Exercise sheet 2 pdf

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Exercise sheet 2

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Dimensões fractais para certos sistemas dinâmicos discretos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Relaxação e decaimento para pontos de equilíbrio em mapeamentos não lineares unidimensionais

We investigate in this work the behaviour of the decay to the fixed points, in particular along the bifurcations, for a family of one-dimensional logistic-like discrete mappings. We start with the logistic map focusing in the transcritical bifurcation. Next we investigate the convergence to the stationary state at the cubic map. At the end we generalise the procedure for a mapping of the logistic-like type. Near the fixed point, the dynamical variable varies slowly. This property allows us to approximate/rewrite the equation of differences, hence natural from discrete mappings, into an ordinary differential equation. We then solve such equation which furnishes the evolution towards the stationary state. Our numerical simulations confirm the theoretical results validating the above mentioned approximation

Ordinal patterns in epileptic brains: Analysis of intracranial EEG and simultaneous EEG-fMRI

Epileptic seizures are associated with high behavioral stereotypy of the patients. In the EEG of epilepsy patients characteristic signal patterns can be found during and between seizures. Here we use ordinal patterns to analyze EEGs of epilepsy patients and quantify the degree of signal determinism. Besides relative signal redundancy and the fraction of forbidden patterns we introduce the fraction of under-represented patterns as a new measure. Using the logistic map, parameter scans are performed to explore the sensitivity of the measures to signal determinism. Thereafter, application is made to two types of EEGs recorded in two epilepsy patients. Intracranial EEG shows pronounced determinism peaks during seizures. Finally, we demonstrate that ordinal patterns may be useful for improving analysis of non-invasive simultaneous EEG-fMRI.

Linear chaos for the Quick-Thinking-Driver model.

In recent years, the topic of car-following has experimented an increased importance in traffic engineering and safety research. This has become a very interesting topic because of the development of driverless cars (Google driverless cars, http://en.wikipedia.org/wiki/Google_driverless_car). Driving models which describe the interaction between adjacent vehicles in the same lane have a big interest in simulation modeling, such as the Quick-Thinking-Driver model. A non-linear version of it can be given using the logistic map, and then chaos appears. We show that an infinite-dimensional version of the linear model presents a chaotic behaviour using the same approach as for studying chaos of death models of cell growth.

Diffusive models and chaos indicators for non-linear betatron motion in circular hadron accelerators

Understanding the complex dynamics of beam-halo formation and evolution in circular particle accelerators is crucial for the design of current and future rings, particularly those utilizing superconducting magnets such as the CERN Large Hadron Collider (LHC), its luminosity upgrade HL-LHC, and the proposed Future Circular Hadron Collider (FCC-hh). A recent diffusive framework, which describes the evolution of the beam distribution by means of a Fokker-Planck equation, with diffusion coefficient derived from the Nekhoroshev theorem, has been proposed to describe the long-term behaviour of beam dynamics and particle losses. In this thesis, we discuss the theoretical foundations of this framework, and propose the implementation of an original measurement protocol based on collimator scans in view of measuring the Nekhoroshev-like diffusive coefficient by means of beam loss data. The available LHC collimator scan data, unfortunately collected without the proposed measurement protocol, have been successfully analysed using the proposed framework. This approach is also applied to datasets from detailed measurements of the impact on the beam losses of so-called long-range beam-beam compensators also at the LHC. Furthermore, dynamic indicators have been studied as a tool for exploring the phase-space properties of realistic accelerator lattices in single-particle tracking simulations. By first examining the classification performance of known and new indicators in detecting the chaotic character of initial conditions for a modulated Hénon map and then applying this knowledge to study the properties of realistic accelerator lattices, we tried to identify a connection between the presence of chaotic regions in the phase space and Nekhoroshev-like diffusive behaviour, providing new tools to the accelerator physics community.

