18,755 research outputs found

    On the Law of Large Numbers for Discrete Fourier Transform

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    We establish the rate of convergence in the strong law of large numbers of discrete Fourier Transform of the identically distributed random variables with finite moment of order p, where 1<p<2.Comment: 7 page

    Central limit theorem for Fourier transform and periodogram of random fields

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    In this paper we show that the limiting distribution of the real and the imaginary part of the double Fourier transform of a stationary random field is almost surely an independent vector with Gaussian marginal distributions, whose variance is, up to a constant, the field's spectral density. The dependence structure of the random field is general and we do not impose any restrictions on the speed of convergence to zero of the covariances, or smoothness of the spectral density. The only condition required is that the variables are adapted to a commuting filtration and are regular in some sense. The results go beyond the Bernoulli fields and apply to both short range and long range dependence. They can be easily applied to derive the asymptotic behavior of the periodogram associated to the random field. The method of proof is based on new probabilistic methods involving martingale approximations and also on borrowed and new tools from harmonic analysis.Comment: 20 page

    Capped Lp approximations for the composite L0 regularization problem

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    The composite L0 function serves as a sparse regularizer in many applications. The algorithmic difficulty caused by the composite L0 regularization (the L0 norm composed with a linear mapping) is usually bypassed through approximating the L0 norm. We consider in this paper capped Lp approximations with p>0p>0 for the composite L0 regularization problem. For each p>0p>0, the capped Lp function converges to the L0 norm pointwisely as the approximation parameter tends to infinity. We point out that the capped Lp approximation problem is essentially a penalty method with an Lp penalty function for the composite L0 problem from the viewpoint of numerical optimization. Our theoretical results stated below may shed a new light on the penalty methods for solving the composite L0 problem and help the design of innovative numerical algorithms. We first establish the existence of optimal solutions to the composite L0 regularization problem and its capped Lp approximation problem under conditions that the data fitting function is asymptotically level stable and bounded below. Asymptotically level stable functions cover a rich class of data fitting functions encountered in practice. We then prove that the capped Lp problem asymptotically approximates the composite L0 problem if the data fitting function is a level bounded function composed with a linear mapping. We further show that if the data fitting function is the indicator function on an asymptotically linear set or the L0 norm composed with an affine mapping, then the composite L0 problem and its capped Lp approximation problem share the same optimal solution set provided that the approximation parameter is large enough

    Two-step Fixed-point proximity algorithms for multi-block separable convex problems

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    Multi-block separable convex problems recently received considerable attention. This class of optimization problems minimizes a separable convex objective function with linear constraints. The algorithmic challenges come from the fact that the classic alternating direction method of multipliers (ADMM) for the problem is not necessarily convergent. However, it is observed that ADMM outperforms numerically many of its variants with guaranteed theoretical convergence. The goal of this paper is to develop convergent and computationally efficient algorithms for solving multi-block separable convex problems. We first characterize the solutions of the optimization problems by proximity operators of the convex functions involved in their objective function. We then design a two-step fixed-point iterative scheme for solving these problems based on the characterization. We further prove convergence of the iterative scheme and show that it has O(1/k) convergence rate in the ergodic sense and the sense of the partial primal-dual gap, where k denotes the iteration number. Moreover, we derive specific two-step fixed-point proximity algorithms (2SFPPA) from the proposed iterative scheme and establish their global convergence. Numerical experiments for solving the sparse MRI problem demonstrate the numerical efficiency of the proposed 2SFPPA.Comment: 22 pages, 6 figue

    On the quenched CLT for stationary random fields under projective criteria

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    Motivated by random evolutions which do not start from equilibrium, in a recent work, Peligrad and Voln\'{y} (2018) showed that the quenched CLT (central limit theorem) holds for ortho-martingale random fields. In this paper, we study the quenched CLT for a class of random fields larger than the ortho-martingales. To get the results, we impose sufficient conditions in terms of projective criteria under which the partial sums of a stationary random field admit an ortho-martingale approximation. More precisely, the sufficient conditions are of the Hannan's projective type. As applications, we establish quenched CLT's for linear and nonlinear random fields with independent innovations

    Inhomogeneous dynamic nuclear polarization and suppression of electron-polarization decay in a quantum dot

