Fourier Neural Operator with Learned Deformations for PDEs on General Geometries

Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is significantly faster compared to numerical solvers, on a variety of PDEs, such as fluid flows. However, the FNO uses the Fast Fourier transform (FFT), which is limited to rectangular domains with uniform grids. In this work, we propose a new framework, viz., geo-FNO, to solve PDEs on arbitrary geometries. Geo-FNO learns to deform the input (physical) domain, which may be irregular, into a latent space with a uniform grid. The FNO model with the FFT is applied in the latent space. The resulting geo-FNO model has both the computation efficiency of FFT and the flexibility of handling arbitrary geometries. Our geo-FNO is also flexible in terms of its input formats, viz., point clouds, meshes, and design parameters are all valid inputs. We consider a variety of PDEs such as the Elasticity, Plasticity, Euler's, and Navier-Stokes equations, and both forward modeling and inverse design problems. Geo-FNO is $10^5$ times faster than the standard numerical solvers and twice more accurate compared to direct interpolation on existing ML-based PDE solvers such as the standard FNO

Conceptual approach study of a 200 watt per kilogram solar array

Solar array candidate configurations (flexible rollup, flexible flat-pact, semi-rigid panel, semi-rigid flat-pack) were analyzed with particular attention to the specific power (W/kg) requirement. Two of these configurations (flexible rollup and flexible flat-pack) are capable of delivering specific powers equal to or exceeding the baseline requirement of 200 W/kg. Only the flexible rollup is capable of in-flight retraction and subsequent redeployment. The wrap-around contact photovoltaic cell configuration has been chosen over the conventional cell. The demand for ultra high specific power forces the selection of ultra-thin cells and cover material. Based on density and mass range considerations, it was concluded that 13 micrometers of FEP Teflon is sufficient to protect the cell from a total proton fluency of 2(10 to the 12th power) particles/sq cm over a three-year interplanetary mission. The V-stiffened, lattice boom deployed, flexible substrate rollup array holds the greatest promise of meeting the baseline requirements set for this study

Hands-On with NE STEM 4U: For budding STEMers in grades 4-8

Character Biographies 5 Chemistry: The Crystal Tree 10 Biology: Fruitful DNA 15 • Honey Purity Test 22 • Human DNA Extraction 26 • Model Cell 32 • Stethoscopes and Heart Rate 36 Engineering: Build a Catapult 41 • Building Bridges 47 Physics: Battling Balloons 51 • Balloon Popping 57 • Divin\u27 Challenge 60 • Life Jackets and Buoyancy 65 • Simple Circuits 69 • Newton\u27s Tower 75 Geology: Aquifers and Artesian Wells 80 • The Center of the Earth 84 • Mapping and Location Intelligence 88 • Seismology and Earthquakes 92 • Volcanoes 98 Mathematics: Hexaflexagons 102 • Stick Puzzle 107 Stem EXTRAS: Cloud Formation 110 • Nervous about Neurons 113 • Constellations 118 • Fish Supply 128 • Ecology 143 • Genealogy 151 • Play Dough Liaisons 159 • NE STEM 4U FIND IT game 16

Generic Project Plan for a Mobile Robotics System

This thesis discussed the mobile land robots for the robotic competitions. The topics discussed in this thesis are robotic systems, mobile land robots, robot competitions, and example of robot designs. Question-answer sections are added to help understand the requirements to build the robot. Examples include three different teams who participated in different robotic competitions to provide a context for robotic competitions. The thesis was divided into the five chapters. The first and second chapters explained the different kind of robotics systems, and opportunities. The focus of the information was the mobile land robots, which was explained under the third chapter, mobile land robots. The aim of the thesis was to guide those who want to design, build, and compete in the mobile robot competition. As a result, the information from various resources been gathered and has been given a form of thesis to help individuals or group of individuals to guide them through the robotic competitions

Testing Convexity and Acyclicity, and New Constructions for Dense Graph Embeddings

