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Yu Gu

Publications and source records attributed to Yu Gu.

At least 271 records · Page 15Linked to original sources
arXiv2018

Energy-aware Adaptive Spectrum Access and Power Allocation in LAA Networks via Lyapunov Optimization

To relieve the traffic burden and improve the system capacity, licensed-assisted access (LAA) has been becoming a promising technology to the supplementary utilization of the unlicensed spectrum. However, due to the densification of small base stations (SBSs) and the dynamic variety of the number of Wi-Fi nodes in the overlapping areas, the licensed channel interference and the unlicensed channel collision could seriously influence the Quality of Service (QoS) and the energy consumption. In this paper, jointly considering time-variant wireless channel conditions, dynamic traffic loads, and random numbers of Wi-Fi nodes, we address an adaptive spectrum access and power allocation problem that enables minimizing the system power consumption under a certain queue stability constraint in the LAA-enabled SBSs and Wi-Fi networks. The complex stochastic optimization problem is rewritten as the difference of two convex (D.C.) program in the framework of Lyapunov optimization, thus developing an online energy-aware optimal algorithm. We also characterize the performance bounds of the proposed algorithm with a tradeoff of [O(1=V ); O(V )] between power consumption and delay theoretically. The numerical results verify the tradeoff and show that our scheme can reduce the power consumption over the existing scheme by up to 72.1% under the same traffic delay.

eess.SP↗
arXiv2018

Waveform Modeling and Generation Using Hierarchical Recurrent Neural Networks for Speech Bandwidth Extension

This paper presents a waveform modeling and generation method using hierarchical recurrent neural networks (HRNN) for speech bandwidth extension (BWE). Different from conventional BWE methods which predict spectral parameters for reconstructing wideband speech waveforms, this BWE method models and predicts waveform samples directly without using vocoders. Inspired by SampleRNN which is an unconditional neural audio generator, the HRNN model represents the distribution of each wideband or high-frequency waveform sample conditioned on the input narrowband waveform samples using a neural network composed of long short-term memory (LSTM) layers and feed-forward (FF) layers. The LSTM layers form a hierarchical structure and each layer operates at a specific temporal resolution to efficiently capture long-span dependencies between temporal sequences. Furthermore, additional conditions, such as the bottleneck (BN) features derived from narrowband speech using a deep neural network (DNN)-based state classifier, are employed as auxiliary input to further improve the quality of generated wideband speech. The experimental results of comparing several waveform modeling methods show that the HRNN-based method can achieve better speech quality and run-time efficiency than the dilated convolutional neural network (DCNN)-based method and the plain sample-level recurrent neural network (SRNN)-based method. Our proposed method also outperforms the conventional vocoder-based BWE method using LSTM-RNNs in terms of the subjective quality of the reconstructed wideband speech.

cs.SD↗
arXiv2017

Moments of 2D Parabolic Anderson Model

In this note, we use the Feynman-Kac formula to derive a moment representation for the 2D parabolic Anderson model in small time, which is related to the intersection local time of planar Brownian motions.

math.PR↗
arXiv2017

Preserving Reliability to Heterogeneous Ultra-Dense Distributed Networks in Unlicensed Spectrum

This article investigates the prominent dilemma between capacity and reliability in heterogeneous ultra-dense distributed networks, and advocates a new measure of effective capacity to quantify the maximum sustainable data rate of a link while preserving the quality-of-service (QoS) of the link in such networks. Recent breakthroughs are brought forth in developing the theory of the effective capacity in heterogeneous ultra-dense distributed networks. Potential applications of the effective capacity are demonstrated on the admission control, power control and resource allocation of such networks, with substantial gains revealed over existing technologies. This new measure is of particular interest to ultra-dense deployment of the emerging fifth-generation (5G) wireless networks in the unlicensed spectrum, leveraging the capacity gain brought by the use of the unlicensed band and the stringent reliability sustained by 5G in future heterogeneous network environments.

cs.IT↗
arXiv2017

Effective Capacity of Licensed-Assisted Access in Unlicensed Spectrum for 5G: From Theory to Application

License-assisted access (LAA) is a promising technology to offload dramatically increasing cellular traffic to unlicensed bands. Challenges arise from the provision of quality-of-service (QoS) and the quantification of capacity, due to the distributed and heterogeneous nature of LAA and legacy systems (such as WiFi) coexisting in the bands. In this paper, we develop new theories of the effective capacity to measure LAA under statistical QoS requirements. A new four-state semi-Markovian model is developed to capture transmission collisions, random backoffs, and lossy wireless channels of LAA in distributed heterogeneous network environments. A closed-form expression for the effective capacity is derived to comprehensively analyze LAA. The four-state model is further abstracted to an insightful two-state equivalent which reveals the concavity of the effective capacity in terms of transmit rate. Validated by simulations, the concavity is exploited to maximize the effective capacity and effective energy efficiency of LAA, and provide significant improvements of 62.7% and 171.4%, respectively, over existing approaches. Our results are of practical value to holistic designs and deployments of LAA systems.