Predicting Xerostomia induced by IMRT treatments: A logistic regression approach

Radiotherapy is one of the main treatments used against cancer. Radiotherapy uses radiation to destroy cancerous cells trying, at the same time, to minimize the damages in healthy tissues. The planning of a radiotherapy treatment is patient dependent, resulting in a lengthy trial and error procedure until a treatment complying as most as possible with the medical prescription is found. Intensity Modulated Radiation Therapy (IMRT) is one technique of radiation treatment that allows the achievement of a high degree of conformity between the area to be treated and the dose absorbed by healthy tissues. Nevertheless, it is still not possible to eliminate completely the potential treatments’ side-effects. In this retrospective study we use the clinical data from patients with head-and-neck cancer treated at the Portuguese Institute of Oncology of Coimbra and explore the possibility of classifying new and untreated patients according to the probability of xerostomia 12 months after the beginning of IMRT treatments by using a logistic regression approach. The results obtained show that the classifier presents a high discriminative ability in predicting the binary response “at risk for xerostomia at 12 months”

Validation of Logistic Regression Models for Landslide Susceptibility Maps

A wide range of numerical models and tools have been developed over the last decades to support the decision making process in environmental applications, ranging from physical models to a variety of statistically-based methods. In this study, a landslide susceptibility map of a part of Three Gorges Reservoir region of China was produced, employing binary logistic regression analyses. The available information includes the digital elevation model of the region, geological map and different GIS layers including land cover data obtained from satellite imagery. The landslides were observed and documented during the field studies. The validation analysis is exploited to investigate the quality of mapping.

Performance Tuning of Fenix Logistic Systems

Työn tavoitteena oli selvittää Stora Enso Oyj:llä käytössä olevan Fenix myynnin- ja logistiikanhallintajärjestelmän logistiikkapalveluiden suorituskyky, tuottaa asiakasohjelmisto suorituskykymittauksista muodostuneen tiedon hallintaan sekä tuottaa toteuttamissuunnitelma suorituskyvyn parantamiseksi. Suorituskyky mitattiin käyttämällä TUXEDOn tarjoamia ominaisuuksia. Suorituskykymittausten tuloksien arviointia varten rakennettiin asiakasohjelmisto, jolla pystyttiin tuottamaan tarvittavat yhteenvetotiedot palveluiden kestoista ja rakenteista. Valmiita ratkaisuja ei ollut tarjolla, joten kaikki tarvittavat ohjelmistot on rakennettu osana tätä työtä. Kaikki komponenttiliittymät toteutettiin siten, että myös muitakin kuin logistiikkaan liittyviä palveluita voidaan tarvittaessa mitata. Mittausten tuloksena saatuja keskimääräisiä suoritusaikoja käytettiin hyväksi toteuttamissuunnitelmaa tehdessä. Toteutussuunnitelma sisältää useiden logistiikka-alueiden kehittämisideoita, joilla Fenixin logistiikkapalveluiden suorituskykyä voidaan tehostaa., ja nykyinen järjestelmän toimintanopeus pystytään säilyttämään tulevaisuudessa. Toteuttamissuunnitelmassa esitettyjä toimenpiteitä tullaan toteuttamaan TietoEnator Oyj:ssä vuoden 2003 aikana.

Caractérisation de la MAP kinase atypique Erk4 : activation et fonction physiologique

