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.

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.

Low dimensional behavior in three-dimensional coupled map lattices

The analysis of one-, two-, and three-dimensional coupled map lattices is here developed under a statistical and dynamical perspective. We show that the three-dimensional CML exhibits low dimensional behavior with long range correlation and the power spectrum follows 1/f noise. This approach leads to an integrated understanding of the most important properties of these universal models of spatiotemporal chaos. We perform a complete time series analysis of the model and investigate the dependence of the signal properties by change of dimension. (c) 2008 Elsevier Ltd. All rights reserved.

Stretching and folding mechanism in foams

We have described the stretching and folding of foams in a vertical Hele-Shaw cell containing air and a surfactant solution, from a sequence of upside-down flips. Besides the firactal dimension of the foam, we have observed the logistic growth for the soap film length. The stretching and folding mechanism is present during the foam formation, and this mechanism is observed even after the foam has reached its respective maximum fractal dimension. Observing the motion of bubbles inside the foam, large bubbles present power spectrum associated with random walk motion in both directions, while the small bubbles are scattered like balls in a Galton board. (C) 2008 Published by Elsevier B.V.

Tick saliva induces regulatory dendritic cells: MAP-kinases and Toll-like receptor-2 expression as potential targets

Ticks (Acari: Ixodidae) are bloodsucking ectoparasitic arthropods of human and veterinary medical importance. Tick saliva has been shown to contain a wide range of bioactive molecules with vasodilatory, antihemostatic, and immunomodulatory activities. We have previously demonstrated that saliva from Rhipicephalus sanguineus ticks inhibits the maturation of dendritic cells (DCs) stimulated with LPS. Here we examined the mechanism of this immune subversion, evaluating the effect of tick saliva on Toll-like receptor (TLR)-4 signalling pathway in bone marrow-derived DCs. We demonstrated that R. sanguineus tick saliva impairs maturation of DCs stimulated with LIPS, a TLR-4 ligand, leading to increased production of interleukin (IL)-10 and reduced synthesis of IL-12p70 and TNF-alpha. The immunomodulatory effect of the tick saliva on the production of pro-inflammatory cytokines by DCs stimulated with LPS was associated with the observation that tick saliva inhibits the activation of the ERK 1/2 and p38 MAP kinases. These effects were independent of the expression of TLR-4 on the surface of DCs. Additionally, saliva-treated DCs also presented a similar pattern of cytokine modulation in response to other TLR ligands. Since the recent literature reports that several parasites evade immune responses through TLR-2-mediated production of IL-10, we evaluated the effect of tick saliva on the percentage of TLR-2(+) DCs stimulated with the TLR-2 ligand lipoteicoic acid (LTA). The data showed that the population of DCs expressing TLR-2 was significantly increased in DCs treated with LTA plus saliva. In addition, tick saliva alone increased the expression of TLR-2 in a dose- and time-dependent manner. Our data suggest that tick saliva induces regulatory DCs, which secrete IL-10 and low levels of IL-12 and TNF-alpha when stimulated by TLR ligands. Such regulatory DCs are associated with expression of TLR-2 and inhibition of ERK and p38, which promotes the production of IL-10 and thus down-modulates the host`s immune response, possibly favouring susceptibility to tick infestations. (C) 2009 Elsevier B.V. All rights reserved.

New prediction methods for CO2 evaporation inside tubes: Part I - A two-phase flow pattern map and a flow pattern based phenomenological model for two-phase flow frictional pressure drops

