Modal interpolation via nested sequents

The main method of proving the Craig Interpolation Property (CIP) constructively uses cut-free sequent proof systems. Until now, however, no such method has been known for proving the CIP using more general sequent-like proof formalisms, such as hypersequents, nested sequents, and labelled sequents. In this paper, we start closing this gap by presenting an algorithm for proving the CIP for modal logics by induction on a nested-sequent derivation. This algorithm is applied to all the logics of the so-called modal cube.

The effects of erythritol air-polishing powder on microbiologic and clinical outcomes during supportive periodontal therapy: Six-month results of a randomized controlled clinical trial.

OBJECTIVES To characterize the physical characteristics of a new low abrasive erythritol powder (EPAP) and to evaluate its influence on the clinical and microbiologic parameters over a period of 6 months in patients undergoing supportive periodontal therapy (SPT). METHOD AND MATERIALS Prior to the clinical application, the particle size and abrasion level of EPAP were compared to glycine air-polishing powder (GPAP) ex vivo. Subsequently, 40 chronic periodontitis patients previously enrolled in SPT were randomly assigned into two groups for the treatment with subgingival EPAP or repeated scaling and root planing (SRP). At baseline (BL), bleeding on probing positive (BOP+) sites with probing pocket depth (PPD) of ≥ 4 mm but no detectable calculus were defined as study sites. During SPT, these sites were either treated by EPAP or SRP at BL, 3, and 6 months (3M, 6M). When indicated, additional SRP was provided. Plaque Index, BOP, PPD, clinical attachment level (CAL), and subgingival plaque were evaluated at BL and 6M. RESULTS EPAP yielded lower abrasiveness and smaller particle sizes when compared to GPAP. In 38 patients completing the study, EPAP and SRP resulted in significant reductions of BOP% (EPAP, 40.45%; SRP, 42.53%), PPD (EPAP, -0.67; SRP, -0.68), and increase of CAL (EPAP, 0.48; SRP, 0.61) while at 6M no statistically significant between-group differences were observed (P > .05). Microbiologic evaluation revealed minor shifts in the composition of the subgingival biofilm without influence on periodontopathogenic bacteria. CONCLUSION The subgingival use of EPAP by means of an air-polishing device may be considered safe and may lead to comparable clinical and microbiologic outcomes to those obtained with SRP. CLINICAL RELEVANCE The subgingival use of EPAP appears to represent a promising modality for the removal of subgingival biofilm during SPT.

EARLINET: potential operationality of a research network

In the framework of ACTRIS (Aerosols, Clouds, and Trace Gases Research Infrastructure Network) summer 2012 measurement campaign (8 June–17 July 2012), EARLINET organized and performed a controlled exercise of feasibility to demonstrate its potential to perform operational, coordinated measurements and deliver products in near-real time. Eleven lidar stations participated in the exercise which started on 9 July 2012 at 06:00 UT and ended 72 h later on 12 July at 06:00 UT. For the first time, the single calculus chain (SCC) – the common calculus chain developed within EARLINET for the automatic evaluation of lidar data from raw signals up to the final products – was used. All stations sent in real-time measurements of a 1 h duration to the SCC server in a predefined netcdf file format. The pre-processing of the data was performed in real time by the SCC, while the optical processing was performed in near-real time after the exercise ended. 98 and 79 % of the files sent to SCC were successfully pre-processed and processed, respectively. Those percentages are quite large taking into account that no cloud screening was performed on the lidar data. The paper draws present and future SCC users' attention to the most critical parameters of the SCC product configuration and their possible optimal value but also to the limitations inherent to the raw data. The continuous use of SCC direct and derived products in heterogeneous conditions is used to demonstrate two potential applications of EARLINET infrastructure: the monitoring of a Saharan dust intrusion event and the evaluation of two dust transport models. The efforts made to define the measurements protocol and to configure properly the SCC pave the way for applying this protocol for specific applications such as the monitoring of special events, atmospheric modeling, climate research and calibration/validation activities of spaceborne observations.

