Explore the vast range of titles available.

Many traffic management and control applications require highly complete and accurate data of traffic flow. However, because of various reasons such as sensor failure or transmission error, it is common that some traffic flow data are lost. As a result, various methods were proposed by using a wide spectrum of techniques to estimate missing traffic data in the last two decades. Generally, these missing data imputation methods can be categorised into three kinds: prediction methods, interpolation methods and statistical learning methods. To assess their performance, these methods are compared from different aspects in this paper, including reconstruction errors, statistical behaviours and running speeds. Results show that statistical learning methods are more effective than the other two kinds of imputation methods when data of a single detector is utilised. Among various methods, the probabilistic principal component analysis (PPCA) yields best performance in all aspects. Numerical tests demonstrate that PPCA can be used to impute data online before making further analysis (e.g. make traffic prediction) and is robust to weather changes.

This 1998 book describes the sampling and statistical methods used most often by behavioral ecologists and field biologists. Written by a biologist and two statisticians, it provides a rigorous discussion together with worked examples of statistical concepts and methods that are generally not covered in introductory courses, and which are consequently poorly understood and applied by field biologists. The first section reviews important issues such as defining the statistical population and the sampling plan when using non-random methods for sample selection, bias, interpretation of statistical tests, confidence intervals and multiple comparisons. After a detailed discussion of sampling methods and multiple regression, subsequent chapters discuss specialized problems such as pseudoreplication, and their solutions. It will quickly become the statistical handbook for all field biologists.

We prove that if ω is uniformly distributed on [0, 1], then as T → ∞, t ↦ ζ(iωT + it + 1/2) converges to a nontrivial random generalized function, which in turn is identified as a product of a very well-behaved random smooth function and a random generalized function known as a complex Gaussian multiplicative chaos distribution. This demonstrates a novel rigorous connection between probabilistic number theory and the theory of multiplicative chaos—the latter is known to be connected to various branches of modern probability theory and mathematical physics. We also investigate the statistical behavior of the zeta function on the mesoscopic scale. We prove that if we let δT approach zero slowly enough as T → ∞, then t ↦ ζ(1/2 + iδTt + iωT) is asymptotically a product of a divergent scalar quantity suggested by Selberg’s central limit theorem and a strictly Gaussian multiplicative chaos. We also prove a similar result for the characteristic polynomial of a Haar distributed random unitary matrix, where the scalar quantity is slightly different but the multiplicative chaos part is identical. This says that up to scalar multiples, the zeta function and the characteristic polynomial of a Haar distributed random unitary matrix have an identical distribution on the mesoscopic scale.

We numerically investigate magnon-mediated spin transport through nonmagnetic metal/ferromagnetic insulator (NM/FI) heterostructures in the presence of Anderson disorder, and discover universal behaviors of the spin conductance in both one-dimensional (1D) and 2D systems. In the localized regime, the variance of logarithmic spin conductance σ 2(ln G T ) shows a universal linear scaling with its average ⟨ln G T ⟩, independent of Fermi energy, temperature, and system size in both 1D and 2D cases. In 2D, the competition between disorder-enhanced density of states at the NM/FI interface and disorder-suppressed spin transport leads to a non-monotonic dependence of average spin conductance on the disorder strength. As a result, in the metallic regime, average spin conductance is enhanced by disorder, and a new linear scaling between spin conductance fluctuation rms( G T ) and average spin conductance G T is revealed which is universal at large system width. These universal scaling behaviors suggest that spin transport mediated by magnon in disordered 2D NM/FI systems belongs to a new universality class, different from that of charge conductance in 2D normal metal systems.