An updated flow pattern map was developed for CO2 on the basis of the previous Cheng-Ribatski-Wojtan-Thome CO2 flow pattern map [1,2] to extend the flow pattern map to a wider range of conditions. A new annular flow to dryout transition (A-D) and a new dryout to mist flow transition (D-M) were proposed here. In addition, a bubbly flow region which generally occurs at high mass velocities and low vapor qualities was added to the updated flow pattern map. The updated flow pattern map is applicable to a much wider range of conditions: tube diameters from 0.6 to 10 mm, mass velocities from 50 to 1500 kg/m(2) s, heat fluxes from 1.8 to 46 kW/m(2) and saturation temperatures from -28 to +25 degrees C (reduced pressures from 0.21 to 0.87). The updated flow pattern map was compared to independent experimental data of flow patterns for CO2 in the literature and it predicts the flow patterns well. Then, a database of CO2 two-phase flow pressure drop results from the literature was set up and the database was compared to the leading empirical pressure drop models: the correlations by Chisholm [3], Friedel [4], Gronnerud [5] and Muller-Steinhagen and Heck [6], a modified Chisholm correlation by Yoon et al. [7] and the flow pattern based model of Moreno Quiben and Thome [8-10]. None of these models was able to predict the CO2 pressure drop data well. Therefore, a new flow pattern based phenomenological model of two-phase flow frictional pressure drop for CO2 was developed by modifying the model of Moreno Quiben and Thome using the updated flow pattern map in this study and it predicts the CO2 pressure drop database quite well overall. (C) 2007 Elsevier Ltd. All rights reserved.

Spectral properties of chaotic signals generated by the skew tent map

Chaotic signals have been considered potentially attractive in many signal processing applications ranging from wideband communication systems to cryptography and watermarking. Besides, some devices as nonlinear adaptive filters and phase-locked loops can present chaotic behavior. In this paper, we derive analytical expressions for the autocorrelation sequence, power spectral density and essential bandwidth of chaotic signals generated by the skew tent map. From these results, we suggest possible applications in communication systems. (C) 2009 Elsevier B.V. All rights reserved.

Extension of the core map of common bean with EST-SSR, RGA, AFLP, and putative functional markers

Microsatellites and gene-derived markers are still underrepresented in the core molecular linkage map of common bean compared to other types of markers. In order to increase the density of the core map, a set of new markers were developed and mapped onto the RIL population derived from the `BAT93` x `Jalo EEP558` cross. The EST-SSR markers were first characterized using a set of 24 bean inbred lines. On average, the polymorphism information content was 0.40 and the mean number of alleles per locus was 2.7. In addition, AFLP and RGA markers based on the NBS-profiling method were developed and a subset of the mapped RGA was sequenced. With the integration of 282 new markers into the common bean core map, we were able to place markers with putative known function in some existing gaps including regions with QTL for resistance to anthracnose and rust. The distribution of the markers over 11 linkage groups is discussed and a newer version of the common bean core linkage map is proposed.

An integrated molecular map of yellow passion fruit based on simultaneous maximum-likelihood estimation of linkage and linkage phases

The development of genetic maps for auto-incompatible species, such as the yellow passion fruit (Passiflora edulis Sims f.flavicarpa Deg.) is restricted due to the unfeasibility of obtaining traditional mapping populations based on inbred lines. For this reason, yellow passion fruit linkage maps were generally constructed using a strategy known as two-way pseudo-testeross, based on monoparental dominant markers segregating in a 1:1 fashion. Due to the lack of information from these markers in one of the parents, two individual (parental) maps were obtained. However, integration of these maps is essential, and biparental markers can be used for such an operation. The objective of our study was to construct an integrated molecular map for a full-sib population of yellow passion fruit combining different loci configuration generated from amplified fragment length polymorphisms (AFLPs) and microsatellite markers and using a novel approach based on simultaneous maximum-likelihood estimation of linkage and linkage phases, specially designed for outcrossing species. Of the total number of loci, approximate to 76%, 21%, 0.7%, and 2.3% did segregate in 1:1, 3:1, 1:2:1, and 1:1:1:1 ratios, respectively. Ten linkage groups (LGs) were established with a logarithm of the odds (LOD) score >= 5.0 assuming a recombination fraction : <= 0.35. On average, 24 markers were assigned per LG, representing a total map length of 1687 cM, with a marker density of 6.9 cM. No markers were placed as accessories on the map as was done with previously constructed individual maps.