Computational Utilities for the Game of Simplicial Nim

Simplicial nim games, a class of impartial games, have very interesting mathematical properties. Winning strategies on a simplicial nim game can be determined by the set of positions in the game whose Sprague-Grundy values are zero (also zero positions). In this work, I provide two major contributions to the study of simplicial nim games. First, I provide a modern and efficient implementation of the Sprague-Grundy function for an arbitrary simplicial complex, and discuss its performance and scope of viability. Secondly, I provide a method to find a simple mathematical expression to model that function if it exists. I show the effectiveness of this method on determining mathematical expressions that classify the set of zero positions onseveral simplicial nim games

Deep Point Correlation Design

Designing point patterns with desired properties can require substantial effort, both in hand-crafting coding and mathematical derivation. Retaining these properties in multiple dimensions or for a substantial number of points can be challenging and computationally expensive. Tackling those two issues, we suggest to automatically generate scalable point patterns from design goals using deep learning. We phrase pattern generation as a deep composition of weighted distance-based unstructured filters. Deep point pattern design means to optimize over the space of all such compositions according to a user-provided point correlation loss, a small program which measures a pattern’s fidelity in respect to its spatial or spectral statistics, linear or non-linear (e. g., radial) projections, or any arbitrary combination thereof. Our analysis shows that we can emulate a large set of existing patterns (blue, green, step, projective, stair, etc.-noise), generalize them to countless new combinations in a systematic way and leverage existing error estimation formulations to generate novel point patterns for a user-provided class of integrand functions. Our point patterns scale favorably to multiple dimensions and numbers of points: we demonstrate nearly 10 k points in 10-D produced in one second on one GPU. All the resources (source code and the pre-trained networks) can be found at https://sampling.mpi-inf.mpg.de/deepsampling.html

Imaging Discontinuities in the Lithospheric Mantle Using a New, Automated Ps and Sp Receiver Function Workflow

Postponed access: the file will be accessible after 2022-11-17Over the last decades, the receiver function technique has been widely established as a standard tool for surveying sharp changes in elastic properties of the Earth’s crust and upper mantle. To date, very few studies have attempted to use receiver functions for global imaging. To overcome the lack of toolsets for global receiver function imaging, I have developed PyGLImER - a Python-based software suite capable of creating global images from both P-to-S and S-to-P converted teleseismic waves via a comprehensive receiver function workflow. In this thesis, I discuss the functionalities of PyGLImER and demonstrate its efficiency, effectiveness, and robustness on synthetic and real earthquake data examples. I show images from receiver functions, binned and stacked by conversion point, from four regions, one of which - North America - is the focus of a more thorough discussion. The receiver function survey of the North American continent presented here is of unprecedented size resulting in high-resolution images which allow to accurately constrain the depth of the cratonic lithosphere-asthenosphere boundary, make new observations of a positive correlation between the number of midlithospheric discontinuities (MLD) and the age of the lithosphere, and identify a sharp transition from the Proterozoic belts dominated by dipping structures to Archean cratons dominated by horizontal and subhorizontal MLDs. Those observations lead me to make the following hypotheses: (1) Thick continental lithosphere is formed by cyclic (i.e., periodic) processes. (2) In hotter Archean times, the formation of continents was dominated by plume-induced mechanisms (subcretion) causing horizontal MLDs, whereas, in the later Precambrian, the dominance shifted towards subduction accretion. (3) Considering (1) and (2), I deem MLDs to be caused by layers of frozen melt as previously suggested by petrological studies.Master's Thesis in Earth ScienceGEOV399MAMN-GEO

Engineering aperiodic spiral order for photonic-plasmonic device applications

Thesis (Ph.D.)--Boston UniversityDeterministic arrays of metal (i.e., Au) nanoparticles and dielectric nanopillars (i.e., Si and SiN) arranged in aperiodic spiral geometries (Vogel's spirals) are proposed as a novel platform for engineering enhanced photonic-plasmonic coupling and increased light-matter interaction over broad frequency and angular spectra for planar optical devices. Vogel's spirals lack both translational and orientational symmetry in real space, while displaying continuous circular symmetry (i.e., rotational symmetry of infinite order) in reciprocal Fourier space. The novel regime of "circular multiple light scattering" in finite-size deterministic structures will be investigated. The distinctive geometrical structure of Vogel spirals will be studied by a multifractal analysis, Fourier-Bessel decomposition, and Delaunay tessellation methods, leading to spiral structure optimization for novel localized optical states with broadband fluctuations in their photonic mode density. Experimentally, a number of designed passive and active spiral structures will be fabricated and characterized using dark-field optical spectroscopy, ellipsometry, and Fourier space imaging. Polarization-insensitive planar omnidirectional diffraction will be demonstrated and engineered over a large and controllable range of frequencies. Device applications to enhanced LEDs, novel lasers, and thin-film solar cells with enhanced absorption will be specifically targeted. Additionally, using Vogel spirals we investigate the direct (i.e. free space) generation of optical vortices, with well-defined and controllable values of orbital angular momentum, paving the way to the engineering and control of novel types of phase discontinuities (i.e., phase dislocation loops) in compact, chip-scale optical devices. Finally, we report on the design, modeling, and experimental demonstration of array-enhanced nanoantennas for polarization-controlled multispectral nanofocusing, nanoantennas for resonant near-field optical concentration of radiation to individual nanowires, and aperiodic double resonance surface enhanced Raman scattering substrates