Newton-Cartan supergravity with torsion and Schrödinger supergravity

We derive a torsionfull version of three-dimensional N=2 Newton-Cartan supergravity using a non-relativistic notion of the superconformal tensor calculus. The “superconformal” theory that we start with is Schrödinger supergravity which we obtain by gauging the Schrödinger superalgebra. We present two non-relativistic N=2 matter multiplets that can be used as compensators in the superconformal calculus. They lead to two different off-shell formulations which, in analogy with the relativistic case, we call “old minimal” and “new minimal” Newton-Cartan supergravity. We find similarities but also point out some differences with respect to the relativistic case.

Guessing Harmonic Oscillator Wavefunctions Using Maple

The guessing of eigenfunctions is not trivial at higher quantum numbers, no matter what the system being considered. Instead of guessing, one can employ a symbolic calculus progam (Maple in this case) to aid in the reasoning process.

Functional data analysis approaches for genotype-phenotype association studies from next-generation sequencing

Next-generation DNA sequencing platforms can effectively detect the entire spectrum of genomic variation and is emerging to be a major tool for systematic exploration of the universe of variants and interactions in the entire genome. However, the data produced by next-generation sequencing technologies will suffer from three basic problems: sequence errors, assembly errors, and missing data. Current statistical methods for genetic analysis are well suited for detecting the association of common variants, but are less suitable to rare variants. This raises great challenge for sequence-based genetic studies of complex diseases.^ This research dissertation utilized genome continuum model as a general principle, and stochastic calculus and functional data analysis as tools for developing novel and powerful statistical methods for next generation of association studies of both qualitative and quantitative traits in the context of sequencing data, which finally lead to shifting the paradigm of association analysis from the current locus-by-locus analysis to collectively analyzing genome regions.^ In this project, the functional principal component (FPC) methods coupled with high-dimensional data reduction techniques will be used to develop novel and powerful methods for testing the associations of the entire spectrum of genetic variation within a segment of genome or a gene regardless of whether the variants are common or rare.^ The classical quantitative genetics suffer from high type I error rates and low power for rare variants. To overcome these limitations for resequencing data, this project used functional linear models with scalar response to develop statistics for identifying quantitative trait loci (QTLs) for both common and rare variants. To illustrate their applications, the functional linear models were applied to five quantitative traits in Framingham heart studies. ^ This project proposed a novel concept of gene-gene co-association in which a gene or a genomic region is taken as a unit of association analysis and used stochastic calculus to develop a unified framework for testing the association of multiple genes or genomic regions for both common and rare alleles. The proposed methods were applied to gene-gene co-association analysis of psoriasis in two independent GWAS datasets which led to discovery of networks significantly associated with psoriasis.^

Cálculo del valor ambiental de los jardines frontales urbanos : Mendoza (Argentina)

Los espacios verdes y, en general, la vegetación que cumple funciones estéticas y de protección ambiental son valorados, medidos y calculados por el área destinada al cultivo, en lugar de basar los cálculos en los elementos vegetales constitutivos. Esto significa una simplificación excesiva de la valoración de la vegetación (actual o proyectada) que no aporta criterios de cuantificación valorativa necesarios, actualmente, tanto para preservar vegetación existente como para políticas de desarrollo urbano y proyectos de ingeniería del mejoramiento ambiental. En el presente trabajo se propone aplicar a la valoración de los jardines frontales urbanos de la ciudad de Mendoza una metodología cuantitativa desarrollada por R. Codina et al., que se apoya en un concepto nuevo que es su influencia como mejoradores ambientales. La ecuación de cálculo se integra con índices de valoración como el Índice de Vegetación Ambientalmente Activa y el Índice Ambiental Urbanístico, que permiten cuantificar la importancia urbanística y ambiental de la vegetación. También se propone una base para implementar una política de incentivo de los jardines frontales mediante la disminución del avalúo valor terreno del impuesto inmobiliario, en una escala progresiva según el Índice Ambiental Urbanístico de cada propiedad, tendiente a la transformación de la ciudad en una ciudad-jardín, mejorando la calidad de vida y el atractivo turístico urbano.

