Root parametrized differential equations

The present thesis is about the inverse problem in differential Galois Theory. Given a differential field, the inverse  problem asks which linear algebraic groups can be realized as differential Galois groups of Picard-Vessiot extensions of this field.   In this thesis we will concentrate on the realization of the classical groups as differential Galois groups. We introduce a method for a very general realization of these groups. This means that we present for the classical groups of Lie rank $l$ explicit linear differential equations where the coefficients are differential polynomials in $l$ differential indeterminates over an algebraically closed field of constants $C$, i.e. our differential ground field is purely differential transcendental over the constants.   For the groups of type $A_l$, $B_l$, $C_l$, $D_l$ and $G_2$ we managed to do these realizations at the same time in terms of Abhyankar's program 'Nice Equations for Nice Groups'. Here the choice of the defining matrix is important. We found out that an educated choice of $l$ negative roots for the parametrization together with the positive simple roots leads to a nice differential equation and at the same time defines a sufficiently general element of the Lie algebra. Unfortunately for the groups of type $F_4$ and $E_6$ the linear differential equations for such elements are of enormous length. Therefore we keep in the case of $F_4$ and $E_6$ the defining matrix differential equation which has also an easy and nice shape.   The basic idea for the realization is the application of an upper and lower bound criterion for the differential Galois group to our parameter equations and to show that both bounds coincide. An upper and lower bound criterion can be found in literature. Here we will only use the upper bound, since for the application of the lower bound criterion an important condition has to be satisfied. If the differential ground field is $C_1$, e.g., $C(z)$ with standard derivation, this condition is automatically satisfied. Since our differential ground field is purely differential transcendental over $C$, we have no information whether this condition holds or not.   The main part of this thesis is the development of an alternative lower bound criterion and its application. We introduce the specialization bound. It states that the differential Galois group of a specialization of the parameter equation is contained in the differential Galois group of the parameter equation. Thus for its application we need a differential equation over $C(z)$ with given differential Galois group. A modification of a result from Mitschi and Singer yields such an equation over $C(z)$ up to differential conjugation, i.e. up to transformation to the required shape. The transformation of their equation to a specialization of our parameter equation is done for each of the above groups in the respective transformation lemma.

Time Discretization of the SST-generalized Navier-Stokes Equations: Positive and Negative Results

In the theory of the Navier-Stokes equations, the proofs of some basic known results, like for example the uniqueness of solutions to the stationary Navier-Stokes equations under smallness assumptions on the data or the stability of certain time discretization schemes, actually only use a small range of properties and are therefore valid in a more general context. This observation leads us to introduce the concept of SST spaces, a generalization of the functional setting for the Navier-Stokes equations. It allows us to prove (by means of counterexamples) that several uniqueness and stability conjectures that are still open in the case of the Navier-Stokes equations have a negative answer in the larger class of SST spaces, thereby showing that proof strategies used for a number of classical results are not sufficient to affirmatively answer these open questions. More precisely, in the larger class of SST spaces, non-uniqueness phenomena can be observed for the implicit Euler scheme, for two nonlinear versions of the Crank-Nicolson scheme, for the fractional step theta scheme, and for the SST-generalized stationary Navier-Stokes equations. As far as stability is concerned, a linear version of the Euler scheme, a nonlinear version of the Crank-Nicolson scheme, and the fractional step theta scheme turn out to be non-stable in the class of SST spaces. The positive results established in this thesis include the generalization of classical uniqueness and stability results to SST spaces, the uniqueness of solutions (under smallness assumptions) to two nonlinear versions of the Euler scheme, two nonlinear versions of the Crank-Nicolson scheme, and the fractional step theta scheme for general SST spaces, the second order convergence of a version of the Crank-Nicolson scheme, and a new proof of the first order convergence of the implicit Euler scheme for the Navier-Stokes equations. For each convergence result, we provide conditions on the data that guarantee the existence of nonstationary solutions satisfying the regularity assumptions needed for the corresponding convergence theorem. In the case of the Crank-Nicolson scheme, this involves a compatibility condition at the corner of the space-time cylinder, which can be satisfied via a suitable prescription of the initial acceleration.

Reforming Cooperative Credit Structure in India for Financial Inclusion

In the drive for financial inclusion in India, cooperative banks assume prime importance as they are much more accessible to the rural poor than commercial banks. While more accessible, cooperative banks' financial health is rather poor and, therefore, might not be able to serve the needy in a sustained manner. A committee led by Prof. Vaidyanathan has outlined a revival package for cooperatives. Besides suggesting an infusion of funds, it called for the adherence to certain stringent norms to ensure the financial viability. The recommendations provided in the committee’s report are under various stages of implementation in India. The book examines the progress of this reform drive in Bihar, a state in Eastern India. It discusses the background for appointing the committee and its recommendations and also presents the findings of a field study conducted in this regard. The findings inform further policy suggestions which are of general interest to the drive for financial inclusion also in other countries.

Differential effects of insulin signaling on individual carbon fluxes for fatty acid synthesis in brown adipocytes

Considering the major role of insulin signaling on fatty acid synthesis via stimulation of lipogenic enzymes, differential effects of insulin signaling on individual carbon fluxes for fatty acid synthesis have been investigated by comparing the individual lipogenic fluxes in WT and IRS-1 knockout (IRS-1 KO) brown adipocytes. Results from experiments on WT and IRS-1 KO cells incubated with [5-¹³C] glutamine were consistent with the existence of reductive carboxylation pathway. Analysis of isotopomer distribution of nine metabolites related to the lipogenic routes from glucose and glutamine in IRS-1 KO cells using [U-¹³C] glutamine as compared to that in WT cells indicated that flux through reductive carboxylation pathway was diminished while flux through conventional TCA cycle was stimulated due to absence of insulin signaling in IRS-1 KO cells. This observation was confirmed by quantitative estimation of individual lipogenic fluxes in IRS-1 KO cells and their comparison with fluxes in WT cells. Thus, these results suggest that glutamine’s substantial contribution to fatty acid synthesis can be directly manipulated by controlling the flux through reductive carboxylation of alpha-ketoglutarate to citrate using hormone (insulin).