cs.IT↗
arXiv2017

Single-Pass PCA of Large High-Dimensional Data

Principal component analysis (PCA) is a fundamental dimension reduction tool in statistics and machine learning. For large and high-dimensional data, computing the PCA (i.e., the singular vectors corresponding to a number of dominant singular values of the data matrix) becomes a challenging task. In this work, a single-pass randomized algorithm is proposed to compute PCA with only one pass over the data. It is suitable for processing extremely large and high-dimensional data stored in slow memory (hard disk) or the data generated in a streaming fashion. Experiments with synthetic and real data validate the algorithm's accuracy, which has orders of magnitude smaller error than an existing single-pass algorithm. For a set of high-dimensional data stored as a 150 GB file, the proposed algorithm is able to compute the first 50 principal components in just 24 minutes on a typical 24-core computer, with less than 1 GB memory cost.

cs.DS↗
arXiv2016

Kardar-Parisi-Zhang equation and large deviations for random walks in weak random environments

We consider the transition probabilities for random walks in $1+1$ dimensional space-time random environments (RWRE). For critically tuned weak disorder we prove a sharp large deviation result: after appropriate rescaling, the transition probabilities for the RWRE evaluated in the large deviation regime, converge to the solution to the stochastic heat equation (SHE) with multiplicative noise (the logarithm of which is the KPZ equation). We apply this to the exactly solvable Beta RWRE and additionally present a formal derivation of the convergence of certain moment formulas for that model to those for the SHE.

math.PR↗
arXiv2016

On generalized Gaussian free fields and stochastic homogenization

We study a generalization of the notion of Gaussian free field (GFF). Although the extension seems minor, we first show that a generalized GFF does not satisfy the spatial Markov property, unless it is a classical GFF. In stochastic homogenization, the scaling limit of the corrector is a possibly generalized GFF described in terms of an "effective fluctuation tensor" that we denote by $\mathsf{Q}$. We prove an expansion of $\mathsf{Q}$ in the regime of small ellipticity ratio. This expansion shows that the scaling limit of the corrector is not necessarily a classical GFF, and in particular does not necessarily satisfy the Markov property.

math.PR↗
arXiv2016

Near-Optimal Disjoint-Path Facility Location Through Set Cover by Pairs

In this paper we consider two special cases of the "cover-by-pairs" optimization problem that arise when we need to place facilities so that each customer is served by two facilities that reach it by disjoint shortest paths. These problems arise in a network traffic monitoring scheme proposed by Breslau et al. and have potential applications to content distribution. The "set-disjoint" variant applies to networks that use the OSPF routing protocol, and the "path-disjoint" variant applies when MPLS routing is enabled, making better solutions possible at the cost of greater operational expense. Although we can prove that no polynomial-time algorithm can guarantee good solutions for either version, we are able to provide heuristics that do very well in practice on instances with real-world network structure. Fast implementations of the heuristics, made possible by exploiting mathematical observations about the relationship between the network instances and the corresponding instances of the cover-by-pairs problem, allow us to perform an extensive experimental evaluation of the heuristics and what the solutions they produce tell us about the effectiveness of the proposed monitoring scheme. For the set-disjoint variant, we validate our claim of near-optimality via a new lower-bounding integer programming formulation. Although computing this lower bound requires solving the NP-hard Hitting Set problem and can underestimate the optimal value by a linear factor in the worst case, it can be computed quickly by CPLEX, and it equals the optimal solution value for all the instances in our extensive testbed.

cs.DS↗
arXiv2016

High order correctors and two-scale expansions in stochastic homogenization

In this paper, we study high order correctors in stochastic homogenization. We consider elliptic equations in divergence form on $\mathbb{Z}^d$, with the random coefficients constructed from i.i.d. random variables. We prove moment bounds on the high order correctors and their gradients under dimensional constraints. It implies the existence of stationary correctors and stationary gradients in high dimensions. As an application, we prove a two-scale expansion of the solutions to the random PDE, which identifies the first and higher order random fluctuations in a strong sense.

math.AP↗
arXiv2016

Stationary patterns and their selection mechanism of Urban crime models with heterogeneous near-repeat victimization effect

