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Understanding microbiome dynamics via interpretable graph representation learning
No full textLarge-scale perturbations in the microbiome constitution are strongly correlated, whether as a driver or a consequence, with the health and functioning of human physiology. However, understanding the difference in the microbiome profiles of healthy and ill individuals can be complicated due to the large number of complex interactions among microbes. We propose to model these interactions as a time-evolving graph whose nodes are microbes and edges are interactions among them. Motivated by the need to analyse such complex interactions, we develop a method that learns a low-dimensional representation of the time-evolving graph and maintains the dynamics occurring in the high-dimensional space. Through our experiments, we show that we can extract graph features such as clusters of nodes or edges that have the highest impact on the model to learn the low-dimensional representation. This information can be crucial to identify microbes and interactions among them that are strongly correlated with clinical diseases. We conduct our experiments on both synthetic and real-world microbiome datasets
Newton's Method for Global Free Flight Trajectory Optimization
No full textGlobally optimal free flight trajectory optimization can be achieved with a combination of discrete and continuous optimization. A key requirement is that Newton's method for continuous optimization converges in a sufficiently large neighborhood around a minimizer. We show in this paper that, under certain assumptions, this is the case
Blending hydrogen into natural gas: An assessment of the capacity of the German gas grid
No full textDie europaische Gasinfrastruktur wird disruptiv in ein zukunftiges dekarbonisiertes Energiesystem verändert; ein Prozess, der angesichts der jüngsten politischen Situation beschleunigt werden muss. Mit einem wachsenden Wasserstoffmarkt wird der pipelinebasierte Transport unter Nutzung der bestehenden Erdgasinfrastruktur wirtschaftlich sinnvoll, trägt zur Erhöhung der öffentlichen Akzeptanz bei und beschleunigt den Umstellungsprozess. In diesem Beitrag wird die maximal technisch machbare Einspeisung von Wasserstoff in das bestehende deutsche Erdgastransportnetz hinsichtlich regulatorischer Grenzwerte der Gasqualität analysiert. Die Analyse erfolgt auf Basis eines transienten Tracking-Modells, das auf dem allgemeinen Pooling-Problem einschließlich Linepack aufbaut. Es zeigt sich, dass das Gasnetz auch bei strengen Grenzwerten gen ̈ugend Kapazität bietet, um für einen großen Teil der bis 2030 geplanten Erzeugungskapazität für grünen Wasserstoff als garantierter Abnehmer zu dienen.The European gas infrastructure is being disruptively transformed into a future decarbonised energy system; a process that needs to be accelerated given the recent political situation. With a growing hydrogen market, pipeline-based transport using the existing natural gas infrastructure becomes economically viable, helps to increase public acceptance and accelerates the transition process. In this paper, the maximum technically feasible feed-in of hydrogen into the existing German natural gas transport network is analysed with regard to regulatory limits of gas quality. Analysis is based on a transient tracking model that builds on the general pooling problem including linepack. It is shown that even with strict limits, the gas grid offers sufficient capacity to serve as a guaranteed customer for a large part of the green hydrogen generation capacity planned until 2030
An Extended 3D Morphable Face Model with Applications in Experimental Psychology
No full textOur faces and facial expressions are an important means of communication and social interaction. One goal of the behavioral sciences is to better understand how the features of the faces that we look at influence our behavior. These include static features like facial proportions or the shape and color of certain parts of a face which primarily constitute facial identity, as well as dynamic movements resulting from the activation of the mimic musculature. Experimental psychology provides an empirical approach to this endeavor. In experiments, participants are typically exposed to images or videos of realistic faces with specifically controlled features. By analysis of the reactions to such stimuli, conclusions can be drawn about the influence of facial features on the participants’ behavior.
Psychologists today mostly generate face stimuli with the help of digital tools. Image editing with Photoshop is highly flexible, but also time-consuming and subjective. Using tools like Psychomorph or Fantamorph is easier and more objective, but does not allow specific control over facial features. In contrast, stimulus generation with 3D Morphable Face Models (3DMMs) offers a better balance between objectivity, ease of use, and flexibility. 3DMMs are statistical models which have been determined from 3D scans of real people’s faces and facial expressions. After these training scans have been brought into correspondence, methods like principal component analysis (PCA) can be used to determine the major modes of variation of facial shape and texture in the data. Such modes typically vary the overall facial proportions, expressions, or skin color. They can be individually controlled and flexibly combined to generate new faces and facial expressions. The plausibility of the generated faces can be ensured by having the mode combinations follow the multivariate distribution of the training data.
3DMMs have been mostly used by psychologists for the generation of stimulus images of faces with neutral expression. Static and dynamic stimuli of facial expressions are also of great interest, but generation with 3DMMs is less common. A problem is that the majority
of current 3DMMs can only generate facial movements according to the six prototypic expressions of anger, disgust, fear, happiness, sadness, and surprise. More diverse or subtle expressions are often impossible. Among other reasons, this is due to the difficulty in establishing accurate correspondence in the training data. Further, the modes of most 3DMMs were created by means of PCA. These modes often lack interpretability, fail to generate facial details, and rarely provide psychologists a specific control over identity
or expression features. Some 3DMMs also generate subtle artifacts that might lead to undesired effects during face perception. They are also less realistic than faces which were designed by artistic experts for recent computer games and animated movies. Last but not least, current 3DMMs have probably not yet been used for interactive experiments in virtual reality (VR) for technical reasons.
Although they provide many advantages also beyond the generation of static or dynamic stimuli, the limitations of current 3DMMs have so far prevented a widespread usage in experimental psychology. The goal of this dissertation is to foster the creation and usage of 3DMMs in this context. To this end, we make three major contributions.
