Elimination in Operator Algebras

A large class of special functions are solutions of systems of linear difference and differential equations with polynomial coefficients. For a given function, these equations considered as operator polynomials generate a left ideal in a noncommutative algebra called Ore algebra. This ideal with finitely many conditions characterizes the function uniquely so that Gröbner basis techniques can be applied. Many problems related to special functions which can be described by such ideals can be solved by performing elimination of appropriate noncommutative variables in these ideals. In this work, we mainly achieve the following: 1. We give an overview of the theoretical algebraic background as well as the algorithmic aspects of different methods using noncommutative Gröbner elimination techniques in Ore algebras in order to solve problems related to special functions. 2. We describe in detail algorithms which are based on Gröbner elimination techniques and perform the creative telescoping method for sums and integrals of special functions. 3. We investigate and compare these algorithms by illustrative examples which are performed by the computer algebra system Maple. This investigation has the objective to test how far noncommutative Gröbner elimination techniques may be efficiently applied to perform creative telescoping.

Certified Rapid Solution of Parametrized Linear Elliptic Equations: Application to Parameter Estimation

We present a technique for the rapid and reliable evaluation of linear-functional output of elliptic partial differential equations with affine parameter dependence. The essential components are (i) rapidly uniformly convergent reduced-basis approximations — Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N (optimally) selected points in parameter space; (ii) a posteriori error estimation — relaxations of the residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs; and (iii) offline/online computational procedures — stratagems that exploit affine parameter dependence to de-couple the generation and projection stages of the approximation process. The operation count for the online stage — in which, given a new parameter value, we calculate the output and associated error bound — depends only on N (typically small) and the parametric complexity of the problem. The method is thus ideally suited to the many-query and real-time contexts. In this paper, based on the technique we develop a robust inverse computational method for very fast solution of inverse problems characterized by parametrized partial differential equations. The essential ideas are in three-fold: first, we apply the technique to the forward problem for the rapid certified evaluation of PDE input-output relations and associated rigorous error bounds; second, we incorporate the reduced-basis approximation and error bounds into the inverse problem formulation; and third, rather than regularize the goodness-of-fit objective, we may instead identify all (or almost all, in the probabilistic sense) system configurations consistent with the available experimental data — well-posedness is reflected in a bounded "possibility region" that furthermore shrinks as the experimental error is decreased.

Evolution of clinical and functional results after arthroscopic treatment of Discoid Meniscus. A case series study of 31 cases.

Purpose: To evaluate the evolution of clinical and functional outcomes of symptomatic discoid lateral meniscus treated arthroscopically over time and to investigate the relationship between associated intra-articular findings and outcomes. Methods: Of all patients treated arthroscopically between 1995 and 2010, patients treated for symptomatic discoid meniscus were identified in the hospital charts. Baseline data (demographics, previous trauma of ipsilateral knee, and associated intra-articular findings) and medium term outcome data from clinical follow-up examinations (pain, locking, snapping and instability of the operated knee) were extracted from clinical records. Telephone interviews were conducted at long term in 28 patients (31 knees). Interviews comprised clinical outcomes as well as functional outcomes as assessed by the International Knee Documentation Committee Subjective Knee Evaluation Form (IKDC). Results: All patients underwent arthroscopic partial meniscectomy. The mean follow-up time for data extracted from clinical records was 11 months (SD ± 12). A significant improvement was found for pain in 77% (p<0.001), locking in 13%, (p=0.045) and snapping in 39 % (p<0.005). The mean follow-up time of the telephone interview was 60 months (SD ± 43). Improvement from baseline was generally less after five years than after one year and functional outcomes of the IKDC indicated an abnormal function after surgery (IKDC mean= 84.5, SD ± 20). In some patients, 5 year-outcomes were even worse than their preoperative condition. Nonetheless, 74% of patients perceived their knee function as improved. Furthermore, better results were seen in patients without any associated intra-articular findings. Conclusions: Arthroscopical partial meniscectomy is an effective intervention to relieve symptoms in patients with discoid meniscus in the medium-term; however, results trend to deteriorate over time. A trend towards better outcome for patients with no associated intra-articular findings was observed.

