Gradient Descent Provably Solves Nonlinear Tomographic Reconstruction.

In computed tomography (CT), the forward model consists of a linear Radon transform followed by an exponential nonlinearity based on the attenuation of light according to the Beer-Lambert Law. Conventional reconstruction often involves inverting this nonlinearity as a preprocessing step and then solving a convex inverse problem. However, this nonlinear measurement preprocessing required to use the Radon transform is poorly conditioned in the vicinity of high-density materials, such as metal. This preprocessing makes CT reconstruction methods numerically sensitive and susceptible to artifacts near high-density regions. In this paper, we study a technique where the signal is directly reconstructed from raw measurements through the nonlinear forward model. Though this optimization is nonconvex, we show that gradient descent provably converges to the global optimum at a geometric rate, perfectly reconstructing the underlying signal with a near minimal number of random measurements. We also prove similar results in the under-determined setting where the number of measurements is significantly smaller than the dimension of the signal. This is achieved by enforcing prior structural information about the signal through constraints on the optimization variables. We illustrate the benefits of direct nonlinear CT reconstruction with cone-beam CT experiments on synthetic and real 3D volumes. We show that this approach reduces metal artifacts compared to a commercial reconstruction of a human skull with metal dental crowns.

Re-analysis on the statistical sampling biases of a mask promotion trial in Bangladesh: a statistical replication.

A recent randomized trial evaluated the impact of mask promotion on COVID-19-related outcomes. We find that staff behavior in both unblinded and supposedly blinded steps caused large and statistically significant imbalances in population sizes. These denominator differences constitute the rate differences observed in the trial, complicating inferences of causality.

A generalizable and accessible approach to machine learning with global satellite imagery.

Combining satellite imagery with machine learning (SIML) has the potential to address global challenges by remotely estimating socioeconomic and environmental conditions in data-poor regions, yet the resource requirements of SIML limit its accessibility and use. We show that a single encoding of satellite imagery can generalize across diverse prediction tasks (e.g., forest cover, house price, road length). Our method achieves accuracy competitive with deep neural networks at orders of magnitude lower computational cost, scales globally, delivers label super-resolution predictions, and facilitates characterizations of uncertainty. Since image encodings are shared across tasks, they can be centrally computed and distributed to unlimited researchers, who need only fit a linear regression to their own ground truth data in order to achieve state-of-the-art SIML performance.

High-throughput fluorescence microscopy using multi-frame motion deblurring.

We demonstrate multi-frame motion deblurring for gigapixel wide-field fluorescence microscopy using fast slide scanning with coded illumination. Our method illuminates the sample with multiple pulses within each exposure, in order to introduce structured motion blur. By deconvolving this known motion sequence from the set of acquired measurements, we recover the object with up to 10× higher SNR than when illuminated with a single pulse (strobed illumination), while performing acquisition at 5× higher frame-rate than a comparable stop-and-stare method. Our coded illumination sequence is optimized to maximize the reconstruction SNR. We also derive a framework for determining when coded illumination is SNR-optimal in terms of system parameters such as source illuminance, noise, and motion stage specifications. This helps system designers to choose the ideal technique for high-throughput microscopy of very large samples.

Saturating Splines and Feature Selection.

We extend the adaptive regression spline model by incorporating saturation, the natural requirement that a function extend as a constant outside a certain range. We fit saturating splines to data via a convex optimization problem over a space of measures, which we solve using an efficient algorithm based on the conditional gradient method. Unlike many existing approaches, our algorithm solves the original infinite-dimensional (for splines of degree at least two) optimization problem without pre-specified knot locations. We then adapt our algorithm to fit generalized additive models with saturating splines as coordinate functions and show that the saturation requirement allows our model to simultaneously perform feature selection and nonlinear function fitting. Finally, we briefly sketch how the method can be extended to higher order splines and to different requirements on the extension outside the data range.

