Quantitative Stability of Linear Infinite Inequality Systems under Block Perturbations with Applications to Convex Systems

The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set $J$. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is $l_{\infty}(J)$. Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel-Legendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system turn on constant-by-blocks perturbations in the linearized system. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map of block-perturbed linear systems, which involves only the system's data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. In this way we extend to the convex setting the results of [3] developed for arbitrary perturbations with no block structure in the linear framework under the boundedness assumption on the system's coefficients. The latter boundedness assumption is removed in this paper when the decision space is reflexive. The last section provides the aimed application to the convex case

Quantitative Stability and Optimality Conditions in Convex Semi-Infinite and Infinite Programming

This paper concerns parameterized convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional Banach (resp. finite-dimensional) spaces and that are indexed by an arbitrary fixed set T . Parameter perturbations on the right-hand side of the inequalities are measurable and bounded, and thus the natural parameter space is $l_{\infty}(T)$. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map, which involves only the system data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. On one hand, in this way we extend to the convex setting the results of [4] developed in the linear framework under the boundedness assumption on the system coefficients. On the other hand, in the case when the decision space is reflexive, we succeed to remove this boundedness assumption in the general convex case, establishing therefore results new even for linear infinite and semi-infinite systems. The last part of the paper provides verifiable necessary optimality conditions for infinite and semi-infinite programs with convex inequality constraints and general nonsmooth and nonconvex objectives. In this way we extend the corresponding results of [5] obtained for programs with linear infinite inequality constraints

Robust Stability and Optimality Conditions for Parametric Infinite and Semi-Infinite Programs

This paper primarily concerns the study of parametric problems of infinite and semi-infinite programming, where functional constraints are given by systems of infinitely many linear inequalities indexed by an arbitrary set T, where decision variables run over Banach (infinite programming) or finite-dimensional (semi-infinite case) spaces, and where objectives are generally described by nonsmooth and nonconvex cost functions. The parameter space of admissible perturbations in such problems is formed by all bounded functions on T equipped with the standard supremum norm. Unless the index set T is finite, this space is intrinsically infinite-dimensional (nonreflexive and nonseparable) of the l(infinity)-type. By using advanced tools of variational analysis and generalized differentiation and largely exploiting underlying specific features of linear infinite constraints, we establish complete characterizations of robust Lipschitzian stability (with computing the exact bound of Lipschitzian moduli) for parametric maps of feasible solutions governed by linear infinite inequality systems and then derive verifiable necessary optimality conditions for the infinite and semi-infinite programs under consideration expressed in terms of their initial data. A crucial part of our analysis addresses the precise computation of coderivatives and their norms for infinite systems of parametric linear inequalities in general Banach spaces of decision variables. The results obtained are new in both frameworks of infinite and semi-infinite programming

Variational Analysis in Semi-Infinite and Infinite Programming, II: Necessary Optimality Conditions

This paper concerns applications of advanced techniques of variational analysis and generalized differentiation to problems of semi-infinite and infinite programming with feasible solution sets defined by parameterized systems of infinitely many linear inequalities of the type intensively studied in the preceding development [5] from our viewpoint of robust Lipschitzian stability. We present meaningful interpretations and practical examples of such models. The main results establish necessary optimality conditions for a broad class of semi-infinite and infinite programs, where objectives are generally described by nonsmooth and nonconvex functions on Banach spaces and where infinite constraint inequality systems are indexed by arbitrary sets. The results obtained are new in both smooth and nonsmooth settings of semi-infinite and infinite programming

Single-ion and exchange anisotropy effects and multiferroic behavior in high-symmetry tetramer single molecule magnets

We study single-ion and exchange anisotropy effects in equal-spin $s_1$ tetramer single molecule magnets exhibiting $T_d$, $D_{4h}$, $D_{2d}$, $C_{4h}$, $C_{4v}$, or $S_4$ ionic point group symmetry. We first write the group-invariant quadratic single-ion and symmetric anisotropic exchange Hamiltonians in the appropriate local coordinates. We then rewrite these local Hamiltonians in the molecular or laboratory representation, along with the Dzyaloshinskii-Moriay (DM) and isotropic Heisenberg, biquadratic, and three-center quartic Hamiltonians. Using our exact, compact forms for the single-ion spin matrix elements, we evaluate the eigenstate energies analytically to first order in the microscopic anisotropy interactions, corresponding to the strong exchange limit, and provide tables of simple formulas for the energies of the lowest four eigenstate manifolds of ferromagnetic (FM) and anitiferromagnetic (AFM) tetramers with arbitrary $s_1$. For AFM tetramers, we illustrate the first-order level-crossing inductions for $s_1=1/2,1,3/2$, and obtain a preliminary estimate of the microscopic parameters in a Ni$_4$ from a fit to magnetization data. Accurate analytic expressions for the thermodynamics, electron paramagnetic resonance absorption and inelastic neutron scattering cross-section are given, allowing for a determination of three of the microscopic anisotropy interactions from the second excited state manifold of FM tetramers. We also predict that tetramers with symmetries $S_4$ and $D_{2d}$ should exhibit both DM interactions and multiferroic states, and illustrate our predictions for $s_1=1/2, 1$.Comment: 30 pages, 14 figures, submitted to Phys. Rev.

