On differential operators of Calabi-Yau type

This thesis is devoted to the study of Picard-Fuchs operators associated to one-parameter families of $n$-dimensional Calabi-Yau manifolds whose solutions are integrals of $(n,0)$-forms over locally constant $n$-cycles. Assuming additional conditions on these families, we describe algebraic properties of these operators which leads to the purely algebraic notion of operators of CY-type. rnMoreover, we present an explicit way to construct CY-type operators which have a linearly rigid monodromy tuple. Therefore, we first usernthe translation of the existence algorithm by N. Katz for rigid local systems to the level of tuples of matrices which was established by M. Dettweiler and S. Reiter. An appropriate translation to the level of differential operators yields families which contain operators of CY-type. rnConsidering additional operations, we are also able to construct special CY-type operators of degree four which have a non-linearly rigid monodromy tuple. This provides both previously known and new examples.

Logarithmically smooth deformations of strict normal crossing logarithmically symplectic varieties

In this thesis we give a definition of the term logarithmically symplectic variety; to be precise, we distinguish even two types of such varieties. The general type is a triple $(f,nabla,omega)$ comprising a log smooth morphism $fcolon Xtomathrm{Spec}kappa$ of log schemes together with a flat log connection $nablacolon LtoOmega^1_fotimes L$ and a ($nabla$-closed) log symplectic form $omegainGamma(X,Omega^2_fotimes L)$. We define the functor of log Artin rings of log smooth deformations of such varieties $(f,nabla,omega)$ and calculate its obstruction theory, which turns out to be given by the vector spaces $H^i(X,B^bullet_{(f,nabla)}(omega))$, $i=0,1,2$. Here $B^bullet_{(f,nabla)}(omega)$ is the class of a certain complex of $mathcal{O}_X$-modules in the derived category $mathrm{D}(X/kappa)$ associated to the log symplectic form $omega$. The main results state that under certain conditions a log symplectic variety can, by a flat deformation, be smoothed to a symplectic variety in the usual sense. This may provide a new approach to the construction of new examples of irreducible symplectic manifolds.

IMEX finite volume methods for the shallow water equations

Die Flachwassergleichungen (SWE) sind ein hyperbolisches System von Bilanzgleichungen, die adäquate Approximationen an groß-skalige Strömungen der Ozeane, Flüsse und der Atmosphäre liefern. Dabei werden Masse und Impuls erhalten. Wir unterscheiden zwei charakteristische Geschwindigkeiten: die Advektionsgeschwindigkeit, d.h. die Geschwindigkeit des Massentransports, und die Geschwindigkeit von Schwerewellen, d.h. die Geschwindigkeit der Oberflächenwellen, die Energie und Impuls tragen. Die Froude-Zahl ist eine Kennzahl und ist durch das Verhältnis der Referenzadvektionsgeschwindigkeit zu der Referenzgeschwindigkeit der Schwerewellen gegeben. Für die oben genannten Anwendungen ist sie typischerweise sehr klein, z.B. 0.01. Zeit-explizite Finite-Volume-Verfahren werden am öftersten zur numerischen Berechnung hyperbolischer Bilanzgleichungen benutzt. Daher muss die CFL-Stabilitätsbedingung eingehalten werden und das Zeitinkrement ist ungefähr proportional zu der Froude-Zahl. Deswegen entsteht bei kleinen Froude-Zahlen, etwa kleiner als 0.2, ein hoher Rechenaufwand. Ferner sind die numerischen Lösungen dissipativ. Es ist allgemein bekannt, dass die Lösungen der SWE gegen die Lösungen der Seegleichungen/ Froude-Zahl Null SWE für Froude-Zahl gegen Null konvergieren, falls adäquate Bedingungen erfüllt sind. In diesem Grenzwertprozess ändern die Gleichungen ihren Typ von hyperbolisch zu hyperbolisch.-elliptisch. Ferner kann bei kleinen Froude-Zahlen die Konvergenzordnung sinken oder das numerische Verfahren zusammenbrechen. Insbesondere wurde bei zeit-expliziten Verfahren falsches asymptotisches Verhalten (bzgl. der Froude-Zahl) beobachtet, das diese Effekte verursachen könnte.Ozeanographische und atmosphärische Strömungen sind typischerweise kleine Störungen eines unterliegenden Equilibriumzustandes. Wir möchten, dass numerische Verfahren für Bilanzgleichungen gewisse Equilibriumzustände exakt erhalten, sonst können künstliche Strömungen vom Verfahren erzeugt werden. Daher ist die Quelltermapproximation essentiell. Numerische Verfahren die Equilibriumzustände erhalten heißen ausbalanciert.rnrnIn der vorliegenden Arbeit spalten wir die SWE in einen steifen, linearen und einen nicht-steifen Teil, um die starke Einschränkung der Zeitschritte durch die CFL-Bedingung zu umgehen. Der steife Teil wird implizit und der nicht-steife explizit approximiert. Dazu verwenden wir IMEX (implicit-explicit) Runge-Kutta und IMEX Mehrschritt-Zeitdiskretisierungen. Die Raumdiskretisierung erfolgt mittels der Finite-Volumen-Methode. Der steife Teil wird mit Hilfe von finiter Differenzen oder au eine acht mehrdimensional Art und Weise approximniert. Zur mehrdimensionalen Approximation verwenden wir approximative Evolutionsoperatoren, die alle unendlich viele Informationsausbreitungsrichtungen berücksichtigen. Die expliziten Terme werden mit gewöhnlichen numerischen Flüssen approximiert. Daher erhalten wir eine Stabilitätsbedingung analog zu einer rein advektiven Strömung, d.h. das Zeitinkrement vergrößert um den Faktor Kehrwert der Froude-Zahl. Die in dieser Arbeit hergeleiteten Verfahren sind asymptotisch erhaltend und ausbalanciert. Die asymptotischer Erhaltung stellt sicher, dass numerische Lösung das "korrekte" asymptotische Verhalten bezüglich kleiner Froude-Zahlen besitzt. Wir präsentieren Verfahren erster und zweiter Ordnung. Numerische Resultate bestätigen die Konvergenzordnung, so wie Stabilität, Ausbalanciertheit und die asymptotische Erhaltung. Insbesondere beobachten wir bei machen Verfahren, dass die Konvergenzordnung fast unabhängig von der Froude-Zahl ist.