Criterio ambiental volumétrico para cálculo de espacios verdes

Los espacios verdes y, en general, la vegetación utilizada para protección, son valorados, medidos y calculados por el área destinada a esa función más que por los elementos vegetales relacionados. Esto significa una simplificación excesiva que no aporta los criterios de cuantificación necesarios tanto para preservar el patrimonio natural existente como para elaborar proyectos de mejoramiento ambiental. En este trabajo se propone un concepto nuevo para la valoración de los elementos vegetales atendiendo a su influencia como mejoradores ambientales. Se determinan dos índices de valoración: el Índice de Vegetación Ambientalmente Activa por unidad de área utilizada y el Índice Ambiental Urbanístico. Ambos permiten cuantificar la importancia urbanística y ambiental de la vegetación. También se introduce un nuevo concepto en el cálculo de la necesidad de espacios verdes en proyectos urbanísticos y en áreas de amortiguación industriales, basado en el volumen vegetativo que debe existir en áreas que normalmente se destinan a espacios verdes.

Examples of PDEs all whose points are characteristic

Let π : FM ! M be the bundle of linear frames of a manifold M. A basis Lijk , j < k, of diffeomorphism invariant Lagrangians on J1 (FM) was determined in [J. Muñoz Masqué, M. E. Rosado, Invariant variational problems on linear frame bundles, J. Phys. A35 (2002) 2013-2036]. The notion of a characteristic hypersurface for an arbitrary first-order PDE system on an ar- bitrary bred manifold π : P → M, is introduced and for the systems dened by the Euler-Lagrange equations of Lijk every hypersurface is shown to be characteristic. The Euler-Lagrange equations of the natural basis of Lagrangian densities Lijk on the bundle of linear frames of a manifold M which are invariant under diffeomorphisms, are shown to be an underdetermined PDEs systems such that every hypersurface of M is characteristic for such equations. This explains why these systems cannot be written in the Cauchy-Kowaleska form, although they are known to be formally integrable by using the tools of geometric theory of partial differential equations, see [J. Muñoz Masqué, M. E. Rosado, Integrability of the eld equations of invariant variational problems on linear frame bundles, J. Geom. Phys. 49 (2004), 119-155]

