Analysis of the Kohn Laplacian on the Heisenberg Group and on Cauchy-Riemann Manifolds

The purpose of this study is to analyse the regularity of a differential operator, the Kohn Laplacian, in two settings: the Heisenberg group and the strongly pseudoconvex CR manifolds. The Heisenberg group is defined as a space of dimension 2n+1 with a product. It can be seen in two different ways: as a Lie group and as the boundary of the Siegel UpperHalf Space. On the Heisenberg group there exists the tangential CR complex. From this we define its adjoint and the Kohn-Laplacian. Then we obtain estimates for the Kohn-Laplacian and find its solvability and hypoellipticity. For stating L^p and Holder estimates, we talk about homogeneous distributions. In the second part we start working with a manifold M of real dimension 2n+1. We say that M is a CR manifold if some properties are satisfied. More, we say that a CR manifold M is strongly pseudoconvex if the Levi form defined on M is positive defined. Since we will show that the Heisenberg group is a model for the strongly pseudo-convex CR manifolds, we look for an osculating Heisenberg structure in a neighborhood of a point in M, and we want this structure to change smoothly from a point to another. For that, we define Normal Coordinates and we study their properties. We also examinate different Normal Coordinates in the case of a real hypersurface with an induced CR structure. Finally, we define again the CR complex, its adjoint and the Laplacian operator on M. We study these new operators showing subelliptic estimates. For that, we don't need M to be pseudo-complex but we ask less, that is, the Z(q) and the Y(q) conditions. This provides local regularity theorems for Laplacian and show its hypoellipticity on M.

Development of models and methods to simulate peptide-assisted nucleation and growth of calcium-minerals

In den vergangenen Jahren wurden einige bislang unbekannte Phänomene experimentell beobachtet, wie etwa die Existenz unterschiedlicher Prä-Nukleations-Strukturen. Diese haben zu einem neuen Verständnis von Prozessen, die auf molekularer Ebene während der Nukleation und dem Wachstum von Kristallen auftreten, beigetragen. Die Auswirkungen solcher Prä-Nukleations-Strukturen auf den Prozess der Biomineralisation sind noch nicht hinreichend verstanden. Die Mechanismen, mittels derer biomolekulare Modifikatoren, wie Peptide, mit Prä-Nukleations-Strukturen interagieren und somit den Nukleationsprozess von Mineralen beeinflussen könnten, sind vielfältig. Molekulare Simulationen sind zur Analyse der Formation von Prä-Nukleations-Strukturen in Anwesenheit von Modifikatoren gut geeignet. Die vorliegende Arbeit beschreibt einen Ansatz zur Analyse der Interaktion von Peptiden mit den in Lösung befindlichen Bestandteilen der entstehenden Kristalle mit Hilfe von Molekular-Dynamik Simulationen.rnUm informative Simulationen zu ermöglichen, wurde in einem ersten Schritt die Qualität bestehender Kraftfelder im Hinblick auf die Beschreibung von mit Calciumionen interagierenden Oligoglutamaten in wässrigen Lösungen untersucht. Es zeigte sich, dass große Unstimmigkeiten zwischen etablierten Kraftfeldern bestehen, und dass keines der untersuchten Kraftfelder eine realistische Beschreibung der Ionen-Paarung dieser komplexen Ionen widerspiegelte. Daher wurde eine Strategie zur Optimierung bestehender biomolekularer Kraftfelder in dieser Hinsicht entwickelt. Relativ geringe Veränderungen der auf die Ionen–Peptid van-der-Waals-Wechselwirkungen bezogenen Parameter reichten aus, um ein verlässliches Modell für das untersuchte System zu erzielen. rnDas umfassende Sampling des Phasenraumes der Systeme stellt aufgrund der zahlreichen Freiheitsgrade und der starken Interaktionen zwischen Calciumionen und Glutamat in Lösung eine besondere Herausforderung dar. Daher wurde die Methode der Biasing Potential Replica Exchange Molekular-Dynamik Simulationen im Hinblick auf das Sampling von Oligoglutamaten justiert und es erfolgte die Simulation von Peptiden verschiedener Kettenlängen in Anwesenheit von Calciumionen. Mit Hilfe der Sketch-Map Analyse konnten im Rahmen der Simulationen zahlreiche stabile Ionen-Peptid-Komplexe identifiziert werden, welche die Formation von Prä-Nukleations-Strukturen beeinflussen könnten. Abhängig von der Kettenlänge des Peptids weisen diese Komplexe charakteristische Abstände zwischen den Calciumionen auf. Diese ähneln einigen Abständen zwischen den Calciumionen in jenen Phasen von Calcium-Oxalat Kristallen, die in Anwesenheit von Oligoglutamaten gewachsen sind. Die Analogie der Abstände zwischen Calciumionen in gelösten Ionen-Peptid-Komplexen und in Calcium-Oxalat Kristallen könnte auf die Bedeutung von Ionen-Peptid-Komplexen im Prozess der Nukleation und des Wachstums von Biomineralen hindeuten und stellt einen möglichen Erklärungsansatz für die Fähigkeit von Oligoglutamaten zur Beeinflussung der Phase des sich formierenden Kristalls dar, die experimentell beobachtet wurde.