Intra-arterial injection of neural stem cells using a microneedle technique does not cause microembolic strokes

Intra-arterial (IA) injection represents an experimental avenue for minimally invasive delivery of stem cells to the injured brain. It has however been reported that IA injection of stem cells carries the risk of reduction in cerebral blood flow (CBF) and microstrokes. Here we evaluate the safety of IA neural progenitor cell (NPC) delivery to the brain. Cerebral blood flow of rats was monitored during IA injection of single cell suspensions of NPCs after stroke. Animals received 1 × 10(6) NPCs either injected via a microneedle (microneedle group) into the patent common carotid artery (CCA) or via a catheter into the proximally ligated CCA (catheter group). Controls included saline-only injections and cell injections into non-stroked sham animals. Cerebral blood flow in the microneedle group remained at baseline, whereas in the catheter group a persistent (15 minutes) decrease to 78% of baseline occurred (P<0.001). In non-stroked controls, NPCs injected via the catheter method resulted in higher levels of Iba-1-positive inflammatory cells (P=0.003), higher numbers of degenerating neurons as seen in Fluoro-Jade C staining (P<0.0001) and ischemic changes on diffusion weighted imaging. With an appropriate technique, reduction in CBF and microstrokes do not occur with IA transplantation of NPCs.

Invariant barriers to reactive front propagation in fluid flows

We present theory and experiments on the dynamics of reaction fronts in two-dimensional, vortex-dominated flows, for both time-independent and periodically driven cases. We find that the front propagation process is controlled by one-sided barriers that are either fixed in the laboratory frame (time-independent flows) or oscillate periodically (periodically driven flows). We call these barriers burning invariant manifolds (BIMs), since their role in front propagation is analogous to that of invariant manifolds in the transport and mixing of passive impurities under advection. Theoretically, the BIMs emerge from a dynamical systems approach when the advection-reaction-diffusion dynamics is recast as an ODE for front element dynamics. Experimentally, we measure the location of BIMs for several laboratory flows and confirm their role as barriers to front propagation.

Barriers to front propagation in ordered and disordered vortex flows

We present experiments on reactive front propagation in a two-dimensional (2D) vortex chain flow (both time-independent and time-periodic) and a 2D spatially disordered (time-independent) vortex-dominated flow. The flows are generated using magnetohydrodynamic forcing techniques, and the fronts are produced using the excitable, ferroin-catalyzed Belousov-Zhabotinsky chemical reaction. In both of these flows, front propagation is dominated by the presence of burning invariant manifolds (BIMs) that act as barriers, similar to invariant manifolds that dominate the transport of passive impurities. Convergence of the fronts onto these BIMs is shown experimentally for all of the flows studied. The BIMs are also shown to collapse onto the invariant manifolds for passive transport in the limit of large flow velocities. For the disordered flow, the measured BIMs are compared to those predicted using a measured velocity field and a three-dimensional set of ordinary differential equations that describe the dynamics of front propagation in advection-reaction-diffusion systems.

