On singularly perturbed Filippov systems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Piecewise Bounded Quadratic Systems in the Plane

In this paper we study the sliding mode of piecewise bounded quadratic systems in the plane given by a non-smooth vector field Z=(X,Y). Analyzing the singular, crossing and sliding sets, we get the conditions which ensure that any solution, including the sliding one, is bounded.

On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Equações diferenciais ordinárias não suaves autônomas e não autônomas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Equações diferenciais ordinárias não suaves autônomas e não autônomas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Solvability near the characteristic set for a special class of complex vector fields

This work deals with the solvability near the characteristic set Sigma = {0} x S-1 of operators of the form L = partial derivative/partial derivative t+(x(n) a(x)+ ix(m) b(x))partial derivative/partial derivative x, b not equivalent to 0 and a(0) not equal 0, defined on Omega(epsilon) = (-epsilon, epsilon) x S-1, epsilon > 0, where a and b are real-valued smooth functions in (-epsilon, epsilon) and m >= 2n. It is shown that given f belonging to a subspace of finite codimension of C-infinity (Omega(epsilon)) there is a solution u is an element of L-infinity of the equation Lu = f in a neighborhood of Sigma; moreover, the L-infinity regularity is sharp.

Modeling random corrosion processes via polynomial chaos expansion

Polynomial Chaos Expansion (PCE) is widely recognized as a flexible tool to represent different types of random variables/processes. However, applications to real, experimental data are still limited. In this article, PCE is used to represent the random time-evolution of metal corrosion growth in marine environments. The PCE coefficients are determined in order to represent data of 45 corrosion coupons tested by Jeffrey and Melchers (2001) at Taylors Beach, Australia. Accuracy of the representation and possibilities for model extrapolation are considered in the study. Results show that reasonably accurate smooth representations of the corrosion process can be obtained. The representation is not better because a smooth model is used to represent non-smooth corrosion data. Random corrosion leads to time-variant reliability problems, due to resistance degradation over time. Time variant reliability problems are not trivial to solve, especially under random process loading. Two example problems are solved herein, showing how the developed PCE representations can be employed in reliability analysis of structures subject to marine corrosion. Monte Carlo Simulation is used to solve the resulting time-variant reliability problems. However, an accurate and more computationally efficient solution is also presented.

Weighted Fourier–Laplace transforms in reproducing kernel Hilbert spaces on the sphere

We study the action of a weighted Fourier–Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness implied by the transform, we show that smoothness of the kernel implies the same smoothness for the generating elements (spherical harmonics) in the Mercer expansion of the kernel. We prove a reproducing property for the weighted Fourier–Laplace transform of the functions in the RKHS and embed the RKHS into spaces of smooth functions. Some relevant properties of the embedding are considered, including compactness and boundedness. The approach taken in the paper includes two important notions of differentiability characterized by weighted Fourier–Laplace transforms: fractional derivatives and Laplace–Beltrami derivatives.

Design and Computation of Warped Time-Frequency Transforms

In this work we introduce an analytical approach for the frequency warping transform. Criteria for the design of operators based on arbitrary warping maps are provided and an algorithm carrying out a fast computation is defined. Such operators can be used to shape the tiling of time-frequency plane in a flexible way. Moreover, they are designed to be inverted by the application of their adjoint operator. According to the proposed mathematical model, the frequency warping transform is computed by considering two additive operators: the first one represents its nonuniform Fourier transform approximation and the second one suppresses aliasing. The first operator is known to be analytically characterized and fast computable by various interpolation approaches. A factorization of the second operator is found for arbitrary shaped non-smooth warping maps. By properly truncating the operators involved in the factorization, the computation turns out to be fast without compromising accuracy.

Direct and inverse transient eddy current problems

Die vorliegende Arbeit behandelt Vorwärts- sowie Rückwärtstheorie transienter Wirbelstromprobleme. Transiente Anregungsströme induzieren elektromagnetische Felder, welche sogenannte Wirbelströme in leitfähigen Objekten erzeugen. Im Falle von sich langsam ändernden Feldern kann diese Wechselwirkung durch die Wirbelstromgleichung, einer Approximation an die Maxwell-Gleichungen, beschrieben werden. Diese ist eine lineare partielle Differentialgleichung mit nicht-glatten Koeffizientenfunktionen von gemischt parabolisch-elliptischem Typ. Das Vorwärtsproblem besteht darin, zu gegebener Anregung sowie den umgebungsbeschreibenden Koeffizientenfunktionen das elektrische Feld als distributionelle Lösung der Gleichung zu bestimmen. Umgekehrt können die Felder mit Messspulen gemessen werden. Das Ziel des Rückwärtsproblems ist es, aus diesen Messungen Informationen über leitfähige Objekte, also über die Koeffizientenfunktion, die diese beschreibt, zu gewinnen. In dieser Arbeit wird eine variationelle Lösungstheorie vorgestellt und die Wohlgestelltheit der Gleichung diskutiert. Darauf aufbauend wird das Verhalten der Lösung für verschwindende Leitfähigkeit studiert und die Linearisierbarkeit der Gleichung ohne leitfähiges Objekt in Richtung des Auftauchens eines leitfähigen Objektes gezeigt. Zur Regularisierung der Gleichung werden Modifikationen vorgeschlagen, welche ein voll parabolisches bzw. elliptisches Problem liefern. Diese werden verifiziert, indem die Konvergenz der Lösungen gezeigt wird. Zuletzt wird gezeigt, dass unter der Annahme von sonst homogenen Umgebungsparametern leitfähige Objekte eindeutig durch die Messungen lokalisiert werden können. Hierzu werden die Linear Sampling Methode sowie die Faktorisierungsmethode angewendet.

