Fast numerical algorithms for the computation of invariant tori in Hamiltonian systems

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of invariant tori in Hamiltonian systems (exact symplectic maps and Hamiltonian vector fields). The algorithms are based on the parameterization method and follow closely the proof of the KAM theorem given in [LGJV05] and [FLS07]. They essentially consist in solving a functional equation satisfied by the invariant tori by using a Newton method. Using some geometric identities, it is possible to perform a Newton step using little storage and few operations. In this paper we focus on the numerical issues of the algorithms (speed, storage and stability) and we refer to the mentioned papers for the rigorous results. We show how to compute efficiently both maximal invariant tori and whiskered tori, together with the associated invariant stable and unstable manifolds of whiskered tori. Moreover, we present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori. Since quasi-periodic cocycles appear in other contexts, this section may be of independent interest. The numerical methods presented here allow to compute in a unified way primary and secondary invariant KAM tori. Secondary tori are invariant tori which can be contracted to a periodic orbit. We present some preliminary results that ensure that the methods are indeed implementable and fast. We postpone to a future paper optimized implementations and results on the breakdown of invariant tori.

Incidencia, pronóstico y evolución clínica, inmunológica y virológica de las infecciones oportunistas del sistema nervioso central en pacientes con infección por VIH en la era del tratamiento antirretroviral de alta eficacia. Relación con el síndrome inflamatorio de reconstitución inmunológica

Després de la introducció de la teràpia antirretroviral d’alta eficàcia, s’ha objectivat a l’hospital vall d’hebron, una disminució progressiva de la incidencia de les principals infeccions oportunistes del sistema nerviós central (toxoplasmosis, meningitis tuberculosa, meningitis criptococócica i de la leucoencefalopatia multifocal progresiva-LMP). La supervivencia global d’aquestes infeccions va ser de 2 mesos, sent la de pitjor pronòstic la LMP, l’estimació de supervivencia de la qual als 36 mesos va ser del 36.4%. L’aparició de la síndrome Inflamatòria de reconstitució immunològica es va asociar a una recuperació immunològica més rápida, sense asociar-se a major mortalitat.

CAC controlled services sharing a link with connectionless data services in an ATM network: a performance evaluation study

In the B-ISDN there is a provision for four classes of services, all of them supported by a single transport network (the ATM network). Three of these services, the connected oriented (CO) ones, permit connection access control (CAC) but the fourth, the connectionless oriented (CLO) one, does not. Therefore, when CLO service and CO services have to share the same ATM link, a conflict may arise. This is because a bandwidth allocation to obtain maximum statistical gain can damage the contracted ATM quality of service (QOS); and vice versa, in order to guarantee the contracted QOS, the statistical gain have to be sacrificed. The paper presents a performance evaluation study of the influence of the CLO service on a CO service (a circuit emulation service or a variable bit-rate service) when sharing the same link

Select-divide-and-conquer method for large-scale configuration interaction

A select-divide-and-conquer variational method to approximate configuration interaction (CI) is presented. Given an orthonormal set made up of occupied orbitals (Hartree-Fock or similar) and suitable correlation orbitals (natural or localized orbitals), a large N-electron target space S is split into subspaces S0,S1,S2,...,SR. S0, of dimension d0, contains all configurations K with attributes (energy contributions, etc.) above thresholds T0={T0egy, T0etc.}; the CI coefficients in S0 remain always free to vary. S1 accommodates KS with attributes above T1≤T0. An eigenproblem of dimension d0+d1 for S0+S 1 is solved first, after which the last d1 rows and columns are contracted into a single row and column, thus freezing the last d1 CI coefficients hereinafter. The process is repeated with successive Sj(j≥2) chosen so that corresponding CI matrices fit random access memory (RAM). Davidson's eigensolver is used R times. The final energy eigenvalue (lowest or excited one) is always above the corresponding exact eigenvalue in S. Threshold values {Tj;j=0, 1, 2,...,R} regulate accuracy; for large-dimensional S, high accuracy requires S 0+S1 to be solved outside RAM. From there on, however, usually a few Davidson iterations in RAM are needed for each step, so that Hamiltonian matrix-element evaluation becomes rate determining. One μhartree accuracy is achieved for an eigenproblem of order 24 × 106, involving 1.2 × 1012 nonzero matrix elements, and 8.4×109 Slater determinants

Risk sharing with the monarch: Excusable defaults and contingent debt in the age of Philip II, 1556-1598

Contingent sovereign debt can create important welfare gains. Nonetheless,there is almost no issuance today. Using hand-collected archival data, we examine thefirst known case of large-scale use of state-contingent sovereign debt in history. Philip IIof Spain entered into hundreds of contracts whose value and due date depended onverifiable, exogenous events such as the arrival of silver fleets. We show that this allowedfor effective risk-sharing between the king and his bankers. The data also stronglysuggest that the defaults that occurred were excusable they were simply contingenciesover which Crown and bankers had not contracted previously.

