Weyl-Heisenberg Frame Wavelets with Basic Supports

Let $a$, $b$ be two fixed non-zero constants. A measurable set $E\subset \mathbb{R}$ is called a Weyl-Heisenberg frame set for $(a, b)$ if the function $g=\chi_{E}$ generates a Weyl-Heisenberg frame for $L^2(\mathbb{R})$ under modulates by $b$ and translates by $a$, i.e., $\{e^{imbt}g(t-na\}_{m,n\in\mathbb{Z}}$ is a frame for $L^2(\mathbb{R})$. It is an open question on how to characterize all frame sets for a given pair $(a,b)$ in general. In the case that $a=2\pi$ and $b=1$, a result due to Casazza and Kalton shows that the condition that the set $F=\bigcup_{j=1}^{k}([0,2\pi)+2n_{j}\pi)$ (where $\{n_{1}<n_{2}<...<n_{k}\}$ are integers) is a Weyl-Heisenberg frame set for $(2\pi,1)$ is equivalent to the condition that the polynomial $f(z)=\sum_{j=1}^{k}z^{n_{j}}$ does not have any unit roots in the complex plane. In this paper, we show that this result can be generalized to a class of more general measurable sets (called basic support sets) and to set theoretical functions and continuous functions defined on such sets.Comment: 11 pages, 2 figure

From Weyl-Heisenberg Frames to Infinite Quadratic Forms

Let $a$, $b$ be two fixed positive constants. A function $g\in L^2({\mathbb R})$ is called a \textit{mother Weyl-Heisenberg frame wavelet} for $(a,b)$ if $g$ generates a frame for $L^2({\mathbb R})$ under modulates by $b$ and translates by $a$, i.e., $\{e^{imbt}g(t-na\}_{m,n\in\mathbb{Z}}$ is a frame for $L^2(\mathbb{R})$. In this paper, we establish a connection between mother Weyl-Heisenberg frame wavelets of certain special forms and certain strongly positive definite quadratic forms of infinite dimension. Some examples of application in matrix algebra are provided

Stability and electronic properties of small BN nanotubes

We report the stability and electronic structures of the boron nitride nanotubes (BNNTs) with diameters below 4 A by semi-empirical quantum mechanical molecular dynamics simulations and ab initio calculations. Among them (3,0), (3,1), (2,2), (4,0), (4,1) and (3,2) BNNTs can be stable well over room temperature. These small BNNTs become globally stable when encapsulated in a larger BNNT. It is found that the energy gaps and work functions of these small BNNTs are strongly dependent on their chirality and diameters. The small zigzag BNNTs become desirable semiconductors and have peculiar distribution of nearly free electron states due to strong hybridization effect. When such a small BNNT is inserted in a larger one, the energy gap of the formed double-walled BNNT can even be much reduced due to the coupled effect of wall buckling difference and NFE-pi hybridization.Comment: 28 pages, 9 figures, 1 tabl

Projected Performance Advantage of Multilayer Graphene Nanoribbon as Transistor Channel Material

The performance limits of the multilayer graphene nanoribbon (GNR) field-effect transistor (FET) are assessed and compared to those of monolayer GNR FET and carbon nanotube (CNT) FET. The results show that with a thin high-k gate insulator and reduced interlayer coupling, multilayer GNR FET can significantly outperform its CNT counterpart with a similar gate and bandgap in terms of the ballistic on-current. In the presence of optical phonon scattering, which has a short mean free path in the graphene-derived nanostructures, the advantage of the multilayer GNRFET is even more significant. The simulation results indicate multilayer GNRs with incommensurate non-AB stacking and weak interlayer coupling are the best candidate for high performance GNR FETs.Comment: 22 pages, 6 figure

Production of the Extreme-Ultraviolet Late Phase of an X Class Flare in a Three-Stage Magnetic Reconnection Process

We report observations of an X class flare on 2011 September 6 by the instruments onboard the Solar Dynamics Observatory (SDO). The flare occurs in a complex active region with multiple polarities. The Extreme-Ultraviolet (EUV) Variability Experiment (EVE) observations in the warm coronal emission reveal three enhancements, of which the third one corresponds to an EUV late phase. The three enhancements have a one-to-one correspondence to the three stages in flare evolution identified by the spatially-resolved Atmospheric Imaging Assembly (AIA) observations, which are characterized by a flux rope eruption, a moderate filament ejection, and the appearance of EUV late phase loops, respectively. The EUV late phase loops are spatially and morphologically distinct from the main flare loops. Multi-channel analysis suggests the presence of a continuous but fragmented energy injection during the EUV late phase resulting in the warm corona nature of the late phase loops. Based on these observational facts, We propose a three-stage magnetic reconnection scenario to explain the flare evolution. Reconnections in different stages involve different magnetic fields but show a casual relationship between them. The EUV late phase loops are mainly produced by the least energetic magnetic reconnection in the last stage.Comment: 6 pages, 4 figures, 1 table. Accepted for Publication in ApJ

Deep Neural Network Embeddings with Gating Mechanisms for Text-Independent Speaker Verification