Resonancia magnética cardiaca: medidas lineales y volumétricas en adultos sanos

Introducción: La gran mayoría de las medidas de normalidad utilizadas para la interpretación de resonancia cardiaca son extrapoladas de las medidas de ecocardiografía. Los limitados registros de medidas de normalidad se encuentran ajustados en poblaciones extranjeras, no hay registros en latinoamericanos. Objetivo: Determinar las dimensiones cardiacas utilizando resonancia magnética en una población de personas sin antecedente médicos con repercusión cardiaca para lograr una muestra de valores que permitan ajustar las medidas de normalidad utilizadas por nuestro servicio. Materiales y métodos: se analizaron 45 sujetos sanos con edad comprendida entre los 21 y 45 años, las adquisiciones se realizaron utilizando un equipo de RM de 1,5 teslas, el análisis de las imágenes se realizó mediante el programa Cardiac Volume Vx. Se evaluaron múltiples parámetros morfofuncionales a través de análisis estadístico por medio del sistema SPSS versión 23. Resultados: Mediciones obtenidas de ventrículo izquierdo principales fueron volumen diastólico en mujeres de 62 ml +/- 7.1 y en hombres de 65 ml +/- 11.2 y fracción de eyección de 60 % +/- 5 en mujeres y de 62 % +/- 9 en hombres. En ventrículo derecho el volumen diastólico final se encontró 81.8 ml +/- 14.6 en mujeres y 100 ml +/- 24.8 en hombres y fracción de eyección de 53 % +/- 17 en mujeres y de 45 % +/- 12 en hombres. Volumen de fin de diástole de 50 +/- 12.7 ml en mujeres y de 49 ml +/- 19 ml en hombres y fracción de eyección de aurícula izquierda de 55 % +/- 0.08 en mujeres y de 50 % +/- 0.07 en hombres. Volumen de fin de diástole de 44.1 ml +/- 18.5 en mujeres y de 49.2 ml +/- 22.9 en hombres y fracción de eyección de aurícula derecha de 50 % +/- 11 en mujeres y de 45 % +/- 8 en hombres. Se obtuvieron otras medidas lineales y volumétricas adicionales de cavidades cardiacas y de grandes vasos supracardiacos. Conclusiones: se describen los valores de referencia de los parámetros morfofuncionales de las cavidades cardiacas y de vasos supracardiacos. El sexo fue tenido en cuenta como covariable relacionada con la modificación de los parámetros evaluados. Se sugieren variaciones en las medidas de cavidades cardiacas para la población estudiada relacionada con aclimatación crónica a la altitud de la ciudad de Bogotá.

Density functional energy decomposition into one- and two-atom contributions

The present work provides a generalization of Mayer's energy decomposition for the density-functional theory (DFT) case. It is shown that one- and two-atom Hartree-Fock energy components in Mayer's approach can be represented as an action of a one-atom potential VA on a one-atom density ρ A or ρ B. To treat the exchange-correlation term in the DFT energy expression in a similar way, the exchange-correlation energy density per electron is expanded into a linear combination of basis functions. Calculations carried out for a number of density functionals demonstrate that the DFT and Hartree-Fock two-atom energies agree to a reasonable extent with each other. The two-atom energies for strong covalent bonds are within the range of typical bond dissociation energies and are therefore a convenient computational tool for assessment of individual bond strength in polyatomic molecules. For nonspecific nonbonding interactions, the two-atom energies are low. They can be either repulsive or slightly attractive, but the DFT results more frequently yield small attractive values compared to the Hartree-Fock case. The hydrogen bond in the water dimer is calculated to be between the strong covalent and nonbonding interactions on the energy scale

Operator expansion: definition and molecular integral applications

Es defineix l'expansió general d'operadors com una combinació lineal de projectors i s'exposa la seva aplicació generalitzada al càlcul d'integrals moleculars. Com a exemple numèric, es fa l'aplicació al càlcul d'integrals de repulsió electrònica entre quatre funcions de tipus s centrades en punts diferents, i es mostren tant resultats del càlcul com la definició d'escalat respecte a un valor de referència, que facilitarà el procés d'optimització de l'expansió per uns paràmetres arbitraris. Es donen resultats ajustats al valor exacte

Linear viscoelasticity from molecular dynamics simulation of entangled polymers

The linear viscoelastic (LVE) spectrum is one of the primary fingerprints of polymer solutions and melts, carrying information about most relaxation processes in the system. Many single chain theories and models start with predicting the LVE spectrum to validate their assumptions. However, until now, no reliable linear stress relaxation data were available from simulations of multichain systems. In this work, we propose a new efficient way to calculate a wide variety of correlation functions and mean-square displacements during simulations without significant additional CPU cost. Using this method, we calculate stress−stress autocorrelation functions for a simple bead−spring model of polymer melt for a wide range of chain lengths, densities, temperatures, and chain stiffnesses. The obtained stress−stress autocorrelation functions were compared with the single chain slip−spring model in order to obtain entanglement related parameters, such as the plateau modulus or the molecular weight between entanglements. Then, the dependence of the plateau modulus on the packing length is discussed. We have also identified three different contributions to the stress relaxation:  bond length relaxation, colloidal and polymeric. Their dependence on the density and the temperature is demonstrated for short unentangled systems without inertia.

