arXiv subjects

Peng Xu

Publications and source records attributed to Peng Xu.

At least 415 records · Page 23Linked to original sources

arXiv2017

Frequency-difference-dependent stochastic resonance in neural systems

Biological neurons receive multiple noisy oscillatory signals, and their dynamical response to the superposition of these signals is of fundamental importance for information processing in the brain. Here we study the response of neural systems to the weak envelope modulation signal, which is superimposed by two periodic signals with different frequencies. We show that stochastic resonance occurs at the beat frequency in neural systems at the single-neuron as well as the population level. The performance of this frequency-difference-dependent stochastic resonance is influenced by both the beat frequency and the two forcing frequencies. Compared to a single neuron, a population of neurons is more efficient in detecting the information carried by the weak envelope modulation signal at the beat frequency. Furthermore, an appropriate fine-tuning of the excitation-inhibition balance can further optimize the response of a neural ensemble to the superimposed signal. Our results thus introduce and provide insights into the generation and modulation mechanism of the frequency-difference-dependent stochastic resonance in neural systems.

q-bio.NC↗

arXiv2017

Optimal Power Allocation Scheme for Non-Orthogonal Multiple Access with $α$-Fairness

This paper investigates the optimal power allocation scheme for sum throughput maximization of non-orthogonal multiple access (NOMA) system with $α$-fairness. In contrast to the existing fairness NOMA models, $α$-fairness can only utilize a single scalar to achieve different user fairness levels. Two different channel state information at the transmitter (CSIT) assumptions are considered, namely, statistical and perfect CSIT. For statistical CSIT, fixed target data rates are predefined, and the power allocation problem is solved for sum throughput maximization with $α$-fairness, through characterizing several properties of the optimal power allocation solution. For perfect CSIT, the optimal power allocation is determined to maximize the instantaneous sum rate with $α$-fairness, where user rates are adapted according to the instantaneous channel state information (CSI). In particular, a simple alternate optimization (AO) algorithm is proposed, which is demonstrated to yield the optimal solution. Numerical results reveal that, at the same fairness level, NOMA significantly outperforms the conventional orthogonal multiple access (MA) for both the scenarios with statistical and perfect CSIT.

cs.IT↗

arXiv2017

Accelerated Stochastic Power Iteration

Principal component analysis (PCA) is one of the most powerful tools in machine learning. The simplest method for PCA, the power iteration, requires $\mathcal O(1/Δ)$ full-data passes to recover the principal component of a matrix with eigen-gap $Δ$. Lanczos, a significantly more complex method, achieves an accelerated rate of $\mathcal O(1/\sqrtΔ)$ passes. Modern applications, however, motivate methods that only ingest a subset of available data, known as the stochastic setting. In the online stochastic setting, simple algorithms like Oja's iteration achieve the optimal sample complexity $\mathcal O(σ^2/Δ^2)$. Unfortunately, they are fully sequential, and also require $\mathcal O(σ^2/Δ^2)$ iterations, far from the $\mathcal O(1/\sqrtΔ)$ rate of Lanczos. We propose a simple variant of the power iteration with an added momentum term, that achieves both the optimal sample and iteration complexity. In the full-pass setting, standard analysis shows that momentum achieves the accelerated rate, $\mathcal O(1/\sqrtΔ)$. We demonstrate empirically that naively applying momentum to a stochastic method, does not result in acceleration. We perform a novel, tight variance analysis that reveals the "breaking-point variance" beyond which this acceleration does not occur. By combining this insight with modern variance reduction techniques, we construct stochastic PCA algorithms, for the online and offline setting, that achieve an accelerated iteration complexity $\mathcal O(1/\sqrtΔ)$. Due to the embarassingly parallel nature of our methods, this acceleration translates directly to wall-clock time if deployed in a parallel environment. Our approach is very general, and applies to many non-convex optimization problems that can now be accelerated using the same technique.

math.OC↗

arXiv2017

Measurement of the topological Chern number by continuous probing of a qubit subject to a slowly varying Hamiltonian

We analyze a measurement scheme that allows determination of the Berry curvature and the topological Chern number of a Hamiltonian with parameters exploring a two-dimensional closed manifold. Our method uses continuous monitoring of the gradient of the Hamiltonian with respect to one parameter during a quasi-adiabatic quench of the other. Measurement back-action leads to disturbance of the system dynamics, but we show that this can be compensated by a feedback Hamiltonian. As an example, we analyze the implementation with a superconducting qubit subject to time varying, near resonant microwave fields; equivalent to a spin 1/2 particle in a magnetic field.