Well-Being Tracking via Smartphone-Measured Activity and Sleep: Cohort Study.

BACKGROUND: Automatically tracking mental well-being could facilitate personalization of treatments for mood disorders such as depression and bipolar disorder. Smartphones present a novel and ubiquitous opportunity to track individuals' behavior and may be useful for inferring and automatically monitoring mental well-being. OBJECTIVE: The aim of this study was to assess the extent to which activity and sleep tracking with a smartphone can be used for monitoring individuals' mental well-being. METHODS: A cohort of 106 individuals was recruited to install an app on their smartphone that would track their well-being with daily surveys and track their behavior with activity inferences from their phone's accelerometer data. Of the participants recruited, 53 had sufficient data to infer activity and sleep measures. For this subset of individuals, we related measures of activity and sleep to the individuals' well-being and used these measures to predict their well-being. RESULTS: We found that smartphone-measured approximations for daily physical activity were positively correlated with both mood (P=.004) and perceived energy level (P<.001). Sleep duration was positively correlated with mood (P=.02) but not energy. Our measure for sleep disturbance was not found to be significantly related to either mood or energy, which could imply too much noise in the measurement. Models predicting the well-being measures from the activity and sleep measures were found to be significantly better than naive baselines (P<.01), despite modest overall improvements. CONCLUSIONS: Measures of activity and sleep inferred from smartphone activity were strongly related to and somewhat predictive of participants' well-being. Whereas the improvement over naive models was modest, it reaffirms the importance of considering physical activity and sleep for predicting mood and for making automatic mood monitoring a reality.

Meaningless comparisons lead to false optimism in medical machine learning.

A new trend in medicine is the use of algorithms to analyze big datasets, e.g. using everything your phone measures about you for diagnostics or monitoring. However, these algorithms are commonly compared against weak baselines, which may contribute to excessive optimism. To assess how well an algorithm works, scientists typically ask how well its output correlates with medically assigned scores. Here we perform a meta-analysis to quantify how the literature evaluates their algorithms for monitoring mental wellbeing. We find that the bulk of the literature (∼77%) uses meaningless comparisons that ignore patient baseline state. For example, having an algorithm that uses phone data to diagnose mood disorders would be useful. However, it is possible to explain over 80% of the variance of some mood measures in the population by simply guessing that each patient has their own average mood-the patient-specific baseline. Thus, an algorithm that just predicts that our mood is like it usually is can explain the majority of variance, but is, obviously, entirely useless. Comparing to the wrong (population) baseline has a massive effect on the perceived quality of algorithms and produces baseless optimism in the field. To solve this problem we propose "user lift" that reduces these systematic errors in the evaluation of personalized medical monitoring.

3D imaging in volumetric scattering media using phase-space measurements.

We demonstrate the use of phase-space imaging for 3D localization of multiple point sources inside scattering material. The effect of scattering is to spread angular (spatial frequency) information, which can be measured by phase space imaging. We derive a multi-slice forward model for homogenous volumetric scattering, then develop a reconstruction algorithm that exploits sparsity in order to further constrain the problem. By using 4D measurements for 3D reconstruction, the dimensionality mismatch provides significant robustness to multiple scattering, with either static or dynamic diffusers. Experimentally, our high-resolution 4D phase-space data is collected by a spectrogram setup, with results successfully recovering the 3D positions of multiple LEDs embedded in turbid scattering media.

Robust efficiency and actuator saturation explain healthy heart rate control and variability.

