Wasserstein Covariance for Multiple Random Densities

A common feature of methods for analyzing samples of probability density functions is that they respect the geometry inherent to the space of densities. Once a metric is specified for this space, the Fr\'echet mean is typically used to quantify and visualize the average density from the sample. For one-dimensional densities, the Wasserstein metric is popular due to its theoretical appeal and interpretive value as an optimal transport metric, leading to the Wasserstein-Fr\'echet mean or barycenter as the mean density. We extend the existing methodology for samples of densities in two key directions. First, motivated by applications in neuroimaging, we consider dependent density data, where a $p$-vector of univariate random densities is observed for each sampling unit. Second, we introduce a Wasserstein covariance measure and propose intuitively appealing estimators for both fixed and diverging $p$, where the latter corresponds to continuously-indexed densities. We also give theory demonstrating consistency and asymptotic normality, while accounting for errors introduced in the unavoidable preparatory density estimation step. The utility of the Wasserstein covariance matrix is demonstrated through applications to functional connectivity in the brain using functional magnetic resonance imaging data and to the secular evolution of mortality for various countries.Comment: 12 pages, 4 figure

On the limits of the communication complexity technique for proving lower bounds on the size of minimal NFA’s

AbstractIn contrast to the minimization of deterministic finite automata (DFA’s), the task of constructing a minimal nondeterministic finite automaton (NFA) for a given NFA is PSPACE-complete. Moreover, there are no polynomial approximation algorithms with a constant approximation ratio for estimating the number of states of minimal NFA’s.Since one is unable to efficiently estimate the size of a minimal NFA in an efficient way, one should ask at least for developing mathematical proof methods that help to prove good lower bounds on the size of a minimal NFA for a given regular language. Here we consider the robust and most successful lower bound proof technique that is based on communication complexity. In this paper it is proved that even a strong generalization of this method fails for some concrete regular languages.“To fail” is considered here in a very strong sense. There is an exponential gap between the size of a minimal NFA and the achievable lower bound for a specific sequence of regular languages.The generalization of the concept of communication protocols is also strong here. It is shown that cutting the input word into 2O(n1/4) pieces for a size n of a minimal nondeterministic finite automaton and investigating the necessary communication transfer between these pieces as parties of a multiparty protocol does not suffice to get good lower bounds on the size of minimal nondeterministic automata. It seems that for some regular languages one cannot really abstract from the automata model that cuts the input words into particular symbols of the alphabet and reads them one by one using its input head

Risk Taking, Principal Agent Problems and Breakdown of Corporate Social Responsibility (CSR): How to Reestablish Safe-Assets and Capital Funding for Social Security?

The breakdown of the financial markets in fall 2007 and the following debt crisis in the EU has produced an enormous mistrust in financial products and the monetary system. The paper describes the background of the crisis induced by functional failures in risk management and the multifold principal agent problems existing in the financial market structures. The innovated nontransparent financial products have mixed up different risk weights and puzzled, or even fooled formerly loyal customers. Contemporaneously abundant liquidity on the international financial market accompanied by easy money policies of the Fed in the US and the ECB in the euro zone have depressed the real interest rate to zero or even negative values. Desperate investors are seeking for safe-assets, but their demand remains unsatisfied. Low real interest rates and the consequently lacking compound interest effect in the same time jeopardize private as well as public insurance schemes being dependent on capital funding: the demographic crisis becomes gloomy. Therefore, the managers of the financial markets have to reestablish CSR and to divide the markets into safe-asset areas for the usual clients and “casino” areas for those who like to play with high risks. Only with transparency and risk adequate financial products can the lost commitment be regained

Financial Markets and the Global Debt Crisis: Toward a New Architecture for A More Reliable Financial Sector

AbstractThe breakdown of the financial markets in 2007 and the ensuing debt crisis in the EU has produced enormous mistrust in financial products and the monetary system. The emergence of shadow banking also changed the behavior patterns of management so that its self-interest dominated the interests of shareholders and the other stakeholders. These false incentives led to merger processes in the financial system resulting in market structures in which single institutions became too big or too connected to fail. The empirical developments and the political counter-measures described in this article point to the fact that the macro-perspective has been dominant, neglecting individual irresponsibility and failure

Die Hydrologie des Sudd: hydrologische Untersuchungen und Auswertung des Wasserhaushaltes in den Sudd Sümpfen des Süd Sudan

