Conditional Probabilities of Multivariate Poisson Distributions

Multivariate Poisson distributions have numerous applications. Fast computation of these distributions, holding constant a fixed set of linear combinations of these variables, has been explored by Sontag and Zeilberger. This elaborates on their work

Discriminative Bayesian filtering lends momentum to the stochastic Newton method for minimizing log-convex functions

To minimize the average of a set of log-convex functions, the stochastic Newton method iteratively updates its estimate using subsampled versions of the full objective's gradient and Hessian. We contextualize this optimization problem as sequential Bayesian inference on a latent state-space model with a discriminatively-specified observation process. Applying Bayesian filtering then yields a novel optimization algorithm that considers the entire history of gradients and Hessians when forming an update. We establish matrix-based conditions under which the effect of older observations diminishes over time, in a manner analogous to Polyak's heavy ball momentum. We illustrate various aspects of our approach with an example and review other relevant innovations for the stochastic Newton method

The Short Rotation Period of Hi'iaka, Haumea's Largest Satellite

Hi'iaka is the larger outer satellite of the dwarf planet Haumea. Using relative photometry from the Hubble Space Telescope and Magellan and a phase dispersion minimization analysis, we have identified the rotation period of Hi'iaka to be ~9.8 hrs (double-peaked). This is ~120 times faster than its orbital period, creating new questions about the formation of this system and possible tidal evolution. The rapid rotation suggests that Hi'iaka could have a significant obliquity and spin precession that could be visible in light curves within a few years. We then turn to an investigation of what we learn about the (presently unclear) formation of the Haumea system and family based on this unexpectedly rapid rotation rate. We explore the importance of the initial semi-major axis and rotation period in tidal evolution theory and find they strongly influence the time required to despin to synchronous rotation, relevant to understanding a wide variety of satellite and binary systems. We find that despinning tides do not necessarily lead to synchronous spin periods for Hi'iaka, even if it formed near the Roche limit. Therefore the short rotation period of Hi'iaka does not rule out significant tidal evolution. Hi'iaka's spin period is also consistent with formation near its current location and spin up due to Haumea-centric impactors.Comment: 21 pages with 6 figures, to be published in The Astronomical Journa

Unsupervised multimodal modeling of cognitive and brain health trajectories for early dementia prediction

Predicting the course of neurodegenerative disorders early has potential to greatly improve clinical management and patient outcomes. A key challenge for early prediction in real-world clinical settings is the lack of labeled data (i.e., clinical diagnosis). In contrast to supervised classification approaches that require labeled data, we propose an unsupervised multimodal trajectory modeling (MTM) approach based on a mixture of state space models that captures changes in longitudinal data (i.e., trajectories) and stratifies individuals without using clinical diagnosis for model training. MTM learns the relationship between states comprising expensive, invasive biomarkers (β-amyloid, grey matter density) and readily obtainable cognitive observations. MTM training on trajectories stratifies individuals into clinically meaningful clusters more reliably than MTM training on baseline data alone and is robust to missing data (i.e., cognitive data alone or single assessments). Extracting an individualized cognitive health index (i.e., MTM-derived cluster membership index) allows us to predict progression to AD more precisely than standard clinical assessments (i.e., cognitive tests or MRI scans alone). Importantly, MTM generalizes successfully from research cohort to real-world clinical data from memory clinic patients with missing data, enhancing the clinical utility of our approach. Thus, our multimodal trajectory modeling approach provides a cost-effective and non-invasive tool for early dementia prediction without labeled data (i.e., clinical diagnosis) with strong potential for translation to clinical practice

The orbits of the quadruple star system 88 Tau A from PHASES differential astrometry and radial velocity

We have used high precision differential astrometry from the Palomar High-precision Astrometric Search for Exoplanet Systems (PHASES) project and radial velocity measurements covering a time-span of 20 years to determine the orbital parameters of the 88 Tau A system. 88 Tau is a complex hierarchical multiple system comprising a total of six stars; we have studied the brightest 4, consisting of two short-period pairs orbiting each other with an 18-year period. We present the first orbital solution for one of the short-period pairs, and determine the masses of the components and distance to the system to the level of a few percent. In addition, our astrometric measurements allow us to make the first determination of the mutual inclinations of the orbits. We find that the sub-systems are not coplanar.Comment: Corrected Author Ordering; 12 Pages, Accepted for publication in Ap

