A Technique for Characterizing the Development of Rhythms in Bird Song

The developmental trajectory of nervous system dynamics shows hierarchical structure on time scales spanning ten orders of magnitude from milliseconds to years. Analyzing and characterizing this structure poses significant signal processing challenges. In the context of birdsong development, we have previously proposed that an effective way to do this is to use the dynamic spectrum or spectrogram, a classical signal processing tool, computed at multiple time scales in a nested fashion. Temporal structure on the millisecond timescale is normally captured using a short time Fourier analysis, and structure on the second timescale using song spectrograms. Here we use the dynamic spectrum on time series of song features to study the development of rhythm in juvenile zebra finch. The method is able to detect rhythmic structure in juvenile song in contrast to previous characterizations of such song as unstructured. We show that the method can be used to examine song development, the accuracy with which rhythm is imitated, and the variability of rhythms across different renditions of a song. We hope that this technique will provide a standard, automated method for measuring and characterizing song rhythm

Wavelet packets based denoising method for measurement domain repeat-time multipath filtering in GPS static high-precision positioning

Repeatable satellite orbits can be used for multipath mitigation in GPS-based deformation monitoring and other high-precision GPS applications that involve continuous observation with static antennas. Multipath signals at a static station repeat when the GPS constellation repeats given the same site environment. Repeat-time multipath filtering techniques need noise reduction methods to remove the white noise in carrier phase measurement residuals in order to retrieve the carrier phase multipath corrections for the next day. We propose a generic and robust three-level wavelet packets based denoising method for repeat-time-based carrier phase multipath filtering in relative positioning; the method does not need tuning to work with different data sets. The proposed denoising method is tested rigorously and compared with two other denoising methods. Three rooftop data sets collected at the University of Nottingham Ningbo China and two data sets collected at three Southern California Integrated GPS Network high-rate stations are used in the performance assessment. Test results of the wavelet packets denoising method are compared with the results of the resistor–capacitor (RC) low-pass filter and the single-level discrete wavelet transform (DWT) denoising method. Multipath mitigation efficiency in carrier phase measurement domain is shown by spectrum analysis of two selected satellites in two data sets. The positioning performance of the repeat-time-based multipath filtering techniques is assessed. The results show that the performance of the three noise reduction techniques is about 1–46 % improvement on positioning accuracy when compared with no multipath filtering. The statistical results show that the wavelet packets based denoising method is always better than the RC filter by 2–4 %, and better than the DWT method by 6–15 %. These results suggest that the proposed wavelet packets based denoising method is better than both the DWT method and the relatively simple RC low-pass filter for noise reduction in multipath filtering. However, the wavelet packets based denoising method is not significantly better than the RC filter

WAVOS: a MATLAB toolkit for wavelet analysis and visualization of oscillatory systems

<p>Abstract</p> <p>Background</p> <p>Wavelets have proven to be a powerful technique for the analysis of periodic data, such as those that arise in the analysis of circadian oscillators. While many implementations of both continuous and discrete wavelet transforms are available, we are aware of no software that has been designed with the nontechnical end-user in mind. By developing a toolkit that makes these analyses accessible to end users without significant programming experience, we hope to promote the more widespread use of wavelet analysis.</p> <p>Findings</p> <p>We have developed the WAVOS toolkit for wavelet analysis and visualization of oscillatory systems. WAVOS features both the continuous (Morlet) and discrete (Daubechies) wavelet transforms, with a simple, user-friendly graphical user interface within MATLAB. The interface allows for data to be imported from a number of standard file formats, visualized, processed and analyzed, and exported without use of the command line. Our work has been motivated by the challenges of circadian data, thus default settings appropriate to the analysis of such data have been pre-selected in order to minimize the need for fine-tuning. The toolkit is flexible enough to deal with a wide range of oscillatory signals, however, and may be used in more general contexts.</p> <p>Conclusions</p> <p>We have presented WAVOS: a comprehensive wavelet-based MATLAB toolkit that allows for easy visualization, exploration, and analysis of oscillatory data. WAVOS includes both the Morlet continuous wavelet transform and the Daubechies discrete wavelet transform. We have illustrated the use of WAVOS, and demonstrated its utility for the analysis of circadian data on both bioluminesence and wheel-running data. WAVOS is freely available at <url>http://sourceforge.net/projects/wavos/files/</url></p

Slepian functions and their use in signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and on the surface of a sphere.Comment: Submitted to the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verla

Objective surface evaluation of fiber reinforced polymer composites

The mechanical properties of advanced composites are essential for their structural performance, but the surface finish on exterior composite panels is of critical importance for customer satisfaction. This paper describes the application of wavelet texture analysis (WTA) to the task of automatically classifying the surface finish properties of two fiber reinforced polymer (FRP) composite construction types (clear resin and gel-coat) into three quality grades. Samples were imaged and wavelet multi-scale decomposition was used to create a visual texture representation of the sample, capturing image features at different scales and orientations. Principal components analysis was used to reduce the dimensionality of the texture feature vector, permitting successful classification of the samples using only the first principal component. This work extends and further validates the feasibility of this approach as the basis for automated non-contact classification of composite surface finish using image analysis.<br /