On the recurrence of random walks in Lévy random environments

This thesis investigates one-dimensional random walks in random environment whose transition probabilities might have an infinite variance. The ergodicity of the dynamical system ''from the point of view of the particle'' is proved under the assumptions of transitivity and existence of an absolutely continuous steady state on the space of the environments. We show that, if the average of the local drift over the environments is summable and null, then the RWRE is recurrent. We provide an example satisfying all the hypotheses.

The effects of dynamic loading on the intervertebral disc

Loading is important to maintain the balance of matrix turnover in the intervertebral disc (IVD). Daily cyclic diurnal assists in the transport of large soluble factors across the IVD and its surrounding circulation and applies direct and indirect stimulus to disc cells. Acute mechanical injury and accumulated overloading, however, could induce disc degeneration. Recently, there is more information available on how cyclic loading, especially axial compression and hydrostatic pressure, affects IVD cell biology. This review summarises recent studies on the response of the IVD and stem cells to applied cyclic compression and hydrostatic pressure. These studies investigate the possible role of loading in the initiation and progression of disc degeneration as well as quantifying a physiological loading condition for the study of disc degeneration biological therapy. Subsequently, a possible physiological/beneficial loading range is proposed. This physiological/beneficial loading could provide insight into how to design loading regimes in specific system for the testing of various biological therapies such as cell therapy, chemical therapy or tissue engineering constructs to achieve a better final outcome. In addition, the parameter space of 'physiological' loading may also be an important factor for the differentiation of stem cells towards most ideally 'discogenic' cells for tissue engineering purpose.

Computations of Vector-Valued Siegel Modular Forms

We carry out some computations of vector-valued Siegel modular forms of degree two, weight (k, 2) and level one, and highlight three experimental results: (1) we identify a rational eigenform in a three-dimensional space of cusp forms; (2) we observe that non-cuspidal eigenforms of level one are not always rational; (3) we verify a number of cases of conjectures about congruences between classical modular forms and Siegel modular forms. Our approach is based on Satoh's description of the module of vector-valued Siegel modular forms of weight (k, 2) and an explicit description of the Hecke action on Fourier expansions. (C) 2013 Elsevier Inc. All rights reserved.

Influence of Partial Lateral Corpectomy with and without Hemilaminectomy on Canine Thoracolumbar Stability: A Biomechanical Study

OBJECTIVE: To analyze the biomechanical changes induced by partial lateral corpectomy (PLC) and a combination of PLC and hemilaminectomy in a T13-L3 spinal segment in nonchondrodystrophic dogs. STUDY DESIGN: In vitro biomechanical cadaveric study. SAMPLE POPULATION: T13-L3 spinal segments (n = 10) of nonchondrodystrophic dogs (weighing, 25-38 kg). METHODS: A computed tomography (CT) scan of each T13-L3 spinal segment was performed. A loading simulator for flexibility analysis was used to determine the range of motion (ROM) and neutral zone (NZ) during flexion/extension, lateral bending, and axial rotation. A servohydraulic testing machine was used to determine the changes in stiffness during compression, dorsoventral, and lateral shear. All spines were tested intact, after PLC in the left intervertebral space of L1-L2, and after a combination of PLC and hemilaminectomy. RESULTS: Statistically significant increases in ROM and NZ (P < .05) were detected during flexion/extension and lateral bending when PLC was performed. A significant increase in ROM (P < .001) was noted during axial rotation and flexion after PLC and hemilaminectomy. Stiffness decreased significantly during compression and dorsoventral shear after each procedure. Decreased stiffness during lateral shear was only significant after a combination of both procedures. CONCLUSION: PLC might lead to some spinal instability; these changes are enhanced when a hemilaminectomy is added.

Zeros of Weakly Holomorphic Modular Forms of Levels 2 and 3

Let M-k(#)(N) be the space of weakly holomorphic modular forms for Gamma(0)(N) that are holomorphic at all cusps except possibly at infinity. We study a canonical basis for M-k(#)(2) and M-k(#)(3) and prove that almost all modular forms in this basis have the property that the majority of their zeros in a fundamental domain lie on a lower boundary arc of the fundamental domain.