The correlation of healthy states with heart rate variability (HRV) using time series analyses is well documented. Whereas these studies note the accepted proximal role of autonomic nervous system balance in HRV patterns, the responsible deeper physiological, clinically relevant mechanisms have not been fully explained. Using mathematical tools from control theory, we combine mechanistic models of basic physiology with experimental exercise data from healthy human subjects to explain causal relationships among states of stress vs. health, HR control, and HRV, and more importantly, the physiologic requirements and constraints underlying these relationships. Nonlinear dynamics play an important explanatory role--most fundamentally in the actuator saturations arising from unavoidable tradeoffs in robust homeostasis and metabolic efficiency. These results are grounded in domain-specific mechanisms, tradeoffs, and constraints, but they also illustrate important, universal properties of complex systems. We show that the study of complex biological phenomena like HRV requires a framework which facilitates inclusion of diverse domain specifics (e.g., due to physiology, evolution, and measurement technology) in addition to general theories of efficiency, robustness, feedback, dynamics, and supporting mathematical tools.

Alterations in cerebrospinal fluid proteins in a presymptomatic primary glioma model.

BACKGROUND: Understanding the early relationship between brain tumor cells and their environment could lead to more sensitive biomarkers and new therapeutic strategies. We have been using a rodent model of neurocarcinogenesis in which all animals develop brain tumors by six months of age to establish two early landmarks in glioma development: the appearance of a nestin(+) cell at thirty days of age and the appearance of cellular hyperplasia between 60 and 120 days of age. We now report an assessment of the CSF proteome to determine the changes in protein composition that occur during this period. MATERIALS AND METHODS: Nestin(+) cell clusters and microtumors were assessed in 63 ethylnitrosourea-exposed rats on 30, 60, and 90 days of age. CSF was obtained from the cisterna magna from 101 exposed and control rats at 30, 60, and 90 days and then analyzed using mass spectrometry. Differentially expressed peaks were isolated and identified. RESULTS: Nestin(+) cells were noted in all ethylnitrosourea-exposed rats assessed pathologically. Small microtumors were noted in 0%, 18%, and 67% of 30-, 60-, and 90-day old rats, respectively (p<0.05, Chi square). False Discovery Rate analysis of peak intensities showed that the number of true discoveries with p<0.05 increased markedly with increasing age. Isolation and identification of highly differentially detected proteins at 90 days of age revealed increases in albumin and a fragment of α1 macroglobulin and alterations in glutathionylated transthyretin. CONCLUSIONS: The presence of increased albumin, fragments of cerebrospinal fluid proteins, and glutathione breakdown in temporal association with the development of cellular hyperplasia, suggests that, similar to many other systemic cancers, inflammation and oxidative stress is playing an important early role in the host's response to brain tumor development and may be involved in affecting the early growth of brain tumor.

A distinct phenotypic change in gliomas at the time of magnetic resonance imaging detection.

OBJECT: Although gliomas remain refractory to treatment, it is not clear whether this characteristic is fixed at the time of its origin or develops later. The authors have been using a model of neurocarcinogenesis to determine whether a time exists during a glioma's evolution during which it is detectable but still curable, thus providing a justification for exploring the clinical merits of an early detection and treatment strategy. The authors recently reported the presence of 2 distinct cellular subsets, 1 expressing nestin and the other both glial fibrillary acidic protein (GFAP) and osteopontin (OPN), within all examined gliomas that developed after in utero exposure to ethylnitrosourea. METHODS: In this study, the authors used magnetic resonance (MR) imaging to assess when these 2 subpopulations appeared during glioma evolution. RESULTS: Using T2-weighted and diffusion-weighted MR imaging, the authors observed that gliomas grew exponentially once detected at rates that were location-dependent. Despite large differences in growth rates, however, they determined by correlating histochemistry with imaging in a second series of animals, that all lesions initially detected on T2-weighted images contained both subsets of cells. In contrast, lesions containing only nestin-positive cells, which appeared on average 40 days before detection on MR images, were not detected. CONCLUSIONS: The sequential appearance of first the nestin-positive cells followed several weeks later by those expressing GFAP/OPN suggests that all gliomas arise through common early steps in this model. Furthermore, the authors hypothesize that the expression of OPN, a molecule associated with cancer aggressiveness, at the time of T2-weighted detection signals a time during glioma development when the lesion becomes refractory to treatment.