Relational and Allegorical Semantics for Constraint Logic Programming

El cálculo de relaciones binarias fue creado por De Morgan en 1860 para ser posteriormente desarrollado en gran medida por Peirce y Schröder. Tarski, Givant, Freyd y Scedrov demostraron que las álgebras relacionales son capaces de formalizar la lógica de primer orden, la lógica de orden superior así como la teoría de conjuntos. A partir de los resultados matemáticos de Tarski y Freyd, esta tesis desarrolla semánticas denotacionales y operacionales para la programación lógica con restricciones usando el álgebra relacional como base. La idea principal es la utilización del concepto de semántica ejecutable, semánticas cuya característica principal es el que la ejecución es posible utilizando el razonamiento estándar del universo semántico, este caso, razonamiento ecuacional. En el caso de este trabajo, se muestra que las álgebras relacionales distributivas con un operador de punto fijo capturan toda la teoría y metateoría estándar de la programación lógica con restricciones incluyendo los árboles utilizados en la búsqueda de demostraciones. La mayor parte de técnicas de optimización de programas, evaluación parcial e interpretación abstracta pueden ser llevadas a cabo utilizando las semánticas aquí presentadas. La demostración de la corrección de la implementación resulta extremadamente sencilla. En la primera parte de la tesis, un programa lógico con restricciones es traducido a un conjunto de términos relacionales. La interpretación estándar en la teoría de conjuntos de dichas relaciones coincide con la semántica estándar para CLP. Las consultas contra el programa traducido son llevadas a cabo mediante la reescritura de relaciones. Para concluir la primera parte, se demuestra la corrección y equivalencia operacional de esta nueva semántica, así como se define un algoritmo de unificación mediante la reescritura de relaciones. La segunda parte de la tesis desarrolla una semántica para la programación lógica con restricciones usando la teoría de alegorías—versión categórica del álgebra de relaciones—de Freyd. Para ello, se definen dos nuevos conceptos de Categoría Regular de Lawvere y _-Alegoría, en las cuales es posible interpretar un programa lógico. La ventaja fundamental que el enfoque categórico aporta es la definición de una máquina categórica que mejora e sistema de reescritura presentado en la primera parte. Gracias al uso de relaciones tabulares, la máquina modela la ejecución eficiente sin salir de un marco estrictamente formal. Utilizando la reescritura de diagramas, se define un algoritmo para el cálculo de pullbacks en Categorías Regulares de Lawvere. Los dominios de las tabulaciones aportan información sobre la utilización de memoria y variable libres, mientras que el estado compartido queda capturado por los diagramas. La especificación de la máquina induce la derivación formal de un juego de instrucciones eficiente. El marco categórico aporta otras importantes ventajas, como la posibilidad de incorporar tipos de datos algebraicos, funciones y otras extensiones a Prolog, a la vez que se conserva el carácter 100% declarativo de nuestra semántica. ABSTRACT The calculus of binary relations was introduced by De Morgan in 1860, to be greatly developed by Peirce and Schröder, as well as many others in the twentieth century. Using different formulations of relational structures, Tarski, Givant, Freyd, and Scedrov have shown how relation algebras can provide a variable-free way of formalizing first order logic, higher order logic and set theory, among other formal systems. Building on those mathematical results, we develop denotational and operational semantics for Constraint Logic Programming using relation algebra. The idea of executable semantics plays a fundamental role in this work, both as a philosophical and technical foundation. We call a semantics executable when program execution can be carried out using the regular theory and tools that define the semantic universe. Throughout this work, the use of pure algebraic reasoning is the basis of denotational and operational results, eliminating all the classical non-equational meta-theory associated to traditional semantics for Logic Programming. All algebraic reasoning, including execution, is performed in an algebraic way, to the point we could state that the denotational semantics of a CLP program is directly executable. Techniques like optimization, partial evaluation and abstract interpretation find a natural place in our algebraic models. Other properties, like correctness of the implementation or program transformation are easy to check, as they are carried out using instances of the general equational theory. In the first part of the work, we translate Constraint Logic Programs to binary relations in a modified version of the distributive relation algebras used by Tarski. Execution is carried out by a rewriting system. We prove adequacy and operational equivalence of the semantics. In the second part of the work, the relation algebraic approach is improved by using allegory theory, a categorical version of the algebra of relations developed by Freyd and Scedrov. The use of allegories lifts the semantics to typed relations, which capture the number of logical variables used by a predicate or program state in a declarative way. A logic program is interpreted in a _-allegory, which is in turn generated from a new notion of Regular Lawvere Category. As in the untyped case, program translation coincides with program interpretation. Thus, we develop a categorical machine directly from the semantics. The machine is based on relation composition, with a pullback calculation algorithm at its core. The algorithm is defined with the help of a notion of diagram rewriting. In this operational interpretation, types represent information about memory allocation and the execution mechanism is more efficient, thanks to the faithful representation of shared state by categorical projections. We finish the work by illustrating how the categorical semantics allows the incorporation into Prolog of constructs typical of Functional Programming, like abstract data types, and strict and lazy functions.

Could it be possible to replace DERIVE with MAXIMA?

In recent years, a considerable number of teachers in Spain have been using DERIVE to teach math subjects in High Schools and Universities. This software has been used by the authors of this work as a support tool in Mathematics courses for Engineering. Since Texas Instruments does not support DERIVE, we were faced with finding an alternative software product, and considering the possibility of using a public-domain software such as MAXIMA. Here we make a comparative study of DERIVE and MAXIMA as support tools for a Calculus course for first year Engineering students.

Efficient management of backtracking in and-parallelism

A backtracking algorithm for AND-Parallelism and its implementation at the Abstract Machine level are presented: first, a class of AND-Parallelism models based on goal independence is defined, and a generalized version of Restricted AND-Parallelism (RAP) introduced as characteristic of this class. A simple and efficient backtracking algorithm for R A P is then discussed. An implementation scheme is presented for this algorithm which offers minimum overhead, while retaining the performance and storage economy of sequent ial implementations and taking advantage of goal independence to avoid unnecessary backtracking ("restricted intelligent backtracking"). Finally, the implementation of backtracking in sequential and AND-Parallcl systems is explained through a number of examples.

