions in which the ports are located. It is precisely for this reason that the reform instituted in 1992 aimed to combine balanced development of the national port system with the defence of the interests of autonomous regions. To this end the current regulatory framework provides for the possibility of port authorities drawing up their own competitive strategies, but makes their implementation conditional upon approval of their business plan by the Spanish state port authority. The latter body coordinates the national port system to ensure the guidelines set by the central government authorities are followed in the field of transport. However, the scale of the differences which exist among both the size of facilities and their relevant markets on the one hand, and the financial and economic circumstances of each of them on the other, suggest that each port authority's needs must be very different. Consequently, their competitive strategies must also be very different. It is therefore valid to ask whether coping with this diversity calls for different guidelines to regulate their freedom of action. Key words: Competition, regulation, port sector JEL classification numbers: L1, L5, L9

Desarrollo de una aplicación web para representación de datos de posicionamiento

En aquesta memòria s’explica el desenvolupament d’una eina útil que permet a l’usuari visualitzar en l’aplicació Google Maps les dades de posicionament captats en una sessió GPS. En aquest projecte, hem dissenyat una aplicació Web en la qual recollim les dades ingressades per l’usuari mitjançant un formulari. Un cop emmagatzemades aquestes dades en el servidor, la nostra eina hi executa l’aplicació encarregada del càlcul de les posicions. Aquesta és un script desenvolupat en MATLAB, que s’encarrega d’interpretar les dades subministrades per l’usuari, amb les quals es poden calcular les coordenades captades pel receptor GPS. Una vegada calculades, el software les emmagatzema en el servidor, en un arxiu .xml, que serà el que posteriorment interpretarà Google Maps gràcies al seu API. D’aquesta manera, l’usuari obtindrà el resultat visual de la sessió GPS que hagi decidit carregar sense necessitat des disposar de cap software específic per a la interpretació i el càlcul de les dades que hi ha capturat.

Generic super-exponential stability of invariant tori in Hamiltonian systems

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.

Los col·loquis de la insigne ciutat de Tortosa, de Crisfòfor Despuig

Aquest treball té per finalitat facilitar el coneixement d'una obra cabdal de la literatura catalana; entendre'n el context temporal -el Renaixement i les seues convulsions polítiques, religioses i culturals, l'època del concili de Trento- i espacial -Tortosa, la Corona d'Aragó, l'Imperi espanyol-, per tal de situar-la dins d'unes coordenades espaciotemporals que facilitin la comprensió de l'obra per a estudiants i estudiosos.

10 años de repositorios cooperativos

El 1999 van començar els treballs que van culminar amb la posada en funcionament de TDX / TDX, el primer dipòsit creat a Espanya. Des de llavors la cooperació entre les universitats de Catalunya i la Biblioteca de Catalunya ha permès posar en funcionament 5 repositoris cooperatius (TDX / TDR, RECERCAT, RACO, MDC i MDX). Això ha estat possible per una divisió de tasques en la qual les biblioteques són les responsables de la introducció de continguts, el CESCA de la preparació del programari i el maquinari i el CBUC de la coordinació dels processos.Aquest taller dividit en 4 parts, té la finalitat d'explicar les diferents fases que han viscut els repositoris cooperatius, les actuacions dutes a terme en aquests 10 anys per omplir de contingut (estàndards, aspectes legals, ajuts de digitalització, etc.), La experiència d'una de les universitats -la UPF- que participa en aquests dipòsits cooperatius i que alhora disposa del seu propi i la infraestructura tècnica en la qual s'han desenvolupat i evolucionat.

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