SCAPA (Spacially Addressable Protein Array) – a Novel Protein Array for the Differential Profiling of Ligand-receptor Induced Signalling

While protein microarray technology has been successful in demonstrating its usefulness for large scale high-throughput proteome profiling, performance of antibody/antigen microarrays has been only moderately productive. Immobilization of either the capture antibodies or the protein samples on solid supports has severe drawbacks. Denaturation of the immobilized proteins as well as inconsistent orientation of antibodies/ligands on the arrays can lead to erroneous results. This has prompted a number of studies to address these challenges by immobilizing proteins on biocompatible surfaces, which has met with limited success. Our strategy relates to a multiplexed, sensitive and high-throughput method for the screening quantification of intracellular signalling proteins from a complex mixture of proteins. Each signalling protein to be monitored has its capture moiety linked to a specific oligo ‘tag’. The array involves the oligonucleotide hybridization-directed localization and identification of different signalling proteins simultaneously, in a rapid and easy manner. Antibodies have been used as the capture moieties for specific identification of each signaling protein. The method involves covalently partnering each antibody/protein molecule with a unique DNA or DNA derivatives oligonucleotide tag that directs the antibody to a unique site on the microarray due to specific hybridization with a complementary tag-probe on the array. Particular surface modifications and optimal conditions allowed high signal to noise ratio which is essential to the success of this approach.

Differential epipolar constraint in mobile robot egomotion estimation

The estimation of camera egomotion is a well established problem in computer vision. Many approaches have been proposed based on both the discrete and the differential epipolar constraint. The discrete case is mainly used in self-calibrated stereoscopic systems, whereas the differential case deals with a unique moving camera. The article surveys several methods for mobile robot egomotion estimation covering more than 0.5 million samples using synthetic data. Results from real data are also given

Replicated nil associations of digit ratio (2D:4D) and absolute finger lengths with implicit and explicit measures of aggression. 'Replicaci??n de asociaciones nulas del ratio del segundo y cuarto dedo (2D:4D) y la longitud absoluta de los dedos con medidas de agresi??n impl??citas y expl??citas'

Resumen tomado de la publicaci??n

Local model predictive control experiences with differential driven wheeled mobile robots

This work extends a previously developed research concerning about the use of local model predictive control in differential driven mobile robots. Hence, experimental results are presented as a way to improve the methodology by considering aspects as trajectory accuracy and time performance. In this sense, the cost function and the prediction horizon are important aspects to be considered. The aim of the present work is to test the control method by measuring trajectory tracking accuracy and time performance. Moreover, strategies for the integration with perception system and path planning are briefly introduced. In this sense, monocular image data can be used to plan safety trajectories by using goal attraction potential fields

Use of multilevel logistic regression to identify the causes of differential item functioning

Resumen tomado de la publicaci??n

The Challenges of didactics on scholar inclusion: specialized teachers perceptions

This study is a section of the GP-FOREESP - Formation of Human Resources and Learning in Special Education Group’s agenda. This Group is engaged in the development of researches with the intent to contribute on the process to universalize the access to school as well as on the improvement of education system that is currently available to the target population of Special Education. Nowadays, the inclusion process subject has been prioritized by that research group, as they consider that, along with other reasons, the efforts to establish an inclusive education system would be the unique alternative to solve the problem regarding the access to school, which is currently limited, and also to improve the quality on special education, since the level presented in the country is low. Guided by such premise, the present work is a supplementary project developed within the group extent to generate knowledge on school inclusion matter

Diferencias en la sedación de pacientes pediátricos con dos formas de preparar Fentany

En la unidad de cuidado intensivo pediátrico (UCIP) es esencial garantizar una adecuada sedación y analgesia del paciente en ventilación mecánica para mejorar su adaptación, disminuyendo el estrés y ansiedad de la situación crítica. Una estrategia utilizada es la combinación de midazolam más fentanyl, sin embargo no se encuentra en la literatura estudios sobre la repercusión de la forma de preparación sobre los grados de sedación, objetivo principal de este estudio. Materiales y métodos: Se realizó un estudio analítico retrospectivo para evaluar las diferencias sobre la escala Comfort de sedación con dos medicamentos: fentanyl y midazolam diluidos en solución salina y sin diluir. Se revisaron 1321 historias clínicas desde enero del 2005 a junio del 2010; 70 cumplieron con los criterios de inclusión y se agruparon en 2 cohorte. La cohorte No 1 fueron los pacientes que recibieron medicamentos puros y la cohorte 2 aquellos que los recibieron diluidos en solución salina. Se hizo un análisis estadístico mediante chi cuadrado y regresión logística. Resultados: Se encontró una diferencia estadísticamente significativa a favor de medicamentos sin diluir en términos de grado de “sedación óptima” (p< 0.01). No hubo diferencias al evaluar tiempo de estancia en UCIP (p=0.67), duración de ventilación mecánica (p=0.15), número de medicamentos coadyuvantes utilizados (p=0.1) ni de la frecuencia de presentación del síndrome de abstinencia (p=0.77). Conclusión: Se encontró una diferencia en el número de pacientes que alcanzaron el puntaje óptimo en la escala Comfort utilizando la estrategia de sedación con medicamentos preparados sin diluir.

MA160exam01

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files

MA160exam01pdf

Exam questions and solutions in PDF

Ordinary Differential Equations

Exercises and solutions about ordinary differential equations.