First, we describe a matching method that establishes correspondence for 3D face scans with a very high accuracy. Unlike the most commonly used methods, it transforms the facial features into a 2D intermediate representation so that they can be aligned to a reference using image registration. We perform experiments with a large database of 3D scans of faces and facial expressions showing that our method outperforms previous approaches.
Second, the 3D scans which were previously brought into correspondence are used for the creation of a 3DMM whose resolution is an order of magnitude higher than that of most existing models. We learn a variety of meaningful modes that, e.g., vary features only in specific regions of the face, or that are related to demographic factors such as ethnicity and age. Further, modes of local facial movements are established that can be flexibly combined into a large variety of expressions. We evaluate the quality of the newly created 3DMM in two experiments. Our results show its advantages over previous models, especially the higher degree of realism of dynamic stimuli of facial expressions which were created with our model.
Third, we demonstrate that 3DMMs can not only be used for the generation of stimuli. We develop two experimental methods that are readily applicable in experimental psychology. Initially, we create 3D avatar faces with our 3DMM that are readily applicable in VR.
They are used in a new open source framework for virtual mirror experiments on self-face perception. A study is conducted which demonstrates the advantages of the framework over previous methods. Furthermore, our 3DMM is used to create a method for improved control of facial asymmetry in existing stimulus photographs. We show that the method accounts for different dimensions of facial asymmetry and is less sensitive than previous approaches to extrinsic factors like the posture of the head. The different methods are evaluated in a study investigating the influence of facial asymmetry on ratings of attractiveness, femininity, and masculinity. The results indicate the benefits and validity of our method
How Many Clues To Give? A Bilevel Formulation For The Minimum Sudoku Clue Problem
No full textIt has been shown that any 9 by 9 Sudoku puzzle must contain at least 17 clues to have a unique solution. This paper investigates the more specific question: given a particular completed Sudoku grid, what is the minimum number of clues in any puzzle whose unique solution is the given grid? We call this problem the Minimum Sudoku Clue Problem (MSCP). We formulate MSCP as a binary bilevel linear program, present a class of globally valid inequalities, and provide a computational study on 50 MSCP instances of 9 by 9 Sudoku grids. Using a general bilevel solver, we solve 95\% of instances to optimality, and show that the solution process benefits from the addition of a moderate amount of inequalities. Finally, we extend the proposed model to other combinatorial problems in which uniqueness of the solution is of interest
VoronoiGraph.jl
No full textThis Package implements a variation of the Voronoi Graph Traversal algorithm by Polianskii and Pokorny [1]. It constructs a Voronoi Diagram from a set of points by performing a random walk on the graph of the vertices of the diagram. Unlike many other Voronoi implementations this algorithm is not limited to 2 or 3 dimensions and promises good performance even in higher dimensions
On the Numerical Treatment of Interlaced Target Values - Modeling, Optimization and Simulation of Regulating Valves in Gas Networks
No full textDue to the current and foreseeable shifts towards carbon dioxide neutral energy production, which will likely result in balancing fluctuating renewable energy generation by transforming power-to-gas-to-power as well as building a large-scale hydrogen transport infrastructure, the trading and transport operations of gas will become more dynamic, volatile, and hence also less predictable.
Therefore, computer-aided support in terms of rapid simulation and control optimization will further broaden its importance for gas network dispatching.
In this paper, we aim to contribute and openly publish two new mathematical models for regulators, also referred to as control valves, which together with compressors make up the most complex and involved types of active elements in gas network infrastructures.
They provide direct control over gas networks but are in turn controlled via target values, also known as set-point values, themselves.
Our models incorporate up to six dynamical target values to define desired transient states for the elements' local vicinity within the network.
That is, each pair of every two target values defines a bounding box for the inlet pressure, outlet pressure as well as the passing mass flow of gas.
In the proposed models, those target values are prioritized differently and are constantly in competition with each other, which can only be resolved dynamically at run-time of either a simulation or optimization process.
Besides careful derivation, we compare simulation and optimization results with predictions of the widely adopted commercial simulation tool SIMONE, serving as our substitute for actual real-world transport operations
Simulation-based inference for efficient identification of generative models in computational connectomics
No full textRecent advances in connectomics research enable the acquisition of increasing amounts of data about the connectivity patterns of neurons. How can we use this wealth of data to efficiently derive and test hypotheses about the principles underlying these patterns? A common approach is to simulate neuronal networks using a hypothesized wiring rule in a generative model and to compare the resulting synthetic data with empirical data. However, most wiring rules have at least some free parameters, and identifying parameters that reproduce empirical data can be challenging as it often requires manual parameter tuning. Here, we propose to use simulation-based Bayesian inference (SBI) to address this challenge. Rather than optimizing a fixed wiring rule to fit the empirical data, SBI considers many parametrizations of a rule and performs Bayesian inference to identify the parameters that are compatible with the data. It uses simulated data from multiple candidate wiring rule parameters and relies on machine learning methods to estimate a probability distribution (the 'posterior distribution over parameters conditioned on the data') that characterizes all data-compatible parameters. We demonstrate how to apply SBI in computational connectomics by inferring the parameters of wiring rules in an in silico model of the rat barrel cortex, given in vivo connectivity measurements. SBI identifies a wide range of wiring rule parameters that reproduce the measurements. We show how access to the posterior distribution over all data-compatible parameters allows us to analyze their relationship, revealing biologically plausible parameter interactions and enabling experimentally testable predictions. We further show how SBI can be applied to wiring rules at different spatial scales to quantitatively rule out invalid wiring hypotheses. Our approach is applicable to a wide range of generative models used in connectomics, providing a quantitative and efficient way to constrain model parameters with empirical connectivity data