This dissertation describes the hydrology of the Sudd swamps in southern Sudan, comprising a hydrologic investigation and evaluation of its water balance. The study improves historical interpretations and unveils so far unknown conditions and interdependencies in the swamp and floodplain system, considering the area morphology, vegetation dynamics, water balance, flow conditions and hydrodynamic processes in the system. The assessment is based on field works carried out in the swamps over a three year period between 2004 and 2006 as well as historical and remote sensing data. Interdependencies between morphology and hydrology are described considering the effect of ground slopes and morphological features on spill and flooding of the seasonally flooded grasslands. Bathymetric depth profiles and cross sectional depth and flow distributions have been established for the Sudds inland delta and the question of spill into the Bahr el Ghazal basin has been assessed. Vegetation dynamics in the swamp have been described and quantified assessing the extent of changes in the channel and lagoon system of the Sudd using Landsat satellite images for water body delineation. Changes in-between years and as well compared to Lake Victoria outflow data have been established and quantified; correlation was found for the largely water level dependent lagoon system. Variations in the channel system were interpreted to happen in a certain pattern but the extent of changes could not be correlated to the outflow data as they are influenced by additional, here not considered factors like wind drift and channel blockages by vegetation. The water balances of the floodplains, while controlled by river levels, were found to be dependent on a complex interaction between soil, vegetation, topography and seasonal trends in rainfall and evapotranspiration. Based on field measurements, these components have been assessed in detail and evaluated regarding their function in the seasonal cycle of flooding and drying. An analysis of the soil and evapotranspiration conditions as well as the interaction with vegetation and meteorological conditions using field and laboratory experiments was conducted. Sources, processes, flow directions and the fate of the floodwaters on both the river fed seasonal floodplains and the rainfed grasslands have been established showing that river spill is responsible for area flooding while no return flow occurs and drying is caused by evapotranspiration alone. Additionally it was found that rainfall can only cause temporary flooding in extreme events. To obtain missing flow data for important but ungauged locations, methods have been established to derive these, combining upstream flows from Lake Albert and torrential runoff derived from the Collaborative Historical African Rainfall Model (CHARM) rainfall data in the catchment between Lake Albert and Mongalla. The results provide previously unavailable flow data at Mongalla, the entry to the Sudd swamp, with a high level of confidence; data which are essential for detailed hydrological assessments of the swamp system. In addition to evaluations based on measurements, a numerical hydrodynamic assessment has been carried out with the DHI MIKE21 model. The study has established water level gradients, flow directions and velocities in the swamp as well as on the seasonal floodplains.Diese Dissertation beschreibt die Hydrologie der Sudd Sümpfe im Süd-Sudan und besteht aus einer hydrologischen Untersuchung und Auswertung der Wasserbilanz. Die Arbeit verfeinert historische Interpretationen und beschreibt bisher unbekannte Bedingungen und Zusammenhänge in den Sumpf- und Überschwemmungsgebieten unter Berücksichtigung von Morphologie, Vegetationsdynamik, Wasserbilanz, Fließbedingungen, und hydrodynamischen Prozessen. Die Untersuchungen basieren auf dreijährigen Feldarbeiten von 2004 bis 2006 sowie historischen- und Fernerkundungsdaten. Zusammenhänge zwischen der Morphologie und Hydrologie sind unter Berücksichtigung der Effekte von Gefälle und morphologischen Besonderheiten auf die Überflutungscharakteristik in den saisonal überfluteten Grassflächen beschrieben. Wassertiefenprofile, Querschnittstiefen und Fließprofile wurden für das Sudd Inland-Delta erstellt und die Frage nach Überlauf in das Bahr el Ghazal Becken untersucht. Die Vegetationsdynamik in den Sümpfen wurde durch Untersuchungen von Veränderungen des Kanal- und Lagunensystems beschrieben und quantifiziert; Die Untersuchungen basieren auf Landsat Satellitenbildern welche zur Feststellung von Veränderungen zwischen verschiedenen Jahren und im Vergleich zum Lake Victoria Ausfluss benutzt wurden. Eine Übereinstimmung für das hauptsächlich wasserspiegel¬abhängige Lagunensystem wurde gefunden. Bei Veränderungen im Kanalsystem konnte ein Änderungsmuster festgestellt werden, ein direkter Zusammenhang mit Änderungen des Lake Victoria Ausflusses wurde nicht gefunden, da noch andere, hier nicht untersuchte Faktoren wie Winddrift und Kanalblockaden durch Vegetation eine Rolle spielen. Die Wasserbilanz der Überflutungsflächen ist, obwohl grundsätzlich abhängig von Fluss-Wasserständen, von komplexen Interaktionen zwischen Boden, Vegetation, Topographie, und saisonalen Trends von Niederschlag und Evapotranspiration bestimmt. Diese Komponenten wurden, basierend auf Feldmessungen, detailliert untersucht und bezüglich ihrer Funktion im saisonalen Überflutungs- und Trocknungskreislauf ausgewertet. Eine Analyse von Boden und Evapotranspiration und deren Interaktion mit der Vegetation und meteorologischen Bedingungen wurde unter Nutzung von Feld- und Laborexperimenten durchgeführt. Ursprung, Prozesse, Fließrichtungen und Verbleib des Wassers auf sowohl den saisonalen Überflutungs-flächen sowie den regengespeisten Grasebenen wurden festgestellt. Die Ergebnisse zeigen, dass Flusswasser für die Überflutungen verantwortlich ist und Flutwasser nicht ablaufen, sondern die Trocknung durch Evapotranspiration erfolgt. Es wurde des Weiteren festgestellt, dass auch extreme Niederschläge nur kurzfristige Überflutungen verursachen können. Um Abflussdaten für wichtige, nicht gemessene Punkte zu erstellen, wurden Methoden zur Interpolation aus den Abflussdaten des flussaufwärts gelegenen Albert See Abflussdaten und Zuflüssen aus dem zwischen dem Albert See und Mongalla gelegenen Einzugsgebiet basierend auf CHARM (Collaborative Historical African Rainfall Model) entwickelt. Die Ergebnisse liefern neue Abflussdaten für das am Eingang der Sümpfe liegende Mongalla mit einem hohen Vertrauensniveau. Diese Daten sind für eine detaillierte hydrologische Untersuchung des Sumpfsystems unerlässlich. Zusätzlich zur Auswertung der Feldmessungen wurden numerisch-hydrodynamische Untersuchungen mit dem DHI MIKE21 Modell durchgeführt. Durch diese Studien wurden Wasserspiegelgradienten, Fließrichtungen und Strömungen in den Sümpfen und auf den saisonalen Überflutungsflächen berechnet

