Zur Konvergenz der Randpunktmethode

Das von Maz'ya eingeführte Approximationsverfahren, die Methode der näherungsweisen Näherungen (Approximate Approximations), kann auch zur numerischen Lösung von Randintegralgleichungen verwendet werden (Randpunktmethode). In diesem Fall hängen die Komponenten der Matrix des resultierenden Gleichungssystems zur Berechnung der Näherung für die Dichte nur von der Position der Randpunkte und der Richtung der äußeren Einheitsnormalen in diesen Punkten ab. Dieses numerisches Verfahren wird am Beispiel des Dirichlet Problems für die Laplace Gleichung und die Stokes Gleichungen in einem beschränkten zweidimensionalem Gebiet untersucht. Die Randpunktmethode umfasst drei Schritte: Im ersten Schritt wird die unbekannte Dichte durch eine Linearkombination von radialen, exponentiell abklingenden Basisfunktionen approximiert. Im zweiten Schritt wird die Integration über den Rand durch die Integration über die Tangenten in Randpunkten ersetzt. Für die auftretende Näherungspotentiale können sogar analytische Ausdrücke gewonnen werden. Im dritten Schritt wird das lineare Gleichungssystem gelöst, und eine Näherung für die unbekannte Dichte und damit auch für die Lösung der Randwertaufgabe konstruiert. Die Konvergenz dieses Verfahrens wird für glatte konvexe Gebiete nachgewiesen.

Semi-algebraic methods for symbolic analysis of complex reaction networks

The identification of chemical mechanism that can exhibit oscillatory phenomena in reaction networks are currently of intense interest. In particular, the parametric question of the existence of Hopf bifurcations has gained increasing popularity due to its relation to the oscillatory behavior around the fixed points. However, the detection of oscillations in high-dimensional systems and systems with constraints by the available symbolic methods has proven to be difficult. The development of new efficient methods are therefore required to tackle the complexity caused by the high-dimensionality and non-linearity of these systems. In this thesis, we mainly present efficient algorithmic methods to detect Hopf bifurcation fixed points in (bio)-chemical reaction networks with symbolic rate constants, thereby yielding information about their oscillatory behavior of the networks. The methods use the representations of the systems on convex coordinates that arise from stoichiometric network analysis. One of the methods called HoCoQ reduces the problem of determining the existence of Hopf bifurcation fixed points to a first-order formula over the ordered field of the reals that can then be solved using computational-logic packages. The second method called HoCaT uses ideas from tropical geometry to formulate a more efficient method that is incomplete in theory but worked very well for the attempted high-dimensional models involving more than 20 chemical species. The instability of reaction networks may lead to the oscillatory behaviour. Therefore, we investigate some criterions for their stability using convex coordinates and quantifier elimination techniques. We also study Muldowney's extension of the classical Bendixson-Dulac criterion for excluding periodic orbits to higher dimensions for polynomial vector fields and we discuss the use of simple conservation constraints and the use of parametric constraints for describing simple convex polytopes on which periodic orbits can be excluded by Muldowney's criteria. All developed algorithms have been integrated into a common software framework called PoCaB (platform to explore bio- chemical reaction networks by algebraic methods) allowing for automated computation workflows from the problem descriptions. PoCaB also contains a database for the algebraic entities computed from the models of chemical reaction networks.

Intro to Matlab for Oceanography: Micro-lectures

This is a collection of 12 micro-lectures, to be used by students in advance of practical sessions. Durations range for 3 min to 10 min. Topics include: ****** 1. Introduction ****** 2. Data classes ****** 3. Matrices ****** 4. Getting help ****** 5. Index notation ****** 6. 1- and 2-dimensional data ****** 7. 3-dimensional data ****** 8. Booleans (True/False) ****** 9. Designing a programme (Algorithms) ****** 10. Flow control: If-then statements ****** 11. Flow control: For-do loops ****** 12. Making nicer figures ******

Evaluación de la mecánica ventricular izquierda mediante speckle tracking en pacientes sanos en la Clínica Shaio