Deep analysis of perception through dynamic structures that emerge in cortical activity from self-regulated noise

The statistical properties of the spontaneous background electrocorticogram (ECoG) were modeled, starting with random numbers, constraining the distributions, and identifying characteristic deviations from randomness in ECoG from subjects at rest and during intentional behaviors. The ECoG had been recorded through 8 × 8 arrays of 64 electrodes, from the surfaces of auditory, visual, or somatic cortices of 9 rabbits, and from the inferotemporal cortex of a human subject. Power spectral densities (PSD) in coordinates of log10 power versus log10 frequency of ECoG from subjects at rest usually conformed to noise in power-law distributions in a continuum. PSD of ECoG from active subjects usually deviated from noise in having peaks in log10 power above the power-law line in various frequency bands. The analytic signals from the Hilbert transform after band pass filtering in the beta and gamma ranges revealed beats from interference among distributed frequencies in band pass filtered noise called Rayleigh noise. The beats were displayed as repetitive down spikes in log10 analytic power. Repetition rates were proportional to filter bandwidths for all center frequencies. Resting ECoG often gave histograms of the magnitudes and intervals of down spikes that conformed to noise. Histograms from active ECoG often deviated from noise in Rayleigh distributions of down spike intervals by giving what are called Rice (Mathematical analysis of random noise—and appendixes—technical publications monograph B-1589. Bell Telephone Labs Inc., New York, 1950) distributions. Adding power to noise as signals at single frequencies simulated those deviations. The beats in dynamic theory are deemed essential for perception, by gating beta and gamma bursts at theta rates through enhancement of the cortical signal-to-noise ratio in exceptionally deep down spikes called null spikes

Scalar and vector Slepian functions, spherical signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and, particularly for applications in the geosciences, for scalar and vectorial signals defined on the surface of a unit sphere.Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verlag. This is a slightly modified but expanded version of the paper arxiv:0909.5368 that appeared in the 1st Edition of the Handbook, when it was called: Slepian functions and their use in signal estimation and spectral analysi

ChIP-PaM: an algorithm to identify protein-DNA interaction using ChIP-Seq data

<p>Abstract</p> <p>Background</p> <p>ChIP-Seq is a powerful tool for identifying the interaction between genomic regulators and their bound DNAs, especially for locating transcription factor binding sites. However, high cost and high rate of false discovery of transcription factor binding sites identified from ChIP-Seq data significantly limit its application.</p> <p>Results</p> <p>Here we report a new algorithm, ChIP-PaM, for identifying transcription factor target regions in ChIP-Seq datasets. This algorithm makes full use of a protein-DNA binding pattern by capitalizing on three lines of evidence: 1) the tag count modelling at the peak position, 2) pattern matching of a specific tag count distribution, and 3) motif searching along the genome. A novel data-based two-step eFDR procedure is proposed to integrate the three lines of evidence to determine significantly enriched regions. Our algorithm requires no technical controls and efficiently discriminates falsely enriched regions from regions enriched by true transcription factor (TF) binding on the basis of ChIP-Seq data only. An analysis of real genomic data is presented to demonstrate our method.</p> <p>Conclusions</p> <p>In a comparison with other existing methods, we found that our algorithm provides more accurate binding site discovery while maintaining comparable statistical power.</p

The landscape of Neandertal ancestry in present-day humans

Analyses of Neandertal genomes have revealed that Neandertals have contributed genetic variants to modern humans1–2. The antiquity of Neandertal gene flow into modern humans means that regions that derive from Neandertals in any one human today are usually less than a hundred kilobases in size. However, Neandertal haplotypes are also distinctive enough that several studies have been able to detect Neandertal ancestry at specific loci1,3–8. Here, we have systematically inferred Neandertal haplotypes in the genomes of 1,004 present-day humans12. Regions that harbor a high frequency of Neandertal alleles in modern humans are enriched for genes affecting keratin filaments suggesting that Neandertal alleles may have helped modern humans adapt to non-African environments. Neandertal alleles also continue to shape human biology, as we identify multiple Neandertal-derived alleles that confer risk for disease. We also identify regions of millions of base pairs that are nearly devoid of Neandertal ancestry and enriched in genes, implying selection to remove genetic material derived from Neandertals. Neandertal ancestry is significantly reduced in genes specifically expressed in testis, and there is an approximately 5-fold reduction of Neandertal ancestry on chromosome X, which is known to harbor a disproportionate fraction of male hybrid sterility genes20–22. These results suggest that part of the reduction in Neandertal ancestry near genes is due to Neandertal alleles that reduced fertility in males when moved to a modern human genetic background