Compressive and Noncompressive Power Spectral Density Estimation from Periodic Nonuniform Samples

This paper presents a novel power spectral density estimation technique for band-limited, wide-sense stationary signals from sub-Nyquist sampled data. The technique employs multi-coset sampling and incorporates the advantages of compressed sensing (CS) when the power spectrum is sparse, but applies to sparse and nonsparse power spectra alike. The estimates are consistent piecewise constant approximations whose resolutions (width of the piecewise constant segments) are controlled by the periodicity of the multi-coset sampling. We show that compressive estimates exhibit better tradeoffs among the estimator's resolution, system complexity, and average sampling rate compared to their noncompressive counterparts. For suitable sampling patterns, noncompressive estimates are obtained as least squares solutions. Because of the non-negativity of power spectra, compressive estimates can be computed by seeking non-negative least squares solutions (provided appropriate sampling patterns exist) instead of using standard CS recovery algorithms. This flexibility suggests a reduction in computational overhead for systems estimating both sparse and nonsparse power spectra because one algorithm can be used to compute both compressive and noncompressive estimates.Comment: 26 pages, single spaced, 9 figure

Bayesian latent time joint mixed-effects model of progression in the Alzheimer's Disease Neuroimaging Initiative.

IntroductionWe characterize long-term disease dynamics from cognitively healthy to dementia using data from the Alzheimer's Disease Neuroimaging Initiative.MethodsWe apply a latent time joint mixed-effects model to 16 cognitive, functional, biomarker, and imaging outcomes in Alzheimer's Disease Neuroimaging Initiative. Markov chain Monte Carlo methods are used for estimation and inference.ResultsWe find good concordance between latent time and diagnosis. Change in amyloid positron emission tomography shows a moderate correlation with change in cerebrospinal fluid tau (ρ = 0.310) and phosphorylated tau (ρ = 0.294) and weaker correlation with amyloid-β 42 (ρ = 0.176). In comparison to amyloid positron emission tomography, change in volumetric magnetic resonance imaging summaries is more strongly correlated with cognitive measures (e.g., ρ = 0.731 for ventricles and Alzheimer's Disease Assessment Scale). The average disease trends are consistent with the amyloid cascade hypothesis.DiscussionThe latent time joint mixed-effects model can (1) uncover long-term disease trends; (2) estimate the sequence of pathological abnormalities; and (3) provide subject-specific prognostic estimates of the time until onset of symptoms

Predicting the course of Alzheimer's progression.

Alzheimer's disease is the most common neurodegenerative disease and is characterized by the accumulation of amyloid-beta peptides leading to the formation of plaques and tau protein tangles in brain. These neuropathological features precede cognitive impairment and Alzheimer's dementia by many years. To better understand and predict the course of disease from early-stage asymptomatic to late-stage dementia, it is critical to study the patterns of progression of multiple markers. In particular, we aim to predict the likely future course of progression for individuals given only a single observation of their markers. Improved individual-level prediction may lead to improved clinical care and clinical trials. We propose a two-stage approach to modeling and predicting measures of cognition, function, brain imaging, fluid biomarkers, and diagnosis of individuals using multiple domains simultaneously. In the first stage, joint (or multivariate) mixed-effects models are used to simultaneously model multiple markers over time. In the second stage, random forests are used to predict categorical diagnoses (cognitively normal, mild cognitive impairment, or dementia) from predictions of continuous markers based on the first-stage model. The combination of the two models allows one to leverage their key strengths in order to obtain improved accuracy. We characterize the predictive accuracy of this two-stage approach using data from the Alzheimer's Disease Neuroimaging Initiative. The two-stage approach using a single joint mixed-effects model for all continuous outcomes yields better diagnostic classification accuracy compared to using separate univariate mixed-effects models for each of the continuous outcomes. Overall prediction accuracy above 80% was achieved over a period of 2.5 years. The results further indicate that overall accuracy is improved when markers from multiple assessment domains, such as cognition, function, and brain imaging, are used in the prediction algorithm as compared to the use of markers from a single domain only

Neuroanatomical spread of amyloid β and tau in Alzheimer's disease: implications for primary prevention.