Property testing, especially that of geometric and graph properties, is an ongoing area of research. In this thesis, we present a result from each of the two areas. For the problem of convexity testing in high dimensions, we give nearly matching upper and lower bounds for the sample complexity of algorithms have one-sided and two-sided error, where algorithms only have access to labeled samples independently drawn from the standard multivariate Gaussian. In the realm of graph property testing, we give an improved lower bound for testing acyclicity in directed graphs of bounded degree. Central to the area of topological graph theory is the genus parameter, but the complexity of determining the genus of a graph is poorly understood when graphs become nearly complete. We summarize recent progress in understanding the space of minimum genus embeddings of such dense graphs. In particular, we classify all possible face distributions realizable by minimum genus embeddings of complete graphs, present new constructions for genus embeddings of the complete graphs, and find unified constructions for minimum triangulations of surfaces

Geostatistical evaluation of the eastern ore field one (EF1) orebody, Rosh Pinah zinc mine, Namibia

A Dissertation submitted in fulfilment of the requirements for the degree of Master of Science in Engineering to the Faculty of Engineering and the Built Environment, School of Mining Engineering, University of the Witwatersrand, Johannesburg, 2018The geometry, size and quality of a deposit are key parameters required for decision-making regarding mining methods, capital investments or divestments, economic viability and processing methods. The dissertation uses a quantitative approach to assess three geological modelling methods for orebody geometry. It applies Principal Components Analysis (PCA) in order to understand the variability and correlation in the data. The dissertation aims to determine the significance of increasing the composite size to 3 m for grade estimation and to estimate the tonnes and grades of the Eastern Ore Field 1 in-situ resource as on 31 December 2016. A MineSight, a Leapfrog and a hybrid of MineSight and Leapfrog modelling method were assessed, aiming to reduce the modelling time. The Minesight and Leapfrog hybrid model is recommended for modelling complex sedimentary exhalative deposits. The PCA was carried out using Matlab. Based on the correlation of 0.998, the first principal component increases with increasing Ag, Zn and Pb and it correlates most strongly with Ag. The second principal component increases with Zn, with a correlation of 0.985. With a correlation of 0.927, the third component increases with Mg. A 3 m composite size is recommended for estimating EF1 because the generated block-model estimates have lower means, standard deviations, variances and numbers of extreme outliers. The 3 m composite size is closer to the SMU at Rosh Pinah, and produces a better block estimate than 1.5 m composites, the later gives more tonnes and higher grade due to the volume-variance effect, which ultimately leads to overestimation of the mineral deposit. The total in-situ EF1 resource estimated using the Ordinary Kriging interpolation method as on 31 December 2016 was 814,100 tonnes at 8.58% Zn, 3.19% Pb and 79.22 ppm Ag.MT201

New Algorithms for Fast and Economic Assembly: Advances in Transcriptome and Genome Assembly