Les MAP kinases sont des enzymes essentielles impliquées dans 7 voies de signalisation distinctes qui permettent à la cellule de répondre de manière adéquate aux stimuli extra-cellulaires. Chez les mammifères, les MAP kinases les mieux caractérisées sont Erk1/2, Jnk, p38 et Erk5. Ces enzymes jouent un rôle important dans l’embryogenèse, la prolifération et la différenciation cellulaire ainsi que dans la réponse au stress. Erk4 est un membre atypique de la famille MAP kinase. D’une part, la boucle d’activation de Erk4 possède un motif SEG au lieu du motif TXY, très conservé chez les MAP kinases. D’autre part, Erk4 possède une extension en C-terminal du domaine kinase qui n’est pas présente chez les MAP kinases classiques. Jusqu’à présent aucune fonction n’a été attribuée à Erk4. De plus, la voie de signalisation ainsi que le mode de régulation conduisant à l’activation de Erk4 ne sont pas connus. Le seul substrat de Erk4 identifié jusqu’à maintenant est la MAPKAP kinase MK5. L’impact fonctionnel de cette interaction n’est également pas connu. Afin d’en apprendre davantage sur la MAP kinase atypique Erk4, nous avons étudié le mécanisme d’activation de cette kinase ainsi que sa fonction physiologique par une approche de délétion génique chez la souris. En ce qui concerne l’activation de Erk4, nous avons montré que la boucle d’activation de Erk4 (S186EG) est constitutivement phosphorylée in vivo et que cette phosphorylation n’est pas modulée par les stimuli classiques des MAP kinases dont le sérum et le sorbitol. Cependant, nous avons observé que la phosphorylation de la S186 augmente en présence de MK5 et que cette augmentation est indépendante de l’activité kinase de l’une ou l’autre de ces kinases. De plus, nous avons établi que la phosphorylation de la boucle d’activation de Erk4 est requise pour l’interaction stable entre Erk4 et MK5 ainsi que pour l’activation, et la relocalisation cytoplasmique de MK5. Ainsi, notre étude a permis de révéler que Erk4 est régulée de manière différente des MAP kinases classiques et que la phosphorylation de la boucle d’activation de Erk4 joue un rôle essentiel dans la régulation de l’activité de MK5. Parallèlement, nos résultats mettent en évidence l’existence d’une “Erk4 kinase”, dont le recrutement et/ou l’activation semble être facilité par MK5. Afin identifier la fonction physiologique de Erk4, nous avons généré des souris Erk4-déficientes. L’inactivation génique de Erk4 est viable et les souris ne présentent aucune anomalie apparente. Dans le but d’expliquer l’absence de phénotype, nous avons regardé si l’expression de Erk3, le paralogue de Erk4, pouvait compenser la perte de Erk4. Notre analyse a révélé que l’expression de Erk3 dans les souris Erk4-/- n’augmente pas au cours du développement embryonnaire ou dans les tissus adultes afin de compenser pour la perte de Erk4. Par la suite, nous avons adressé la question de redondance entre Erk4 et Erk3. Dans notre laboratoire, les souris Erk3-déficientes ont également été générées et le phénotype de ces souris a récemment été analysé. Cette étude a révélé que l’inactivation génique de Erk3 entraîne un retard de croissance intra-utérin, un défaut de maturation pulmonaire et la mort néo-natale des souriceaux. Nous avons donc regardé la contribution de Erk4 dans ces phénotypes. L’analyse des souris Erk4-/- a révélé que l’inactivation de Erk4 n’entraîne pas de retard de croissance ou de maturation du poumon. De plus, nous avons montré que l’inactivation additionnelle de Erk4 dans les souris Erk3-/- n’accentue pas le phénotype des souris Erk3-déficientes. Ainsi, notre étude a révélé que contrairement à Erk3, Erk4 n’est pas essentielle au développement murin dans des conditions physiologiques. Parallèlement, nous avons montré que Erk4 et Erk3 possèdent des fonctions non-redondantes in vivo.

Regulation of the ERK subgroup of MAP kinase cascades through G protein-coupled receptors.

The extracellularly-responsive kinase (ERK) subfamily of mitogen-activated protein kinases (MAPKs) has been implicated in the regulation of cell growth and differentiation. Activation of ERKs involves a two-step protein kinase cascade lying upstream from ERK, in which the Raf family are the MAPK kinase kinases and the MEK1/MEK2 isoforms are the MAPK kinases. The linear sequence of Raf --> MEK --> ERK constitutes the ERK cascade. Although the ERK cascade is activated through growth factor-regulated receptor protein tyrosine kinases, they are also modulated through G protein-coupled receptors (GPCRs). All four G protein subfamilies (Gq/11 Gi/o, Gs and G12/13) influence the activation state of ERKs. In this review, we describe the ERK cascade and characteristics of its activation through GPCRs. We also discuss the identity of the intervening steps that may couple agonist binding at GPCRs to activation of the ERK cascade.