Autophagy in cells of the blood

Autophagy is a conserved proteolytic mechanism that degrades cytoplasmic material including cell organelles. The importance of autophagy for cell homeostasis and survival has long been appreciated. Recent data suggest that autophagy is also involved in non-metabolic functions that particularly concern blood cells. Here, we review these findings, which point to an important role of autophagy in several cellular functions related to host defense.

Estrogen receptor subtype beta2 is involved in neuromast development in zebrafish (Danio rerio) larvae

Estrogens are known to play a role in both reproductive and non-reproductive functions in mammals. Estrogens and their receptors are involved in the development of the central nervous system (brain development, neuronal survival and differentiation) as well as in the development of the peripheral nervous system (sensory-motor behaviors). In order to decipher possible functions of estrogens in early development of the zebrafish sensory system, we investigated the role of estrogen receptor beta(2) (ERbeta(2)) by using a morpholino (MO) approach blocking erbeta(2) RNA translation. We further investigated the development of lateral line organs by cell-specific labeling, which revealed a disrupted development of neuromasts in morphants. The supporting cells developed and migrated normally. Sensory hair cells, however, were absent in morphants' neuromasts. Microarray analysis and subsequent in situ hybridizations indicated an aberrant activation of the Notch signaling pathway in ERbeta(2) morphants. We conclude that signaling via ERbeta(2) is essential for hair cell development and may involve an interaction with the Notch signaling pathway during cell fate decision in the neuromast maturation process.

ROLE OF THE GCN5 HISTONE ACETYLTRANSFERASE IN SPINOCEREBELLAR ATAXIA TYPE 7 AND IN IMMATURE NEURONS

Spinocerebellar Ataxia type 7 (SCA7) is a neurodegenerative disease caused by expansion of a CAG repeat encoding a polyglutamine tract in ATXN7, a component of the SAGA histone acetyltransferase (HAT) complex. Previous studies provided conflicting evidence regarding the effects of polyQ-ATXN7 on the activity of Gcn5, the HAT catalytic subunit of SAGA. Here I showed that reducing Gcn5 expression accelerates both cerebellar and retinal degeneration in a mouse model of SCA7. Deletion of Gcn5 in Purkinje cells in mice expressing wild type Atxn7, however, causes only mild ataxia and does not lead to the early lethality observed in SCA7 mice. Reduced Gcn5 expression strongly enhances retinopathy in SCA7 mice, but does not affect the transcriptional targets of Atxn7, as expression of these genes is not further altered by Gcn5 depletion. These findings demonstrate that loss of Gcn5 functions can contribute to the time of onset and severity of SCA7 phenotypes, but suggest that non-transcriptional functions of SAGA may play a role in neurodegeneration in this disease.

Neuropsychological long-term sequelae after posterior fossa tumour resection during childhood

The importance of the cerebellum for non‐motor functions is becoming more and more evident. The influence on cognitive functions from acquired cerebellar lesions during childhood, however, is not well known. We present follow‐up data from 24 patients, who were operated upon during childhood for benign cerebellar tumours. The benign histology of these tumours required neither radiotherapy nor chemotherapy. Post‐operatively, these children were of normal intelligence with a mean IQ of 99.1, performance intelligence quotient (PIQ) of 101.3 and verbal intelligence quotient (VIQ) of 96.8. However, 57% of patients showed abnormalities in subtesting. In addition, more extensive neuropsychological testing revealed significant problems for attention, memory, processing speed and interference. Visuo‐constructive problems were marked for copying the Rey figure, but less pronounced for recall of the figure. Verbal fluency was more affected than design fluency. Behavioural deficits could be detected in 33% of patients. Attention deficit problems were marked in 12.5%, whereas others demonstrated psychiatric symptoms such as mutism, addiction problems, anorexia, uncontrolled temper tantrums and phobia. Age at tumour operation and size of tumour had no influence on outcome. Vermis involvement was related to an increase in neuropsychological and psychiatric problems. The observation that patients with left‐sided cerebellar tumours were more affected than patients with right‐sided tumours is probably also influenced by a more pronounced vermian involvement in the former group. In summary, this study confirms the importance of the cerebellum for cognitive development and points to the necessity of careful follow‐up for these children to provide them with the necessary help to achieve full integration into professional life.

Improving children’s cognitive performance – Effect of a memory strategy training in children born very preterm

Aims: To examine the effect of memory strategy training on different aspects of memory in children born very preterm and to determine whether there is a generalization of the training effect to non-trained functions. The influence of individual factors such as age and performance level on the training success will be determined. Methods: In a randomized, controlled and blinded clinical trial, 46 children born very preterm (aged 7-12 years) were allocated to a memory strategy training (MEMO-Training, n=23) or a control group (n=23). Neuropsychological assessment was performed before, immediately after the training and at a 6-month follow-up. In the MEMO-Training, five different memory strategies were introduced and practiced in a one-to-one setting (4 hour-long training sessions over 4 weeks, 20 homework sessions). Results: A significant training-related improvement occurred in trained aspects of memory (verbal and visual learning and recall, verbal working memory) and in non-trained functions (inhibition, mental arithmetic). No performance increase was observed in the control group. At six months follow-up, there was a significant training-related improvement of visual working memory. Age and performance level before the training predicted the training success significantly. Conclusion: Teaching memory strategies is an effective way to improve different aspects of memory but also non-trained functions such as inhibition and mental arithmetic in children born very preterm. Age and performance level influence the success of memory strategy training. These results highlight the importance of teaching children memory strategies to reduce scholastic problems.