Sex-dependent age modulation of frontostriatal and temporo-parietal activation during cognitive control

Developmental functional imaging studies of cognitive control show progressive age-related increase in task-relevant fronto-striatal activation in male development from childhood to adulthood. Little is known, however, about how gender affects this functional development. In this study, we used event related functional magnetic resonance imaging to examine effects of sex, age, and their interaction on brain activation during attentional switching and interference inhibition, in 63 male and female adolescents and adults, aged 13 to 38. Linear age correlations were observed across all subjects in task-specific frontal, striatal and temporo-parietal activation. Gender analysis revealed increased activation in females relative to males in fronto-striatal areas during the Switch task, and laterality effects in the Simon task, with females showing increased left inferior prefrontal and temporal activation, and males showing increased right inferior prefrontal and parietal activation. Increased prefrontal activation clusters in females and increased parietal activation clusters in males furthermore overlapped with clusters that were age-correlated across the whole group, potentially reflecting more mature prefrontal brain activation patterns for females, and more mature parietal activation patterns for males. Gender by age interactions further supported this dissociation, revealing exclusive female-specific age correlations in inferior and medial prefrontal brain regions during both tasks, and exclusive male-specific age correlations in superior parietal (Switch task) and temporal regions (Simon task). These findings show increased recruitment of age-correlated prefrontal activation in females, and of age-correlated parietal activation in males, during tasks of cognitive control. Gender differences in frontal and parietal recruitment may thus be related to gender differences in the neurofunctional maturation of these brain regions.

Towards an assessment of multiple ecosystem processes and services via functional traits

Managing ecosystems to ensure the provision of multiple ecosystem services is a key challenge for applied ecology. Functional traits are receiving increasing attention as the main ecological attributes by which different organisms and biological communities influence ecosystem services through their effects on underlying ecosystem processes. Here we synthesize concepts and empirical evidence on linkages between functional traits and ecosystem services across different trophic levels. Most of the 247 studies reviewed considered plants and soil invertebrates, but quantitative trait–service associations have been documented for a range of organisms and ecosystems, illustrating the wide applicability of the trait approach. Within each trophic level, specific processes are affected by a combination of traits while particular key traits are simultaneously involved in the control of multiple processes. These multiple associations between traits and ecosystem processes can help to identify predictable trait–service clusters that depend on several trophic levels, such as clusters of traits of plants and soil organisms that underlie nutrient cycling, herbivory, and fodder and fibre production. We propose that the assessment of trait–service clusters will represent a crucial step in ecosystem service monitoring and in balancing the delivery of multiple, and sometimes conflicting, services in ecosystem management.

Modeling chemotaxis reveals the role of reversed phosphotransfer and a bi-functional kinase-phosphatase

Understanding how multiple signals are integrated in living cells to produce a balanced response is a major challenge in biology. Two-component signal transduction pathways, such as bacterial chemotaxis, comprise histidine protein kinases (HPKs) and response regulators (RRs). These are used to sense and respond to changes in the environment. Rhodobacter sphaeroides has a complex chemosensory network with two signaling clusters, each containing a HPK, CheA. Here we demonstrate, using a mathematical model, how the outputs of the two signaling clusters may be integrated. We use our mathematical model supported by experimental data to predict that: (1) the main RR controlling flagellar rotation, CheY6, aided by its specific phosphatase, the bifunctional kinase CheA3, acts as a phosphate sink for the other RRs; and (2) a phosphorelay pathway involving CheB2 connects the cytoplasmic cluster kinase CheA3 with the polar localised kinase CheA2, and allows CheA3-P to phosphorylate non-cognate chemotaxis RRs. These two mechanisms enable the bifunctional kinase/phosphatase activity of CheA3 to integrate and tune the sensory output of each signaling cluster to produce a balanced response. The signal integration mechanisms identified here may be widely used by other bacteria, since like R. sphaeroides, over 50% of chemotactic bacteria have multiple cheA homologues and need to integrate signals from different sources.