Great efforts have been devoted to decipher the sequence composition of the genomes and transcriptomes of diverse organisms. Continuing advances in high-throughput sequencing technologies have led to a decline in associated costs, facilitating a rapid increase in the amount of available genetic data. In particular genome studies have undergone a fundamental paradigm shift where genome projects are no longer limited by sequencing costs, but rather by computational problems associated with assembly. There is an urgent demand for more efficient and more accurate methods. Most recently, “hybrid” methods that integrate short- and long-read data have been devised to address this need. LazyB is a new, low-cost hybrid genome assembler. It starts from a bipartite overlap graph between long reads and restrictively filtered short-read unitigs. This graph is translated into a long-read overlap graph. By design, unitigs are both unique and almost free of assembly errors. As a consequence, only few spurious overlaps are introduced into the graph. Instead of the more conventional approach of removing tips, bubbles, and other local features, LazyB extracts subgraphs whose global properties approach a disjoint union of paths in multiple steps, utilizing properties of proper interval graphs. A prototype implementation of LazyB, entirely written in Python, not only yields significantly more accurate assemblies of the yeast, fruit fly, and human genomes compared to state-of-the-art pipelines, but also requires much less computational effort. An optimized C++ implementation dubbed MuCHSALSA further significantly reduces resource demands. Advances in RNA-seq have facilitated tremendous insights into the role of both coding and non-coding transcripts. Yet, the complete and accurate annotation of the transciptomes of even model organisms has remained elusive. RNA-seq produces reads significantly shorter than the average distance between related splice events and presents high noise levels and other biases The computational reconstruction remains a critical bottleneck. Ryūtō implements an extension of common splice graphs facilitating the integration of reads spanning multiple splice sites and paired-end reads bridging distant transcript parts. The decomposition of read coverage patterns is modeled as a minimum-cost flow problem. Using phasing information from multi-splice and paired-end reads, nodes with uncertain connections are decomposed step-wise via Linear Programming. Ryūtōs performance compares favorably with state-of-the-art methods on both simulated and real-life datasets. Despite ongoing research and our own contributions, progress on traditional single sample assembly has brought no major breakthrough. Multi-sample RNA-Seq experiments provide more information which, however, is challenging to utilize due to the large amount of accumulating errors. An extension to Ryūtō enables the reconstruction of consensus transcriptomes from multiple RNA-seq data sets, incorporating consensus calling at low level features. Benchmarks show stable improvements already at 3 replicates. Ryūtō outperforms competing approaches, providing a better and user-adjustable sensitivity-precision trade-off. Ryūtō consistently improves assembly on replicates, demonstrable also when mixing conditions or time series and for differential expression analysis. Ryūtōs approach towards guided assembly is equally unique. It allows users to adjust results based on the quality of the guide, even for multi-sample assembly.:1 Preface 1.1 Assembly: A vast and fast evolving field 1.2 Structure of this Work 1.3 Available 2 Introduction 2.1 Mathematical Background 2.2 High-Throughput Sequencing 2.3 Assembly 2.4 Transcriptome Expression 3 From LazyB to MuCHSALSA - Fast and Cheap Genome Assembly 3.1 Background 3.2 Strategy 3.3 Data preprocessing 3.4 Processing of the overlap graph 3.5 Post Processing of the Path Decomposition 3.6 Benchmarking 3.7 MuCHSALSA – Moving towards the future 4 Ryūtō - Versatile, Fast, and Effective Transcript Assembly 4.1 Background 4.2 Strategy 4.3 The Ryūtō core algorithm 4.4 Improved Multi-sample transcript assembly with Ryūtō 5 Conclusion & Future Work 5.1 Discussion and Outlook 5.2 Summary and Conclusio

Design, Control, and Evaluation of a Human-Inspired Robotic Eye

Schulz S. Design, Control, and Evaluation of a Human-Inspired Robotic Eye. Bielefeld: Universität Bielefeld; 2020.The field of human-robot interaction deals with robotic systems that involve humans and robots closely interacting with each other. With these systems getting more complex, users can be easily overburdened by the operation and can fail to infer the internal state of the system or its ”intentions”. A social robot, replicating the human eye region with its familiar features and movement patterns, that are the result of years of evolution, can counter this. However, the replication of these patterns requires hard- and software that is able to compete with the human characteristics and performance. Comparing previous systems found in literature with the human capabili- ties reveal a mismatch in this regard. Even though individual systems solve single aspects, the successful combination into a complete system remains an open challenge. In contrast to previous work, this thesis targets to close this gap by viewing the system as a whole — optimizing the hard- and software, while focusing on the replication of the human model right from the beginning. This work ultimately provides a set of interlocking building blocks that, taken together, form a complete end-to-end solution for the de- sign, control, and evaluation of a human-inspired robotic eye. Based on the study of the human eye, the key driving factors are identified as the success- ful combination of aesthetic appeal, sensory capabilities, performance, and functionality. Two hardware prototypes, each based on a different actua- tion scheme, have been developed in this context. Furthermore, both hard- ware prototypes are evaluated against each other, a previous prototype, and the human by comparing objective numbers obtained by real-world mea- surements of the real hardware. In addition, a human-inspired and model- driven control framework is developed out, again, following the predefined criteria and requirements. The quality and human-likeness of the motion, generated by this model, is evaluated by means of a user study. This frame- work not only allows the replication of human-like motion on the specific eye prototype presented in this thesis, but also promotes the porting and adaption to less equipped humanoid robotic heads. Unlike previous systems found in literature, the presented approach provides a scaling and limiting function that allows intuitive adjustments of the control model, which can be used to reduce the requirements set on the target platform. Even though a reduction of the overall velocities and accelerations will result in a slower motion execution, the human characteristics and the overall composition of the interlocked motion patterns remain unchanged