quant-ph↗

arXiv2017

Chang'e 3 lunar mission and upper limit on stochastic background of gravitational wave around the 0.01 Hz band

The Doppler tracking data of the Chang'e 3 lunar mission is used to constrain the stochastic background of gravitational wave in cosmology within the 1 mHz to 0.05 Hz frequency band. Our result improves on the upper bound on the energy density of the stochastic background of gravitational wave in the 0.02 Hz to 0.05 Hz band obtained by the Apollo missions, with the improvement reaching almost one order of magnitude at around 0.05 Hz. Detailed noise analysis of the Doppler tracking data is also presented, with the prospect that these noise sources will be mitigated in future Chinese deep space missions. A feasibility study is also undertaken to understand the scientific capability of the Chang'e 4 mission, due to be launched in 2018, in relation to the stochastic gravitational wave background around 0.01 Hz. The study indicates that the upper bound on the energy density may be further improved by another order of magnitude from the Chang'e 3 mission, which will fill the gap in the frequency band from 0.02 Hz to 0.1 Hz in the foreseeable future.

astro-ph.IM↗

arXiv2017

Efficient generation of many-body singlet states of spin-1 bosons in optical superlattices

We propose an efficient stepwise adiabatic merging (SAM) method to generate many-body singlet states in antiferromagnetic spin-1 bosons in concatenated optical superlattices with isolated double-well arrays, by adiabatically ramping up the double-well bias. With an appropriate choice of bias sweeping rate and magnetic field, the SAM protocol predicts a fidelity as high as 90% for a sixteen-body singlet state and even higher fidelities for smaller even-body singlet states. During their evolution, the spin-1 bosons exhibit interesting squeezing dynamics, manifested by an odd-even oscillation of the experimentally observable squeezing parameter. The generated many-body singlet states may find practical applications in precision measurement of magnetic field gradient and in quantum information processing.

cond-mat.quant-gas↗

arXiv2017

Cross-modal Subspace Learning for Fine-grained Sketch-based Image Retrieval

Sketch-based image retrieval (SBIR) is challenging due to the inherent domain-gap between sketch and photo. Compared with pixel-perfect depictions of photos, sketches are iconic renderings of the real world with highly abstract. Therefore, matching sketch and photo directly using low-level visual clues are unsufficient, since a common low-level subspace that traverses semantically across the two modalities is non-trivial to establish. Most existing SBIR studies do not directly tackle this cross-modal problem. This naturally motivates us to explore the effectiveness of cross-modal retrieval methods in SBIR, which have been applied in the image-text matching successfully. In this paper, we introduce and compare a series of state-of-the-art cross-modal subspace learning methods and benchmark them on two recently released fine-grained SBIR datasets. Through thorough examination of the experimental results, we have demonstrated that the subspace learning can effectively model the sketch-photo domain-gap. In addition we draw a few key insights to drive future research.

cs.CV↗

arXiv2017

Rogozin's convolution inequality for locally compact groups

General extensions of an inequality due to Rogozin, concerning the essential supremum of a convolution of probability density functions on the real line, are obtained. While a weak version of the inequality is proved in the very general context of Polish $σ$-compact groups, particular attention is paid to the group $\mathbb{R}^d$, where the result can combined with rearrangement inequalities for certain linear images for a strong generalization. As a consequence, we obtain a unification and sharpening of both the $\infty$-Renyi entropy power inequality for sums of independent random vectors, due to Bobkov and Chistyakov, and the bounds on marginals of projections of product measures due to Rudelson and Vershynin (matching and extending the sharp improvement of Livshyts, Paouris and Pivovarov). The proof is elementary and relies on a characterization of extreme points of a class of probability measures in the general setting of Polish measure spaces, as well as the development of a generalization of Ball's cube slicing bounds for products of $d$-dimensional Euclidean balls (where the "co-dimension 1" case had been recently settled by Brzezinski).

math.PR↗

arXiv2017

Physical Layer Security Jamming: Theoretical Limits and Practical Designs in Wireless Networks

