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Numerical treatment of seismic accelerograms and of inelastic seismic structural responses using harmonic wavelets
The harmonic wavelet transform is employed to analyze various kinds of nonstationary signals common in aseismic design. The effectiveness of the harmonic wavelets for capturing the temporal evolution of the frequency content of strong ground motions is demonstrated. In this regard, a detailed study of important earthquake accelerograms is undertaken and smooth joint time-frequency spectra are provided for two near-field and two far-field records; inherent in this analysis is the concept of the mean instantaneous frequency. Furthermore, as a paradigm of usefulness for aseismic structural purposes, a similar analysis is conducted for the response of a 20-story steel frame benchmark building considering one of the four accelerograms scaled by appropriate factors as the excitation to simulate undamaged and severely damaged conditions for the structure. The resulting joint time-frequency representation of the response time histories captures the influence of nonlinearity on the variation of the effective natural frequencies of a structural system during the evolution of a seismic event. In this context, the potential of the harmonic wavelet transform as a detection tool for global structural damage is explored in conjunction with the concept of monitoring the mean instantaneous frequency of records of critical structural responses
Multiresolution analysis in statistical mechanics. II. The wavelet transform as a basis for Monte Carlo simulations on lattices
In this paper, we extend our analysis of lattice systems using the wavelet
transform to systems for which exact enumeration is impractical. For such
systems, we illustrate a wavelet-accelerated Monte Carlo (WAMC) algorithm,
which hierarchically coarse-grains a lattice model by computing the probability
distribution for successively larger block spins. We demonstrate that although
the method perturbs the system by changing its Hamiltonian and by allowing
block spins to take on values not permitted for individual spins, the results
obtained agree with the analytical results in the preceding paper, and
``converge'' to exact results obtained in the absence of coarse-graining.
Additionally, we show that the decorrelation time for the WAMC is no worse than
that of Metropolis Monte Carlo (MMC), and that scaling laws can be constructed
from data performed in several short simulations to estimate the results that
would be obtained from the original simulation. Although the algorithm is not
asymptotically faster than traditional MMC, because of its hierarchical design,
the new algorithm executes several orders of magnitude faster than a full
simulation of the original problem. Consequently, the new method allows for
rapid analysis of a phase diagram, allowing computational time to be focused on
regions near phase transitions.Comment: 11 pages plus 7 figures in PNG format (downloadable separately
Quantitative Regular Expressions for Arrhythmia Detection Algorithms
Motivated by the problem of verifying the correctness of arrhythmia-detection
algorithms, we present a formalization of these algorithms in the language of
Quantitative Regular Expressions. QREs are a flexible formal language for
specifying complex numerical queries over data streams, with provable runtime
and memory consumption guarantees. The medical-device algorithms of interest
include peak detection (where a peak in a cardiac signal indicates a heartbeat)
and various discriminators, each of which uses a feature of the cardiac signal
to distinguish fatal from non-fatal arrhythmias. Expressing these algorithms'
desired output in current temporal logics, and implementing them via monitor
synthesis, is cumbersome, error-prone, computationally expensive, and sometimes
infeasible.
In contrast, we show that a range of peak detectors (in both the time and
wavelet domains) and various discriminators at the heart of today's
arrhythmia-detection devices are easily expressible in QREs. The fact that one
formalism (QREs) is used to describe the desired end-to-end operation of an
arrhythmia detector opens the way to formal analysis and rigorous testing of
these detectors' correctness and performance. Such analysis could alleviate the
regulatory burden on device developers when modifying their algorithms. The
performance of the peak-detection QREs is demonstrated by running them on real
patient data, on which they yield results on par with those provided by a
cardiologist.Comment: CMSB 2017: 15th Conference on Computational Methods for Systems
Biolog
Multiresolution analysis in statistical mechanics. I. Using wavelets to calculate thermodynamic properties
The wavelet transform, a family of orthonormal bases, is introduced as a
technique for performing multiresolution analysis in statistical mechanics. The
wavelet transform is a hierarchical technique designed to separate data sets
into sets representing local averages and local differences. Although
one-to-one transformations of data sets are possible, the advantage of the
wavelet transform is as an approximation scheme for the efficient calculation
of thermodynamic and ensemble properties. Even under the most drastic of
approximations, the resulting errors in the values obtained for average
absolute magnetization, free energy, and heat capacity are on the order of 10%,
with a corresponding computational efficiency gain of two orders of magnitude
for a system such as a Ising lattice. In addition, the errors in
the results tend toward zero in the neighborhood of fixed points, as determined
by renormalization group theory.Comment: 13 pages plus 7 figures (PNG
Discrepancy between sub-critical and fast rupture roughness: a cumulant analysis
We study the roughness of a crack interface in a sheet of paper. We
distinguish between slow (sub-critical) and fast crack growth regimes. We show
that the fracture roughness is different in the two regimes using a new method
based on a multifractal formalism recently developed in the turbulence
literature. Deviations from monofractality also appear to be different in both
regimes
Construction of Parseval wavelets from redundant filter systems
We consider wavelets in L^2(R^d) which have generalized multiresolutions.
