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The wavelet transform, which is the decomposition of a signal into a set of independent frequency channels, is shown to be a useful diagnostic tool in the analysis of heartbeat sounds. In particular, the wavelet transform enables the experimentalist to obtain qualitative and quantitative measurements of time-frequency characteristics of phonocardiogram (PCG) signals.
The thesis of this paper emerges from the fact that mental states are generated by neural processes that also produce an associated electroencephalogram (EEG). Thus, it is logical to expect correlations between mental state and EEG. The corollary is that the EEG can serve as an index of mental state, which can be particularly useful for studies in animals, where mental states are much less accessible for objective study than in humans. Herein, I briefly review the traditional approaches that have informed our attitudes about animal mental states. Virtually all of our conclusions about mental states in animals are drawn by inference from behavioral observation, a process that is highly and unavoidably subject to anthropomorphism. Traditionally, the electroencephalogram (EEG) has been used in a crude way as an objective indication of physical and behavioral state in animals. This, however, has led to substantial controversy, because there are several situations in which EEG patterns and behavior seem to be dissociated. We not only fail to understand these dissociated states, but there are also important humane animal-welfare issues that remain unresolved because we do not fully understand the extent to which the EEG can reflect mental state. At issue is whether EEG-behavioral dissociations, to the extent that they exist, are proof that the EEG is dissociated from mental states. Powerful new EEG methods, such as topographical EEG mapping, wavelet analysis, and testing for nonlinear ('chaotic') dynamical properties and short-term serial dependencies, are now available for studying the extent to which the EEG can index thinking and feeling in humans and, by extrapolation, in animals. Critics who have become disenchanted with the utility of the EEG should at least concede that fresh approaches to old problems are now available and should therefore be thoughtfully considered. If such research does nothing more than improve the rigor of the debate over animal welfare and rights issues, it will be worth the effort.
The recently introduced wavelet transform is a member of the class of time-frequency representations which include the Gabor short-time Fourier transform and Wigner-Ville distribution. Such techniques are of significance because of their ability to display the spectral content of a signal as time elapses. The value of the wavelet transform as a signal analysis tool has been demonstrated by its successful application to the study of turbulence and processing of speech and music. Since, in common with these subjects, both the time and frequency content of physiological signals are often of interest (the ECG being an obvious example), the wavelet transform represents a particularly relevant means of analysis. Following a brief introduction to the wavelet transform and its implementation, this paper describes a preliminary investigation into its application to the study of both ECG and heart rate variability data. In addition, the wavelet transform can be used to perform multiresolution signal decomposition. Since this process can be considered as a sub-band coding technique, it offers the opportunity for data compression, which can be implemented using efficient pyramidal algorithms. Results of the compression and reconstruction of ECG data are given which suggest that the wavelet transform is well suited to this task.
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MOTIVATION: The mapping from codon to amino acid is surjective due to codon degeneracy, suggesting that codon space might harbor higher information content. Embeddings from the codon language model have recently demonstrated success in various protein downstream tasks. However, predictive models for residue-level tasks such as phosphorylation sites, arguably the most studied Post-Translational Modification (PTM), and PTM sites prediction in general, have predominantly relied on representations in amino acid space. RESULTS: We introduce a novel approach for predicting phosphorylation sites by utilizing codon-level information through embeddings from the codon adaptation language model (CaLM), trained on protein-coding DNA sequences. Protein sequences are first reverse-translated into reliable coding sequences by mapping UniProt sequences to their corresponding NCBI reference sequences and extracting the exact coding sequences from their GenBank format using a dynamic programming-based global pairwise alignment. The resulting coding sequences are encoded using the CaLM encoder to generate codon-aware embeddings, which are subsequently integrated with amino acid-aware embeddings obtained from a protein language model, through an early fusion strategy. Next, a window-level representation of the site of interest, retaining the full sequence context, is constructed from the fused embeddings. A ConvBiGRU network extracts feature maps that capture spatiotemporal correlations between proximal residues within the window. This is followed by a prediction head based on a Kolmogorov-Arnold network (KAN) using the derivative of gaussian wavelet transform to generate the inference for the site. The overall model, dubbed CaLMPhosKAN, performs better than the existing approaches across multiple datasets. AVAILABILITY AND IMPLEMENTATION: CaLMPhosKAN is publicly available at https://github.com/KCLabMTU/CaLMPhosKAN.
