Instantaneous frequency and amplitude of complex signals based on quaternion Fourier transform

The ideas of instantaneous amplitude and phase are well understood for signals with real-valued samples, based on the analytic signal which is a complex signal with one-sided Fourier transform. We extend these ideas to signals with complex-valued samples, using a quaternion-valued equivalent of the analytic signal obtained from a one-sided quaternion Fourier transform which we refer to as the hypercomplex representation of the complex signal. We present the necessary properties of the quaternion Fourier transform, particularly its symmetries in the frequency domain and formulae for convolution and the quaternion Fourier transform of the Hilbert transform. The hypercomplex representation may be interpreted as an ordered pair of complex signals or as a quaternion signal. We discuss its derivation and properties and show that its quaternion Fourier transform is one-sided. It is shown how to derive from the hypercomplex representation a complex envelope and a phase. A classical result in the case of real signals is that an amplitude modulated signal may be analysed into its envelope and carrier using the analytic signal provided that the modulating signal has frequency content not overlapping with that of the carrier. We show that this idea extends to the complex case, provided that the complex signal modulates an orthonormal complex exponential. Orthonormal complex modulation can be represented mathematically by a polar representation of quaternions previously derived by the authors. As in the classical case, there is a restriction of non-overlapping frequency content between the modulating complex signal and the orthonormal complex exponential. We show that, under these conditions, modulation in the time domain is equivalent to a frequency shift in the quaternion Fourier domain. Examples are presented to demonstrate these concepts

Multiperiodicity, modulations and flip-flops in variable star light curves I. Carrier fit method

The light curves of variable stars are commonly described using simple trigonometric models, that make use of the assumption that the model parameters are constant in time. This assumption, however, is often violated, and consequently, time series models with components that vary slowly in time are of great interest. In this paper we introduce a class of data analysis and visualization methods which can be applied in many different contexts of variable star research, for example spotted stars, variables showing the Blazhko effect, and the spin-down of rapid rotators. The methods proposed are of explorative type, and can be of significant aid when performing a more thorough data analysis and interpretation with a more conventional method.Our methods are based on a straightforward decomposition of the input time series into a fast "clocking" periodicity and smooth modulating curves. The fast frequency, referred to as the carrier frequency, can be obtained from earlier observations (for instance in the case of photometric data the period can be obtained from independently measured radial velocities), postulated using some simple physical principles (Keplerian rotation laws in accretion disks), or estimated from the data as a certain mean frequency. The smooth modulating curves are described by trigonometric polynomials or splines. The data approximation procedures are based on standard computational packages implementing simple or constrained least-squares fit-type algorithms.Comment: 14 pages, 23 figures, submitted to Astronomy and Astrophysic

Women using a web‐based digital health coaching programme for stress management: stress sources, symptoms and soping strategies

Researchers have proposed and tested many theories to understand gender differences in stress experiences. However, little research has identified differences between subgroups of women in terms of stress sources, symptoms, coping strategies and help‐seeking behaviour. The purpose of this study was to examine these characteristics of women seeking help for stress management through a digital health coaching programme. We examined cross‐sectional data from 63,690 women between the ages of 18 and 59 years who participated in the stress management programme from 2001 to 2008. We divided the sample into age groups to identify developmental patterns in their stress characteristics. Work , time demands and psychological reactions to stress were consistent concerns, whereas between‐group comparisons indicated diverse stress characteristics by age group. Importantly, women at all ages reported being uncomfortable asking for help. The findings suggest that technology‐based solutions like digital health coaching may reach women who may not otherwise seek or receive help for stress management. The results also emphasize the importance of considering the unique characteristics of women when providing them stress management interventions. Copyright © 2011 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87059/1/smi1389.pd

Evaluation of sensitivity to endocrine herapy index (SET2,3) for response to neoadjuvant endocrine therapy and longer-term breast cancer patient outcomes (Alliance Z1031)

PURPOSE: To evaluate prediction of response and event-free survival (EFS) following neoadjuvant endocrine therapy by SET2,3 index of nonproliferation gene expression related to estrogen and progesterone receptors adjusted for baseline prognosis. EXPERIMENTAL DESIGN: A correlative study was conducted of SET2,3 measured from gene expression profiles of diagnostic tumor (Agilent microarrays) in 379 women with cStage II-III breast cancer from the American College of Surgeons Oncology Group Z1031 neoadjuvant aromatase inhibitor trial SET2,3 was dichotomized using the previously published cutoff. Fisher exact test was used to assess the association between SET2,3 and low proliferation at week 2-4 [Ki67 ≤ 10% or complete cell-cycle arrest (CCCA; Ki67 ≤ 2.7%)] and PEPI-0 rate in cohort B, and the association between SET2,3 and ypStage 0/I in all patients. Cox models were used to assess EFS with respect to SET2,3 excluding cohort B patients who switched to chemotherapy. RESULTS: Patients with high SET2,3 had higher rate of pharmacodynamic response than patients with low SET2,3 (Ki67 ≤ 10% in 88.2% vs. 56.9%, P \u3c 0.0001; CCCA in 50.0% vs. 26.2%, P = 0.0054), but rate of ypStage 0/I (24.0% vs. 20.4%, P = 0.4580) or PEPI = 0 (28.4% vs. 20.6%, P = 0.3419) was not different. Patients with high SET2,3 had longer EFS than patients with low SET2,3 (HR, 0.52, 95% confidence interval: 0.34-0.80; P = 0.0026). CONCLUSIONS: This exploratory analysis of Z1031 data demonstrated a higher rate of pharmacodynamic suppression of proliferation and longer EFS in high SET2,3 disease relative to low SET2,3 disease. The ypStage 0/I rate and PEPI = 0 rate were similar with respect to SET2,3

