Nonlinear spectral analysis of Peregrine solitons observed in optics and in hydrodynamic experiments

The data recorded in optical fiber [1] and in hydrodynamic [2] experiments reported the pioneering observation of nonlinear waves with spatiotemporal localization similar to the Peregrine soliton are examined by using nonlinear spectral analysis. Our approach is based on the integrable nature of the one-dimensional focusing nonlinear Schrodinger equation (1D-NLSE) that governs at leading order the propagation of the optical and hydrodynamic waves in the two experiments. Nonlinear spectral analysis provides certain spectral portraits of the analyzed structures that are composed of bands lying in the complex plane. The spectral portraits can be interpreted within the framework of the so-called finite gap theory (or periodic inverse scattering transform). In particular, the number N of bands composing the nonlinear spectrum determines the genus g = N - 1 of the solution that can be viewed as a measure of complexity of the space-time evolution of the considered solution. Within this setting the ideal, rational Peregrine soliton represents a special, degenerate genus 2 solution. While the fitting procedures employed in [1] and [2] show that the experimentally observed structures are quite well approximated by the Peregrine solitons, nonlinear spectral analysis of the breathers observed both in the optical fiber and in the water tank experiments reveals that they exhibit spectral portraits associated with more general, genus 4 finite-gap NLSE solutions. Moreover, the nonlinear spectral analysis shows that the nonlinear spectrum of the breathers observed in the experiments slowly changes with the propagation distance, thus confirming the influence of unavoidable perturbative higher order effects or dissipation in the experiments

Short-range correlations in asymmetric nuclear matter

The spectral function of protons in the asymmetric nuclear matter is calculated in the self-consistent T-matrix approach. The spectral function per proton increases with increasing asymmetry. This effect and the density dependence of the spectral function partially explain the observed increase of the spectral function with the mass number of the target nuclei in electron scattering experiments

Spectral function and fidelity susceptibility in quantum critical phenomena

In this paper, we derive a simple equality that relates the spectral function $I(k,\omega)$ and the fidelity susceptibility $\chi_F$, i.e. $\chi_F=\lim_{\eta\rightarrow 0}\frac{\pi}{\eta} I(0, i\eta)$ with $\eta$ being the half-width of the resonance peak in the spectral function. Since the spectral function can be measured in experiments by the neutron scattering or the angle-resolved photoemission spectroscopy(ARPES) technique, our equality makes the fidelity susceptibility directly measurable in experiments. Physically, our equality reveals also that the resonance peak in the spectral function actually denotes a quantum criticality-like point at which the solid state seemly undergoes a significant change.Comment: 5 pages, 2 figure

Asymmetric discrimination of non-speech tonal analogues of vowels

Published in final edited form as: J Exp Psychol Hum Percept Perform. 2019 February ; 45(2): 285–300. doi:10.1037/xhp0000603.Directional asymmetries reveal a universal bias in vowel perception favoring extreme vocalic articulations, which lead to acoustic vowel signals with dynamic formant trajectories and well-defined spectral prominences due to the convergence of adjacent formants. The present experiments investigated whether this bias reflects speech-specific processes or general properties of spectral processing in the auditory system. Toward this end, we examined whether analogous asymmetries in perception arise with non-speech tonal analogues that approximate some of the dynamic and static spectral characteristics of naturally-produced /u/ vowels executed with more versus less extreme lip gestures. We found a qualitatively similar but weaker directional effect with two-component tones varying in both the dynamic changes and proximity of their spectral energies. In subsequent experiments, we pinned down the phenomenon using tones that varied in one or both of these two acoustic characteristics. We found comparable asymmetries with tones that differed exclusively in their spectral dynamics, and no asymmetries with tones that differed exclusively in their spectral proximity or both spectral features. We interpret these findings as evidence that dynamic spectral changes are a critical cue for eliciting asymmetries in non-speech tone perception, but that the potential contribution of general auditory processes to asymmetries in vowel perception is limited.Accepted manuscrip

Pattern vectors from algebraic graph theory

Graphstructures have proven computationally cumbersome for pattern analysis. The reason for this is that, before graphs can be converted to pattern vectors, correspondences must be established between the nodes of structures which are potentially of different size. To overcome this problem, in this paper, we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a Hermitian property matrix that can be viewed as a complex analogue of the Laplacian. To embed the graphs in a pattern space, we explore whether the vectors of invariants can be embedded in a low- dimensional space using a number of alternative strategies, including principal components analysis ( PCA), multidimensional scaling ( MDS), and locality preserving projection ( LPP). Experimentally, we demonstrate that the embeddings result in well- defined graph clusters. Our experiments with the spectral representation involve both synthetic and real- world data. The experiments with synthetic data demonstrate that the distances between spectral feature vectors can be used to discriminate between graphs on the basis of their structure. The real- world experiments show that the method can be used to locate clusters of graphs