There are two kinds of fast activity in the ERG: fast retinal potentials (FRP), an irregular series of spiky wavelets and oscillatory potentials (OP), a rhythmic sequence of events. Corneal ERG from nine intact young carps, evoked by extended pulses of diffuse white light under mesopic adaptation, displayed two different groups of wavelets related to ON and OFF, respectively. Stimulation and recording conditions were established to permit separate Fourier analysis of both groups of wavelets. Power distributions of normalized ON spectra showed both a wide dispersion and a high inter-subject variability. All normalized OFF spectra showed, instead, components within a narrow band from 52 to 56 Hz, most of them maximum relative power peaks. It is concluded that FRP originating in highly labile sources dominate ON fast activity, while the predominant OFF fast activity are OP originating in a stable discrete source.
This paper discusses a simple application of the wavelet transformation to analyse nerve cell impulse patterns. The action potentials converted into delta, or Dirac, functions were convoluted in the time domain with a modified Gauss (the negative of the second derivative of Gauss) function, varying in width between 0.6 and 384 ms. The width of the Gauss function was varied in 640 steps. Some parts of the transformation were extended, analysed and averaged in the frequency domain to explore oscillatory components of the impulse pattern. The sequences of action potentials of retinal ganglion cells evoked by short flashes are taken as examples. The present analysis demonstrate some properties of mathematical "microscopic" application to transient responses of the central nervous system (CNS), whereby the degree of magnification (steps of transformation) was varied.
The one-dimensional equations of flow in the elastic arteries are hyperbolic and admit nonlinear, wavelike solutions for the mean velocity, U, and the pressure, P. Neglecting dissipation, the solutions can be written in terms of wavelets defined as differences of the Riemann invariants across characteristics. This analysis shows that the product, dUdP, is positive definite for forward running wavelets and negative definite for backward running wavelets allowing the determination of the net magnitude and direction of propagating wavelets from pressure and velocity measured at a point in the artery. With the linearizing assumption that intersecting wavelets are additive, the forward and backward running wavelets can be separately calculated. This analysis, applied to measurements made in the ascending aorta of man, shows that forward running wavelets dominate during both the acceleration and deceleration phases of blood flow in the aorta. The forward and backward running waves calculated using the linearized analysis are similar to the results of an impedance analysis of the data. Unlike the impedance analysis, however, this is a time domain analysis which can be applied to nonperiodic or transient flow.
We would like to propose a method of single evoked potential (EP) extraction free from assumptions and based on a novel approach--the wavelet representation of the signal. Wavelets were introduced by Grossman and Morlet in 1984. The method is based on the multiresolution signal decomposition. Wavelets are already used for speech recognition, geophysics investigations and fractal analysis. This method seems to be a useful improvement upon Fourier Transform analysis, since it provides simultaneous information on frequency and time localization of the signal. We would like to introduce wavelet formalism for the first time to brain signal analysis. One of the most important problems in this field is the analysis of evoked potentials. This signal has an amplitude several times smaller than EEG, therefore stimulus-synchronized averaging is commonly used. This method is based on several assumptions. Namely it is postulated that: 1) EP are characterized by a deterministic repeatable pattern, 2) EEG has purely stochastic character, 3) EEG and EP are independent. These assumptions have been challenged e.g. the variability of the EP pattern was demonstrated by John (1973) by means of factor analysis. In view of the works of Sayers et al. (1974) and Başar (1988) EP reflects the reorganization of the spontaneous activity under the influence of a stimulus and it is connected with the redistribution of EEG phases. Several attempts to overcome the limitation of the averaging method have been made. Heintze and Künkel (1984) used an autoregressive moving average (ARMA) model to extract evoked potentials from 2 segments. This was possible under two conditions: high signal to noise ratio and clear separation of the EEG and EP spectra.(ABSTRACT TRUNCATED AT 250 WORDS)
