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Since age is the most significant risk factor for the development of Alzheimer’s disease (AD), it is important to understand the effect of normal ageing on brain network characteristics before we can accurately diagnose the condition based on information derived from resting state electroencephalogram (EEG) recordings, aiming to detect brain network disruption. This article proposes a novel brain functional connectivity imaging method, particularly targeting the contribution of nonlinear dynamics of functional connectivity, on distinguishing participants with AD from healthy controls (HC). We describe a parametric method established upon a Nonlinear Finite Impulse Response model, and a revised orthogonal least squares algorithm used to estimate the linear, nonlinear and combined connectivity between any two EEG channels without fitting a full model. This approach, where linear and non-linear interactions and their spatial distribution and dynamics can be estimated independently, offered us the means to dissect the dynamic brain network disruption in AD from a new perspective and to gain some insight into the dynamic behaviour of brain networks in two age groups (above and below 70) with normal cognitive function. Although linear and stationary connectivity dominates the classification contributions, quantitative results have demonstrated that nonlinear and dynamic connectivity can significantly improve the classification accuracy, barring the group of participants below the age of 70, for resting state EEG recorded during eyes open. The developed approach is generic and can be used as a powerful tool to examine brain network characteristics and disruption in a user friendly and systematic way. [ABSTRACT FROM AUTHOR]

In this paper, we study the electromagnetic scattering of a conducting and permeable sphere buried in sea sediments. Instead of taking a uniform conducting medium in the previous work, we model marine environments as a layered medium that consists of the air, the sea, and the sediment. We adopt an integral equation technique to compute time-harmonic solutions for background and scattered fields under fundamental source excitations, i.e., vertical and horizontal magnetic dipoles. The corresponding transient scattering responses to causal step waveform are computed through the digital sine transform. The derived fundamental solutions provide convenient formulas tailored for three-layer medium modeling. The numerical experiments demonstrate that the scattered responses computed in the different backgrounds are approaching almost to the same decays at late times. However, the background fields can significantly mask the scattered responses. Subtracting assumed uniform background responses from “measured” total fields in the three-layered medium cannot provide a correct scattering response in the interested time range, i.e., 0.1–25 ms. To remove the background fields, we propose a conceptual gradiometer system that has receiver cubes installed radially symmetric with respect to a transmitting antenna. The results demonstrate that the suitable differential combinations are able to yield the scattering responses that well agree with those of a free space as the layered background fields in these combined receivers are equal and their influence are automatically canceled out. [ABSTRACT FROM PUBLISHER]

We present a new approach for inverting time-domain electromagnetic data to recover the location and magnetic dipole polarizations of a limited number of buried objects. We form the multichannel electromagnetic induction (EMI) sensor data as a spatial-temporal response matrix (STRM). The rows of the STRM correspond to measurements sampled at different time channels from one sensor and the columns correspond to measurements sampled at the same time channel from different sensors. The singular value decomposition of the STRM produces the left and right singular vectors that are related to the sensor and the temporal spaces, respectively. If the effective rank of the STRM is r, then the first r singular vectors span signal subspaces (SS), and the remaining singular vectors span the noise subspaces. The original data are projected onto the SS, and the temporal orthogonal projection inversion (TOPI) uses these data in a nonlinear inverse problem to solve for source locations of the objects. The polarizations of the targets are then obtained by solving a linear optimization problem in the original data domain. We present theoretical and numerical analyses to investigate the singular value system of the STRM and the sensitivity of the TOPI to the size of an SS. Only a few subspace vectors are required to generate locations of the objects. The results are insensitive to the exact choice of rank, and this differs from usual methods that involve selecting the number of time channels to be used in the inversion and carefully estimating associated uncertainties. The proposed approach is evaluated using the synthetic and real multistatic EMI data. [ABSTRACT FROM PUBLISHER]

An important step in the identification of cellular automata (CA) is to detect the correct neighborhood before parameter estimation. Many authors have suggested procedures based on the removal of redundant neighbors from a very large initial neighborhood one by one to find the real model, but this often induces ill conditioning and overfitting. This is true particularly for a large initial neighborhood where there are few significant terms, and this will be demonstrated by an example in this paper. By introducing a new criteria and three new techniques, this paper proposes a new adaptive fast CA orthogonal-least-square (Adaptive-FCA-OLS) algorithm, which cannot only adaptively search for the correct neighborhood without any preset tolerance but can also considerably reduce the computational complexity and memory usage. Several numerical examples demonstrate that the Adaptive-FCA-OLS algorithm has better robustness to noise and to the size of the initial neighborhood than other recently developed neighborhood detection methods in the identification of binary CA. [ABSTRACT FROM AUTHOR]

This brief introduces a new parametric modelling and identification method for linear time-varying systems using a block least mean square (LMS) approach where the time-varying parameters are approximated using multi-wavelet basis functions. This approach can be applied to track rapidly or even sharply varying processes and is developed by combining wavelet approximation theory with a block LMS algorithm. Numerical examples are provided to show the effectiveness of the proposed method for dealing with severely nonstationary processes. Application of the proposed approach to a real mechanical system indicates better tracking capability of the multi-wavelet basis function algorithm compared with the normalized least squares or recursive least squares routines. [ABSTRACT FROM PUBLISHER]

Neighborhood detection and local state vector construction for the identification of spatiotemporal systems is considered in this paper. Determining the neighborhood size both in the space and time domain can considerably reduce the complexity of the set of candidate model terms for the identification of coupled map lattice models. The computation requirements of the model identification algorithm can also be greatly reduced instead of the more direct identification approach of searching over the entire spatiotemporal neighborhood in the original space. In this paper, a new neighborhood detection method is introduced based on embedding theory for nonlinear dynamical systems to produce an initial spatiotemporal neighborhood for the identification of spatiotemporal systems. Numerical examples are provided to demonstrate the feasibility and applicability of the new neighborhood detection method. [ABSTRACT FROM AUTHOR]

In this paper, an algorithm is derived for the determination of the output frequency ranges of nonlinear systems, which extends previous results on the output frequencies of nonlinear systems to a more general situation. The new results are significant for the analysis of the output frequency response of a wide class of non-linear systems. [ABSTRACT FROM AUTHOR]

Extracting the rules from spatio-temporal patterns generated by the evolution of cellular automata (CA) usually requires a priori information about the observed system, but in many applications little information will be known about the pattern. This paper introduces a new neighborhood detection algorithm which can determine the range of the neighborhood without any knowledge of the system by introducing a criterion based on mutual information (and an indication of over-estimation). A coarse-to-fine identification routine is then proposed to determine the CA rule from the observed pattern. Examples, including data from a real experiment, are employed to evaluate the new algorithm. [ABSTRACT FROM AUTHOR]