Climate spectrum estimation in the presence of timescale errors

We introduce an algorithm (called REDFITmc2) for spectrum estimation in the presence of timescale errors. It is based on the Lomb-Scargle periodogram for unevenly spaced time series, in combination with the Welch's Overlapped Segment Averaging procedure, bootstrap bias correction and persistence estimation. The timescale errors are modelled parametrically and included in the simulations for determining (1) the upper levels of the spectrum of the red-noise AR(1) alternative and (2) the uncertainty of the frequency of a spectral peak. Application of REDFITmc2 to ice core and stalagmite records of palaeoclimate allowed a more realistic evaluation of spectral peaks than when ignoring this source of uncertainty. The results support qualitatively the intuition that stronger effects on the spectrum estimate (decreased detectability and increased frequency uncertainty) occur for higher frequencies. The surplus information brought by algorithm REDFITmc2 is that those effects are quantified. Regarding timescale construction, not only the fixpoints, dating errors and the functional form of the age-depth model play a role. Also the joint distribution of all time points (serial correlation, stratigraphic order) determines spectrum estimation.

Hard thermal loop benchmark for the extraction of the nonperturbative QQ[over ¯] potential

The extraction of the finite temperature heavy quark potential from lattice QCD relies on a spectral analysis of the Wilson loop. General arguments tell us that the lowest lying spectral peak encodes, through its position and shape, the real and imaginary parts of this complex potential. Here we benchmark this extraction strategy using leading order hard-thermal loop (HTL) calculations. In other words, we analytically calculate the Wilson loop and determine the corresponding spectrum. By fitting its lowest lying peak we obtain the real and imaginary parts and confirm that the knowledge of the lowest peak alone is sufficient for obtaining the potential. Access to the full spectrum allows an investigation of spectral features that do not contribute to the potential but can pose a challenge to numerical attempts of an analytic continuation from imaginary time data. Differences in these contributions between the Wilson loop and gauge fixed Wilson line correlators are discussed. To better understand the difficulties in a numerical extraction we deploy the maximum entropy method with extended search space to HTL correlators in Euclidean time and observe how well the known spectral function and values for the real and imaginary parts are reproduced. Possible venues for improvement of the extraction strategy are discussed.

Benchmarking the Bayesian reconstruction of the non-perturbative heavy ǪǬ potential

The extraction of the finite temperature heavy quark potential from lattice QCD relies on a spectral analysis of the real-time Wilson loop. Through its position and shape, the lowest lying spectral peak encodes the real and imaginary part of this complex potential. We benchmark this extraction strategy using leading order hard-thermal loop (HTL) calculations. I.e. we analytically calculate the Wilson loop and determine the corresponding spectrum. By fitting its lowest lying peak we obtain the real- and imaginary part and confirm that the knowledge of the lowest peak alone is sufficient for obtaining the potential. We deploy a novel Bayesian approach to the reconstruction of spectral functions to HTL correlators in Euclidean time and observe how well the known spectral function and values for the real and imaginary part are reproduced. Finally we apply the method to quenched lattice QCD data and perform an improved estimate of both real and imaginary part of the non-perturbative heavy ǪǬ potential.

Non-water-suppressed proton MR spectroscopy improves spectral quality in the human spinal cord

Magnetic resonance spectroscopy enables insight into the chemical composition of spinal cord tissue. However, spinal cord magnetic resonance spectroscopy has rarely been applied in clinical work due to technical challenges, including strong susceptibility changes in the region and the small cord diameter, which distort the lineshape and limit the attainable signal to noise ratio. Hence, extensive signal averaging is required, which increases the likelihood of static magnetic field changes caused by subject motion (respiration, swallowing), cord motion, and scanner-induced frequency drift. To avoid incoherent signal averaging, it would be ideal to perform frequency alignment of individual free induction decays before averaging. Unfortunately, this is not possible due to the low signal to noise ratio of the metabolite peaks. In this article, frequency alignment of individual free induction decays is demonstrated to improve spectral quality by using the high signal to noise ratio water peak from non-water-suppressed proton magnetic resonance spectroscopy via the metabolite cycling technique. Electrocardiography (ECG)-triggered point resolved spectroscopy (PRESS) localization was used for data acquisition with metabolite cycling or water suppression for comparison. A significant improvement in the signal to noise ratio and decrease of the Cramér Rao lower bounds of all metabolites is attained by using metabolite cycling together with frequency alignment, as compared to water-suppressed spectra, in 13 healthy volunteers.

Spectral waveform analysis of intranodal arterial blood flow in abnormally large superficial lymph nodes in dogs

Objective-To evaluate pulsed-wave Doppler spectral parameters as a method for distinguishing between neoplastic and inflammatory peripheral lymphadenopathy in dogs. Sample Population-40 superficial lymph nodes from 33 dogs with peripheral lymphadenopathy. Procedures-3 Doppler spectral tracings were recorded from each node. Spectral Doppler analysis including assessment of the resistive index, peak systolic velocity-to-end diastolic velocity (S:D) ratio, diastolic notch velocity-to-peak systolic velocity (N:S) ratio, and end diastolic velocity-to-diastolic notch velocity ratio was performed for each tracing. Several calculation methods were used to determine the Doppler indices for each lymph node. After the ultrasonographic examination, fine needle aspirates or excisional biopsy specimens of the examined lymph nodes were obtained, and lymphadenopathy was classified as either inflammatory or neoplastic (lymphomatous or metastatic) via cytologic or histologic examination. Results of Doppler analysis were compared with cytologic or histopathologic findings. Results-The Doppler index with the highest diagnostic accuracy was the S:D ratio calculated from the first recorded tracing; a cutoff value of 3.22 yielded sensitivity of 91%, specificity of 100%, and negative predictive value of 89% for detection of neoplasia. Overall diagnostic accuracy was 95%. At a sensitivity of 100%, the most accurate index was the N:S ratio calculated from the first recorded tracing; a cutoff value of 0.45 yielded specificity of 67%, positive predictive value of 81%, and overall diagnostic accuracy of 86.5%. Conclusions and Clinical Relevance-Results suggested that noninvasive Doppler spectral analysis may be useful in the diagnosis of neoplastic versus inflammatory peripheral lymphadenopathy in dogs.

A new Bayesian approach to the reconstruction of spectral functions

We present a novel approach for the reconstruction of spectra from Euclidean correlator data that makes close contact to modern Bayesian concepts. It is based upon an axiomatically justified dimensionless prior distribution, which in the case of constant prior function m(ω) only imprints smoothness on the reconstructed spectrum. In addition we are able to analytically integrate out the only relevant overall hyper-parameter α in the prior, removing the necessity for Gaussian approximations found e.g. in the Maximum Entropy Method. Using a quasi-Newton minimizer and high-precision arithmetic, we are then able to find the unique global extremum of P[ρ|D] in the full Nω » Nτ dimensional search space. The method actually yields gradually improving reconstruction results if the quality of the supplied input data increases, without introducing artificial peak structures, often encountered in the MEM. To support these statements we present mock data analyses for the case of zero width delta peaks and more realistic scenarios, based on the perturbative Euclidean Wilson Loop as well as the Wilson Line correlator in Coulomb gauge.