Introducción: La ecocardiografía es actualmente la técnica de imagen diagnóstica más utilizada para la evaluación de la anatomía y la función cardiovascular. En la actualidad se está utilizando la ecocardiografía por speckle tracking la cual permite una evaluación mas objetiva y confiable de la función ventricular, sin embargo se requieren valores de referencia que hagan que los valores obtenidos sean válidos y útiles para determinar en forma mas oportuna conductas previas al deterioro de su función. Objetivo general: Determinar los valores de referencia para mecánica ventricular izquierda mediante ecocardiografía bidimensional por speckle tracking con equipo Toshiba Artida con transductor multifrecuencia de 3 megahertzios en pacientes sin patología cardiaca conocida en la Fundación Clínica Shaio en el año 2014. Metodología: Análisis de una cohorte prospectiva de todos los pacientes que ingresaron a la Fundación Clínica Shaio para evaluación ecocardiográfica sin patología cardiaca conocida entre los meses Agosto y Diciembre del 2014. Resultados: Se presenta este estudio de la evaluación de la mecánica ventricular izquierda en adultos sanos, los resultados son similares a los obtenidos en estudios de referencia, sin embargo se consideran de gran importancia ya que de acuerdo a la guía actual de evaluación de la mecánica ventricular por strain rate es importante que cada equipo se encuentre estandarizado con el fin de tener resultados válidos de acuerdo a las diferentes patologías en las que se puede aplicar y a nuestra población.

Seed dormancy and germination of Ficus lundellii and tropical forest restoration

We investigated seed dormancy and germination in Ficus lundellii Standl. (Moraceae), a native species of Mexico's Los Tuxtlas tropical rain forest. In an 8-h photoperiod at an alternating diurnal (16/8 h) temperature of 20/30 degrees C, germination was essentially complete (96%) within 28 days, whereas in darkness, all seeds remained dormant. Neither potassium nitrate (0.05-0.2%) applied continuously nor gibberellic acid applied either continuously (10-200 ppm) or as a 24 hour pretreatment (2000 ppm) induced germination in the dark. Germination in the light was not reduced by a 24-h hydrochloric acid (0.1-1%) pretreatment, but it was reduced both by a 24-h pretreatment with either H2O2 (0. 1-5 M) or 5% HCl, or by more than 5 days of storage at 40 degrees C (4.5% seed water content). In a study with a 2-dimensional temperature gradient plate, seeds germinated fully and rapidly in the light at a constant temperature of 30 degrees C, and fully but less rapidly in the light at alternating temperatures with low amplitudes (< 12 degrees C) about the optimal constant temperature. The base, optimal and ceiling temperatures for rate of germination were estimated as 13.8, 30.1 and 41.1 degrees C, respectively. In all temperature regimes, light was essential for the germination of F lundellii seeds.

Proteomic biomarkers of peripheral blood mononuclear cells obtained from postmenopausal women undergoing an intervention with soy isoflavones

Background: The incidence of cardiovascular diseases increases after menopause, and soy consumption is suggested to inhibit disease development. Objective: The objective was to identify biomarkers of response to a dietary supplementation with an isoflavone extract in postmenopausal women by proteome analysis of peripheral blood mononuclear cells. Design: The study with healthy postmenopausal woman was performed in a placebo-controlled sequential design. Peripheral mononuclear blood cells were collected from 10 volunteers after 8 wk of receiving daily 2 placebo cereal bars and after a subsequent 8 wk of intervention with 2 cereal bars each providing 25 mg of isoflavones. The proteome of the cells was visualized after 2-dimensional gel electrophoresis, and peptide mass fingerprinting served to identify proteins that by the intervention displayed altered protein concentrations. Results: Twenty-nine proteins were identified that showed significantly altered expression in the mononuclear blood cells under the soy-isoflavone intervention, including a variety of proteins involved in an antiinflammatory response. Heat shock protein 70 or a lymphocyte-specific protein phosphatase and proteins that promote increased fibrinolysis, such as a-enolase, were found at increased intensities, whereas those that mediate adhesion, migration, and proliferation of vascular smooth muscle cells, such as galectin-1, were found at reduced intensities after soy extract consumption. Conclusion: Protcome analysis identified in vivo markers that respond to a dietary intervention with isoflavone-enriched soy extract in postmenopausal women. The nature of the proteins identified suggests that soy isoflavones may increase the anti inflammatory response in blood mononuclear cells that might contribute to the atherosclerosis-preventive activities of a soy-rich diet.

