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When starting an N -body simulation of an isolated galaxy, it is desirable to select particles from a distribution function to ensure that the model is in equilibrium. Random sampling from a DF is widely used, but results in a set of particles that differs by shot noise from that intended. This paper presents a method to reduce sampling noise that has been developed by the author in a many collaborations over a number of years. The technique has been partly described in past papers, though the ideas have not previously been gathered together, nor have its advantages been clearly demonstrated in past work. Of course, sampling errors can also be reduced by a brute force increase in the number of particles, but methods to achieve the same effect with fewer particles have obvious advantages. Here we not only describe the method, but also present three sets of simulations to illustrate the practical advantages of reducing sampling error. The improvements are not dramatic, but are clearly worth having. [ABSTRACT FROM AUTHOR]

In high-speed analog-to-digital converters (ADCs), two main factors contribute to high power consumption. The first is the super linear relationship with the sampling rate; i.e., by doubling the sampling rate, the power consumption more than doubles. The second factor arises from the consumption of analog circuitry responsible to mitigate the jitter noise. By employing a multichannel sampling system, one can achieve high sampling rates by incorporating multiple low sampling-rate channels, which results in a linear scaling of power consumption with the number of channels. The main drawback of this system is the timing mismatch between the sampling channels. In this paper, we intend to jointly compensate the jitter noise and the timing mismatch between the channels using statistical methods. We first approximate the acquisition system and derive a stochastic model. Then, we propose an iterative maximum likelihood algorithm to estimate the parameters of the input signal. We further evaluate the Cramér-Rao lower bound (CRLB) for the estimation error to examine the proposed algorithm. Simulation results indicate that our algorithm is capable of closely following the CRLB curve for reasonable values of jitter noise and a wide range of timing mismatch errors. Moreover, it is shown that the mismatch-compensated multichannel sampling system performs almost equivalently to a single-channel high rate sampler without having its shortcomings. [ABSTRACT FROM AUTHOR]

Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional data set. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional knowledge on the principal vector? We study the case in which the principal vector is known to lie in the positive orthant. Similar constraints arise in a number of applications, ranging from the analysis of gene expression data to spike sorting in neural signal processing. In the unconstrained case, the estimation performances of PCA have been precisely characterized using the random matrix theory, under a statistical model known as the spiked model. It is known that the estimation error undergoes a phase transition as the signal-to-noise ratio crosses a certain threshold. Unfortunately, tools from the random matrix theory have no bearing on the constrained problem. Despite this challenge, we develop an analogous characterization in the constrained case, within a one-spike model. In particular: 1) we prove that the estimation error undergoes a similar phase transition, albeit at a different thresholds in signal-to-noise ratio that we determine exactly; 2) we prove that—unlike in the unconstrained case—the estimation error depends on the spike vector, and characterize the least favorable vectors; and 3) we show that a non-negative principal component can be approximately computed—under the spiked model—in nearly linear time. This despite the fact that the problem is non-convex and, in general, NP-hard to solve exactly. [ABSTRACT FROM AUTHOR]

This paper deals with area-based subpixel image registration under the rotation-isometric scaling-translation transformation hypothesis. Our approach is based on parametrical modeling of geometrically transformed textural image fragments and maximum-likelihood estimation of the transformation vector between them. Due to the parametrical approach based on the fractional Brownian motion modeling of the local fragments' texture, the proposed estimator \mboxML_\mathrmfBm (ML stands for “maximum likelihood” and fBm stands for “fractal Brownian motion”) has the ability to better adapt to real image texture content compared with other methods relying on universal similarity measures such as mutual information or normalized correlation. The main benefits are observed when assumptions underlying the fBm model are fully satisfied, e.g., for isotropic normally distributed textures with stationary increments. Experiments on both simulated and real images and for high and weak correlations between registered images show that the \mboxML_\mathrmfBm estimator offers significant improvement compared with other state-of-the-art methods. It reduces translation vector, rotation angle, and scaling factor estimation errors by a factor of about 1.75–2, and it decreases the probability of false match by up to five times. In addition, an accurate confidence interval for \mboxML_\mathrmfBm estimates can be obtained from the Cramér–Rao lower bound on rotation-scaling-translation parameter estimation error. This bound depends on texture roughness, noise level in reference and template images, correlation between these images, and geometrical transformation parameters. [ABSTRACT FROM AUTHOR]