Physical layer security has been recently recognized as a promising new design paradigm to provide security in wireless networks. In addition to the existing conventional cryptographic methods, physical layer security exploits the dynamics of fading channels to enhance secured wireless links. In this approach, jamming plays a key role by generating noise signals to confuse the potential eavesdroppers, and significantly improves quality and reliability of secure communications between legitimate terminals. This article presents theoretical limits and practical designs of jamming approaches for physical layer security. In particular, the theoretical limits explore the achievable secrecy rates of user cooperation based jamming whilst the centralized, and game theoretic based precoding techniques are reviewed for practical implementations. In addition, the emerging wireless energy harvesting techniques are exploited to harvest the required energy to transmit jamming signals. Future directions of these approaches, and the associated research challenges are also briefly outlined.

cs.IT↗

arXiv2016

Forward and Reverse Entropy Power Inequalities in Convex Geometry

The entropy power inequality, which plays a fundamental role in information theory and probability, may be seen as an analogue of the Brunn-Minkowski inequality. Motivated by this connection to Convex Geometry, we survey various recent developments on forward and reverse entropy power inequalities not just for the Shannon-Boltzmann entropy but also more generally for Rényi entropy. In the process, we discuss connections between the so-called functional (or integral) and probabilistic (or entropic) analogues of some classical inequalities in geometric functional analysis

cs.IT↗

arXiv2016

Preserving coherent spin and squeezed spin states of a spin-1 Bose-Einstein condensate with rotary echoes

A challenge in precision measurement with squeezed spin state arises from the spin dephasing due to stray magnetic fields. To suppress such environmental noises, we employ a continuous driving protocol, rotary echo, to enhance the spin coherence of a spin-1 Bose-Einstein condensate in stray magnetic fields. Our analytical and numerical results show that the coherent and the squeezed spin states are preserved for a significantly long time, compared to the free induction decay time, if the condition $hτ= mπ$ is met with $h$ the pulse amplitude and $τ$ pulse width. In particular, both the spin average and the spin squeezing, including the direction and the amplitude, are simultaneously fixed for a squeezed spin state. Our results point out a practical way to implement quantum measurements based on a spin-1 condensate beyond the standard quantum limit.

cond-mat.quant-gas↗

arXiv2016

The norm of the Fourier transform on compact or discrete abelian groups

We calculate the norm of the Fourier operator from $L^p(X)$ to $L^q(\hat{X})$ when $X$ is an infinite locally compact abelian group that is, furthermore, compact or discrete. This subsumes the sharp Hausdorff-Young inequality on such groups. In particular, we identify the region in $(p,q)$-space where the norm is infinite, generalizing a result of Fournier, and setting up a contrast with the case of finite abelian groups, where the norm was determined by Gilbert and Rzeszotnik. As an application, uncertainty principles on such groups expressed in terms of Rényi entropies are discussed.

math.CA↗

arXiv2016

First-order post-Newtonian analysis of the relativistic tidal effects for satellite gradiometry and the Mashhoon-Theiss anomaly

With continuous advances in technology, future satellite gradiometry missions will be capable of performing precision relativistic experiments and imposing constraints on modern gravity theories. To this end, the full first-order post-Newtonian tidal tensor under inertially guided and Earth-pointing local frames along post-Newtonian orbits is worked out. The physical picture behind the "Mashhoon-Theiss anomaly" is explained at the post-Newtonian level. The relativistic precession of the local frame with respect to the sidereal frame will produce modulations of Newtonian tidal forces along certain bases, which gives rise to two different kinds of secular tidal tensors. The measurements of the secular tidal force from the frame-dragging effect is also discussed.

gr-qc↗

arXiv2016

Role of electron-electron interactions in the charge dynamics of rare-earth-doped CaFe2As2

We have investigated the charge dynamics and the nature of many-body interactions in La- and Pr- doped CaFe2As2. From the infrared part of the optical conductivity, we discover that the scattering rate of mobile carriers above 200 K exhibits saturation at the Mott-Ioffe-Regel limit of metallic transport. However, the dc resistivity continues to increase with temperature above 200 K due to the loss of Drude spectral weight. The loss of Drude spectral weight with increasing temperature is seen in a wide temperature range in the uncollapsed tetragonal phase, and this spectral weight is recovered at energy scales about one order of magnitude larger than the Fermi energy scale in these semimetals. The phenomena noted above have been observed previously in other correlated metals in which the dominant interactions are electronic in origin. Further evidence of significant electron-electron interactions is obtained from the presence of quadratic temperature and frequency-dependent terms in the scattering rate at low temperatures and frequencies in the uncollapsed tetragonal structures of La-doped and Pr-doped CaFe2As2. For temperatures below the structure collapse transition in Pr-doped CaFe2As2 at 70 K, the scattering rate decreases due to weakening of electronic correlations, and the Drude spectral weight decreases due to modification of the low-energy electronic structure.