Lightweight Lempel-Ziv Parsing

We introduce a new approach to LZ77 factorization that uses O(n/d) words of working space and O(dn) time for any d >= 1 (for polylogarithmic alphabet sizes). We also describe carefully engineered implementations of alternative approaches to lightweight LZ77 factorization. Extensive experiments show that the new algorithm is superior in most cases, particularly at the lowest memory levels and for highly repetitive data. As a part of the algorithm, we describe new methods for computing matching statistics which may be of independent interest.Comment: 12 page

Composing JSON-based Web APIs

International audienceThe development of Web APIs has become a discipline that companies have to master to succeed in the Web. The so-called API economy is pushing companies to provide access to their data by means of Web APIs, thus requiring web developers to study and integrate such APIs into their applications. The exchange of data with these APIs is usually performed by using JSON, a schemaless data format easy for computers to parse and use. While JSON data is easy to read, its structure is implicit, thus entailing serious problems when integrating APIs coming from di erent vendors. Web developers have therefore to understand the domain behind each API and study how they can be composed. We tackle this issue by presenting an approach able to both discover the domain of JSON-based Web APIs, and identify composition links among them. Our approach allows developers to easily visualize what is behind APIs and how they can be composed to be used in their applications

CO33 188. Abordaje mínimamente invasivo frente a abordaje estándar en cirugía de recambio valvular aórtico

ObjetivoComparar resultados obtenidos en pacientes sometidos a recambio valvular aórtico aislado por abordaje mínimamente invasivo frente a esternotomía estándar.MétodosEntre enero de 2006 – diciembre de 2011, 524 pacientes fueron sometidos de forma programada a recambio valvular aórtico aislado, de los cuales 454 fueron realizados mediante abordaje estándar (grupo E) y 70 mediante miniesternotomía en «J» (grupo M). Consideradas variables preoperatorias, tiempos de circulación extracorpórea (CEC) y clampaje aórtico, resultados postoperatorios (morbimortalidad, estancias en unidad de cuidados intensivos [UCI] y postoperatoria total) y coste económico global (estancias en UCI, sala, intervención quirúrgica, consumo de fungible, implante y otros recursos).ResultadosLas características preoperatorias de la población fueron similares, sin diferencias significativas en cuanto a edad (68±9 vs 69±8 años) y EuroSCORE I aditivo (6,04±3,00 vs 5,38±2,23) entre grupo E y M, respectivamente. Sin embargo sí hubo diferencias significativas en cuanto a mortalidad (4,2 vs 0%; p < 0,005), tiempo de CEC (95±38 vs 84±21 min; p < 0,001), tiempo de clampaje aórtico (72±28 vs 65±15 min; p < 0,001), días de estancia en UCI (4,31±5,27 vs 3,14±1,2; p < 0,05) y días totales de estancia hospitalaria (9,68±7,6 vs 7,87±4,0; p < 0,05) entre grupo E y M, respectivamente. El grupo M presentó un consumo de 1.771,21 €/paciente inferior al grupo E.ConclusiónLa cirugía mínimamente invasiva para el recambio valvular aórtico puede ser beneficiosa tanto en términos de morbimortalidad como en términos económicos. Dado que el estudio presentado es retrospectivo, creemos que futuros análisis prospectivos aleatorizados serían convenientes para profundizar los hallazgos obtenidos

P15 60. Accidente cerebrovascular tras cirugía coronaria aislada: capacidad predictiva de las escalas de riesgo chads2 y cha2ds2vasc

ObjetivosValidar las escalas de riesgo CHADS2 y CHA2DS2VASC como modelos predictivos de desarrollo de accidente cerebrovascular (ACV) en cirugía coronaria aislada (CCA).MétodosPacientes consecutivos con CCA entre enero de 2003 – octubre de 2011. Puntuaciones CHADS2 y CHA2DS2VASC computadas para todos los pacientes, considerándose variable de resultado la aparición de ACV perioperatorio precoz (primer mes postoperatorio y/o alta hospitalaria). Considerado ACV el evento neurológico con focalidad clínica (ictus/ataque isquémico transitorio [AIT]). Dos modelos específicos ya validados para la predicción de ACV tras CPC, Northern New England Cardiovascular Disease Study Group (NNECDSG) y Multicenter Study of Perioperative Ischemia (McSPI) Research Group, fueron asimismo computados para todos los pacientes y comparados con los previos. La capacidad discriminativa fue cuantificada por el cálculo del área bajo la curva ROC (AUC). Además, dicha capacidad predictiva de los esquemas fue estudiada por distribución de sus puntuaciones en tres estratos atendiendo a la incidencia de ACV postoperatorio: baja (<1%), intermedia (1–3%) y alta (≥ 3%).ResultadosDos mil novecientos diez pacientes, 62 desarrollaron ACV postoperatorio (2,1%). La incidencia de ACV en pacientes igual o mayores de 75 años fue superior (3,9%) que la comparada con los menores de 75 años (1,7%) (odds ratio [OR]: 2,2; p=0,01). La AUC para CHADS2 fue 0,71, CHA2DS2VASC 0,72, NNECDSG 0,69 y McSPI 0,73. NNECDSG y CHA2DS2VASC demostraron mejor asignación de los pacientes a los estratos de bajo y alto riesgo.ConclusionesAmbos sistemas de puntuación CHADS2 y CHA2DS2VASC son modelos utilizados en la práctica clínica cotidiana con capacidad de predicción del desarrollo de ACV postoperatorio tras CCA similar a modelos específicamente preestablecidos