Organized vs. competitive corruption

We study bureaucratic corruption in a model in which a constituencysets required levels for a given set of activities. Each activity iscarried out by an external provider, and its realization is supervisedby a bureaucrat. While bureaucrats are supposed to act on behalf of theconstituency, they can decide to be corrupt and allow providers todeliver lower activity levels than contracted in exchange for a bribe.Given this, the constituency sets the optimal activity levels weighingoff the value of activity levels, their costs, as well as the possibilityfor the bureaucrats to be corrupt. We use this setup to study the impacton equilibrium corruption of the degree of decentralization of corruption.To do this we compute equilibrium corruption in two different settings:1) Each bureaucrat acts in such a way as to maximize his own individualutility (competitive corruption); 2) An illegal syndicate oversee thecorruption decisions of the population of bureaucrats in such a way asto maximize total proceeds from corruption (organized corruption). Weshow that, since average corruption payoff is increasing in the activitylevels set by the constituency, and since the latter responds to highlevels of corruption by reducing required activity levels, in equilibriumthe illegal syndicate acts in such a way as to restrain the total numberof corrupt transactions, so that corruption is lower when it is organizedthan when it is competitive.

Mixed and Hybrid Models of Public Service Delivery

This symposium presents research from different contexts to improve our collective understanding of a variety of aspects of mixed forms of service delivery, be they mixed contracting at the level of the market (which is more common in the U.S.), or mixed management and ownership at the level of the firm (which is more common in Europe). The articles included in this special symposium examine the factors that give rise to mixed forms of service delivery (e.g., economic and fiscal stress, regulatory flexibility, geography, management) and how these factors impact their design and operation. Articles also explore the performance of mixed forms of service delivery relative to more conventional arrangements like contracted or direct service delivery. The articles contribute to a better theoretical and conceptual understanding of mixed/hybrid forms of services delivery.

Infección prenatal

Protocolos terapeuticos. Infección prenatal. Riesgo de infección prenatal. La infección prenatal requiere un alto índice de sospecha, ya que no siempre, los antecedentes se hallan presentes bien porque faltan o bien porque hayan pasado desapercibidos. Dentro del concepto de infección prenatal se encuentran las englobadas en el acrónimo Torches (toxoplasmosis, rubeola, citomegalovirosis, herpes o sífilis) )...

Genome-wide analysis of adaptive molecular evolution in the carnivorous plant Utricularia gibba

The genome of the bladderwort Utricularia gibba provides an unparalleled opportunity to uncover the adaptive landscape of an aquatic carnivorous plant with unique phenotypic features such as absence of roots, development of water-filled suction bladders, and a highly ramified branching pattern. Despite its tiny size, the U. gibba genome accommodates approximately as many genes as other plant genomes. To examine the relationship between the compactness of its genome and gene turnover, we compared the U. gibba genome with that of four other eudicot species, defining a total of 17,324 gene families (orthogroups). These families were further classified as either 1) lineage-specific expanded/contracted or 2) stable in size. The U. gibba-expanded families are generically related to three main phenotypic features: 1) trap physiology, 2) key plant morphogenetic/developmental pathways, and 3) response to environmental stimuli, including adaptations to life in aquatic environments. Further scans for signatures of protein functional specialization permitted identification of seven candidate genes with amino acid changes putatively fixed by positive Darwinian selection in the U. gibba lineage. The Arabidopsis orthologs of these genes (AXR, UMAMIT41, IGS, TAR2, SOL1, DEG9, and DEG10) are involved in diverse plant biological functions potentially relevant for U. gibba phenotypic diversification, including 1) auxin metabolism and signal transduction, 2) flowering induction and floral meristem transition, 3) root development, and 4) peptidases. Taken together, our results suggest numerous candidate genes and gene families as interesting targets for further experimental confirmation of their functional and adaptive roles in the U. gibba's unique lifestyle and highly specialized body plan.

New approximation to the third-order density : application to the calculation of correlated multicenter indices

In this work we present the formulas for the calculation of exact three-center electron sharing indices (3c-ESI) and introduce two new approximate expressions for correlated wave functions. The 3c-ESI uses the third-order density, the diagonal of the third-order reduced density matrix, but the approximations suggested in this work only involve natural orbitals and occupancies. In addition, the first calculations of 3c-ESI using Valdemoro's, Nakatsuji's and Mazziotti's approximation for the third-order reduced density matrix are also presented for comparison. Our results on a test set of molecules, including 32 3c-ESI values, prove that the new approximation based on the cubic root of natural occupancies performs the best, yielding absolute errors below 0.07 and an average absolute error of 0.015. Furthemore, this approximation seems to be rather insensitive to the amount of electron correlation present in the system. This newly developed methodology provides a computational inexpensive method to calculate 3c-ESI from correlated wave functions and opens new avenues to approximate high-order reduced density matrices in other contexts, such as the contracted Schrödinger equation and the anti-Hermitian contracted Schrödinger equation