Fourier Neural Solver for large sparse linear algebraic systems

Large sparse linear algebraic systems can be found in a variety of scientific and engineering fields, and many scientists strive to solve them in an efficient and robust manner. In this paper, we propose an interpretable neural solver, the Fourier Neural Solver (FNS), to address them. FNS is based on deep learning and Fast Fourier transform. Because the error between the iterative solution and the ground truth involves a wide range of frequency modes, FNS combines a stationary iterative method and frequency space correction to eliminate different components of the error. Local Fourier analysis reveals that the FNS can pick up on the error components in frequency space that are challenging to eliminate with stationary methods. Numerical experiments on the anisotropy diffusion equation, convection-diffusion equation, and Helmholtz equation show that FNS is more efficient and more robust than the state-of-the-art neural solver.Comment: 15 pages, 10 figure

Sound Patterns in Mandarin Recycling Repair

The objective of the present research is to investigate the ways in which Mandarin interlocutors utilize prosodic resources as part of the means to achieve interactional actions and sequential-organization in natural conversation. By approaches of interactional prosody and conversational phonetics toward the analysis of sound realization of Mandarin repair in natural conversation, this study provides a preliminary exploration on how the combination of detailed prosodic features forms various sound patterns in reflecting the interactional aspect and sequential organization of Mandarin conversation. The current study examines the particular example of recycling repair, defined as “a repeat of part of a conversational turn,” among all methods used in accomplishing Mandarin same-turn self-repair. The data corpus consists of 260 cases of recycling repair culled from a collection of both video- and audio-taped naturally occurring Mandarin conversation. For each recycling, acoustic measurements, including duration, pitch, silence, cut-off and lengthening were carried out by using Praat. Additional judgments would be made based on the analyst’s impressionistic interpretation of these acoustic cues. After taking measurements, the results were compared and the sound patterns that emerged from recyclings of the same sound manifestation were identified. By a qualitative case-study methodology, this thesis reports 6 sound patterns and 3 sub-patterns based on 112 cases of Mandarin recyclings selected. The findings from the current research highlight the interaction-specific, sequence-specific, and function-specific examples of recyclings in relation to the use of the 6 main prosodic patterns. 3 sub-patterns that share some similarity with 2 of the 6 sound patterns in terms of interactional function were further identified. The result from the current exploratory work on the correlation between sound patterns in Mandarin recyclings and interaction contributes significantly to an interdisciplinary study that focuses on broadening the interactional linguistic theory by paying close attention to the sound patterns in natural conversation

Formation and transportation of sand-heap in an inclined and vertically vibrated container

We report the experimental findings of formation and motion of heap in granular materials in an inclined and vertically vibrated container. We show experimentally how the transport velocity of heap up container is related to the driving acceleration as well as the driving frequency of exciter. An analogous experiment was performed with a heap-shaped Plexiglas block. We propose that cohesion force resulted from pressure gradient in ambient gas plays a crucial role in enhancing and maintaining a heap, and ratchet effect causes the movement of the heap. An equation which governs the transport velocity of the heap is presented.Comment: 9 pages, 5 figures, submitted to PR