In this paper, gating mechanisms are applied in deep neural network (DNN) training for x-vector-based text-independent speaker verification. First, a gated convolution neural network (GCNN) is employed for modeling the frame-level embedding layers. Compared with the time-delay DNN (TDNN), the GCNN can obtain more expressive frame-level representations through carefully designed memory cell and gating mechanisms. Moreover, we propose a novel gated-attention statistics pooling strategy in which the attention scores are shared with the output gate. The gated-attention statistics pooling combines both gating and attention mechanisms into one framework; therefore, we can capture more useful information in the temporal pooling layer. Experiments are carried out using the NIST SRE16 and SRE18 evaluation datasets. The results demonstrate the effectiveness of the GCNN and show that the proposed gated-attention statistics pooling can further improve the performance.Comment: 5 pages, 3 figures, submitted to INTERSPEECH 201

Multi-Task Learning with High-Order Statistics for X-vector based Text-Independent Speaker Verification

The x-vector based deep neural network (DNN) embedding systems have demonstrated effectiveness for text-independent speaker verification. This paper presents a multi-task learning architecture for training the speaker embedding DNN with the primary task of classifying the target speakers, and the auxiliary task of reconstructing the first- and higher-order statistics of the original input utterance. The proposed training strategy aggregates both the supervised and unsupervised learning into one framework to make the speaker embeddings more discriminative and robust. Experiments are carried out using the NIST SRE16 evaluation dataset and the VOiCES dataset. The results demonstrate that our proposed method outperforms the original x-vector approach with very low additional complexity added.Comment: 5 pages,2 figures, submitted to INTERSPEECH 201

Statistical Learning Based Congestion Control for Real-time Video Communication

With the increasing demands on interactive video applications, how to adapt video bit rate to avoid network congestion has become critical, since congestion results in self-inflicted delay and packet loss which deteriorate the quality of real-time video service. The existing congestion control is hard to simultaneously achieve low latency, high throughput, good adaptability and fair bandwidth allocation, mainly because of the hardwired control strategy and egocentric convergence objective. To address these issues, we propose an end-to-end statistical learning based congestion control, named Iris. By exploring the underlying principles of self-inflicted delay, we reveal that congestion delay is determined by sending rate, receiving rate and network status, which inspires us to control video bit rate using a statistical-learning congestion control model. The key idea of Iris is to force all flows to converge to the same queue load, and adjust the bit rate by the model. All flows keep a small and fixed number of packets queuing in the network, thus the fair bandwidth allocation and low latency are both achieved. Besides, the adjustment step size of sending rate is updated by online learning, to better adapt to dynamically changing networks. We carried out extensive experiments to evaluate the performance of Iris, with the implementations of transport layer (UDP) and application layer (QUIC) respectively. The testing environment includes emulated network, real-world Internet and commercial LTE networks. Compared against TCP flavors and state-of-the-art protocols, Iris is able to achieve high bandwidth utilization, low latency and good fairness concurrently. Especially over QUIC, Iris is able to increase the video bitrate up to 25%, and PSNR up to 1dB

On the Nature of the Extreme-Ultraviolet Late Phase of Solar Flares

The extreme-ultraviolet (EUV) late phase of solar flares is a second peak of warm coronal emissions (e.g., Fe XVI) for many minutes to a few hours after the GOES soft X-ray peak. It was first observed by the EUV Variability Experiment (EVE) on board the Solar Dynamics Observatory (SDO). The late phase emission originates from a second set of longer loops (late phase loops) that are higher than the main flaring loops. It is suggested as being caused by either additional heating or long-lasting cooling. In this paper, we study the role of long-lasting cooling and additional heating in producing the EUV late phase using the "enthalpy-based thermal evolution of loops" (EBTEL) model. We find that a long cooling process in late phase loops can well explain the presence of the EUV late phase emission, but we cannot exclude the possibility of additional heating in the decay phase. Moreover, we provide two preliminary methods based on the UV and EUV emissions from the Atmospheric Imaging Assembly (AIA) on board SDO to determine whether an additional heating plays some role or not in the late phase emission. Using nonlinear force-free field modeling, we study the magnetic configuration of the EUV late phase. It is found that the late phase can be generated either in hot spine field lines associated with a magnetic null point or in large-scale magnetic loops of multipolar magnetic fields. In this paper, we also discuss why the EUV late phase is usually observed in warm coronal emissions and why the majority of flares do not exhibit an EUV late phase.Comment: Accepted for publication in Ap

Efficient and Accurate Path Cost Estimation Using Trajectory Data

Using the growing volumes of vehicle trajectory data, it becomes increasingly possible to capture time-varying and uncertain travel costs in a road network, including travel time and fuel consumption. The current paradigm represents a road network as a graph, assigns weights to the graph's edges by fragmenting trajectories into small pieces that fit the underlying edges, and then applies a routing algorithm to the resulting graph. We propose a new paradigm that targets more accurate and more efficient estimation of the costs of paths by associating weights with sub-paths in the road network. The paper provides a solution to a foundational problem in this paradigm, namely that of computing the time-varying cost distribution of a path. The solution consists of several steps. We first learn a set of random variables that capture the joint distributions of sub-paths that are covered by sufficient trajectories. Then, given a departure time and a path, we select an optimal subset of learned random variables such that the random variables' corresponding paths together cover the path. This enables accurate joint distribution estimation of the path, and by transferring the joint distribution into a marginal distribution, the travel cost distribution of the path is obtained. The use of multiple learned random variables contends with data sparseness, the use of multi-dimensional histograms enables compact representation of arbitrary joint distributions that fully capture the travel cost dependencies among the edges in paths. Empirical studies with substantial trajectory data from two different cities offer insight into the design properties of the proposed solution and suggest that the solution is effective in real-world settings.Comment: 16pages, 42 figure