The Two States of Star Forming Clouds

We examine the effects of self-gravity and magnetic fields on supersonic turbulence in isothermal molecular clouds with high resolution simulations and adaptive mesh refinement. These simulations use large root grids (512^3) to capture turbulence and four levels of refinement to capture high density, for an effective resolution of 8,196^3. Three Mach 9 simulations are performed, two super-Alfv\'enic and one trans-Alfv\'enic. We find that gravity splits the clouds into two populations, one low density turbulent state and one high density collapsing state. The low density state exhibits properties similar to non-self-gravitating in this regime, and we examine the effects of varied magnetic field strength on statistical properties: the density probability distribution function is approximately lognormal; velocity power spectral slopes decrease with field strength; alignment between velocity and magnetic field increases with field; the magnetic field probability distribution can be fit to a stretched exponential. The high density state is characterized by self-similar spheres; the density PDF is a power-law; collapse rate decreases with increasing mean field; density power spectra have positive slopes, P({\rho},k) \propto k; thermal-to-magnetic pressure ratios are unity for all simulations; dynamic-to-magnetic pressure ratios are larger than unity for all simulations; magnetic field distribution is a power-law. The high Alfv\'en Mach numbers in collapsing regions explain recent observations of magnetic influence decreasing with density. We also find that the high density state is found in filaments formed by converging flows, consistent with recent Herschel observations. Possible modifications to existing star formation theories are explored.Comment: 19 pages, 20 figure

Tendon–bone contact pressure and biomechanical evaluation of a modified suture-bridge technique for rotator cuff repair

The aim of the study was to evaluate the time-zero mechanical and footprint properties of a suture-bridge technique for rotator cuff repair in an animal model. Thirty fresh-frozen sheep shoulders were randomly assigned among three investigation groups: (1) cyclic loading, (2) load-to-failure testing, and (3) tendon–bone interface contact pressure measurement. Shoulders were cyclically loaded from 10 to 180 N and displacement to gap formation of 5- and 10-mm at the repair site. Cycles to failure were determined. Additionally, the ultimate tensile strength and stiffness were verified along with the mode of failure. The average contact pressure and pressure pattern were investigated using a pressure-sensitive film system. All of the specimens resisted against 3,000 cycles and none of them reached a gap formation of 10 mm. The number of cycles to 5-mm gap formation was 2,884.5 ± 96.8 cycles. The ultimate tensile strength was 565.8 ± 17.8 N and stiffness was 173.7 ± 9.9 N/mm. The entire specimen presented a unique mode of failure as it is well known in using high strength sutures by pulling them through the tendon. We observed a mean contact pressure of 1.19 ± 0.03 MPa, applied on the footprint area. The fundamental results of our study support the use of a suture-bridge technique for optimising the conditions of the healing biology of a reconstructed rotator cuff tendon. Nevertheless, an individual estimation has to be done if using the suture-bridge technique clinically. Further investigation is necessary to evaluate the cell biological healing process in order to achieve further sufficient advancements in rotator cuff repair

Results of matching valve and root repair to aortic valve and root pathology

ObjectiveFor patients with aortic root pathology and aortic valve regurgitation, aortic valve replacement is problematic because no durable bioprosthesis exists, and mechanical valves require lifetime anticoagulation. This study sought to assess outcomes of combined aortic valve and root repair, including comparison with matched bioprosthesis aortic valve replacement.MethodsFrom November 1990 to January 2005, 366 patients underwent modified David reimplantation (n = 72), root remodeling (n = 72), or valve repair with sinotubular junction tailoring (n = 222). Active follow-up was 99% complete, with a mean of 5.6 ± 4.0 years (maximum 17 years); follow-up for vital status averaged 8.5 ± 3.6 years (maximum 19 years). Propensity-adjusted models were developed for fair comparison of outcomes.ResultsThirty-day and 5-, 10-, and 15-year survivals were 98%, 86%, 74%, and 58%, respectively, similar to that of the US matched population and better than that after bioprosthesis aortic valve replacement. Propensity-score–adjusted survival was similar across procedures (P > .3). Freedom from reoperation at 30 days and 5 and 10 years was 99%, 92%, and 89%, respectively, and was similar across procedures (P > .3) after propensity-score adjustment. Patients with tricuspid aortic valves were more likely to be free of reoperation than those with bicuspid valves at 10 years (93% vs 77%, P = .002), equivalent to bioprosthesis aortic valve replacement and superior after 12 years. Bioprostheses increasingly deteriorated after 7 years, and hazard functions for reoperation crossed at 7 years.ConclusionsValve preservation (rather than replacement) and matching root procedures have excellent early and long-term results, with increasing survival benefit at 7 years and fewer reoperations by 12 years. We recommend this procedure for experienced surgical teams