Radiomic and deep learning characterization of breast parenchyma on full field digital mammograms and specimen radiographs: A pilot study of a potential cancer field effect

Purpose: In women with biopsy-proven breast cancer, histologically normal areas of the parenchyma have shown molecular similarity to the tumor, supporting a potential cancer field effect. The purpose of this work was to investigate relationships of human-engineered radiomic and deep learning features between regions across the breast in mammographic parenchymal patterns and specimen radiographs. Approach: This study included mammograms from 74 patients with at least 1 identified malignant tumor, of whom 32 also possessed intraoperative radiographs of mastectomy specimens. Mammograms were acquired with a Hologic system and specimen radiographs were acquired with a Fujifilm imaging system. All images were retrospectively collected under an Institutional Review Board-approved protocol. Regions of interest (ROI) of 128 × 128 pixels were selected from three regions: within the identified tumor, near to the tumor, and far from the tumor. Radiographic texture analysis was used to extract 45 radiomic features and transfer learning was used to extract 20 deep learning features in each region. Kendall’s Tau-b and Pearson correlation tests were performed to assess relationships between features in each region. Results: Statistically significant correlations in select subgroups of features with tumor, near to the tumor, and far from the tumor ROI regions were identified in both mammograms and specimen radiographs. Intensity-based features were found to show significant correlations with ROI regions across both modalities. Conclusions: Results support our hypothesis of a potential cancer field effect, accessible radiographically, across tumor and non-tumor regions, thus indicating the potential for computerized analysis of mammographic parenchymal patterns to predict breast cancer risk.</p

Segmentation of plate coupling, fate of subduction fluids, and modes of arc magmatism in Cascadia, inferred from magnetotelluric resistivity

Author Posting. © American Geophysical Union, 2014. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geochemistry, Geophysics, Geosystems 15 (2014): 4230–4253, doi:10.1002/2014GC005509.Five magnetotelluric (MT) profiles have been acquired across the Cascadia subduction system and transformed using 2-D and 3-D nonlinear inversion to yield electrical resistivity cross sections to depths of ∼200 km. Distinct changes in plate coupling, subduction fluid evolution, and modes of arc magmatism along the length of Cascadia are clearly expressed in the resistivity structure. Relatively high resistivities under the coasts of northern and southern Cascadia correlate with elevated degrees of inferred plate locking, and suggest fluid- and sediment-deficient conditions. In contrast, the north-central Oregon coastal structure is quite conductive from the plate interface to shallow depths offshore, correlating with poor plate locking and the possible presence of subducted sediments. Low-resistivity fluidized zones develop at slab depths of 35–40 km starting ∼100 km west of the arc on all profiles, and are interpreted to represent prograde metamorphic fluid release from the subducting slab. The fluids rise to forearc Moho levels, and sometimes shallower, as the arc is approached. The zones begin close to clusters of low-frequency earthquakes, suggesting fluid controls on the transition to steady sliding. Under the northern and southern Cascadia arc segments, low upper mantle resistivities are consistent with flux melting above the slab plus possible deep convective backarc upwelling toward the arc. In central Cascadia, extensional deformation is interpreted to segregate upper mantle melts leading to underplating and low resistivities at Moho to lower crustal levels below the arc and nearby backarc. The low- to high-temperature mantle wedge transition lies slightly trenchward of the arc.Phil Wannamaker and Virginie Maris gratefully acknowledge funding by the U.S. National Science Foundation under grants EAR08–43725 and EAR08–38043 through the Earthscope and Geophysics programs. The 2D inversion capability received development support under U.S. Department of Energy contract DE-PS36-04GO94001. Rob Evans was supported through Earthscope grant EAR08–44041 and Shane McGary through a National Defense Science and Engineering Graduate (NDSEG) fellowship. Fieldwork in Canada was made possible by an NSERC Discovery Grant and a Canadian Foundation for Innovation award to Martyn Unsworth.2015-05-1

Transient anhedonia phenotype and altered circadian timing of behaviour during night-time dim light exposure in Per3(-/-) mice, but not wildtype mice.

Industrialisation greatly increased human night-time exposure to artificial light, which in animal models is a known cause of depressive phenotypes. Whilst many of these phenotypes are 'direct' effects of light on affect, an 'indirect' pathway via altered sleep-wake timing has been suggested. We have previously shown that the Period3 gene, which forms part of the biological clock, is associated with altered sleep-wake patterns in response to light. Here, we show that both wild-type and Per3(-/-) mice showed elevated levels of circulating corticosterone and increased hippocampal Bdnf expression after 3 weeks of exposure to dim light at night, but only mice deficient for the PERIOD3 protein (Per3(-/-)) exhibited a transient anhedonia-like phenotype, observed as reduced sucrose preference, in weeks 2-3 of dim light at night, whereas WT mice did not. Per3(-/-) mice also exhibited a significantly smaller delay in behavioural timing than WT mice during weeks 1, 2 and 4 of dim light at night exposure. When treated with imipramine, neither Per3(-/-) nor WT mice exhibited an anhedonia-like phenotype, and neither genotypes exhibited a delay in behavioural timing in responses to dLAN. While the association between both Per3(-/-) phenotypes remains unclear, both are alleviated by imipramine treatment during dim night-time light