Geophysical Investigation of Subsurface Three-Dimensional Architecture of Icy Debris Fans With Ground Penetrating Radar in the Wrangell Mountains, Alaska

Icy debris fans have are newly-described landforms (Kochel and Trop, 2008 and 2012) as landforms developed immediately after deglaciation on Earth and similar features have been observed on Mars. Subsurface characteristics of Icy debris fans have not been previously investigated. Ground penetrating radar (GPR) was used to non-invasively investigate the subsurface characteristics of icy debris fans near McCarthy, Alaska, USA. The three fans investigated in Alaska are the East, West, and Middle fans (Kochel and Trop, 2008 and 2012) which below the Nabesna ice cap and on top of the McCarthy Creek Glacier. Icy debris fans in general are a largely unexplored suite of paraglacial landforms and processes in alpine regions. Recent field studies focused on direct observations and depositional processes. Their results showed that the fan's composition is primarily influenced by the type and frequency of depositional processes that supply the fan. Photographic studies show that the East Fan receives far more ice and snow avalanches whereas the Middle and West Fans receive fewer mass wasting events but more clastic debris is deposited on the Middle and West fan from rock falls and icy debris flows. GPR profiles and Wide-angle reflection and refraction (WARR) surveys consisting of both, common mid-point (CMP), and common shot-point (CSP) surveys investigated the subsurface geometry of the fans and the McCarthy Creek Glacier. All GPR surveys were collected in July of 2013 with 100MHz bi-static antennas. Four axial profiles and three cross-fan profiles were done on the West and Middle fans as well as the McCarthy Creek Glacier in order to investigate the relationship between the three features. GPR profiles yielded reflectors that were continuous for 10+ m and hyperbolic reflections in the subsurface. The depth to these reflections in the subsurface requires knowledge of the velocity of the subsurface. To find the velocity of the subsurface eight WARR surveys collected on the fans and on the McCarthy Creek glacier to provide information on variability of subsurface velocities. The profiles of the Middle and West fan have more reflections in their profiles compared to profiles done on the McCarthy Creek Glacier. Based on the WARR surveys, we interpret the lower energy return in the glacier to be caused by two reasons. 1) The increased attenuation due to wet ice versus drier ice and on the fan with GPR velocities >0.15m/ns. 2) Lack of interfaces in the glacier compared to those in the fans which are inferred to be produced by the alternating layers of stratified ice and lithic-rich layers. The GPR profiles on the West and Middle Fans show the shallow subsurface being dominated by lenticular reflections interpreted to be consistent with the shape of surficial deposits. The West Fan is distinguished from the Middle Fan by the nature of its reflections patterns and thicknesses of reflection packages that clearly shows the Middle fan with a greater thickness. The changes in subsurface reflections between the Middle and West Fans as well as the McCarthy Creek Glacier are thought to reflect the type and frequency of depositional processes and surrounding bedrock and talus slopes.

Maximum principle preserving high order schemes for convection-dominated diffusion equations

The maximum principle is an important property of solutions to PDE. Correspondingly, it's of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving(MPP) high order finite volume(FV) WENO scheme, and then propose a new parametrized MPP high order finite difference(FD) WENO framework, which is generalized from the one solving hyperbolic conservation laws. A formal analysis is presented to show that a third order finite difference scheme with this parametrized MPP flux limiters maintains the third order accuracy without extra CFL constraint when the low order monotone flux is chosen appropriately. Numerical tests in both one and two dimensional cases are performed on the simulation of the incompressible Navier-Stokes equations in vorticity stream-function formulation and several other problems to show the effectiveness of the proposed method.

LOCAL DIGITAL CONTROL OF POWER ELECTRONIC CONVERTERS IN A DC MICROGRID BASED ON A-PRIORI DERIVATION OF SWITCHING SURFACES

In power electronic basedmicrogrids, the computational requirements needed to implement an optimized online control strategy can be prohibitive. The work presented in this dissertation proposes a generalized method of derivation of geometric manifolds in a dc microgrid that is based on the a-priori computation of the optimal reactions and trajectories for classes of events in a dc microgrid. The proposed states are the stored energies in all the energy storage elements of the dc microgrid and power flowing into them. It is anticipated that calculating a large enough set of dissimilar transient scenarios will also span many scenarios not specifically used to develop the surface. These geometric manifolds will then be used as reference surfaces in any type of controller, such as a sliding mode hysteretic controller. The presence of switched power converters in microgrids involve different control actions for different system events. The control of the switch states of the converters is essential for steady state and transient operations. A digital memory look-up based controller that uses a hysteretic sliding mode control strategy is an effective technique to generate the proper switch states for the converters. An example dcmicrogrid with three dc-dc boost converters and resistive loads is considered for this work. The geometric manifolds are successfully generated for transient events, such as step changes in the loads and the sources. The surfaces corresponding to a specific case of step change in the loads are then used as reference surfaces in an EEPROM for experimentally validating the control strategy. The required switch states corresponding to this specific transient scenario are programmed in the EEPROM as a memory table. This controls the switching of the dc-dc boost converters and drives the system states to the reference manifold. In this work, it is shown that this strategy effectively controls the system for a transient condition such as step changes in the loads for the example case.

