Number Of Temporal Samples Research Articles

Centrality informed embedding of networks for temporal feature extraction

We propose a two-step methodology for exploring the temporal characteristics of a network. First, we construct a graph time series, where each snapshot is the result of a temporal whole-graph embedding. The embedding is carried out using the degree, Katz and betweenness centralities to characterize first and higher order proximities among vertices. Then a principal component analysis is performed over the collected temporal graph samples, which exhibits eigengraphs, graphs whose temporal weight variations model the sampled graph series. Analysis of the temporal timeline of each of the main eigengraphs reveals moments of importance in terms of structural graph changes. Parameters such as the dimension of the embeddings and the number of temporal samples are explored. Two case studies are presented: a Bitcoin subgraph, where findings are cross-checked by looking at the subgraph behavior itself, and the Enron email network, which allows us to compare our findings with prior studies. In both cases, the proposed methodology successfully identified temporal structural changes in the graph evolution.

Further Results on the Cramér–Rao Bound for Sparse Linear Arrays

Sparse linear arrays, such as co-prime and nested arrays, can identify up $O(M^2)$ uncorrelated sources with only $O(M)$ sensors by utilizing their difference coarray model. In our previous work, we derived closed-form asymptotic mean-squared error (MSE) expressions for two coarray based MUSIC algorithms and analyzed the Cramer-Rao bound (CRB) in high signal-to-noise ratio (SNR) regions, under the assumption of uncorrelated sources. In this paper, we provide further analysis of the CRB presented in our previous work. We first establish the connection between two CRBs, the CRB derived with the assumption that the sources are uncorrelated, and the classical stochastic CRB derived without this assumption. We show that they are asymptotically equal in high SNR regions for uncorrelated sources. Next, we analyze the behavior of the former CRB for co-prime and nested arrays with a large number of sensors. We investigate the effect of configuration parameters on this CRB. We show that, for co-prime and nested arrays, this CRB can decrease at a rate of $O(M^{-5})$ for large values of $M$ , while this rate is only $O(M^{-3})$ for an $M$ -sensor ULA. This finding analytically demonstrates that co-prime and nested arrays can achieve better asymptotic estimation performance when the number of sensors is a limiting factor. We also show that for a fixed aperture, co-prime and nested arrays require more snapshots to achieve the same performance as ULAs, showing the trade-off between the number of spatial samples and the number of temporal samples. Finally, we demonstrate our analytical results with numerical experiments.

Enhanced identification of BOLD-like components with multi-echo simultaneous multi-slice (MESMS) fMRI and multi-echo ICA

The recent introduction of simultaneous multi-slice (SMS) acquisitions has enabled the acquisition of blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) data with significantly higher temporal sampling rates. In a parallel development, the use of multi-echo fMRI acquisitions in conjunction with a multi-echo independent component analysis (ME-ICA) approach has been introduced as a means to automatically distinguish functionally-related BOLD signal components from signal artifacts, with significant gains in sensitivity, statistical power, and specificity. In this work, we examine the gains that can be achieved with a combined approach in which data obtained with a multi-echo simultaneous multi-slice (MESMS) acquisition are analyzed with ME-ICA. We find that ME-ICA identifies significantly more BOLD-like components in the MESMS data as compared to data acquired with a conventional multi-echo single-slice acquisition. We demonstrate that the improved performance of MESMS derives from both an increase in the number of temporal samples and the enhanced ability to filter out high-frequency artifacts.

Adaptive OFDM Radar Waveform Design for Improved Micro-Doppler Estimation

We analyze the performance of a wideband orthogonal frequency division multiplexing (OFDM) signal in estimating the micro-Doppler frequency of a rotating target having multiple scattering centers. The use of a frequency-diverse OFDM signal enables us to independently analyze the micro-Doppler characteristics with respect to a set of orthogonal subcarrier frequencies. We characterize the accuracy of micro-Doppler frequency estimation by computing the Cramer-Rao bound (CRB) on the angular-velocity estimate of the target. Additionally, to improve the accuracy of the estimation procedure, we formulate and solve an optimization problem by minimizing the CRB on the angular-velocity estimate with respect to the OFDM spectral coefficients. We present several numerical examples to demonstrate the CRB variations with respect to the signal-to-noise ratios, number of temporal samples, and number of OFDM subcarriers. The improvement in estimation accuracy due to the adaptive waveform design is also analyzed numerically. A grid-based maximum likelihood estimation technique is applied to evaluate the corresponding mean-squared error performance.

Identifying Sighting Clusters of Endangered Taxa with Historical Records

The probability and time of extinction of taxa is often inferred from statistical analyses of historical records. Many of these analyses require the exclusion of multiple records within a unit of time (i.e., a month or a year). Nevertheless, spatially explicit, temporally aggregated data may be useful for identifying clusters of sightings (i.e., sighting clusters) in space and time. Identification of sighting clusters highlights changes in the historical recording of endangered taxa. I used two methods to identify sighting clusters in historical records: the Ederer-Myers-Mantel (EMM) test and the space-time permutation scan (STPS). I applied these methods to the spatially explicit sighting records of three species of orchids that are listed as endangered in the Republic of Ireland under the Wildlife Act (1976): Cephalanthera longifolia, Hammarbya paludosa, and Pseudorchis albida. Results with the EMM test were strongly affected by the choice of the time interval, and thus the number of temporal samples, used to examine the records. For example, sightings of P. albida clustered when the records were partitioned into 20-year temporal samples, but not when they were partitioned into 22-year temporal samples. Because the statistical power of EMM was low, it will not be useful when data are sparse. Nevertheless, the STPS identified regions that contained sighting clusters because it uses a flexible scanning window (defined by cylinders of varying size that move over the study area and evaluate the likelihood of clustering) to detect them, and it identified regions with high and regions with low rates of orchid sightings. The STPS analyses can be used to detect sighting clusters of endangered species that may be related to regions of extirpation and may assist in the categorization of threat status.

Stealth terrain navigation

A method for solving visibility-based terrain path planning problems using massively parallel hypercube machines is proposed. A typical example is to find a path that is hidden from moving adversaries. This kind of problem can be generalized as a time-varying constrained path planning problem and is proven to be computationally hard. An approximation based on both temporal and, spatial sampling is proposed. Since a 2-D grid cell representation of terrain can be embedded into a hypercube with extra links for fast communication, the method can be very efficient when implemented on hypercube machines. The time complexity is in general O(T*E*log N) using O(N) processors, where T is the number of temporal samples, E is the number of adversary agents, and N is the number of grid cells on the terrain. It is also shown that the method can be applied to several realistic problems with a variety of path optimizations. All algorithms have been implemented on the Connection Machine CM-2 and results of experiments are presented. >