cond-mat.supr-con↗

arXiv2016

Investigation of the high-spin rotational properties of the proton emitter $^{113}$Cs using a particle-number conserving method

The recently observed two high-spin rotational bands in the proton emitter $^{113}$Cs are investigated using the cranked shell model with pairing correlations treated by a particle-number conserving method, in which the Pauli blocking effects are taken into account exactly. By using the configuration assignments of band 1 ($π3/2^+[422], α= -1/2$) and band 2 ($π1/2^+[420], α= 1/2$), the experimental moments of inertia and quasiparticle alignments can be well reproduced by the present calculations, which in turn strongly support these configuration assignments. Furthermore, by analyzing the occupation probability $n_μ$ of each cranked Nilsson level near the Fermi surface and the contribution of each orbital to the angular momentum alignments, the backbending mechanism of these two bands is also investigated.

nucl-th↗

arXiv2016

A New Line Defect in NdTiO3 Perovskite

Perovskite oxides form an eclectic class of materials owing to their structural flexibility in accommodating cations of different sizes and valences. They host well known point and planar defects, but so far no line defect has been identified other than dislocations. Using analytical scanning transmission electron microscopy (STEM) and ab initio calculations we have detected and characterized the atomic and electronic structures of a novel line defect in NdTiO3 perovskite. It appears in STEM images as a perovskite cell rotated by 45 degrees. It consists of self-organized Ti-O vacancy lines replaced by Nd columns surrounding a central Ti-O octahedral chain containing Ti4+ ions, as opposed to Ti3+ in the host. The distinct Ti valence in this line defect introduces the possibility of engineering exotic conducting properties in a single preferred direction and tailoring novel desirable functionalities in this Mott insulator.

cond-mat.mtrl-sci↗

arXiv2016

Relativistic Dynamics of Relative Motions (I): Post-Newtonian Extension of the Hill-Clohessy-Wiltshire Equations

With continuous advances in technologies related to deep space ranging and satellite gravity gradiometry, corrections from general relativity to the dynamics of relative orbital motions will certainly become important. In this work, we extend,in a systematic way, the Hill-Clohessy-Wiltshire Equations to include the complete first order post-Newtonian effects from general relativity. Within certain short time limit, post-Newtonian corrections to general periodic solutions of the Hill-Clohessy-Wiltshire Equations are also worked out.

astro-ph.EP↗

arXiv2016

Sub-sampled Newton Methods with Non-uniform Sampling

We consider the problem of finding the minimizer of a convex function $F: \mathbb R^d \rightarrow \mathbb R$ of the form $F(w) := \sum_{i=1}^n f_i(w) + R(w)$ where a low-rank factorization of $\nabla^2 f_i(w)$ is readily available. We consider the regime where $n \gg d$. As second-order methods prove to be effective in finding the minimizer to a high-precision, in this work, we propose randomized Newton-type algorithms that exploit \textit{non-uniform} sub-sampling of $\{\nabla^2 f_i(w)\}_{i=1}^{n}$, as well as inexact updates, as means to reduce the computational complexity. Two non-uniform sampling distributions based on {\it block norm squares} and {\it block partial leverage scores} are considered in order to capture important terms among $\{\nabla^2 f_i(w)\}_{i=1}^{n}$. We show that at each iteration non-uniformly sampling at most $\mathcal O(d \log d)$ terms from $\{\nabla^2 f_i(w)\}_{i=1}^{n}$ is sufficient to achieve a linear-quadratic convergence rate in $w$ when a suitable initial point is provided. In addition, we show that our algorithms achieve a lower computational complexity and exhibit more robustness and better dependence on problem specific quantities, such as the condition number, compared to similar existing methods, especially the ones based on uniform sampling. Finally, we empirically demonstrate that our methods are at least twice as fast as Newton's methods with ridge logistic regression on several real datasets.

math.OC↗