Thermoreversible hyaluronan-based hydrogel supports in vitro and ex vivo disc-like differentiation of human mesenchymal stem cells

BACKGROUND CONTEXT The fate of human mesenchymal stem cells (hMSCs) supplied to the degenerating intervertebral disc (IVD) is still not fully understood and can be negatively affected by low oxygen, pH, and glucose concentration of the IVD environment. The hMSC survival and yield upon injection of compromised IVD could be improved by the use of an appropriate carrier and/or by predifferentiation of hMSCs before injection. PURPOSE To optimize hMSC culture conditions in thermoreversible hyaluronan-based hydrogel, hyaluronan-poly(N-isopropylacrylamide) (HA-pNIPAM), to achieve differentiation toward the disc phenotype in vitro, and evaluate whether preconditioning contributes to a better hMSC response ex vivo. STUDY DESIGN In vitro and ex vivo whole-organ culture of hMSCs. METHODS In vitro cultures of hMSCs were conducted in HA-pNIPAM and alginate for 1 week under hypoxia in chondropermissive medium alone and with the supplementation of transforming growth factor β1 or growth and differentiation factor 5 (GDF-5). Ex vivo, hMSCs were either suspended in HA-pNIPAM and directly supplied to the IVDs or predifferentiated with GDF-5 for 1 week in HA-pNIPAM and then supplied to the IVDs. Cell viability was evaluated by Live-Dead assay, and DNA, glycosaminoglycan (GAG), and gene expression profiles were used to assess hMSC differentiation toward the disc phenotype. RESULTS The HA-pNIPAM induced hMSC differentiation toward the disc phenotype more effectively than alginate: in vitro, higher GAG/DNA ratio and higher collagen type II, SOX9, cytokeratin-19, cluster of differentiation 24, and forkhead box protein F1 expressions were found for hMSCs cultured in HA-pNIPAM compared with those cultured in alginate, regardless of the addition of growth factors. Ex vivo, direct combination of HA-pNIPAM with the disc environment induced a stronger disc-like differentiation of hMSCs than predifferentiation of hMSCs followed by their delivery to the discs. CONCLUSIONS Hyaluronan-based thermoreversible hydrogel supports hMSC differentiation toward the disc phenotype without the need for growth factor supplementation in vitro and ex vivo. Further in vivo studies are required to confirm the suitability of this hydrogel as an effective stem cell carrier for the treatment of IVD degeneration.

Malignant nail tumors

Because of the large number of different tissues making up the distal phalanx of fingers and toes, a large variety of malignant tumors can be found in and around the nail apparatus. Bowen disease is probably the most frequent nail malignancy. It is usually seen as a verrucous plaque of the nail fold and nail bed in persons above the age of 40 years. It slowly grows over a period of years or even decades before degenerating to an invasive squamous cell carcinoma. The latter may also occur primarily often as a weeping onycholysis. The next most frequent nail malignancy is ungual melanoma. Those arising from the matrix are usually pigmented and often start with a longitudinal melanonychia whereas those originating from the nail bed remain amelanotic, are often nodular and mistaken for an ingrown nail in an elderly person. The treatment of choice for in situ and early invasive subungual melanomas is generous extirpation of the nail apparatus whereas distal amputation is only indicated for advanced melanomas. In addition to these frequent nail malignancies, nail-specific carcinomas, malignant vascular and osseous tumors, other sarcomas, nail involvement in malignant systemic disorders and metastases may occur. In most cases, they cannot be diagnosed accurately on clinical grounds. Therefore, a high degree of suspicion is necessary in all isolated or single-digit proliferations that do not respond to conservative treatment.

Organ Culture Bioreactors - Platforms to Study Human Intervertebral Disc Degeneration and Regenerative Therapy.

