The Generalized DCell Network Structures and Their Graph Properties

DCell~\cite{guo} has been proposed as a server centric network structure for data centers. DCell can support millions of servers with high network capacity and provide good fault tolerance by only using commodity mini-switches. In this paper, we show that DCell is only a special case of a more generalized DCell structure. We give the generalized DCell construction rule and several new DCell structures. We analyze the graph properties, including the closed form of number of servers, bisection width, diameter, and symmetry, of the generalized DCell structure. Furthermore, we show that the new structures are more symmetric, have much smaller diameter, and provide much better load-balancing than the original DCell by using shortest-path routing. We demonstrate the load-balancing property of the new structures by analysis and extensive simulations.Postprint (published version

Convolutional Recurrent Neural Networks for Small-Footprint Keyword Spotting

Keyword spotting (KWS) constitutes a major component of human-technology interfaces. Maximizing the detection accuracy at a low false alarm (FA) rate, while minimizing the footprint size, latency and complexity are the goals for KWS. Towards achieving them, we study Convolutional Recurrent Neural Networks (CRNNs). Inspired by large-scale state-of-the-art speech recognition systems, we combine the strengths of convolutional layers and recurrent layers to exploit local structure and long-range context. We analyze the effect of architecture parameters, and propose training strategies to improve performance. With only ~230k parameters, our CRNN model yields acceptably low latency, and achieves 97.71% accuracy at 0.5 FA/hour for 5 dB signal-to-noise ratio.Comment: Accepted to Interspeech 201

Note on Global Regularity for 2D Oldroyd-B Fluids with Diffusive Stress

We prove global regularity of solutions of Oldroyd-B equations in 2 spatial dimensions with spatial diffusion of the polymeric stresses

Explorations in the Mathematics of Inviscid Incompressible Fluids

The main subject of this dissertation is smooth incompressible fluids. The emphasis is on the incompressible Euler equations in all of R^2 or R^3, but many of the ideas and results can also be adapted to other hydrodynamic systems, such as the Navier-Stokes or surface quasi-geostrophic (SQG) equations. A second subject is the modeling of moving contact lines and dynamic contact angles in inviscid liquid-vapor-solid systems under surface tension. The dissertation is divided into three independent parts: First, we introduce notation and prove useful identities for studying incompressible fluids in a pointwise Lagrangian sense. The main purpose is to provide a unified treatment of results scattered across the literature. Furthermore, we prove several analogs of Constantin’s local pressure formula for other nonlocal operators, such as the Biot-Savart law and Leray projection. Also, we define and study properties of a Lagrangian locally compact Abelian group in terms of which some nonlocal formulas encountered in fluid dynamics may be interpreted as convolutions. Second, we apply the algebraic theory of scalar polynomial orthogonal invariants to the incompressible Euler equations in two and three dimensions. Using this framework, we give simplified proofs of results of Chae and Vieillefosse. We also investigate other uses of orthogonal transformations, such as diagonalizing the deformation tensor along a particle trajectory, and comment on relative advantages and disadvantages. These techniques are likely to be useful in other orthogonally invariant PDE systems as well. Third, we propose an idealized inviscid liquid-vapor-solid model for the macroscopic study of moving contact lines and dynamic contact angles. Previous work mostly addresses viscous systems and frequently ignores a singular stress present when the contact angle is not at its equilibrium value. We also examine and clarify the role that disjoining pressure plays and outline a program for further research

Frequency and predictability effects on event-related potentials during reading

Effects of frequency, predictability, and position of words on event-related potentials were assessed during word-by-word sentence reading in 48 subjects in an early and in a late time window corresponding to P200 and N400. Repeated measures multiple regression analyses revealed a P200 effect in the high-frequency range; also the P200 was larger on words at the beginning and end of sentences than on words in the middle of sentences (i.e., a quadratic effect of word position). Predictability strongly affected the N400 component; the effect was stronger for low than for high-frequency words. The P200 frequency effect indicates that high-frequency words are lexically accessed very fast, independent of context information. Effects on the N400 suggest that predictability strongly moderates the late access especially of low-frequency words. Thus, contextual facilitation on the N400 appears to reflect both lexical and post-lexical stages of word recognition, questioning a strict classification into lexical and post-lexical processes