BMP2 and mechanical loading cooperatively regulate immediate early signalling events in the BMP pathway

<p>Abstract</p> <p>Background</p> <p>Efficient osteogenic differentiation is highly dependent on coordinated signals arising from growth factor signalling and mechanical forces. Bone morphogenetic proteins (BMPs) are secreted proteins that trigger Smad and non-Smad pathways and thereby influence transcriptional and non-transcriptional differentiation cues. Crosstalk at multiple levels allows for promotion or attenuation of signalling intensity and specificity. Similar to BMPs, mechanical stimulation enhances bone formation. However, the molecular mechanism by which mechanical forces crosstalk to biochemical signals is still unclear.</p> <p>Results</p> <p>Here, we use a three-dimensional bioreactor system to describe how mechanical forces are integrated into the BMP pathway. Time-dependent phosphorylation of Smad, mitogen-activated protein kinases and Akt in human fetal osteoblasts was investigated under loading and/or BMP2 stimulation conditions. The phosphorylation of R-Smads is increased both in intensity and duration under BMP2 stimulation with concurrent mechanical loading. Interestingly, the synergistic effect of both stimuli on immediate early Smad phosphorylation is reflected in the transcription of only a subset of BMP target genes, while others are differently affected. Together this results in a cooperative regulation of osteogenesis that is guided by both signalling pathways.</p> <p>Conclusions</p> <p>Mechanical signals are integrated into the BMP signalling pathway by enhancing immediate early steps within the Smad pathway, independent of autocrine ligand secretion. This suggests a direct crosstalk of both mechanotransduction and BMP signalling, most likely at the level of the cell surface receptors. Furthermore, the crosstalk of both pathways over longer time periods might occur on several signalling levels.</p

The Degradation of Synthetic Polymeric Scaffolds With Strut-like Architecture Influences the Mechanics-dependent Repair Process of an Osteochondral Defect in Silico

Current clinical treatments of osteochondral defects in articulating joints are frequently not successful in restoring articular surfaces. Novel scaffold-based tissue engineering strategies may help to improve current treatment options and foster a true regeneration of articulating structures. A frequently desired property of scaffolds is their ability to degrade over time and allow a full restoration of tissue and function. However, it remains largely unknown how scaffold degradation influences the mechanical stability of the tissue in a defect region and, in turn, the regenerative process. Such differing goals-supporting regeneration by degrading its own structure-can hardly be analyzed for tissue engineered constructs in clinical trials and in vivo preclinical experiments. Using an in silico analysis, we investigated the degradation-induced modifications in material and architectural properties of a scaffold with strut-like architecture over the healing course and their influence on the mechanics-dependent tissue formation in osteochondral defects. The repair outcome greatly varied depending on the degradation modality, i.e. surface erosion or bulk degradation with and without autocatalysis, and of the degradation speed, i.e. faster, equal or slower than the expected repair time. Bulk degradation with autocatalysis, independently of degradation speed, caused the mechanical failure of the scaffold prior to osteochondral defect repair and was thereby deemed inappropriate for further application. On the other hand, scaffolds with strut-like architecture degrading by both surface erosion and bulk degradation with slow degradation speed resulted in comparably good repair outcomes, thereby indicating such degradation modalities as favorable for the application in osteochondral defects