On differential operators of Calabi-Yau type

This thesis is devoted to the study of Picard-Fuchs operators associated to one-parameter families of $n$-dimensional Calabi-Yau manifolds whose solutions are integrals of $(n,0)$-forms over locally constant $n$-cycles. Assuming additional conditions on these families, we describe algebraic properties of these operators which leads to the purely algebraic notion of operators of CY-type. rnMoreover, we present an explicit way to construct CY-type operators which have a linearly rigid monodromy tuple. Therefore, we first usernthe translation of the existence algorithm by N. Katz for rigid local systems to the level of tuples of matrices which was established by M. Dettweiler and S. Reiter. An appropriate translation to the level of differential operators yields families which contain operators of CY-type. rnConsidering additional operations, we are also able to construct special CY-type operators of degree four which have a non-linearly rigid monodromy tuple. This provides both previously known and new examples.

Prevalence and types of pitfall in the assessment of mitral isthmus linear conduction block

To identify and understand clinically encountered pitfalls in the assessment of transmitral conduction block using differential coronary sinus and left atrial appendage pacing techniques in patients with left mitral isthmus linear ablation.

From episodic to habitual prospective memory: ERP-evidence for a linear transition

Performing a prospective memory task repeatedly changes the nature of the task from episodic to habitual. The goal of the present study was to investigate the neural basis of this transition. In two experiments, we contrasted event-related potentials (ERPs) evoked by correct responses to prospective memory targets in the first, more episodic part of the experiment with those of the second, more habitual part of the experiment. Specifically, we tested whether the early, middle, or late ERP-components, which are thought to reflect cue detection, retrieval of the intention, and post-retrieval processes, respectively, would be changed by routinely performing the prospective memory task. The results showed a differential ERP effect in the middle time window (450 - 650 ms post-stimulus). Source localization using low resolution brain electromagnetic tomography analysis (LORETA) suggests that the transition was accompanied by an increase of activation in the posterior parietal and occipital cortex. These findings indicate that habitual prospective memory involves retrieval processes guided more strongly by parietal brain structures. In brief, the study demonstrates that episodic and habitual prospective memory tasks recruit different brain areas.

Fully Adaptive Newton--Galerkin Methods for Semilinear Elliptic Partial Differential Equations

In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both prediction-type adaptive Newton methods and a linear adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton–Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples

Differential effectiveness of integrated cognitive remediation therapy for schizophrenbia outpatients: The impact oft he duration of illness

Background Nowadays there is extensive evidence available showing the efficacy of cognitive remediation (CR). To date, only limited evidence is available about the impact of the duration of illness on CR effects. The Integrated Neurocognitive Therapy (INT) represents a new developed CR approach. It is a manualized group therapy targeting all 11 NIMH-MATRICS domains. Methods In an international multicenter study, 166 schizophrenia outpatients (DSM-IV-TR) were randomly assigned either to INT or to Treatment-As-Usual (TAU). 60 patients were defined as Early Course group (EC) characterized by less than 5 years of illness, 40 patients were in the Long-Term group (LT) characterized by more than 15 years of illness, and 76 patients were in the Medium-Long-Term group (MLT) characterized by an illness of 5-15 years. Treatment comprised of 15 biweekly sessions. Assessments were conducted before and after treatment and at follow up (1 year). Multivariate General Linear Models (GLM) examined our hypothesis, whether EC, LT, and MLT groups differ under INT and TAU from each other in outcome. Results First of all, the attendance rate of 65% was significantly lower and the drop out rate of 18.5% during therapy was higher in the EC group compared to the other groups. Interaction effects regarding proximal outcome showed that the duration of illness has a strong impact on neurocognitive functioning in speed of processing (F>2.4) and attention (F>2.8). But INT intervention compared to TAU only had a significant effect in more chronically ill patients of MLT and LT, but not in younger patients in EC. In social cognitive domains, only the EC group showed a significant change in attribution (hostility; F>2.5), LT and MLT groups did not. However, no differences between the 3 groups were evident in memory, problem solving, and emotion perception. Regarding more distal outcome, LT patients had more symptoms compared to EC (F>4.4). Finally, EC patients showed higher improvements in psychosocial functioning compared to LT and MLT (F=1.8). Conclusions Against common expectations, long-term, more chronically ill patients showed higher effects in basal cognitive functions compared to younger patients and patients without any active therapy (TAU). On the other hand, early-course patients had a greater potential to change in attribution, symptoms and psychosocial functioning. Consequently, more integrated therapy offers are also recommended for long-term course schizophrenia patients.