Constrained least mean square (CLMS) algorithm is the most popular constrained adaptive filtering algorithm due to its simple structure and easy implementation. However, its convergence slows down when the input signal is colored. To address this issue, this paper firstly introduces the normalized subband adaptive filter (NSAF) into the constrained filtering problem and derives a constrained NSAF (CNSAF) algorithm using the Lagrange multiplier method. Benefiting from the good decorrelation capability of the NSAF, the proposed CNSAF algorithm significantly improves the convergence performance of the CLMS algorithm under colored inputs. Then, the mean and mean-square stability of the CNSAF algorithm is analyzed, and the theoretical models to characterize the transient and steady-state mean square deviation (MSD) behaviors of the CNSAF algorithm are derived utilizing the Kronecker product property and vectorization method. Further to extend the CNSAF algorithm to the problem of sparse system identification, a sparse version of the CNSAF algorithm (S-CNSAF) is derived. Finally, the validity of the derived theoretical MSD prediction models and the superiority of the proposed algorithms are confirmed by extensive computer simulations on system identification with colored inputs.

The knowledge of the spatial power spectra of the main geomagnetic field and of its secular variation makes it possible to define typical timescales τn for each spherical harmonic degree n. Investigating both observations and numerical dynamos, we show that a one‐parameter law of the form τn = τSV/n is satisfied for the non‐dipole field, given the statistical way the observed τn are expected to fluctuate. Consequently, we determine the corresponding secular‐variation timescale τSV from either instantaneous or time‐averaged spectra, leading to a value of 415 ±4555 yr for recent satellite field models. In the broader context of geomagnetic data assimilation, τSV could provide a sensible and convenient means to rescale the time axis of dynamo simulations. Key Points The geomagnetic correlation times follow a universal behaviour This behaviour can be described by a simple one‐parameter law This parameter value allows for a consistent time‐rescaling of numerical models

This study takes a new receiving approach to detect an ultra-wideband (UWB) signal in the presence of multiple access interference (MAI). A generalised normal-Laplace (GNL) distribution is exploited for designing a novel multiuser UWB receiver. To more accurately comply with real statistical behaviours of the MAI-plus-noise in time-hopping multiple access UWB systems, a modified parameter estimator, which is an adaptive method of moments estimation (aMME), is proposed. In the existing studies, the analysis about GNL model shows appropriate results for UWB simulations, while it requires heavy complexity to obtain the precise distribution because of no existence of a closed-form probability density function (PDF) expression. To practically evaluate the GNL PDF, the fast Fourier transform, which can significantly reduce the computational complexity is considered. The GNL using the aMME outperforms the conventional matched filter UWB receiver, the soft-limiting receiver, the Gaussian–Laplace mixture receiver, the p-order metric receiver and the previous GNL receivers, especially in high SNR ranges. Furthermore, the presented GNL receiving method is applied to each finger of the conventional Rake receiver for signal detection in IEEE UWB multipath channels. The proposed Rake receiver based on the GNL distribution performs better than the conventional Rake receiver in multipath fading channels.

An analytical scheme to determine the statistical behavior of a stochastic system including two terms of fractional derivative with real, arbitrary, fractional orders is proposed. In this approach, Green’s functions obtained are based on a Laplace transform approach and the weighted generalized Mittag–Leffler function. The responses of the system can be subsequently described as a Duhamel integral-type close-form expression. These expressions are applied to obtain the statistical behavior of a dynamical system excited by stationary stochastic processes. The numerical simulation based on the modified Euler method and Monte Carlo approach is developed. Three examples of single-degree-of-freedom system with fractional derivative damping under Gaussian white noise excitation are presented to illustrate application of the proposed method.

The third edition of Van Kampen's standard work has been revised and updated.The main difference with the second edition is that the contrived application of the quantum master equation in section 6 of chapter XVII has been replaced with a satisfactory treatment of quantum fluctuations.

Asymptotic unbiasedness and L2-consistency are established for various statistical estimates of mutual information in the mixed models framework. Such models are important, e.g., for analysis of medical and biological data. The study of the conditional Shannon entropy as well as new results devoted to statistical estimation of the differential Shannon entropy are employed essentially. Theoretical results are completed by computer simulations for logistic regression model with different parameters. The numerical experiments demonstrate that new statistics, proposed by the authors, have certain advantages.