Using the Cayley-Hamilton theorem with N-partitioned matrices

A definition is given for the characteristic equation of anN-partitioned matrix. It is then proved that this matrix satisfies its own characteristic equation. This can then be regarded as a version of the Cayley-Hamilton theorem, of use withN-dimensional systems.

Characterising the variability and extremes of the stratospheric polar vortices using 2D moment analysis

The mean state, variability and extreme variability of the stratospheric polar vortices, with an emphasis on the Northern Hemisphere vortex, are examined using 2-dimensional moment analysis and Extreme Value Theory (EVT). The use of moments as an analysis to ol gives rise to information about the vortex area, centroid latitude, aspect ratio and kurtosis. The application of EVT to these moment derived quantaties allows the extreme variability of the vortex to be assessed. The data used for this study is ECMWF ERA-40 potential vorticity fields on interpolated isentropic surfaces that range from 450K-1450K. Analyses show that the most extreme vortex variability occurs most commonly in late January and early February, consistent with when most planetary wave driving from the troposphere is observed. Composites around sudden stratospheric warming (SSW) events reveal that the moment diagnostics evolve in statistically different ways between vortex splitting events and vortex displacement events, in contrast to the traditional diagnostics. Histograms of the vortex diagnostics on the 850K (∼10hPa) surface over the 1958-2001 period are fitted with parametric distributions, and show that SSW events comprise the majority of data in the tails of the distributions. The distribution of each diagnostic is computed on various surfaces throughout the depth of the stratosphere, and shows that in general the vortex becomes more circular with higher filamentation at the upper levels. The Northern Hemisphere (NH) and Southern Hemisphere (SH) vortices are also compared through the analysis of their respective vortex diagnostics, and confirm that the SH vortex is less variable and lacks extreme events compared to the NH vortex. Finally extreme value theory is used to statistically mo del the vortex diagnostics and make inferences about the underlying dynamics of the polar vortices.

Efficient non-linear data assimilation in geophysical fluid dynamics

New ways of combining observations with numerical models are discussed in which the size of the state space can be very large, and the model can be highly nonlinear. Also the observations of the system can be related to the model variables in highly nonlinear ways, making this data-assimilation (or inverse) problem highly nonlinear. First we discuss the connection between data assimilation and inverse problems, including regularization. We explore the choice of proposal density in a Particle Filter and show how the ’curse of dimensionality’ might be beaten. In the standard Particle Filter ensembles of model runs are propagated forward in time until observations are encountered, rendering it a pure Monte-Carlo method. In large-dimensional systems this is very inefficient and very large numbers of model runs are needed to solve the data-assimilation problem realistically. In our approach we steer all model runs towards the observations resulting in a much more efficient method. By further ’ensuring almost equal weight’ we avoid performing model runs that are useless in the end. Results are shown for the 40 and 1000 dimensional Lorenz 1995 model.

WAXS studies of global molecular orientation induced in nematic liquid crystals by simple shear flow

Global molecular orientation function coefficients for the nematic liquid crystal 4-cyano 4'-nn -pentylbiphenyl (5CB) in shear flow are presented, being extracted from 2-dimensional Wide-Angle X-ray Scattering data. A linear increase in orientation parameter P2 is observed with a logarithmic increase in shear rate. It is proposed that this arises from an increased number of LC directors aligning to the shear axis. Upon cessation of shear flow, the anisotropy is seen to relax away completely, over a time scale which is inversely proportional to the previously applied shear rate.

The Mathematics of Control Theory

This text contains papers presented at the Institute of Mathematics and its Applications Conference on Control Theory, held at the University of Strathclyde in Glasgow. The contributions cover a wide range of topics of current interest to theoreticians and practitioners including algebraic systems theory, nonlinear control systems, adaptive control, robustness issues, infinite dimensional systems, applications studies and connections to mathematical aspects of information theory and data-fusion.