Flash visual evoked potentials (VEPs) in unanesthetized monkeys were recorded from the cortical surface and from closely spaced intracortical sites together with associated multiple unit activity (MUA). The VEP depth profiles were subjected to current source density (CSD) analysis to delineate the laminar pattern of transmembrane current flows manifested by extracellular source and sinks. The initial surface recorded components (P15 and P18) were generated subcortically within the thalamocortical radiations. The distribution of current sources and sinks associated with two subsequent surface negative components. N24 and N40. demonstrates their generation within laminae IVA and IVCb respectively, both parvocellular thalamorecipient layers. Oscillatory potentials resembling those seen in human VEPs are observed riding on N40; analysis of MUA in conjunction with sources and sinks coincident with these wavelets provides evidence that they derive from both thalamocortical and cortical activity. MUA in the 20-60 msec range shows phasic increases throughout lamina IV, which are maximum in amplitude within lamina IVA. This increased firing is concurrent with the sinks observed within the parvocellular thalamorecipient sublaminae IVCb and IVA. A subsequent component, P65, coincident with a decrease in MUA to below the spontaneous level co-located with a lamina IVCb current source, probably arises from intracortically generated inhibitory activity within IVCb. The next VEP component, a surface negative potential at 95 msec, is coincident with current sources and sinks in lamina III, and is consistent with stellate cell input to supragranular elements. VEP components after N95 are not associated with either MUA or CSD activity and are probably generated in extrastriate cortex. Human counterparts of the simian VEP are proposed.
A method has been developed for tracking irregularities in the acoustic waveform of a sustained phonation using the adaptive Wiener filter. Irregularities are determined by the technique of correlation cancellation. The algorithm is evaluated using sustained vowels produced by a formant synthesizer and by subjects with and without phonatary disorders. Results indicate that the method is capable of differentiating between normal and abnormal voices. Most significantly, however, it can also track sporadic or nonstationary irregularities in the shape of an individual acoustic wavelet. This method is expected to be a useful tool for the acoustics analysis of voice production.
Recent studies of cortical simple cell function suggest that the primitives of image representation in vision have a wavelet form similar to Gabor elementary functions (EF's). It is shown that textures and fully-textured images can be practically decomposed into, and synthesized from, a finite set of EF's. Textured-images can be synthesized from a set of EF's using image coefficient library. Alternatively, texturing of contoured (cartoon-like) images is analogous to adding chromaticity information to contoured images. A method for texture discrimination and image segmentation using local features based on the Gabor approach is introduced. Features related to the EF's parameters provide efficient means for texture discrimination and classification. This method is invariant under rotation and translation. The performance of the classification appears to be robust with respect to noisy conditions. The results show an insensitivity of the discrimination to relatively high noise levels, comparable to the performances of the human observer.
Frequency-domain techniques have been extensively investigated for the analysis of high-resolution electrocardiograms (ECGs), although the merit of frequency-domain analysis is still subject to controversy. Time-frequency analysis methods, which estimate the frequency content of a signal as a function of time, potentially provide even more information for improved ECG analysis. Some researchers report impressive results in predicting the outcome of electrophysiologic studies using the short-time Fourier transform (spectrogram). Other time-frequency representations, such as the Wigner distribution, short-time spectral estimators, and the wavelet transform, have also been investigated. The authors present a unified overview of time-frequency representations, showing that only four classes characterize most time-frequency representations. The authors describe the advantages and drawbacks of the various approaches and speculate on their promise for ECG analysis. Very preliminary experiments in applying some of these techniques to the prediction of the outcome of electrophysiologic studies have suggested some possible new research directions.
MOTIVATION: Pangenome indexing is a critical supporting technology in biological sequence analysis such as read alignment applications. The need to accurately identify billions of small sequencing fragments carrying sequencing errors and genomic variants drives the development of scalable and efficient pangenome indexing approach. RESULTS: We propose a new wavelet tree-based approach, called Panaln, for indexing pangenome and introduce a batch computation approach for fast count query over Panaln. We present a simple and effective seeding strategy and develop a pangenome program that uses the seed-and-extend paradigm for read alignment. Experimental results on simulated and real data demonstrate that Panaln uses significantly less space for the compared pangenome methods with generally higher accuracy. We provide a scalable index construction by representing pangenome with a linear model. Additionally, Panaln brings enhanced accuracy compared to the popular single reference methods. AVAILABILITY AND IMPLEMENTATION: Package: https://anaconda.org/bioconda/panaln and source code: https://github.com/Lilu-guo/Panaln.
