Computationally Tractable Riemannian Manifolds for Graph Embeddings

Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic geometry. However, going beyond embedding spaces of constant sectional curvature, while potentially more representationally powerful, proves to be challenging as one can easily lose the appeal of computationally tractable tools such as geodesic distances or Riemannian gradients. Here, we explore computationally efficient matrix manifolds, showcasing how to learn and optimize graph embeddings in these Riemannian spaces. Empirically, we demonstrate consistent improvements over Euclidean geometry while often outperforming hyperbolic and elliptical embeddings based on various metrics that capture different graph properties. Our results serve as new evidence for the benefits of non-Euclidean embeddings in machine learning pipelines.Comment: Submitted to the Thirty-fourth Conference on Neural Information Processing System

The Holographic Entropy Cone

We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory

Digital mixing consoles: parallel architectures and taskforce scheduling strategies

This thesis is concerned specifically with the implementation of large-scale professional DMCs. The design of such multi-DSP audio products is extremely challenging: one cannot simply lash together n DSPs and obtain /7-times the performance of a sole device. M-P models developed here show that topology and IPC mechanisms have critical design implications. Alternative processor technologies are investigated with respect to the requirements of DMC architectures. An extensive analysis of M-P topologies is undertaken using the metrics provided by the TPG tool. Novel methods supporting DSP message-passing connectivity lead to the development of a hybrid audio M-P (HYMIPS) employing these techniques. A DMC model demonstrates the impact of task allocation on ASP M-P architectures. Five application-specific heuristics and four static-labelling schemes are developed for scheduling console taskforces on M-Ps. An integrated research framework and DCS engine enable scheduling strategies to be analysed with regard to the DMC problem domain. Three scheduling algorithms — CPM, DYN and AST — and three IPC mechanisms — FWE, NSL and NML — are investigated. Dynamic-labelling strategies and mix-bus granularity issues are further studied in detail. To summarise, this thesis elucidates those topologies, construction techniques and scheduling algorithms appropriate to professional DMC systems

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

The Design of Cube Calculus Machine Using Sram-Based Fpga Reconfigurable Hardware Dec’s Perle-1 Board

Presented in this thesis are new approaches to column compatibility checking and column-based input/output encoding for Curtis decompositions of switching functions. These approaches can be used in Curtis-type functional decomposition programs for applications in several scientific disciplines. Examples of applications are: minimization of combinational and sequential logic) mapping of logic functions to programmable logic devices such as CPLDs, MPGAs, and FPGAs, data encryption, data compression, pattern recognition) and image refinement. Presently, Curtis-type functional decomposition programs are used primarily for experimental purposes due to performance, quality, and compatibility issues. However) in the past few years a renewal of interest in the area of functional decomposition has resulted in significant improvements in performance and quality of multi-level decomposition programs. The goal of this thesis is to introduce algorithms that can significantly improve the performance and quality of Curtis-type decomposition programs. In doing so, it is hoped that a Curtis-type decomposition program, complete with efficient, high quality algorithms for decomposition, will be a feasible tool for use in one or more practical applications. Various testing and analyses were performed in order to evaluate the potential of algorithms presented in this thesis for use in a high quality Curtis-type decomposition program. Testing was done using a binary input, binary output Curtis-type decomposition program MULTIS/GUD. This program was implemented here at Portland State University by the Portland Oregon Logic Optimization Group

Parallel and Distributed Computing

The 14 chapters presented in this book cover a wide variety of representative works ranging from hardware design to application development. Particularly, the topics that are addressed are programmable and reconfigurable devices and systems, dependability of GPUs (General Purpose Units), network topologies, cache coherence protocols, resource allocation, scheduling algorithms, peertopeer networks, largescale network simulation, and parallel routines and algorithms. In this way, the articles included in this book constitute an excellent reference for engineers and researchers who have particular interests in each of these topics in parallel and distributed computing

Effective influences in neuronal networks : attentional modulation of effective influences underlying flexible processing and how to measure them

Selective routing of information between brain areas is a key prerequisite for flexible adaptive behaviour. It allows to focus on relevant information and to ignore potentially distracting influences. Selective attention is a psychological process which controls this preferential processing of relevant information. The neuronal network structures and dynamics, and the attentional mechanisms by which this routing is enabled are not fully clarified. Based on previous experimental findings and theories, a network model is proposed which reproduces a range of results from the attention literature. It depends on shifting of phase relations between oscillating neuronal populations to modulate the effective influence of synapses. This network model might serve as a generic routing motif throughout the brain. The attentional modifications of activity in this network are investigated experimentally and found to employ two distinct channels to influence processing: facilitation of relevant information and independent suppression of distracting information. These findings are in agreement with the model and previously unreported on the level of neuronal populations. Furthermore, effective influence in dynamical systems is investigated more closely. Due to a lack of a theoretical underpinning for measurements of influence in non-linear dynamical systems such as neuronal networks, often unsuited measures are used for experimental data that can lead to erroneous conclusions. Based on a central theorem in dynamical systems, a novel theory of effective influence is developed. Measures derived from this theory are demonstrated to capture the time dependent effective influence and the asymmetry of influences in model systems and experimental data. This new theory holds the potential to uncover previously concealed interactions in generic non-linear systems studied in a range of disciplines, such as neuroscience, ecology, economy and climatology