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Previous algorithms for decoding AG codes up to the designed distance all assumed existence of an extra rational place on the base algebraic curve. The place is used to solve the decoding problem by linear algebra over the base field of the curve. The rationality of the place is essential, and therefore AG codes supported by all rational places on the curve are excluded from the domain of applicability of the decoding algorithms. This paper presents a decoding algorithm for those AG codes using an extra place of higher degree. Hence finally all AG codes, as Goppa defined 40 years ago, are equipped with a fast decoding algorithm. [ABSTRACT FROM AUTHOR]

Many graph-based algorithms in high performance computing (HPC) use approximate solutions due to having algorithms that are computationally expensive or serial in nature. Neural acceleration, i.e., the process of speeding up approximation computation elements via artificial neural networks, is relatively new and has not focused on HPC graph-based algorithms. In this paper, we propose a starting point for applying models for neural acceleration to graph-based HPC algorithms utilizing an understanding of the connectivity computational pattern, recursive neural networks, and graph neural networks. We demonstrate these techniques on the problem related to the utility functions of sparse matrix ordering and fill-in (i.e., zero elements becoming nonzero during factorization) calculations. The problem of sparse matrix ordering is commonly used for issues related to load balancing, improving memory reuse, or reducing computational and memory costs in direct sparse linear solver methods. These utility functions are ideal for demonstration as they comprise a number of different graph-based subproblems, and thus demonstrate the usefulness of our method over a wide range. We show that we can accurately approximate the best ordering and the nonzero count of the sparse factorization matrix while speeding up the calculation by as much as $30.3\times $ over the traditional serial method.

The matrix-multiply assist (MMA) facility is the latest addition to IBM's power instruction set architecture and first shipped in the recently introduced POWER10 processor. MMA is designed to accelerate matrix–matrix operations, such as matrix multiplication and convolution, using instructions that compute the outer product of vector-register operands. Outer product computations have been used for decades in linear algebra libraries to deliver high-performance implementations of matrix operations. Such libraries use conventional single-instruction–multiple-data (SIMD) instructions to emulate outer product operations. MMA in POWER10 is the first hardware with direct support for outer product operations released in the market. MMA operates with the widest diversity of data types compared to any accelerator design currently announced. Unleashing the high-performance enabled by MMA requires careful code generation. Two key considerations for optimal MMA code performance are 1) the choice of accumulation layout when maximizing the using the accumulators and 2) the selection of matrix access order. This article shows that over 92% of peak performance in POWER10 with MMA can be achieved when the code generation makes the right choices. [ABSTRACT FROM AUTHOR]

Thomson’s multitaper method estimates the power spectrum of a signal from $N$ equally spaced samples by averaging $K$ tapered periodograms. Discrete prolate spheroidal sequences (DPSS) are used as tapers since they provide excellent protection against spectral leakage. Thomson’s multitaper method is widely used in applications, but most of the existing theory is qualitative or asymptotic. Furthermore, many practitioners use a DPSS bandwidth $W$ and number of tapers that are smaller than what the theory suggests is optimal because the computational requirements increase with the number of tapers. We revisit Thomson’s multitaper method from a linear algebra perspective involving subspace projections. This provides additional insight and helps us establish nonasymptotic bounds on some statistical properties of the multitaper spectral estimate, which are similar to existing asymptotic results. We show using $K=2NW-O(\log (NW))$ tapers instead of the traditional $2NW-O(1)$ tapers better protects against spectral leakage, especially when the power spectrum has a high dynamic range. Our perspective also allows us to derive an $\epsilon $ -approximation to the multitaper spectral estimate which can be evaluated on a grid of frequencies using $O\left({\log (NW)\log \tfrac {1}{ \epsilon }}\right)$ FFTs instead of $K=O(NW)$ FFTs. This is useful in problems where many samples are taken, and thus, using many tapers is desirable. [ABSTRACT FROM AUTHOR]

High performance and, at the same time, energy efficiency are important yet often conflicting requirements in many fields of emerging applications. Those applications range from multi-dimensional and multi-sensor digital signal processing to machine learning, such as neural network processing. Whereas conventional fixed-point and floating-point processor architectures cannot adapt to quite diverging demands related to required precision and accuracy of computations, even within a single application, e.g., in different layers of a neural network, domain-specific accelerators may be much too specific and thus rigid to cover a wide enough spectrum of applications. In this tutorial brief, we give an overview of existing processor solutions that are reconfigurable or tunable in precision or accuracy of computations. The spectrum of reviewed architectures ranges from processors with vectorizable processors over multi- and trans-precision solutions, including GPUs to any-time instruction-set processors. The latter works with a fixed precision, but the accuracy of the result of floating-point operations is encoded in the instruction word. It can thus vary from instruction to instruction. This allows realizing accuracy vs. execution time or energy tradeoffs. Subsequently, we investigate several application domains, including neural network processing, linear algebra, and approximate computing, where such emerging processor architectures can be beneficially used. [ABSTRACT FROM AUTHOR]

The operation and maintenance of infrastructure components and systems can be modeled as a Markov process, partially or fully observable. Information about the current condition can be summarized by the “inner” state of a finite state controller. When a control policy is assigned, the stochastic evolution of the system is completely described by a Markov transition function. This article applies finite state Markov chain analyses to identify relevant features of the time evolution of a controlled system. We focus on assessing if some critical conditions are reachable (or if some actions will ever be taken), in identifying the probability of these critical events occurring within a time period, their expected time of occurrence, their long-term frequency, and the probability that some events occur before others. We present analytical methods based on linear algebra to address these questions, discuss their computational complexity and the structure of the solution. The analyses can be performed after a policy is selected for a Markov decision process (MDP) or a partially observable MDP. Their outcomes depend on the selected policy and examining these outcomes can provide the decision makers with deeper understanding of the consequences of following that policy, and may also suggest revising it. [ABSTRACT FROM AUTHOR]

Contribution: In this study, an alternative educational approach for introducing quantum computing to a wider audience is highlighted. The proposed methodology considers quantum computing as a generalized probability theory rather than a field emanating from physics and utilizes quantum programming as an educational tool to reinforce the learning process. Background: Quantum computing is a topic mainly rooted in physics, and it has been gaining rapid popularity in recent years. A need for extending the educational reach to groups outside of physics has also been becoming a necessity. Intended Outcomes: This study aims to inform academics and organizations interested in introducing quantum computing to a diverse group of participants on an educational approach. It is intended that the proposed methodology would facilitate people from diverse backgrounds to enter the field. Application Design: The introductory quantum physics content is bypassed and the quantum computing concepts are introduced through linear algebra instead. Quantum programming tasks are prepared in line with the content. Pre/post-test design method and Likert scale satisfaction surveys are utilized to measure knowledge acquisition and to evaluate the perception of the learning process by the participants. Findings: Conducted pre/post-test design survey shows that there is a statistically significant increase in the basic knowledge levels of the participants on quantum computing concepts. Furthermore, no significant difference in the gain scores is observed between the participants from different STEM-related educational backgrounds. The majority of the participants were satisfied and provided positive feedback. [ABSTRACT FROM AUTHOR]