Evaluación del comportamiento mecánico, estructural y frente a la corrosión, de una nueva armadura de acero inoxidable dúplex bajo en níquel

La durabilidad de las estructuras de hormigón armado no es ilimitada, en especial en determinados ambientes. El ingreso de agentes agresivos en el hormigón, fundamentalmente dióxido de carbono e iones cloruros, rebasando el espesor del recubrimiento y alcanzando las armaduras, reducen el alto pH del hormigón hasta alcanzar un umbral crítico, por debajo del cual, el acero queda despasivado. Posteriormente, si existe el suficiente aporte de humedad y oxígeno, el acero se corroe, lo que supone drásticas reducciones de la vida de servicio de estas estructuras y su inevitable reparación. La utilización de armaduras de acero inoxidable es una alternativa que está recibiendo cada vez más consideración. Su resistencia a la corrosión en los ambientes más agresivos, incluso con ataque de cloruros, lo convierte en el material idóneo para prolongar de forma muy considerable la vida útil de la estructura. En este trabajo se ha evaluado el comportamiento mecánico y estructural, y de resistencia a la corrosión, de un nuevo acero inoxidable dúplex de bajo contenido en níquel, el EN 1.4482 (AISI 2001), y se ha comparado con el inoxidable austenítico más utilizado, el EN 1.4301 (AISI 304), con el dúplex EN 1.4362 (AISI 2304) y con el tradicional acero al carbono B-500-SD. El estudio mecánico y estructural se ha realizado en tres niveles diferentes: a nivel de barra, estudiando las propiedades mecánicas y de ductilidad de los cuatro aceros citados; a nivel de sección, estudiando su comportamiento a flexión con diferentes cuantías de armado por medio de los diagramas momento-curvatura; y a nivel de pieza, ensayando una serie de vigas armadas con diferentes aceros y cuantías, y comprobando su comportamiento a desplazamiento y resistencia por medio de los diagramas carga-desplazamiento. El estudio de resistencia a la corrosión se ha realizado embebiendo barras corrugadas, de los tres aceros inoxidables mencionados, en probetas de mortero contaminadas con diferentes cantidades de cloruros, y realizando mediciones electroquímicas durante un periodo de al menos un año. Se han preparado probetas de mortero para dos comparativas diferentes. La primera, manteniendo las probetas en un desecador con el 95 % de humedad relativa durante todo el periodo de mediciones. La segunda, sumergiendo parcialmente las probetas en una solución tampón para carbonatar el mortero. Los resultados de los ensayos mecánicos han demostrado dos aspectos diferentes. Uno, que las armaduras de acero inoxidable tienen un comportamiento muy similar a las de acero al carbono en lo referente a las resistencias alcanzadas, en el límite elástico y en rotura, pero distinto en cuanto al módulo de deformación longitudinal, cuyo valor es claramente inferior al del acero al carbono, por lo que su utilización en las estructuras de hormigón necesita tener en cuenta ese dato en los análisis lineales de cálculo. El segundo aspecto es que las armaduras de acero inoxidable laminadas en caliente presentan una ductilidad muy superior a las de acero al carbono, por lo que ofrecen una mayor seguridad frente a su rotura o al colapso de la estructura, lo que se debe tener en cuenta en el análisis de cálculo plástico. En cambio, las armaduras de acero inoxidable laminadas en frío sólo cumplen con los límites mínimos de ductilidad establecidos en la instrucción EHE-08 para los aceros soldables, y no para los aceros con características especiales de ductilidad. El estudio a nivel de sección refleja la paradoja de obtener secciones menos dúctiles con las armaduras de acero inoxidable laminadas en caliente que con las armaduras de acero al carbono. Para subsanarlo, se definen los conceptos de curvatura última de rotura y ductilidad de la sección en rotura, que tienen en cuenta las altas deformaciones alcanzadas por las armaduras de acero inoxidable. Los resultados a nivel de pieza permiten identificar el comportamiento estructural del hormigón armado con barras corrugadas de acero inoxidable y compararlo con el de las estructuras de hormigón armado convencionales, verificando los resultados experimentales con los teóricos obtenidos con la formulación recogida en la instrucción EHE- 08. Los ensayos de resistencia a la corrosión por cloruros demuestran, durante el primer año y medio de vida de las probetas, un comportamiento muy similar entre el nuevo acero inoxidable dúplex bajo en níquel y el austenítico y el dúplex utilizados para la comparación, incluso para las probetas carbonatadas. Por último, se añade una comparativa económica, realizada sobre dos edificaciones tipo, para cuantificar el sobrecoste que supone la utilización de armaduras de acero inoxidable respecto a las