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    We investigate the dynamic nuclear polarization process by frequently injecting polarized electron spins into a quantum dot. Due to the suppression of the direct dipolar and indirect electron-mediated nuclear spin interactions, by the frequently injected electron spins, the analytical predictions under the independent spin approximation agree well with quantum numerical simulations. Our results show that the acquired nuclear polarization is highly inhomogeneous, proportional to the square of the local electron-nuclear hyperfine interaction constant, if the injection frequency is high. Utilizing the inhomogeneously polarized nuclear spins as an initial state, we further show that the electron-polarization decay time can be extended 100 times even at a relatively low nuclear polarization (<20%), without much suppression of the fluctuation of the Overhauser field. Our results lay the foundation for future investigations of the effect of DNP in more complex spin systems, such as double quantum dots and nitrogen vacancy centers in diamonds.Comment: 10 pages, 12 eps figures, in Rev. Tex 4 forma

    Shared control schematic for brain controlled vehicle based on fuzzy logic

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    Brain controlled vehicle refers to the vehicle that obtains control commands by analyzing the driver's EEG through Brain-Computer Interface (BCI). The research of brain controlled vehicles can not only promote the integration of brain machines, but also expand the range of activities and living ability of the disabled or some people with limited physical activity, so the research of brain controlled vehicles is of great significance and has broad application prospects. At present, BCI has some problems such as limited recognition accuracy, long recognition time and limited number of recognition commands in the process of analyzing EEG signals to obtain control commands. If only use the driver's EEG signals to control the vehicle, the control performance is not ideal. Based on the concept of Shared control, this paper uses the fuzzy control (FC) to design an auxiliary controller to realize the cooperative control of automatic control and brain control. Designing a Shared controller which evaluates the current vehicle status and decides the switching mechanism between automatic control and brain control to improve the system control performance. Finally, based on the joint simulation platform of Carsim and MATLAB, with the simulated brain control signals, the designed experiment verifies that the control performance of the brain control vehicle can be improved by adding the auxiliary controller

    Quantum walks accompanied by spin flipping in one-dimensional optical lattices

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    We investigate continuous-time quantum walks of two fermionic atoms loaded in one-dimensional optical lattices with on-site interaction and subjected to a Zeeman field. The quantum walks are accompanied by spin-flipping processes. We calculate the time-dependent density distributions of the two fermions with opposite spins which are initially positioned on the center site by means of exact numerical method. Besides the usual fast linear expansion behavior, we find an interesting spin-flipping induced localization in the time-evolution of density distributions. We show that the fast linear expansion behavior could be restored by simply ramping on the Zeeman field or further increasing the spin-flipping strength. The intrinsic origin of this exotic phenomenon is attributed to the emergence of a flat band in the single particle spectrum of the system. Furthermore, we investigate the effect of on-site interaction on the dynamics of the quantum walkers. The two-particle correlations are calculated and signal of localization is also shown therein. A simple potential experimental application of this interesting phenomenon is proposed.Comment: 8 pages, 11 figure

    Research on fuzzy PID Shared control method of small brain-controlled uav

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    Brain-controlled unmanned aerial vehicle (uav) is a uav that can analyze human brain electrical signals through BCI to obtain flight commands. The research of brain-controlled uav can promote the integration of brain-computer and has a broad application prospect. At present, BCI still has some problems, such as limited recognition accuracy, limited recognition time and small number of recognition commands in the acquisition of control commands by analyzing eeg signals. Therefore, the control performance of the quadrotor which is controlled only by brain is not ideal. Based on the concept of Shared control, this paper designs an assistant controller using fuzzy PID control, and realizes the cooperative control between automatic control and brain control. By evaluating the current flight status and setting the switching rate, the switching mechanism of automatic control and brain control can be decided to improve the system control performance. Finally, a rectangular trajectory tracking control experiment of the same height is designed for small quadrotor to verify the algorithm

    A Stochastic Geometry Approach to Energy Efficiency in Relay-Assisted Cellular Networks

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    Though cooperative relaying is believed to be a promising technology to improve the energy efficiency of cellular networks, the relays' static power consumption might worsen the energy efficiency therefore can not be neglected. In this paper, we focus on whether and how the energy efficiency of cellular networks can be improved via relays. Based on the spatial Poisson point process, an analytical model is proposed to evaluate the energy efficiency of relay-assisted cellular networks. With the aid of the technical tools of stochastic geometry, we derive the distributions of signal-to-interference-plus-noise ratios (SINRs) and mean achievable rates of both non-cooperative users and cooperative users. The energy efficiency measured by "bps/Hz/W" is expressed subsequently. These established expressions are amenable to numerical evaluation and corroborated by simulation results.Comment: 6 pages, 5 figures, accepted by IEEE Globecom'12. arXiv admin note: text overlap with arXiv:1108.1257 by other author
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