Riemann-Theta Boltzmann Machine

A general Boltzmann machine with continuous visible and discrete integer valued hidden states is introduced. Under mild assumptions about the connection matrices, the probability density function of the visible units can be solved for analytically, yielding a novel parametric density function involving a ratio of Riemann-Theta functions. The conditional expectation of a hidden state for given visible states can also be calculated analytically, yielding a derivative of the logarithmic Riemann-Theta function. The conditional expectation can be used as activation function in a feedforward neural network, thereby increasing the modelling capacity of the network. Both the Boltzmann machine and the derived feedforward neural network can be successfully trained via standard gradient- and non-gradient-based optimization techniques.Comment: 29 pages, 11 figures, final version published in Neurocomputin

Implementing societal values as drivers for performance indicators to improve resilience analysis of critical infrastructures

The resilience of critical infrastructures is assessed with key performance indicators that are unavoidably based on the underlying societal values of the stakeholders. Though societal values are under constant change and critically determine the resilience management of critical infrastructures they are difficult to consider in decision-making approaches. This research presents a proof-of-concept approach to highlight the relevance of societal values for decision-making and resilience management. Previous research proposed to use abstract worldviews to solve the complex decision problem presented by the lake model, a human and nature coupled system model simulating the intricacy of societal decision problems and providing scenarios for research on decision-making under uncertainty. By replacing the abstract worldviews with a reduced set of societal values we establish a formalized relationship between the societal values and the lake model. We show that even slight changes in the societal values can lead to significantly different behavior of the lake model. Though the approach is extremely simplified it serves to highlight the sensitivity of decision problems to societal value changes

Анализ современных технологий водогазового воздействия на продуктивный пласт

Объектом исследования является оборудование для обратной закачки газа в пласт с целью увеличения нефтеотдачи а также утилизации попутного нефтяного газа. Цель работы – анализ эффективности внедрения новой технологической схемы по подготовке водогазовой смеси для закачки в пласт. В выпускной квалификационной работе приведены сведения о современном состоянии технологии обратной закачки газа в пласт. На основе промышленных испытаний на месторождениях и лабораторных исследований были проанализированы технологические схемы закачки водогазовой смеси в пласт с целью увеличения нефтеотдачи. Рассчитано устьевое давление необходимое для закачки раннее подготовленной смеси воды, газа. Приведены экономические расчеты, подтверждающие положительный эффект предлагаемой технологической схемы.Object of a research is the equipment for the return pumping gas in layer for the purpose of increase in oil recovery and also utilization of associated petroleum gas. The work purpose – the analysis of efficiency of introduction of the new technological scheme on preparation of water gas mix for downloading in layer. In final qualification work data on the current state of technology of the return pumping gas are provided to layer. On the basis of industrial tests on fields and laboratory researches technological schemes of pumping water gas mix in layer for the purpose of increase in oil recovery have been analysed

Knee-Deep in Two "bathtubs'': Extending Holling's Ecological Resilience Concept for Critical Infrastructure Modeling and Applying It to an Offshore Wind Farm

Multistability is a common phenomenon which naturally occurs in complex networks. Many engineered infrastructures can be represented as complex networks of interacting components and sub-systems which possess the tendency to exhibit multistability. For analyzing infrastructure resilience, it thus seems fitting to consider a conceptual framework which incorporates the phenomenon of multistability – the ecological resilience provides such a framework. However, we note that the ecological resilience misses some aspects of infrastructure resilience. We therefore propose to complement the concept by two model extensions which consider the generation of perturbations to the infrastructure service and the remedial actions of service restoration after regime shifts. The result is a three-layer framework for modeling infrastructure resilience. We demonstrate this framework in an exemplary disturbance scenario in an offshore wind farm. Based on this use case, we further demonstrate that infrastructure resilience can benefit a lot from the notion of multistability

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.In the past years, several so far unknown phenomena - such as the existence of different pre-nucleation structures - have been observed experimentally, and have generated a new understanding of the processes that occur at the molecular scale during nucleation and growth of crystals. The implications that pre-nucleation structures might have in the process of biomineralisation are not yet well-understood. The mechanisms, by which biomolecular modifiers such as peptides might interact with pre-nucleation structures and thus influence the nucleation process of minerals, are numerous. Molecular simulations are well suited for the analysis of the formation of pre-nucleation structures in the presence of modifiers. This thesis presents an approach to study the interactions of peptides with the solvated constituents of the forming crystals by means of Molecular Dynamics simulations. rnAs a first step towards informative simulations, the quality of existing forcefields with respect to the description of oligoglutamates interacting with calcium ions in aqueous solution was tested. It was found that large discrepancies between well-established forcefields exist, and that non of the tested forcefields gave a realistic description of the ion-pairing of these complex ions. Therefore, a strategy to optimise existing biomolecular forcefields in this respect was developed and it was found that relatively small changes in the parameters of the ion–peptide van-der-Waals interactions were sufficient to obtain a reliable model for the system of interest.rnThe comprehensive sampling of the phase space of the systems is particularly challenging due to the large number of degrees of freedom and the strong interactions between calcium ions and glutamate in solution. The Biasing Potential Replica Exchange Molecular Dynamics method was therefore adapted to the enhanced sampling of oligoglutamates, and peptides of different chain lengths were simulated in the presence of calcium ions. With the help of the sketch-map analysis method numerous stable ion–peptide clusters, which might affect the formation of pre-nucleation structures, were identified from these simulations. Depending on the chain length of the peptide, these clusters exhibit characteristic distances between the calcium ions. These distances resemble some of the distances between calcium ions in those phases of calcium oxalate crystals, which are grown in the presence of oligoglutamates. The analogy of distances between calcium ions in solvated ion–peptide clusters and in calcium oxalate crystals might be interpreted as an indication for the importance of ion–peptide clusters in the nucleation and growth of biominerals and it is a possible explanation for the ability of oligoglutamates to influence the phase of the forming crystals, as it has been observed in experiments

Riemann-Theta Boltzmann Machine

A general Boltzmann machine with continuous visible and discrete integer valued hidden states is introduced. Under mild assumptions about the connection matrices, the probability density function of the visible units can be solved for analytically, yielding a novel parametric density function involving a ratio of Riemann-Theta functions. The conditional expectation of a hidden state for given visible states can also be calculated analytically, yielding a derivative of the logarithmic Riemann-Theta function. The conditional expectation can be used as activation function in a feedforward neural network, thereby increasing the modelling capacity of the network. Both the Boltzmann machine and the derived feedforward neural network can be successfully trained via standard gradient- and non-gradient-based optimization techniques