Linear Approach to the Orbiting Spacecraft Thermal Problem

A linear method is developed for solving the nonlinear differential equations of a lumped-parameter thermal model of a spacecraft moving in a closed orbit. This method, based on perturbation theory, is compared with heuristic linearizations of the same equations. The essential feature of the linear approach is that it provides a decomposition in thermal modes, like the decomposition of mechanical vibrations in normal modes. The stationary periodic solution of the linear equations can be alternately expressed as an explicit integral or as a Fourier series. This method is applied to a minimal thermal model of a satellite with ten isothermal parts (nodes), and the method is compared with direct numerical integration of the nonlinear equations. The computational complexity of this method is briefly studied for general thermal models of orbiting spacecraft, and it is concluded that it is certainly useful for reduced models and conceptual design but it can also be more efficient than the direct integration of the equations for large models. The results of the Fourier series computations for the ten-node satellite model show that the periodic solution at the second perturbative order is sufficiently accurate.

Linear latent force models using Gaussian Processes

Purely data-driven approaches for machine learning present difficulties when data are scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data-driven modeling with a physical model of the system. We show how different, physically inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology, and geostatistics.

Discrete linear stability and sensitivity analysis of fluid flows

Este trabajo presenta un método discreto para el cálculo de estabilidad hidrodinámica y análisis de sensibilidad a perturbaciones externas para ecuaciones diferenciales y en particular para las ecuaciones de Navier-Stokes compressible. Se utiliza una aproximación con variable compleja para obtener una precisión analítica en la evaluación de la matriz Jacobiana. Además, mapas de sensibilidad para la sensibilidad a las modificaciones del flujo de base y a una fuerza constante permiten identificar las regiones del campo fluido donde una modificacin (ej. fuerza puntual) tiene un efecto estabilizador del flujo. Se presentan cuatro casos de prueba: (1) un caso analítico para comprobar la derivación discreta, (2) una cavidad cerrada a bajo Reynolds para mostrar la mayor precisión en el cálculo de los valores propios con la aproximación de paso complejo, (3) flujo 2D en un cilindro circular para validar la metodología, y (4) flujo en un cavidad abierta, presentado para validar el método en casos de inestabilidades convectivamente inestables. Los tres últimos casos mencionados (2-4) se resolvieron con las ecuaciones de Navier-Stokes compresibles, utilizando un método Discontinuous Galerkin Spectral Element Method. Se obtuvo una buena concordancia para el caso de validación (3), cuando se comparó el nuevo método con resultados de la literatura. Además, este trabajo muestra que para el cálculo de los modos propios directos y adjuntos, así como para los mapas de sensibilidad, el uso de variables complejas es de suprema importancia para obtener una predicción precisa. El método descrito es aplicado al análisis para la estabilización de la estela generada por un disco actuador, que representa un modelo sencillo para hélices, rotores de helicópteros o turbinas eólicas. Se explora la primera bifurcación del flujo para un disco actuador, y se sugiere que está asociada a una inestabilidad de tipo Kelvin-Helmholtz, cuya estabilidad se controla con en el número de Reynolds y en la resistencia del disco actuador (o fuerza resistente). En primer lugar, se verifica que la disminución de la resistencia del disco tiene un efecto estabilizador parecido a una disminución del Reynolds. En segundo lugar, el análisis hidrodinmico discreto identifica dos regiones para la colocación de una fuerza puntual que controle las inestabilidades, una cerca del disco y otra en una zona aguas abajo. En tercer lugar, se muestra que la inclusión de un forzamiento localizado cerca del actuador produce una estabilización más eficiente que al forzar aguas abajo. El análisis de los campos de flujo controlados confirma que modificando el gradiente de velocidad cerca del actuador es más eficiente para estabilizar la estela. Estos resultados podrían proporcionar nuevas directrices para la estabilización de la estela de turbinas de viento o de marea cuando estén instaladas en un parque eólico y minimizar las interacciones no estacionarias entre turbinas. ABSTRACT A discrete framework for computing the global stability and sensitivity analysis to external perturbations for any set of partial differential equations is presented. In particular, a complex-step approximation is used to achieve near analytical accuracy for the evaluation of the Jacobian matrix. Sensitivity maps for the sensitivity to base flow modifications and to a steady force are computed to identify regions of the flow field where an input could have a stabilising effect. Four test cases are presented: (1) an analytical test case to prove the theory of the discrete framework, (2) a lid-driven cavity at low Reynolds case to show the improved accuracy in the calculation of the eigenvalues when using the complex-step approximation, (3) the 2D flow past a circular cylinder at just below the critical Reynolds number is used to validate the methodology, and finally, (4) the flow past an open cavity is presented to give an example of the discrete method applied to a convectively unstable case. The latter three (2–4) of the aforementioned cases were solved with the 2D compressible Navier–Stokes equations using a Discontinuous Galerkin Spectral Element Method. Good agreement was obtained for the validation test case, (3), with appropriate results in the literature. Furthermore, it is shown that for the calculation of the direct and adjoint eigenmodes and their sensitivity maps to external perturbations, the use of complex variables is paramount for obtaining an accurate prediction. An analysis for stabilising the wake past an actuator disc, which represents a simple model for propellers, helicopter rotors or wind turbines is also presented. We explore the first flow bifurcation for an actuator disc and it suggests that it is associated to a Kelvin- Helmholtz type instability whose stability relies on the Reynolds number and the flow resistance applied through the disc (or actuator forcing). First, we report that decreasing the disc resistance has a similar stabilising effect to an decrease in the Reynolds number. Second, a discrete sensitivity analysis identifies two regions for suitable placement of flow control forcing, one close to the disc and one far downstream where the instability originates. Third, we show that adding a localised forcing close to the actuator provides more stabilisation that forcing far downstream. The analysis of the controlled flow fields, confirms that modifying the velocity gradient close to the actuator is more efficient to stabilise the wake than controlling the sheared flow far downstream. An interesting application of these results is to provide guidelines for stabilising the wake of wind or tidal turbines when placed in an energy farm to minimise unsteady interactions.

Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

Differential fluorescence labeling of cysteinyl clusters uncovers high tissue levels of thionein

The isolation of thionein (T) from tissues has not been reported heretofore. T contains 20 cysteinyl residues that react with 7-fluorobenz-2-oxa-1,3-diazole-4-sulfonamide to form fluorescent adducts. In metallothionein (MT) the cysteinyl residues, which are bound to zinc, do not react. However, they do react in the presence of a chelating agent such as EDTA. The resultant difference in chemical reactivity provides a means to measure T in the absence of EDTA, (MT + T) in its presence, and, of course, MT by difference. The 7-fluorobenz-2-oxa-1,3-diazole-4-sulfonamide derivative of T can be isolated from tissue homogenates by HPLC and quantified fluorimetrically with a detection limit in the femtomolar range and a linear response over 3 orders of magnitude. Analysis of liver, kidney, and brain of rats reveals almost as much T as MT. Moreover, in contrast to earlier views, MT in tissue extracts appears to be less stable than T. The existence of T in tissues under normal physiological conditions has important implications for its function both in zinc metabolism and the redox balance of the cell.

Kinetic study of thermal 1,3-dipolar cycloaddition of azomethine ylides using differential scanning calorimetry as monitoring window

Kinetics of 1,3-dipolar cycloaddition involving azomethine ylides, generated from thermal [1,2]-prototropy of the corresponding imino ester, employing differential scanning calorimetry (DSC), is surveyed. Glycine and phenylalanine derived imino esters have different behavior. The first one prefers reacting with itself at 75 ºC, rather than with the dipolarophile. However, the α-substituted imino ester gives the cycloadduct at higher temperatures. The thermal dynamic analysis by 1H NMR of the neat reaction mixture of the glycine derivative reveals the presence of signals corresponding to the dipole in very small proportion. The non-isothermal and isothermal DSC curves of the cycloaddition of phenylalaninate and diisobutyl fumarate are obtained from freshly prepared samples. The application of known kinetic models and mathematical multiple non-linear regressions (NLR) allow to determine and to compare Ea, lnA, reaction orders, and reaction enthalpy. Finally a rate equation for each different temperature can be established for this particular thermal cycloaddition.

An iterative method for solving nonsymmetric linear systems with dynamic estimation of parameters /

Vita.

Blended linear multistep methods /

Bibliography: p. 64-65.

A search for better linear multistep methods for stiff problems /

Thesis--Illinois.

Ueber die integration der differential gleichung (t-a)(t-b)(t-c) d²y/dt² + (a+bt+ct²) dy/dt + (d+et)y=0 ...

Inaug.-dis.--Göttingen.