This means that the initial resolution subspace V_0 in L^2(R^d) is not singly
generated. As a result, the representation of the integer lattice Z^d
restricted to V_0 has a nontrivial multiplicity function. We show how the
corresponding analysis and synthesis for these wavelets can be understood in
terms of unitary-matrix-valued functions on a torus acting on a certain vector
bundle. Specifically, we show how the wavelet functions on R^d can be
constructed directly from the generalized wavelet filters.Comment: 34 pages, AMS-LaTeX ("amsproc" document class) v2 changes minor typos
in Sections 1 and 4, v3 adds a number of references on GMRA theory and
wavelet multiplicity analysis; v4 adds material on pages 2, 3, 5 and 10, and
two more reference
Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: numerical study
We study scalar and vector modulation instabilities induced by the vacuum
fluctuations in birefringent optical fibers. To this end, stochastic coupled
nonlinear Schrodinger equations are derived. The stochastic model is equivalent
to the quantum field operators equations and allow for dispersion,
nonlinearity, and arbitrary level of birefringence. Numerical integration of
the stochastic equations is compared to analytical formulas in the case of
scalar modulation instability and non depleted pump approximation. The effect
of classical noise and its competition with vacuum fluctuations for inducing
modulation instability is also addressed.Comment: 33 pages, 5 figure
Study of the spectral properties of ELM precursors by means of wavelets
The high confinement regime (H-mode) in tokamaks is accompanied by the occurrence of bursts of MHD activity at the plasma edge, so-called edge localized modes (ELMs), lasting less than 1 ms. These modes are often preceded by coherent oscillations in the magnetic field, the ELM precursors, whose mode numbers along the toroidal and the poloidal directions can be measured from the phase shift between Mirnov pickup coils. When the ELM precursors have a lifetime shorter than a few milliseconds, their toroidal mode number and their nonlinear evolution before the ELM crash cannot be studied reliably with standard techniques based on Fourier analysis, since averaging in time is implicit in the computation of the Fourier coefficients. This work demonstrates significant advantages in studying spectral features of the short-lived ELM precursors by using Morlet wavelets. It is shown that the wavelet analysis is suitable for the identification of the toroidal mode numbers of ELM precursors with the shortest lifetime, as well as for studying their nonlinear evolution with a time resolution comparable to the acquisition rate of the Mirnov coils
Multiresolution Analysis of Substructure in Dark Matter Halos
Multiresolution analysis is applied to the problem of halo identification in
cosmological N-body simulations. The procedure makes use of a discrete wavelet
transform known as the algorithme a trous and segmentation analysis. It has the
ability to find subhalos in the dense regions of a parent halo and can discern
the multiple levels of substructure expected in the hierarchical clustering
scenario. As an illustration, a 500,000 particle dark matter halo is analyzed
and over 600 subhalos are found. Statistical properties of the subhalo
population are discussed.Comment: 22 pages, 12 figures, substantial changes and additions over original
submission, to be published in the Astrophysical Journal, Oct, 200
Wavelet Formulation of Path Integral Monte Carlo
A wavelet formulation of path integral Monte Carlo (PIMC)is constructed. Comparison with Fourier path integral Monte Carlo is presented using simple one-dimensional examples. Wavelet path integral Monte Carlo exhibits a few advantages over previous methods for PIMC. The efficiency of the current method is at least comparable to other techniques
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