We show that the rate regions achieved by linear-feedback coding schemes over dual multi-antenna Gaussian multi-access channels (MACs) and broadcast channels (BCs) with independent noises coincide. By dual here we mean: •

the channel matrices of the MAC and the BC are transposes of each other and [ABSTRACT FROM PUBLISHER]

A first-order partial differential equation is derived for the cumulative distribution function of the terminal state value in a scalar linear continuous-time system with random disturbance and noise corrupted measurements. The system is subject to a saturated linear control strategy. The cumulative distribution functions of the initial state, the estimator error and the disturbance are assumed to be known. Illustrative examples are presented. [ABSTRACT FROM AUTHOR]

This paper considers the problem of resource-constrained and noise-limited localization and estimation of dynamic targets that are sparsely distributed over a large area. We generalize an existing framework [Bashan , 2008] for adaptive allocation of sensing resources to the dynamic case, accounting for time-varying target behavior such as transitions to neighboring cells and varying amplitudes over a potentially long time horizon. The proposed adaptive sensing policy is driven by minimization of a surrogate function for mean squared error within locations containing targets. We provide theoretical upper bounds on the performance of adaptive sensing policies by analyzing solutions with oracle knowledge of target locations, gaining insight into the effect of target motion and amplitude variation as well as sparsity. Exact minimization of the multistage objective function is infeasible, but myopic optimization yields a closed-form solution. We propose a simple non-myopic extension, the Dynamic Adaptive Resource Allocation Policy (D-ARAP), that allocates a fraction of resources for exploring all locations rather than solely exploiting the current belief state. Our numerical studies indicate that D-ARAP has the following advantages: (a) it is more robust than the myopic policy to noise, missing data, and model mismatch; (b) it performs comparably to well-known approximate dynamic programming solutions but at significantly lower computational complexity; and (c) it improves greatly upon nonadaptive uniform resource allocation in terms of estimation error and probability of detection. [ABSTRACT FROM PUBLISHER]

This paper establishes a nearly optimal algorithm for denoising a mixture of sinusoids from noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a sparse recovery problem with a continuous, infinite dictionary. We show how to compute the estimator via semidefinite programming and provide guarantees on its mean-squared error rate. We derive a complementary minimax lower bound on this estimation rate, demonstrating that our approach nearly achieves the best possible estimation error. Furthermore, we establish bounds on how well our estimator localizes the frequencies in the signal, showing that the localization error tends to zero as the number of samples grows. We verify our theoretical results in an array of numerical experiments, demonstrating that the semidefinite programming approach outperforms three classical spectral estimation techniques. [ABSTRACT FROM PUBLISHER]

We study the theoretical performance of two full-duplex multiple-input multiple-output (MIMO) radio systems: a full-duplex bi-directional communication system and a full-duplex relay system. We focus on the effect of a (digitally manageable) residual self-interference due to imperfect channel estimation (with independent and identically distributed (i.i.d.) Gaussian channel estimation error) and transmitter noise. We assume that the instantaneous channel state information (CSI) is not available the transmitters. To maximize the system ergodic mutual information, which is a nonconvex function of power allocation vectors at the nodes, a gradient projection algorithm is developed to optimize the power allocation vectors. This algorithm exploits both spatial and temporal freedoms of the source covariance matrices of the MIMO links between transmitters and receivers to achieve higher sum ergodic mutual information. It is observed through simulations that the full-duplex mode is optimal when the nominal self-interference is low, and the half-duplex mode is optimal when the nominal self-interference is high. In addition to an exact closed-form ergodic mutual information expression, we introduce a much simpler asymptotic closed-form ergodic mutual information expression, which in turn simplifies the computation of the power allocation vectors. [ABSTRACT FROM PUBLISHER]