Algorithmic options for joint time-frequency analysis in structural dynamics applications

The purpose of this paper is to present recent research efforts by the authors supporting the superiority of joint time-frequency analysis over the traditional Fourier transform in the study of non-stationary signals commonly encountered in the fields of earthquake engineering, and structural dynamics. In this respect, three distinct signal processing techniques appropriate for the representation of signals in the time-frequency plane are considered. Namely, the harmonic wavelet transform, the adaptive chirplet decomposition, and the empirical mode decomposition, are utilized to analyze certain seismic accelerograms, and structural response records. Numerical examples associated with the inelastic dynamic response of a seismically-excited 3-story benchmark steel-frame building are included to show how the mean-instantaneous-frequency, as derived by the aforementioned techniques, can be used as an indicator of global structural damage

Joint time-frequency representation of simulated earthquake accelerograms via the adaptive chirplet transform

Seismic accelerograms are inherently nonstationary signals since both the intensity and frequency content of seismic events evolve in time. The adaptive chirplet transform is a signal processing technique for joint time-frequency representation of nonstationary data. Analysis of a signal via the adaptive chirplet decomposition in conjunction with the Wigner-Ville distribution yields the so-called adaptive spectrogram which constitutes a valid representation of the signal in the time-frequency plane. In this paper the potential of this technique for capturing the temporal evolution of the frequency content of strong ground motions is assessed. In this regard, simulated nonstationary earthquake accelerograms compatible with an exponentially modulated and appropriately filtered Kanai-Tajimi spectrum are processed using the adaptive chirplet transform. These are samples of a random process whose evolutionary power spectrum can be represented by an analytical expression. It is suggested that the average of the ensemble of the adaptive chirplet spectrograms can be construed as an estimate of the underlying evolutionary power spectrum. The obtained numerical results show, indeed, that the estimated evolutionary power spectrum is in a good agreement with the one defined analytically. This fact points out the potential of the adaptive chirplet analysis for as a tool for capturing localized frequency content of arbitrary data- banks of real seismic accelerograms

A non-abelian quasi-particle model for gluon plasma

We propose a quasi-particle model for the thermodynamic description of the gluon plasma which takes into account non-abelian characteristics of the gluonic field. This is accomplished utilizing massive non-linear plane wave solutions of the classical equations of motion with a variable mass parameter, reflecting the scale invariance of the Yang-Mills Lagrangian. For the statistical description of the gluon plasma we interpret these non-linear waves as quasi-particles with a temperature dependent mass distribution. Quasi-Gaussian distributions with a common variance but different temperature dependent mean masses for the longitudinal and transverse modes are employed. We use recent Lattice results to fix the mean transverse and longitudinal masses while the variance is fitted to the equation of state of pure $SU(3)$ on the Lattice. Thus, our model succeeds to obtain both a consistent description of the gluon plasma energy density as well as a correct behaviour of the mass parameters near the critical point.Comment: 7 pages, 2 figure

K-sample subsampling in general spaces: The case of independent time series

AbstractThe problem of subsampling in two-sample and K-sample settings is addressed where both the data and the statistics of interest take values in general spaces. We focus on the case where each sample is a stationary time series, and construct subsampling confidence intervals and hypothesis tests with asymptotic validity. Some examples are also given, and the problem of optimal block size choice is discussed

Dyskinesias after neural transplantation in Parkinson's disease: what do we know and what is next?

Since the 1980 s, when cell transplantation into the brain as a cure for Parkinson's disease hit the headlines, several patients with Parkinson's disease have received transplantation of cells from aborted fetuses with the aim of replacing the dopamine cells destroyed by the disease. The results in human studies were unpredictable and raised controversy. Some patients showed remarkable improvement, but many of the patients who underwent transplantation experienced serious disabling adverse reactions, putting an end to human trials since the late 1990 s. These side effects consisted of patients' developing troublesome involuntary, uncontrolled movements in the absence of dopaminergic medication, so-called off-phase, graft-induced dyskinesias. Notwithstanding the several mechanisms having been proposed, the pathogenesis of this type of dyskinesias remained unclear and there was no effective treatment. It has been suggested that graft-induced dyskinesias could be related to fiber outgrowth from the graft causing increased dopamine release, that could be related to the failure of grafts to restore a precise distribution of dopaminergic synaptic contacts on host neurons or may also be induced by inflammatory and immune responses around the graft. A recent study, however, hypothesized that an important factor for the development of graft-induced dyskinesias could include the composition of the cell suspension and specifically that a high proportion of serotonergic neurons cografted in these transplants engage in nonphysiological properties such as false transmitter release. The findings from this study showed serotonergic hyperinnervation in the grafted striatum of two patients with Parkinson's disease who exhibited major motor recovery after transplantation with fetal mesencephalic tissue but later developed graft-induced dyskinesias. Moreover, the dyskinesias were significantly attenuated by administration of a serotonin agonist, which activates the inhibitory serotonin autoreceptors and attenuates transmitter release from serotonergic neurons, indicating that graft-induced dyskinesias were caused by the dense serotonergic innervation engaging in false transmitter release. Here the implications of the recent findings for the development of new human trials testing the safety and efficacy of cell transplantation in patients with Parkinson's disease are discussed

On the asymptotic theory of subsampling

A general approach to constructing confidence intervals by subsampling was presented in Politis and Romano (1994). The crux of the method is based on recomputing a statistic over subsamples of the data, and these recomputed values are used to build up an estimated sampling distribution. The method works under extremely weak conditions, it applies to independent, identically distributed (LLd.) observations as well as to dependent data situations, such as time series (possible non stationary) , random fields, and marked point processes. In this article, we present some new theorems showing: a new construction for confidence intervals that removes a previous condition, a general theorem showing the validity of subsampling for datadependent choices of the block size, and a general theorem for the construction of hypothesis tests (which is not necessarily derived from a confidence interval construction). The arguments apply to both the Li.d. setting as well as the dependent data case

Subsampling, symmetrization, and robust interpolation

The recently developed subsampling methodology has been shown to be valid for the construction of large-sample confidence regions for a general unknown parameter e under very minimal conditions. Nevertheless, in some specific cases -e.g. in the case of the sample mean of Li.d. data- it has been noted that the subsampling distribution estimators underperform as compared to alternative estimators such as the bootstrap or the asymptotic normal distribution (with estimated variance). In the present report we investigate the extent to which the performance of subsampling distribution estimators can be improved by a (partial) symmetrization technique, while at the same time retaining the robustness property of consistent distribution estimation even in nonregular cases; both i.i.d. and weakly dependent (mixing) observations are considered