The Ideology, Politics and Autonomous Art of Richard Weiner: (An Event in Discourse)"

The first aim of the project was to compile documentation on the life and work of Richard Weiner, a Czech journalist, writer and poet who spent the best part of his life as Paris correspondent for Lidove noviny. Langerova looked at the contexts and the growing independence of certain parts of his work, the distribution of thematic compositional elements into different parts of discourse and their position in the autonomous space of a work of art. Looking at the features of minority literature and the contemporary contexts of Weiner's life and work Langerova focuses on the situation of the Jewish community (Wiener came from an assimilated Jewish family). For this minorities, the function of language as a medium of communication which is able to create an autonomous world became increasingly important. Literature, which is based on this function of language, is a political matter par excellence before it begins forming as an autonomous, independent and divergent place. This means that everything private and intimate is closely connected to political and social responsibility, while supposedly objective genres contain subjective features. Another important characteristic is "nomadism", which asks the question of "Where do I belong". This was very important in Czechoslovakia after World War I , as in the issue of Zionism. Although Weiner rejected Zionism, he asks this question in his writing and it is reflected at a symbolic level in his work, which shows a fundamental thematic and compositional plan of a journey, cross-roads and wandering. These theses were reflected in Weiner's life, which was a series of continuous transfers and unplanned moves, often when he thought he had found his place. As well as tracing the course of his life, and his relations with and views of other writers, Langerova looks at his writings in various areas. Her major focus is the divergence of trivial and great events into different types of discourse in Richard Weiner's work, their transfer (small into great, trivial into mythical) and their historical context.

Melting of Northern Greenland during the last interglaciation

Using simulated climate data from the comprehensive coupled climate model IPSL CM4, we simulate the Greenland ice sheet (GrIS) during the Eemian interglaciation with the three-dimensional ice sheet model SICOPOLIS. The Eemian is a period 126 000 yr before present (126 ka) with Arctic temperatures comparable to projections for the end of this century. In our simulation, the northeastern part of the GrIS is unstable and retreats significantly, despite moderate melt rates. This result is found to be robust to perturbations within a wide parameter space of key parameters of the ice sheet model, the choice of initial ice temperature, and has been reproduced with climate forcing from a second coupled climate model, the CCSM3. It is shown that the northeast GrIS is the most vulnerable. Even a small increase in melt removes many years of ice accumulation, giving a large mass imbalance and triggering the strong ice-elevation feedback. Unlike the south and west, melting in the northeast is not compensated by high accumulation. The analogy with modern warming suggests that in coming decades, positive feedbacks could increase the rate of mass loss of the northeastern GrIS, exceeding the recent observed thinning rates in the south.

Enumerating constrained elementary flux vectors of metabolic networks

The concept of elementary vector is generalised to the case where the steady-state space of the metabolic network is not a flux cone but is a general polyhedron due to further inhomogeneous constraints on the flows through some of the reactions. On one hand, this allows to selectively enumerate elementary modes which satisfy certain optimality criteria and this can yield a large computational gain compared with full enumeration. On the other hand, in contrast to the single optimum found by executing a linear program, this enables a comprehensive description of the set of alternate optima often encountered in flux balance analysis. The concepts are illustrated on a metabolic network model of human cardiac mitochondria.

The stereochemistry of the amino acid side chain influences the inflammatory potential of muramyl dipeptide in experimental meningitis

Intrathecal injections of 50 to 100 micro g of (N-acetylmuramyl-L-alanyl-D-isoglutamine) muramyl dipeptide (MDP)/rabbit dose-dependently triggered tumor necrosis factor alpha (TNF-alpha) secretion (12 to 40,000 pg/ml) preceding the influx of leukocytes in the subarachnoid space of rabbits. Intrathecal instillation of heat-killed unencapsulated R6 pneumococci produced a comparable leukocyte influx but only a minimal level of preceding TNF-alpha secretion. The stereochemistry of the first amino acid (L-alanine) of the MDP played a crucial role with regard to its inflammatory potential. Isomers harboring D-alanine in first position did not induce TNF-alpha secretion and influx of leukocytes. This stereospecificity of MDPs was also confirmed by measuring TNF-alpha release from human peripheral mononuclear blood cells stimulated in vitro. These data show that the inflammatory potential of MDPs depends on the stereochemistry of the first amino acid of the peptide side chain and suggest that intact pneumococci and MDPs induce inflammation by different pathways.

