Decimation and harmonic inversion of periodic orbit signals

Main, Jörg; Dando, P. A.; Belkić, Dževad; Taylor, Howard S.

doi:10.1088/0305-4470/33/6/311

Cited by 38 publications

(66 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…to a sum of exponentials [8,14,15,11]. If we consider a dynamical system with the PF operator L, then in the linear prediction (LP) approach we assume that an auto-correlation function C(t) of some observable u(x) with a zero phase-space average µ(u) = 0 can, for t ≥ 0, be represented by a finite sum of exponentials as…”

Section: Discussion Of the Linear Predictor Approach To Ruelle-pollicmentioning

confidence: 99%

A hybrid method for calculation of Ruelle–Pollicott resonances

Horvat¹,

Veble²

2009

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

Section: Discussion Of the Linear Predictor Approach To Ruelle-pollicmentioning

confidence: 99%

A hybrid method for calculation of Ruelle–Pollicott resonances

Horvat¹,

Veble²

2009

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…The condition G 1j (0, τ ′ ) = G 1j (T 0 , τ ′ ), which is expected from equation (10), is also fulfilled. The discontinuities in the elementṡ G 2j , which appear due to equation (16), are clearly visible. Figure 3 (c) shows the classical Green's function for the same orbit, which is not restricted to the fundamental domain but closed by a rotation of its final point (see figure 3 (d)).…”

Section: An Example For a Symmetry Reduced Orbitmentioning

confidence: 96%

ℏ expansions in semiclassical theories for systems with smooth potentials and discrete symmetries

Cartarius

Main

2007

Annals of Physics

View full text Add to dashboard Cite

We extend a theory of first order corrections to Gutzwiller's trace formula for systems with a smooth potential to systems with discrete symmetries and, as an example, apply the method to the two-dimensional hydrogen atom in a uniform magnetic field. We exploit the C 4v -symmetry of the system in the calculation of the correction terms. The numerical results for the semiclassical values will be compared with values extracted from exact quantum mechanical calculations. The comparison shows an excellent agreement and demonstrates the power of the expansion method.

show abstract

“…Not so long ago, however, researchers in this community began to take a closer look at the other disciplines also dealing with time signals. Eventually, among the many remarkable achievements, they encountered the recent advances in quantum chemistry within the realm of the so-named "quantum-mechanical signal processing" [2,[79][80][81][82][83][84]. Therein, their main attention was caught by signal processors based upon rational functions, notably those from the vast family belonging to the Padé approximant [85][86][87][88][89][90][91][92][93].…”

Section: Conclusion and Future Outlooksmentioning

confidence: 99%

Robust identification of the cancer biomarker phosphocholine through partitioned envelopes in noisy magnetic resonance spectroscopic data by the non-parametric fast Padé transform

Belkić

2017

J Math Chem

View full text Add to dashboard Cite

The recently introduced concept of envelope partitioning for shape estimation within the fast Padé transform (FPT) is presently further explored and solidified. Earlier, noise-free time signals were used and the results were reported for a single model order K . Currently, partitioned envelopes are computed for several values of model orders K by employing noise-corrupted time signals of increasing standard deviations, σ = 0.0289, 0.289, 2.89 in units of root-mean-square of the noise-free time signal. Moreover, spectra averaging is exploited to stabilize shape estimation in face of sensitivity to changes in model order. The main goal of this study is to establish the robustness of the non-parametric FPT for reconstructions of partitioned average envelopes computed with noisy time signals. Both the previous and present illustrations concern synthesized time signals typically encountered in single-voxel magnetic resonance spectroscopy (MRS), akin to in vitro encoding from malignant breast tissue. This particular problem area is chosen for a twofold reason: clinical urgency in cancer medicine, and a huge challenge to reliably identify a key cancer biomarker (phosphocholine), completely hidden underneath a dominant peak (phosphoethanolamine), with a separation of mere 0.001 parts per million of chemical shift. signals, the road would be paved for applications of this special shape estimation to the associated data from in vivo encodings. Partitioned envelopes are important since they offer possibilities to peer into the tightly overlapped resonances by splitting their components apart already at the level of sole total shape spectra. Although constrained by non-parametric estimations, they can still qualitatively decompose the regions of higher spectral density. This would enable subsequent focusing on the most critical spectral regions of interest when solving the local quantification problem by parametric estimations. Such a stepwise strategy is expected to be especially beneficial for multi-voxel magnetic resonance spectroscopic imaging (MRSI), where thousands of noisy spectra need to be processed. The FPT-based partitioned envelopes, followed by accurate local spectral analysis in narrow frequency intervals are poised to help MRSI become an efficient diagnostic modality for everyday clinical practice.

show abstract

Decimation and harmonic inversion of periodic orbit signals

Cited by 38 publications

References 32 publications

A hybrid method for calculation of Ruelle–Pollicott resonances

A hybrid method for calculation of Ruelle–Pollicott resonances

ℏ expansions in semiclassical theories for systems with smooth potentials and discrete symmetries

Robust identification of the cancer biomarker phosphocholine through partitioned envelopes in noisy magnetic resonance spectroscopic data by the non-parametric fast Padé transform

Contact Info

Product

Resources

About