With recent advances in our understanding of the continuous pathophysiological changes that begin many years prior to symptom onset, it is now apparent that Alzheimer's disease cannot be adequately described by discrete clinical stages, but should also incorporate the continuum of biological changes that precede and underlie the clinical representation of the disease. By jointly considering longitudinal changes of all available biomarkers and clinical assessments, variation within individuals can be integrated into a single continuous measure of disease progression and used to identify the earliest pathophysiological changes. Disease time, a measure of disease severity, was estimated using a Bayesian latent time joint mixed-effects model applied to an array of imaging, biomarker and neuropsychological data. Trajectories of regional amyloid β and tau PET uptake were estimated as a function of disease time. Regions with early signs of elevated amyloid β uptake were used to form an early, focal composite and compared to a commonly used global composite, in a separate validation sample. Disease time was estimated in 279 participants (183 cognitively unimpaired individuals, 61 mild cognitive impairment and 35 Alzheimer's disease dementia patients) with available amyloid β and tau PET data. Amyloid β PET uptake levels in the posterior cingulate and precuneus start high and immediately increase with small increases of disease time. Early elevation in tau PET uptake was found in the inferior temporal lobe, amygdala, banks of the superior temporal sulcus, entorhinal cortex, middle temporal lobe, inferior parietal lobe and the fusiform gyrus. In a separate validation sample of 188 cognitively unimpaired individuals, the early, focal amyloid β PET composite showed a 120% increase in the accumulation rate of amyloid β compared to the global composite (P < 0.001), resulting in a 60% increase in the power to detect a treatment effect in a primary prevention trial design. Ordering participants on a continuous disease time scale facilitates the inspection of the earliest signs of amyloid β and tau pathology. To detect early changes in amyloid β pathology, focusing on the earliest sites of amyloid β accumulation results in more powerful and efficient study designs in early Alzheimer's disease. Targeted composites could be used to re-examine the thresholds for amyloid β-related study inclusion, especially as the field shifts to focus on primary and secondary prevention. Clinical trials of anti-amyloid β treatments may benefit from the use of focal composites when estimating drug effects on amyloid β and tau changes in populations with minimal amyloid β and tau pathology and limited expected short-term accumulation

The relative efficiency of time-to-progression and continuous measures of cognition in presymptomatic Alzheimer's disease.

IntroductionClinical trials on preclinical Alzheimer's disease are challenging because of the slow rate of disease progression. We use a simulation study to demonstrate that models of repeated cognitive assessments detect treatment effects more efficiently than models of time to progression.MethodsMultivariate continuous data are simulated from a Bayesian joint mixed-effects model fit to data from the Alzheimer's Disease Neuroimaging Initiative. Simulated progression events are algorithmically derived from the continuous assessments using a random forest model fit to the same data.ResultsWe find that power is approximately doubled with models of repeated continuous outcomes compared with the time-to-progression analysis. The simulations also demonstrate that a plausible informative missing data pattern can induce a bias that inflates treatment effects, yet 5% type I error is maintained.DiscussionGiven the relative inefficiency of time to progression, it should be avoided as a primary analysis approach in clinical trials of preclinical Alzheimer's disease

Defect-Seeded Atomic Layer Deposition of Metal Oxides on the Basal Plane of 2D Layered Materials

Atomic layer deposition (ALD) on mechanically exfoliated 2D layered materials spontaneously produces network patterns of metal oxide nanoparticles in triangular and linear deposits on the basal surface. The network patterns formed under a range of ALD conditions and were independent of the orientation of the substrate in the ALD reactor. The patterns were produced on MoS2 or HOPG when either tetrakis(dimethylamido)titanium or bis(ethylcyclopentadienyl)manganese were used as precursors, suggesting that the phenomenon is general for 2D materials. Transmission electron microscopy revealed the presence, prior to deposition, of dislocation networks along the basal plane of mechanically exfoliated 2D flakes, indicating that periodical basal plane defects related to disruptions in the van der Waals stacking of layers, such as perfect line dislocations and triangular extended stacking faults networks, introduce a surface reactivity landscape that leads to the emergence of patterned deposition

Shear-dependent apparent slip on hydrophobic surfaces: The Mattress Model

Recent experiments (Zhu & Granick (2001) Phys. Rev. Lett. 87 096105) have measured a large shear dependent fluid slip at partially wetting fluid-solid surfaces. We present a simple model for such slip, motivated by the recent observations of nanobubbles on hydrophobic surfaces. The model considers the dynamic response of bubbles to change in hydrodynamic pressure due to the oscillation of a solid surface. Both the compression and diffusion of gas in the bubbles decrease the force on the oscillating surface by a ``leaking mattress'' effect, thereby creating an apparent shear-dependent slip. With bubbles similar to those observed by atomic force microscopy to date, the model is found to lead to force decreases consistent with the experimental measurements of Zhu & Granick