Study of accelerometer assisted single key positioning user input systems

New designs of user input systems have resulted from the developing technologies and specialized user demands. Conventional keyboard and mouse input devices still dominate the input speed, but other input mechanisms are demanded in special application scenarios. Touch screen and stylus input methods have been widely adopted by PDAs and smartphones. Reduced keypads are necessary for mobile phones. A new design trend is exploring the design space in applications requiring single-handed input, even with eyes-free on small mobile devices. This requires as few keys on the input device to make it feasible to operate. But representing many characters with fewer keys can make the input ambiguous. Accelerometers embedded in mobile devices provide opportunities to combine device movements with keys for input signal disambiguation. Recent research has explored its design space for text input. In this dissertation an accelerometer assisted single key positioning input system is developed. It utilizes input device tilt directions as input signals and maps their sequences to output characters and functions. A generic positioning model is developed as guidelines for designing positioning input systems. A calculator prototype and a text input prototype on the 4+1 (5 positions) positioning input system and the 8+1 (9 positions) positioning input system are implemented using accelerometer readings on a smartphone. Users use one physical key to operate and feedbacks are audible. Controlled experiments are conducted to evaluate the feasibility, learnability, and design space of the accelerometer assisted single key positioning input system. This research can provide inspiration and innovational references for researchers and practitioners in the positioning user input designs, applications of accelerometer readings, and new development of standard machine readable sign languages.

Automated design of self-stabilization

Self-stabilization is a property of a distributed system such that, regardless of the legitimacy of its current state, the system behavior shall eventually reach a legitimate state and shall remain legitimate thereafter. The elegance of self-stabilization stems from the fact that it distinguishes distributed systems by a strong fault tolerance property against arbitrary state perturbations. The difficulty of designing and reasoning about self-stabilization has been witnessed by many researchers; most of the existing techniques for the verification and design of self-stabilization are either brute-force, or adopt manual approaches non-amenable to automation. In this dissertation, we first investigate the possibility of automatically designing self-stabilization through global state space exploration. In particular, we develop a set of heuristics for automating the addition of recovery actions to distributed protocols on various network topologies. Our heuristics equally exploit the computational power of a single workstation and the available parallelism on computer clusters. We obtain existing and new stabilizing solutions for classical protocols like maximal matching, ring coloring, mutual exclusion, leader election and agreement. Second, we consider a foundation for local reasoning about self-stabilization; i.e., study the global behavior of the distributed system by exploring the state space of just one of its components. It turns out that local reasoning about deadlocks and livelocks is possible for an interesting class of protocols whose proof of stabilization is otherwise complex. In particular, we provide necessary and sufficient conditions – verifiable in the local state space of every process – for global deadlock- and livelock-freedom of protocols on ring topologies. Local reasoning potentially circumvents two fundamental problems that complicate the automated design and verification of distributed protocols: (1) state explosion and (2) partial state information. Moreover, local proofs of convergence are independent of the number of processes in the network, thereby enabling our assertions about deadlocks and livelocks to apply on rings of arbitrary sizes without worrying about state explosion.

SPATIAL UNDERSTANDING OF MATRIX INVERSION FOR INVERSE FORCE ESTIMATION

A basic approach to study a NVH problem is to break down the system in three basic elements – source, path and receiver. While the receiver (response) and the transfer path can be measured, it is difficult to measure the source (forces) acting on the system. It becomes necessary to predict these forces to know how they influence the responses. This requires inverting the transfer path. Singular Value Decomposition (SVD) method is used to decompose the transfer path matrix into its principle components which is required for the inversion. The usual approach to force prediction requires rejecting the small singular values obtained during SVD by setting a threshold, as these small values dominate the inverse matrix. This assumption of the threshold may be subjected to rejecting important singular values severely affecting force prediction. The new approach discussed in this report looks at the column space of the transfer path matrix which is the basis for the predicted response. The response participation is an indication of how the small singular values influence the force participation. The ability to accurately reconstruct the response vector is important to establish a confidence in force vector prediction. The goal of this report is to suggest a solution that is mathematically feasible, physically meaningful, and numerically more efficient through examples. This understanding adds new insight to the effects of current code and how to apply algorithms and understanding to new codes.

Interference during the implicit learning of two different motor sequences

It has been demonstrated that learning a second motor task after having learned a first task may interfere with the long-term consolidation of the first task. However, little is known about immediate changes in the representation of the motor memory in the early acquisition phase within the first minutes of the learning process. Therefore, we investigated such early interference effects with an implicit serial reaction time task in 55 healthy subjects. Each subject performed either a sequence learning task involving two different sequences, or a random control task. The results showed that learning the first sequence led to only a slight, short-lived interference effect in the early acquisition phase of the second sequence. Overall, learning of neither sequence was impaired. Furthermore, the two processes, sequence-unrelated task learning (i.e. general motor training) and the sequence learning itself did not appear to interfere with each other. In conclusion, although the long-term consolidation of a motor memory has been shown to be sensitive to other interfering memories, the present study suggests that the brain is initially able to acquire more than one new motor sequence within a short space of time without significant interference.