In recent decades the application of bioreactors has revolutionized the concept of culturing tissues and organs that require mechanical loading. In intervertebral disc (IVD) research, collaborative efforts of biomedical engineering, biology and mechatronics have led to the innovation of new loading devices that can maintain viable IVD organ explants from large animals and human cadavers in precisely defined nutritional and mechanical environments over extended culture periods. Particularly in spine and IVD research, these organ culture models offer appealing alternatives, as large bipedal animal models with naturally occurring IVD degeneration and a genetic background similar to the human condition do not exist. Latest research has demonstrated important concepts including the potential of homing of mesenchymal stem cells to nutritionally or mechanically stressed IVDs, and the regenerative potential of "smart" biomaterials for nucleus pulposus or annulus fibrosus repair. In this review, we summarize the current knowledge about cell therapy, injection of cytokines and short peptides to rescue the degenerating IVD. We further stress that most bioreactor systems simplify the real in vivo conditions providing a useful proof of concept. Limitations are that certain aspects of the immune host response and pain assessments cannot be addressed with ex vivo systems. Coccygeal animal disc models are commonly used because of their availability and similarity to human IVDs. Although in vitro loading environments are not identical to the human in vivo situation, 3D ex vivo organ culture models of large animal coccygeal and human lumbar IVDs should be seen as valid alternatives for screening and feasibility testing to augment existing small animal, large animal, and human clinical trial experiments.

Retinal Cell Death Caused by Sodium Iodate Involves Multiple Caspase-Dependent and Caspase-Independent Cell-Death Pathways

Herein, we have investigated retinal cell-death pathways in response to the retina toxin sodium iodate (NaIO3) both in vivo and in vitro. C57/BL6 mice were treated with a single intravenous injection of NaIO3 (35 mg/kg). Morphological changes in the retina post NaIO3 injection in comparison to untreated controls were assessed using electron microscopy. Cell death was determined by TdT-mediated dUTP-biotin nick end labeling (TUNEL) staining. The activation of caspases and calpain was measured using immunohistochemistry. Additionally, cytotoxicity and apoptosis in retinal pigment epithelial (RPE) cells, primary retinal cells, and the cone photoreceptor (PRC) cell line 661W were assessed in vitro after NaIO3 treatment using the ApoToxGlo™ assay. The 7-AAD/Annexin-V staining was performed and necrostatin (Nec-1) was administered to the NaIO3-treated cells to confirm the results. In vivo, degenerating RPE cells displayed a rounded shape and retracted microvilli, whereas PRCs featured apoptotic nuclei. Caspase and calpain activity was significantly upregulated in retinal sections and protein samples from NaIO3-treated animals. In vitro, NaIO3 induced necrosis in RPE cells and apoptosis in PRCs. Furthermore, Nec-1 significantly decreased NaIO3-induced RPE cell death, but had no rescue effect on treated PRCs. In summary, several different cell-death pathways are activated in retinal cells as a result of NaIO3.

Flexibility Properties in Complex Analysis and Affine Algebraic Geometry

In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of them imply that the manifold in question is an Oka–Forstnerič manifold. This important notion has also recently merged from the intensive studies around the homotopy principle in Complex Analysis. This homotopy principle, which goes back to the 1930s, has had an enormous impact on the development of the area of Several Complex Variables and the number of its applications is constantly growing. In this overview chapter we present three classes of properties: (1) density property, (2) flexibility, and (3) Oka–Forstnerič. For each class we give the relevant definitions, its most significant features and explain the known implications between all these properties. Many difficult mathematical problems could be solved by applying the developed theory, we indicate some of the most spectacular ones.

Higher order parametric excitation modes for spaceborne quadrupole mass spectrometers

This paper describes a technique to significantly improve upon the mass peak shape and mass resolution of spaceborne quadrupolemass spectrometers (QMSs) through higher order auxiliary excitation of the quadrupole field. Using a novel multiresonant tank circuit, additional frequency components can be used to drive modulating voltages on the quadrupole rods in a practical manner, suitable for both improved commercial applications and spaceflight instruments. Auxiliary excitation at frequencies near twice that of the fundamental quadrupole RF frequency provides the advantages of previously studied parametric excitation techniques, but with the added benefit of increased sensed excitation amplitude dynamic range and the ability to operate voltage scan lines through the center of upper stability islands. Using a field programmable gate array, the amplitudes and frequencies of all QMS signals are digitally generated and managed, providing a robust and stable voltage control system. These techniques are experimentally verified through an interface with a commercial Pfeiffer QMG422 quadrupole rod system. When operating through the center of a stability island formed from higher order auxiliary excitation, approximately 50% and 400% improvements in 1% mass resolution and peak stability were measured, respectively, when compared with traditional QMS operation. Although tested with a circular rod system, the presented techniques have the potential to improve the performance of both circular and hyperbolic rod geometry QMS sensors.