de acero al carbono. El alto coste inicial de las armaduras de acero inoxidable se ve compensado en el coste final de la estructura de muy diferentes formas, principalmente dependiendo del grado de acero elegido y de si se emplean en el total de la estructura o solamente en los elementos más expuestos. The durability of the concrete structures is limited, especially in certain environments. The attack of aggressive agents in the concrete, mainly carbon dioxide and chloride ions, penetrating the thickness of concrete cover and reaching the reinforcements, reduce the high pH of concrete to the point of reaching a critical threshold, under which, the steel despasivates. Therefore, if there is enough humidity and oxygen, the steel corroes, causing drastic reductions in the service life of these structures and its inevitable repair. Despite the high initial cost compared to carbon steel, the usage of stainless steel reinforcements is an alternative with a major consideration nowadays. Its resistance to corrosion in the most aggressive atmospheres, including chlorides attack, makes the stainless steel a suitable material to extend considerably its lifetime. In this study, it’s been evaluated the mechanical and structural behaviour, and the corrosion resistance, of a new low-nickel duplex stainless steel EN 1.4482 (AISI 2001), and it has been compared with the most widely used austenitic type EN 1.4301 (AISI 304), with duplex steel EN 1.4362 (AISI 2304) and with the traditional carbon steel B-500-SD. The mechanical and structural study has been carried out in three different levels: bar level, studying mechanical properties and ductility of the four steels; section level, studying its behaviour when blending with different amounts of reinforcement through the moment-curvature diagrams; and structural element level, testing a series of reinforced beams with different steels and amounts, and checking its sag and resistance through the load-deflection diagrams. The corrosion resistance study was performed by embedding ribbed bars, using the three stainless steel listed, on mortar specimens contaminated with different amounts of chlorides, and taking electrochemical measurements over a period of at least one year. Mortar specimens have been prepared for two different comparisons. The first, keeping the specimens at 95% of relative humidity during the measurement period. The second, immersing the specimens partially in a carbonate buffer solution. The results of those tests have proved two different aspects. Firstly, that stainless steel reinforcements show a very similar behaviour to carbon steel, according to the reached levels of mechanical resistance, yield stress and steel strength, but a different behaviour in Young’s modulus, which value is clearly lower than the carbon steel. Therefore, when using in concrete structures it is need to consider on that point the existing calculus of linear analysis. The second aspect is that stainless steel reinforcement manufactured by hot-rolling process show a very higher ductility than carbon steel, offering a better security on cracks or structure collapse, which it has to be taken into account on plastic calculus analysis. However, the stainless steel reinfor9 cement cold-rolled bars only meet the minimum thresholds of ductility established by EHE-08 for welded steel, and not for steels with special ductility. The results at the section level reflect the paradox of getting less ductile sections with hot rolled stainless steel reinforcement than with carbon steel reinforcements. To overcome that, the concepts of last break curvature and break ductility section have been defined, which take into account the high deformation value achieved by stainless steel reinforcements. The results at the structural element level allow to identify the structural behaviour of reinforced concrete with stainless steel reinforcements and compared with that of conventional steel reinforcement, contrasting the experimental with the theoretical results obtained from the formulation contained in the instruction EHE-08. Tests on resistance of chloride corrosion show during the first year and a half of specimens life, a similar behaviour between the new low nickel duplex stainless steel and austenitic and duplex used for comparison, even for carbonated specimens. Finally, it has been included an economic comparison on two differents building types, to quantify the additional cost involved on the use of stainless steel reinforcement compared to that of carbon steel. The high initial cost of stainless steel reinforcements is offset in the final cost of the structure in many different ways, mainly depending on the chosen steel grade and whether the reinforcement is used in the total structure or only in risky structural elements.