The harmonics-to-noise ratio (HNR) has been widely accepted for quantifying the irregular or noise component of voice. HNR, however, is usually inflated by cycle-to-cycle variations of fundamental frequency period because zero padding is used for time normalization of the wavelet. In this study, a new method was developed for analyzing waveform perturbations of voice. In this method, noise components of voice were calculated from the discrepancies between wavelets after they had been optimally aligned in time. The optimal time normalization of wavelets was accomplished using procedures of dynamic time warping (DTW). This method was evaluated using both synthetic and natural voices, and significant reductions in noise were obtained. The harmonics-to-noise ratio obtained using DTW for time normalization was also shown to be independent of fundamental frequency perturbations.
Recordings were obtained from rods and horizontal cells of Xenopus, using an eyecup preparation. The enhancement of cone signals produced by rod backgrounds was measured using flickering red spots of varying intensity and diameter, and the experiments were repeated with cone stimuli consisting of alteration of wavelengths of 660 and 605 nm, adjusted for equal effects on rods or cones ("silent substitution"). Rods responded to red flicker with discrete wavelets up to 5 Hz. The characteristics of suppressive rod-cone interaction (SRCI) depend on the precise stimulus parameters. In particular, the reported low-pass attenuation of SRCI is absent with silent substitution. An analysis of the responses to backgrounds in horizontal cells, and the effects of the red light flashes in rods, led to the conclusion that the characteristics of SRCI are determined partially by the fact that "cone" stimuli excite rods and vice versa. This result simplifies the mechanism of SRCI and permits a comparison between the studies of SRCI using electroretinograms and horizontal cells.
1. Electrical potentials in the cat lumbosacral spinal cord evoked by the action of single medial gastrocnemius Ia afferent fibres were recorded using low impedance, bevelled micropipette electrodes and the spike triggered averaging technique. 2. Axonal potentials from the Ia fibres recorded extracellularly appeared as brief triphasic predominantly negative potentials. 3. Terminal potentials recorded in regions of Ia afferent termination appeared as brief diphasic positive-negative waves, often with additional wavelets. 4. Focal synaptic potentials, recorded extracellularly in regions of the medial gastrocnemius Ia afferent termination, appeared as slow (about 10 msec duration) negative potentials following terminal potentials. 5. Excitatory post-synaptic potentials, recorded intracellularly in Ia target cells of the medial gastrocnemius, appeared as slow (about 10 msec duration) positive potentials following terminal potentials. 6. Analysis of the temporal progression of these potentials through the spinal cord allowed calculations of the Ia conduction velocity in the dorsal funiculus stem axon (50-60 m/sec), in major collateral branches (8-19 m/sec) and in terminal branches (0.2-1.0 m/sec). 7. The number of major collateral branches (nine or fewer) and their spacing along the spinal cord (1071 micron mean value) were determined by analysing the extent of the triceps surae motoneurone column. 8. The structural and functional properties of medial gastrocnemius Ia afferent fibres are discussed in relation to recent single fibre anatomical data and the present single fibre electrophysiological data.
The dark-adapted and light-adapted electroretinograms of 13 subjects with 23 normal eyes were analyzed by means of Fourier spectrum. The oscillatory potentials in the time domain were filtered out from the electroretinogram after a corresponding bandpass was given in the frequency domain. The coefficient of variation of total power, dominant power and dominant frequency of the isolated oscillatory potentials in the frequency domain, summed amplitudes and area of the isolated oscillatory potentials, each amplitude and implicit time of the first four major oscillatory potential wavelets in the time domain were compared. The implicit time showed the smallest coefficient of variation; summed amplitudes of OP1 to OP4 showed smaller coefficients of variation than those of the area, the amplitude of each oscillatory potential wavelet, dominant frequency and dominant and total power. The coefficient of variation of these measurement parameters in light-adapted electroretinograms was smaller than those in dark-adapted electroretinograms.