A Composite Initialization Method for Phase Retrieval

Phase retrieval is a classical inverse problem with respect to recovering a signal from a system of phaseless constraints. Many recently proposed methods for phase retrieval such as PhaseMax and gradient-descent algorithms enjoy benign theoretical guarantees on the condition that an elaborate estimate of true solution is provided. Current initialization methods do not perform well when number of measurements are low, which deteriorates the success rate of current phase retrieval methods. We propose a new initialization method that can obtain an estimate of the original signal with uniformly higher accuracy which combines the advantages of the null vector method and maximal correlation method. The constructed spectral matrix for the proposed initialization method has a simple and symmetrical form. A lower error bound is proved theoretically as well as verified numerically.

Temporal Correlation of CSF and Neuroimaging in the Amyloid-Tau-Neurodegeneration Model of Alzheimer Disease

Objective:Temporal correlations between CSF and neuroimaging (PET and MRI) measures of amyloid, tau, and neurodegeneration were evaluated in relation to Alzheimer disease (AD) progression.Methods:Three hundred seventy-one cognitively unimpaired and impaired participants enrolled in longitudinal studies of AD had both CSF (amyloid-β42, phosphorylated tau181, total tau, and neurofilament light chain) and neuroimaging (PiB PET, flortaucipir PET, and structural MRI) measures. The pairwise time interval between CSF and neuroimaging measures was binned into two year periods. Spearman correlations identified the time bin when CSF and neuroimaging measures most strongly correlated. CSF and neuroimaging measures were then binarized as biomarker-positive or biomarker-negative using Gaussian mixture modelling. Cohen’s kappa coefficient identified the time bin when CSF measures best agreed with corresponding neuroimaging measures when determining amyloid, tau, and neurodegeneration biomarker positivity.Results:CSF amyloid-β42 and PiB PET showed maximal correlation when collected within six years of each other (R ≈ -0.5). CSF phosphorylated tau181 and flortaucipir PET showed maximal correlation when CSF was collected four to eight years prior to PET (R ≈ 0.4). CSF neurofilament light chain and cortical thickness showed low correlation, regardless of time interval (Ravg ≈ -0.3). Similarly, CSF total tau and cortical thickness had low correlation, regardless of time interval (Ravg < -0.2).Conclusions:CSF amyloid-β42 and PiB PET best agree when acquired in close temporal proximity, whereas CSF phosphorylated tau precedes flortaucipir PET by four to eight years. CSF and neuroimaging measures of neurodegeneration have low correspondence and are not interchangeable at any time interval.

Relationships Between 24-h LH and Testosterone Concentrations and With Other Pituitary Hormones in Healthy Older Men

Objective To investigate the relationship between LH and T, which characteristics associate with the strength of this relationship, and their interrelationships with GH, TSH, cortisol, and ACTH. Design Hormones were measured in serum samples collected every 10 min during 24 h from 20 healthy men, comprising 10 offspring of long-lived families and 10 control subjects, with a mean (SD) age of 65.6 (5.3) years. We performed cross-correlation analyses to assess the relative strength between two timeseries for all possible time shifts. Results Mean (95% CI) maximal correlation was 0.21 (0.10–0.31) at lag time 60 min between LH and total T concentrations. Results were comparable for calculated free, bioavailable, or secretion rates of T. Men with strong LH-T cross-correlations had, compared to men with no cross-correlation, lower fat mass (18.5 (14.9–19.7) vs. 22.3 (18.4–29.4) kg), waist circumference (93.6 (5.7) vs. 103.1 (12.0) cm), hsCRP (0.7 (0.4–1.3) vs. 1.8 (0.8–12.3) mg/L), IL-6 (0.8 (0.6–1.0) vs. 1.2 (0.9–3.0) pg/mL), and 24-h mean LH (4.3 (2.0) vs. 6.1 (1.5) U/L), and stronger LH-T feedforward synchrony (1.5 (0.3) vs. 1.9 (0.2)). Furthermore, T was positively cross-correlated with TSH (0.32 (0.21–0.43)), cortisol (0.26 (0.19–0.33)), and ACTH (0.26 (0.19–0.32)). Conclusions LH is followed by T with a delay of 60 min in healthy older men. Men with a strong LH-T relationship had more favorable body composition, inflammatory markers, LH levels, and LH-T feedforward synchrony. We observed positive correlations between T and TSH, cortisol, and ACTH.