Winter and Summer Northern Hemisphere blocking in CMIP5 models

The frequencies of atmospheric blocking in both winter and summer and the changes in them from the 20th to the 21st centuries as simulated in twelve CMIP5 models is analysed. The RCP 8.5 high emission scenario runs are used to represent the 21st century. The analysis is based on the wave-breaking methodology of Pelly and Hoskins (2003a). It differs from the Tibaldi and Molteni (1990) index in viewing equatorward cut-off lows and poleward blocking highs in equal manner as indicating a disruption to the westerlies. 1-dimensional and 2-dimensional diagnostics are applied to identify blocking of the mid-latitude storm-track and also at higher latitudes. Winter blocking frequency is found to be generally underestimated. The models give a decrease in the European blocking maximum in the 21st century, consistent with the results in other studies. There is a mean 21st century winter poleward shift of high- latitude blocking, but little agreement between the models on the details. In summer, Eurasian blocking is also underestimated in the models, whereas it is now too large over the high-latitude ocean basins. A decrease in European blocking frequency in the 21st century model runs is again found. However in summer there is a clear eastward shift of blocking over Eastern Europe and Western Russia, in a region close to the blocking that dominated the Russian summer of 2010. While summer blocking decreases in general, the poleward shift of the storm track into the region of frequent high latitude blocking may mean that the incidence of storms being obstructed by blocks may actually increase.

Seasonal cycles and variability of O3 and H2O in the UT/LMS during SPURT

Airborne high resolution in situ measurements of a large set of trace gases including ozone (O3) and total water (H2O) in the upper troposphere and the lowermost stratosphere (UT/LMS) have been performed above Europe within the SPURT project. SPURT provides an extensive data coverage of the UT/LMS in each season within the time period between November 2001 and July 2003. In the LMS a distinct spring maximum and autumn minimum is observed in O3, whereas its annual cycle in the UT is shifted by 2–3 months later towards the end of the year. The more variable H2O measurements reveal a maximum during summer and a minimum during autumn/winter with no phase shift between the two atmospheric compartments. For a comprehensive insight into trace gas composition and variability in the UT/LMS several statistical methods are applied using chemical, thermal and dynamical vertical coordinates. In particular, 2-dimensional probability distribution functions serve as a tool to transform localised aircraft data to a more comprehensive view of the probed atmospheric region. It appears that both trace gases, O3 and H2O, reveal the most compact arrangement and are best correlated in the view of potential vorticity (PV) and distance to the local tropopause, indicating an advanced mixing state on these surfaces. Thus, strong gradients of PV seem to act as a transport barrier both in the vertical and the horizontal direction. The alignment of trace gas isopleths reflects the existence of a year-round extra-tropical tropopause transition layer. The SPURT measurements reveal that this layer is mainly affected by stratospheric air during winter/spring and by tropospheric air during autumn/summer. Normalised mixing entropy values for O3 and H2O in the LMS appear to be maximal during spring and summer, respectively, indicating highest variability of these trace gases during the respective seasons.

An exploration of the equivalent weights particle filter

Particle filters are fully non-linear data assimilation techniques that aim to represent the probability distribution of the model state given the observations (the posterior) by a number of particles. In high-dimensional geophysical applications the number of particles required by the sequential importance resampling (SIR) particle filter in order to capture the high probability region of the posterior, is too large to make them usable. However particle filters can be formulated using proposal densities, which gives greater freedom in how particles are sampled and allows for a much smaller number of particles. Here a particle filter is presented which uses the proposal density to ensure that all particles end up in the high probability region of the posterior probability density function. This gives rise to the possibility of non-linear data assimilation in large dimensional systems. The particle filter formulation is compared to the optimal proposal density particle filter and the implicit particle filter, both of which also utilise a proposal density. We show that when observations are available every time step, both schemes will be degenerate when the number of independent observations is large, unlike the new scheme. The sensitivity of the new scheme to its parameter values is explored theoretically and demonstrated using the Lorenz (1963) model.

The contribution of flux transfer events to convection

It is shown from flux transfer event (FTE) occurrence statistics, observed as a function of MLT by the ISEE satellites, that recent 2-dimensional analytic theories of the effects of pulsed Petschek reconnection predict FTEs to contribute between 50 and 200 kV to the total reconnection voltage when the magnetosheath field points southward. The upper limit (200 kV) allows the possibility that FTEs provide all the antisunward transport of open field lines into the tail lobe. This range is compared with the voltages associated with series of FTEs signatures, as inferred from ground-based observations, which are in the range 10–60 kV. We conclude that the contribution could sometimes be made by a series of single, large events; however, the voltage is often likely to be contributed by several FTEs at different MLT.