Identification of the signal pathways modulated by expression of p210$\rm\sp{bcr-abl}$ and the inhibition of p210$\rm\sp{bcr-abl}$ transforming activity by polypeptides interacting with p210$\rm\sp{bcr-abl}$ in murine myeloid 32D cells

The Bcr-Abl fusion oncogene which resulted from a balanced reciprocal translocation between chromosome 9 and 22, t(9;22)(q11, q34), encodes a 210 KD elevated tyrosine specific protein kinase that is found in more than 95 percent of chronic myelogenous leukemia patients (CML). Increase of level of phosphorylation of tyrosine is observed on cell cycle regulatory proteins in cells overexpressing the Bcr-Abl oncogene, which activates multiple signaling pathways. In addition, distinct signals are required for transforming susceptible fibroblast and hematopoietic cells, and the minimal signals essential for transforming hematopoietic cells are yet to be defined. In the present study, we first established a tetracycline repressible p210$\rm\sp{bcr-abl}$ expression system in a murine myeloid cell line 32D c13, which depends on IL3 to grow in the presence of tetracycline and proliferate independent of IL3 in the absence of tetracycline. Interestingly, one of these sublines does not form tumors in athymic nude mice suggesting that these cells may not be completely transformed. These cells also exhibit a dose-dependent growth and expression of p210$\rm\sp{bcr-abl}$ at varying concentrations of tetracycline in the culture. However, p210$\rm\sp{bcr-abl}$ rescues IL3 deprivation induced apoptosis in a non-dose dependent fashion. DNA genotoxic damage induced by gamma-irradiation activates c-Abl tyrosine kinase, the cellular homologue of p210$\rm\sp{bcr-abl},$ and leads to activation of p38 MAP kinase in the cells. However, in the presence of p210$\rm\sp{bcr-abl}$ the irradiation failed to activate the p38 MAP kinase as examined by an antibody against phosphorylated p38 MAP kinase. Similarly, an altered tyrosine phosphorylation of the JAK1-STAT1 pathways was identified in cells constitutively overexpressing p210$\rm\sp{bcr-abl}.$ This may provided a molecular mechanism for altered therapeutic response of CML patients to IFN-$\alpha.$^ Bcr-Abl oncoprotein has multiple functional domains which have been identified by the work of others. The Bcr tetramerization domain, which may function to stabilize the association of the Bcr-Abl with actin filaments in p210$\rm\sp{bcr-abl}$ susceptible cells, are essential for transforming both fibroblast and hematopoietic cells. We designed a transcription unit encoding first 160 amino acids polypeptide of Bcr protein to test if this polypeptide can inhibit the transforming activity of the p210$\rm\sp{bcr-abl}$ oncoprotein in the 32D c13 cells. When this vector was transfected transiently along with the p210$\rm\sp{bcr-abl}$ expression vector, it can block the transforming activity of p210$\rm\sp{bcr-abl}.$ On the other hand, the retinoblastoma tumor suppressor protein (Rb), a naturally occurring negative regulator of the c-Abl kinase, the cellular homologue of Bcr-Abl oncoprotein, binds to and inhibits the c-Abl kinase in a cell cycle dependent manner. A polypeptide obtained from the carboxyl terminal end of the retinoblastoma tumor suppressor protein, in which the nuclear localization signal was mutated, was used to inhibit the kinase activity of the p210$\rm\sp{bcr-abl}$ in the cytoplasm. This polypeptide, called Rb MC-box, and its wild type form, Rb C-box, when overexpressed in the 32D cells are mainly localized in the cytoplasm. Cotransfection of a plasmid transcription unit coding for this polypeptide and the gene for the p210$\rm\sp{bcr-abl}$ resulted in reduced plating efficiency of p210$\rm\sp{bcr-abl}$ transfected IL3 independent 32D cells. Together, these results may lead to a molecular approach to therapy of CML and an in vitro assay system to identify new targets to which an inhibitory polypeptide transcription unit may be directed. ^