In this paper, we study two PDEs that generalize the urban crime model proposed by Short \emph{et al}. [Math. Models Methods Appl. Sci., 18 (2008), pp. 1249-1267]. Our modifications are made under assumption of the spatial heterogeneity of both the near-repeat victimization effect and the dispersal strategy of criminal agents. We investigate pattern formations in the reaction-advection-diffusion systems with nonlinear diffusion over multi-dimensional bounded domains subject to homogeneous Neumann boundary conditions. It is shown that the positive homogeneous steady state loses its stability as the intrinsic near-repeat victimization rate $ε$ decreases and spatially nonconstant solutions emerge through bifurcation. Moreover, we find the wavemode selection mechanism through rigorous stability analysis of these nontrivial patterns, which shows that the only stable pattern must have wavenumber that maximizes the bifurcation value. Based on this wavemode selection mechanism, we will be able to precisely predict the formation of stable aggregates of the house attractiveness and criminal population density, at least when the diffusion rate $ε$ is around the principal bifurcation value. Our theoretical results also suggest that large domains support more stable aggregates than small domains. Finally, we perform extensive numerical simulations over 1D intervals and 2D squares to illustrate and verify our theoretical findings. Our numerics also include some interesting phenomena such as the merging of two interior spikes and the emerging of new spikes, etc. These nontrivial solutions can model the well observed aggregation phenomenon in urban criminal activities.

math.AP↗
arXiv2015

Scaling limit of fluctuations in stochastic homogenization

We investigate the global fluctuations of solutions to elliptic equations with random coefficients in the discrete setting. In dimension $d\geq 3$ and for i.i.d.\ coefficients, we show that after a suitable scaling, these fluctuations converge to a Gaussian field that locally resembles a (generalized) Gaussian free field. The paper begins with a heuristic derivation of the result, which can be read independently and was obtained jointly with Scott Armstrong.

math.PR↗
arXiv2015

The random Schrödinger equation: homogenization in time-dependent potentials

We analyze the solutions of the Schrödinger equation with the low frequency initial data and a time-dependent weakly random potential. We prove a homogenization result for the low frequency component of the wave field. We also show that the dynamics generates a non-trivial energy in the high frequencies, which do not homogenize -- the high frequency component of the wave field remains random and the evolution of its energy is described by a kinetic equation. The transition from the homogenization of the low frequencies to the random limit of the high frequencies is illustrated by understanding the size of the small random fluctuations of the low frequency component.

math-ph↗
arXiv2015

Pointwise two-scale expansion for parabolic equations with random coefficients

We investigate the first-order correction in the homogenization of linear parabolic equations with random coefficients. In dimension $3$ and higher and for coefficients having a finite range of dependence, we prove a pointwise version of the two-scale expansion. A similar expansion is derived for elliptic equations in divergence form. The result is surprising, since it was not expected to be true without further symmetry assumptions on the law of the coefficients.

math.PR↗
arXiv2015

A central limit theorem for fluctuations in one dimensional stochastic homogenization

In this paper, we analyze the random fluctuations in a one dimensional stochastic homogenization problem and prove a central limit result, i.e., the first order fluctuations can be described by a Gaussian process that solves an SPDE with additive spatial white noise. Using a probabilistic approach, we obtain a precise error decomposition up to the first order, which helps to decompose the limiting Gaussian process, with one of the components corresponding to the corrector obtained by a formal two scale expansion.

math.PR↗
arXiv2015

The random Schrödinger equation: slowly decorrelating time-dependent potentials

We analyze the weak-coupling limit of the random Schrödinger equation with low frequency initial data and a slowly decorrelating random potential. For the probing signal with a sufficiently long wavelength, we prove a homogenization result, that is, the properly compensated wave field admits a deterministic limit in the "very low" frequency regime. The limit is "anomalous" in the sense that the solution behaves as $\exp(-Dt^{s})$ with $s>1$ rather than the "usual"~$\exp(-Dt)$ homogenized behavior when the random potential is rapidly decorrelating. Unlike in rapidly decorrelating potentials, as we decrease the wavelength of the probing signal, stochasticity appears in the asymptotic limit -- there exists a critical scale depending on the random potential which separates the deterministic and stochastic regimes.

math-ph↗
arXiv2015

Magnetic rotational spectroscopy for probing rheology of nanoliter droplets and thin films

In-situ characterization of minute amounts of complex fluids is a challenge. Magnetic Rotational Spectroscopy (MRS) with submicron probes offers flexibility and accuracy providing desired spatial and temporal resolution in characterization of nanoliter droplets and thin films when other methods fall short. MRS analyzes distinct features of the in-plane rotation of a magnetic probe, when its magnetic moment makes full revolution following an external rotating magnetic field. The probe demonstrates a distinguishable movement which changes from rotation to tumbling to trembling as the frequency of rotation of the driving magnetic field changes. In practice, MRS has been used in analysis of gelation of thin polymer films, ceramic precursors, and nanoliter droplets of insect biofluids. MRS is a young field, but it has many potential applications requiring rheological characterization of scarcely available, chemically reacting complex fluids.

cond-mat.mtrl-sci↗