Advancing Operating Systems via Aspect-Oriented Programming

Operating system kernels are among the most complex pieces of software in existence to- day. Maintaining the kernel code and developing new functionality is increasingly compli- cated, since the amount of required features has risen significantly, leading to side ef fects that can be introduced inadvertedly by changing a piece of code that belongs to a completely dif ferent context. Software developers try to modularize their code base into separate functional units. Some of the functionality or “concerns” required in a kernel, however, does not fit into the given modularization structure; this code may then be spread over the code base and its implementation tangled with code implementing dif ferent concerns. These so-called “crosscutting concerns” are especially dif ficult to handle since a change in a crosscutting concern implies that all relevant locations spread throughout the code base have to be modified. Aspect-Oriented Software Development (AOSD) is an approach to handle crosscutting concerns by factoring them out into separate modules. The “advice” code contained in these modules is woven into the original code base according to a pointcut description, a set of interaction points (joinpoints) with the code base. To be used in operating systems, AOSD requires tool support for the prevalent procedu- ral programming style as well as support for weaving aspects. Many interactions in kernel code are dynamic, so in order to implement non-static behavior and improve performance, a dynamic weaver that deploys and undeploys aspects at system runtime is required. This thesis presents an extension of the “C” programming language to support AOSD. Based on this, two dynamic weaving toolkits – TOSKANA and TOSKANA-VM – are presented to permit dynamic aspect weaving in the monolithic NetBSD kernel as well as in a virtual- machine and microkernel-based Linux kernel running on top of L4. Based on TOSKANA, applications for this dynamic aspect technology are discussed and evaluated. The thesis closes with a view on an aspect-oriented kernel structure that maintains coherency and handles crosscutting concerns using dynamic aspects while enhancing de- velopment methods through the use of domain-specific programming languages

Compressing Labels of Dynamic XML Data using Base-9 Scheme and Fibonacci Encoding

The flexibility and self-describing nature of XML has made it the most common mark-up language used for data representation over the Web. XML data is naturally modelled as a tree, where the structural tree information can be encoded into labels via XML labelling scheme in order to permit answers to queries without the need to access original XML files. As the transmission of XML data over the Internet has become vibrant, it has also become necessary to have an XML labelling scheme that supports dynamic XML data. For a large-scale and frequently updated XML document, existing dynamic XML labelling schemes still suffer from high growth rates in terms of their label size, which can result in overflow problems and/or ambiguous data/query retrievals. This thesis considers the compression of XML labels. A novel XML labelling scheme, named “Base-9”, has been developed to generate labels that are as compact as possible and yet provide efficient support for queries to both static and dynamic XML data. A Fibonacci prefix-encoding method has been used for the first time to store Base-9’s XML labels in a compressed format, with the intention of minimising the storage space without degrading XML querying performance. The thesis also investigates the compression of XML labels using various existing prefix-encoding methods. This investigation has resulted in the proposal of a novel prefix-encoding method named “Elias-Fibonacci of order 3”, which has achieved the fastest encoding time of all prefix-encoding methods studied in this thesis, whereas Fibonacci encoding was found to require the minimum storage. Unlike current XML labelling schemes, the new Base-9 labelling scheme ensures the generation of short labels even after large, frequent, skewed insertions. The advantages of such short labels as those generated by the combination of applying the Base-9 scheme and the use of Fibonacci encoding in terms of storing, updating, retrieving and querying XML data are supported by the experimental results reported herein

Advanced semantics for accelerated graph processing

Large-scale graph applications are of great national, commercial, and societal importance, with direct use in fields such as counter-intelligence, proteomics, and data mining. Unfortunately, graph-based problems exhibit certain basic characteristics that make them a poor match for conventional computing systems in terms of structure, scale, and semantics. Graph processing kernels emphasize sparse data structures and computations with irregular memory access patterns that destroy the temporal and spatial locality upon which modern processors rely for performance. Furthermore, applications in this area utilize large data sets, and have been shown to be more data intensive than typical floating-point applications, two properties that lead to inefficient utilization of the hierarchical memory system. Current approaches to processing large graph data sets leverage traditional HPC systems and programming models, for shared memory and message-passing computation, and are thus limited in efficiency, scalability, and programmability. The research presented in this thesis investigates the potential of a new model of execution that is hypothesized as a promising alternative for graph-based applications to conventional practices. A new approach to graph processing is developed and presented in this thesis. The application of the experimental ParalleX execution model to graph processing balances continuation-migration style fine-grain concurrency with constraint-based synchronization through embedded futures. A collection of parallel graph application kernels provide experiment control drivers for analysis and evaluation of this innovative strategy. Finally, an experimental software library for scalable graph processing, the ParalleX Graph Library, is defined using the HPX runtime system, providing an implementation of the key concepts and a framework for development of ParalleX-based graph applications