The design and evaluation of a 2D dose verification system for intensity modulated radiotherapy

The usage of intensity modulated radiotherapy (IMRT) treatments necessitates a significant amount of patient-specific quality assurance (QA). This research has investigated the precision and accuracy of Kodak EDR2 film measurements for IMRT verifications, the use of comparisons between 2D dose calculations and measurements to improve treatment plan beam models, and the dosimetric impact of delivery errors. New measurement techniques and software were developed and used clinically at M. D. Anderson Cancer Center. The software implemented two new dose comparison parameters, the 2D normalized agreement test (NAT) and the scalar NAT index. A single-film calibration technique using multileaf collimator (MLC) delivery was developed. EDR2 film's optical density response was found to be sensitive to several factors: radiation time, length of time between exposure and processing, and phantom material. Precision of EDR2 film measurements was found to be better than 1%. For IMRT verification, EDR2 film measurements agreed with ion chamber results to 2%/2mm accuracy for single-beam fluence map verifications and to 5%/2mm for transverse plane measurements of complete plan dose distributions. The same system was used to quantitatively optimize the radiation field offset and MLC transmission beam modeling parameters for Varian MLCs. While scalar dose comparison metrics can work well for optimization purposes, the influence of external parameters on the dose discrepancies must be minimized. The ability of 2D verifications to detect delivery errors was tested with simulated data. The dosimetric characteristics of delivery errors were compared to patient-specific clinical IMRT verifications. For the clinical verifications, the NAT index and percent of pixels failing the gamma index were exponentially distributed and dependent upon the measurement phantom but not the treatment site. Delivery errors affecting all beams in the treatment plan were flagged by the NAT index, although delivery errors impacting only one beam could not be differentiated from routine clinical verification discrepancies. Clinical use of this system will flag outliers, allow physicists to examine their causes, and perhaps improve the level of agreement between radiation dose distribution measurements and calculations. The principles used to design and evaluate this system are extensible to future multidimensional dose measurements and comparisons. ^

Transparent heterogeneous terrestrial optical communication networks with phase modulated signals

This thesis presents a large scale numerical investigation of heterogeneous terrestrial optical communications systems and the upgrade of fourth generation terrestrial core to metro legacy interconnects to fifth generation transmission system technologies. Retrofitting (without changing infrastructure) is considered for commercial applications. ROADM are crucial enabling components for future core network developments however their re-routing ability means signals can be switched mid-link onto sub-optimally configured paths which raises new challenges in network management. System performance is determined by a trade-off between nonlinear impairments and noise, where the nonlinear signal distortions depend critically on deployed dispersion maps. This thesis presents a comprehensive numerical investigation into the implementation of phase modulated signals in transparent reconfigurable wavelength division multiplexed fibre optic communication terrestrial heterogeneous networks. A key issue during system upgrades is whether differential phase encoded modulation formats are compatible with the cost optimised dispersion schemes employed in current 10 Gb/s systems. We explore how robust transmission is to inevitable variations in the dispersion mapping and how large the margins are when suboptimal dispersion management is applied. We show that a DPSK transmission system is not drastically affected by reconfiguration from periodic dispersion management to lumped dispersion mapping. A novel DPSK dispersion map optimisation methodology which reduces drastically the optimisation parameter space and the many ways to deploy dispersion maps is also presented. This alleviates strenuous computing requirements in optimisation calculations. This thesis provides a very efficient and robust way to identify high performing lumped dispersion compensating schemes for use in heterogeneous RZ-DPSK terrestrial meshed networks with ROADMs. A modified search algorithm which further reduces this number of configuration combinations is also presented. The results of an investigation of the feasibility of detouring signals locally in multi-path heterogeneous ring networks is also presented.