An introduction to ordinary differential equations by computer algebra-systems

We report on an elementary course in ordinary differential equations (odes) for students in engineering sciences. The course is also intended to become a self-study package for odes and is is based on several interactive computer lessons using REDUCE and MATHEMATICA . The aim of the course is not to do Computer Algebra (CA) by example or to use it for doing classroom examples. The aim ist to teach and to learn mathematics by using CA-systems.

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.

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

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

Ordinary Differential Equations

Exercises and solutions about ordinary differential equations.

Differential Equations II

Exercises and solutions for a second year differential equations course.

INFO6003 (2013) Differential Privacy -- Overview Paper

Cynthia Dwork: A Firm Foundation for Private Data Analysis Required reading

The differential effect on dropout of increasing grades' supply by integrating or expanding schools: evidence from a quasi-experiment in Bogotá

En el año 2002, la Secretaría de Educación de Bogotá estipuló la Resolución 2101 que tenía por objeto asegurar el ciclo de la educación completo en los colegios públicos. El propósito de este trabajo es evaluar el impacto de los mecanismos seguidos a la aplicación de esta política sobre la tasa de deserción escolar. Las escuelas tenían tres mecanismos diferentes para alcanzar el objetivo de la presente resolución: expandir los grados escolares ofertados, integrarse con otros colegios de la zona, o ambos. Para ello, utilizo variables instrumentales para resolver el sesgo causado por el hecho de que los colegios que siguen determinada estrategia eran los que tenían altas tasas de deserción inicialmente. Usando datos sobre las características institucionales y las características socio-demográficas de la población cerca del colegio, evalúo el impacto de estos tres mecanismos sobre las tasas de deserción escolar. Los resultados sugieren que las instituciones que aumentaron los grados experimentan un aumento en el número de estudiantes que abandonan el colegio en 12.1 puntos porcentuales, mientras que las instituciones que complementaron este mecanismo con la integración de un colegio próximo pre existente mostraron una reducción en la tasa de deserción escolar de 9.8 puntos porcentuales.

‘Boots for my Sancho’: structural vulnerability among Latin American day labourers in Berkeley, California

This paper addresses the structural vulnerability of Latin American undocumented day labourers in Northern California, as it is expressed in conversations on street corners where they wait for work. The intimate aspects of migrant experience become exemplified in jokes about the Sancho – a hypothetical character who has moved in on a day labourer's family and who enjoys the money he sends home. Joking turns to more serious topics of nostalgia and tensions with family far away, elements that come together with the fears and threats of labour on the corner and affect the way day labourers see themselves. Sexuality is rearticulated in the absence of women and masculinity becomes enmeshed in the contingencies of unregulated work and long-term separation from the people the men support. Together, these elements result in the articulation of threat to the immigrant body itself, which is exemplified by anxieties over homosexual propositions on the corner. Cet article aborde la vulnérabilité structurelle des travailleurs journaliers latino-américains sans papiers dans le Nord de la Californie, telle qu'ils l'expriment dans leurs conversations en attendant du travail aux coins des rues. Les aspects intimes de l'expérience de la migration sont exemplifiés à travers des blagues sur le Sancho – un personnage hypothétique qui, au pays natal, s'est installé dans la famille d'un journalier pour profiter de l'argent qu'elle reçoit de ce dernier. Les blagues deviennent alors des sujets de conversation plus sérieux, sur un fond de nostalgie et de tensions qui résulte de l'éloignement vis-à-vis de la famille – des éléments qui accompagnent les peurs et les menaces liées aux embauches des coins de rue et ont un impact sur la manière dont les journaliers se perçoivent. La sexualité est articulée par rapport à l'absence des femmes et la virilité s'empêtre dans les contingences du travail illégal et de la séparation sur le long terme d'avec les êtres que ces hommes soutiennent financièrement. Ensemble, tous ces éléments ont pour résultat une articulation de la menace vis-à-vis du corps de l'immigré lui-même, qui est exemplifiée par les angoisses dues aux propositions d'homosexuels aux coins des rues.

The influence of culture on parental styles in social vulnerability contexts

The objectives of this study are: (a) to analyze if the relationship between parenting dimensions and children adjustment regarding coping strategies are similar in Argentinian and Spanish samples within poverty contexts; (b) to compare parental dimensions in the two groups studied, and (c) to determine the efficiency of parenting through the study of their influence in children coping strategies. The Graffar-Méndez Castellano Scale (Méndez-Castellano & Méndez, 1994), that brings a socioeconomic description of the population; an Argentinian Scale of Children Perception of Parental Relationships for 8 to 12 years of age (Richaud, 2007a), and the Argentine Questionnaire of Coping for children (Richaud, 2006) were administered to a sample of 458 Spanish and Argentinian children from 8 to 12 years old. Correlations were carried out to analyze the relationships between parenting dimensions and children coping strategies in both groups, and MANOVA, to study if there were different parental dimensions in the two groups —Argentina and Spain—, and to analyze if there were differences in children coping strategies. The results indicate that correlational pattern is similar in both groups, but parental dimensions are different for each culture, being the Argentinian parents more neglectful than Spanish parents. At the same time, Argentinian children adopt coping strategies less efficient that the Spanish children ones, involving in that way a greater emotional conflict.

Revisiting university students' knowledge that involves basic differential equation questions. 'Conocimiento de los estudiantes universitarios con respecto a preguntas que implican ecuaciones diferenciales : una revisión'.

Resumen basado en el de la publicación