Proposals which speed-up function-space MCMC

Inverse problems lend themselves naturally to a Bayesian formulation, in which the quantity of interest is a posterior distribution of state and/or parameters given some uncertain observations. For the common case in which the forward operator is smoothing, then the inverse problem is ill-posed. Well-posedness is imposed via regularisation in the form of a prior, which is often Gaussian. Under quite general conditions, it can be shown that the posterior is absolutely continuous with respect to the prior and it may be well-defined on function space in terms of its density with respect to the prior. In this case, by constructing a proposal for which the prior is invariant, one can define Metropolis-Hastings schemes for MCMC which are well-defined on function space, and hence do not degenerate as the dimension of the underlying quantity of interest increases to infinity, e.g. under mesh refinement when approximating PDE in finite dimensions. However, in practice, despite the attractive theoretical properties of the currently available schemes, they may still suffer from long correlation times, particularly if the data is very informative about some of the unknown parameters. In fact, in this case it may be the directions of the posterior which coincide with the (already known) prior which decorrelate the slowest. The information incorporated into the posterior through the data is often contained within some finite-dimensional subspace, in an appropriate basis, perhaps even one defined by eigenfunctions of the prior. We aim to exploit this fact and improve the mixing time of function-space MCMC by careful rescaling of the proposal. To this end, we introduce two new basic methods of increasing complexity, involving (i) characteristic function truncation of high frequencies and (ii) hessian information to interpolate between low and high frequencies

The Effects of an Early Motion Protocol for Rehabilitation Following a Massive Rotator Cuff Tear Repair: A Case Report

Background and Purpose: Rotator cuff tears are one of the most common musculoskeletal injuries to occur in the United States. Following a surgical repair, there are two main rehabilitation protocols: early motion and delayed motion. Despite the large number of patients in need of rehab following a rotator cuff tear surgical repair, there is not yet a definitive answer in the literature as far as the best protocol to use. Case Description: The patient was a 68-year-old male who injured himself while slipping and attempting to catch himself with his right arm. He presented to physical therapy following a surgical repair of a massive rotator cuff tear. His active range of motion and strength were within normal limits on his non-involved upper extremity, though severely limited on the surgical side due to a combination of pain and post-surgical precautions. Interventions: The patient received therapeutic exercise, ultrasound, E-stim, patient education, and trigger point release manual therapy over the course of physical therapy. Outcomes: The patient had 18 sessions of physical therapy. By the end, his active range of motion on the surgical arm equaled that of his non-involved extremity, and his strength was making rapid gains as well. Discussion: Research regarding early versus delayed motion protocols is limited. Further research should be performed studying different patient demographics to see if factors such as age, various pathologies, size of tear, etc., can affect which protocol would provide the most benefits and least risk for them. The patient in this case report demonstrated significant improvements over the course of therapy utilizing the early motion protocol

Among underemployed college graduates, the role of class looms large

Compared to past decades, a far higher percentage of Americans now attend college. But those who graduate often must contend with high levels of student debt, and face a more uncertain labor market which can lead to underemployment. In new research which looks at post-college underemployment, Kody Steffy finds that those graduates who considered that they were voluntarily underemployed tended ..

Deterministic Mean-field Ensemble Kalman Filtering

The proof of convergence of the standard ensemble Kalman filter (EnKF) from Legland etal. (2011) is extended to non-Gaussian state space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence $\kappa$ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF when the dimension $d<2\kappa$. The fidelity of approximation of the true distribution is also established using an extension of total variation metric to random measures. This is limited by a Gaussian bias term arising from non-linearity/non-Gaussianity of the model, which exists for both DMFEnKF and standard EnKF. Numerical results support and extend the theory

Optimising Microsatellite Networks for IoT

The Internet of Things (IoT) is having a profound impact on the way we understand the world and its inhabitants. One of the biggest challenges that IoT network providers face is providing global coverage for these IoT devices. Space-based IoT solve this by connecting long-range, low-power, low-bandwidth devices with a constellation of Low Earth Orbit (LEO) microsatellites. These satellite networks typically use store-and-forward communications, where a device uplinks cached data to a passing satellite which is stored on-board until the satellite comes in range of a Ground Station (GS). This data is then downlinked and sent to a cloud platform where it can be accessed by a customer

Plan for Phased Continuity of the Research Enterprise Email

Email from Kody Varahramyan, Vice President for Research and Dean of the Graduate School, University of Maine regarding the Plan for Phased Continuity of the Research Enterprise produced by the Research Continuity Task Force Plan who were responsible for looking at re-opening research at UMaine based on federal, state and UMaine system guidance, and the scientific evidence around COVID-19 infection control. The Task Force was established by Dean Varahramyan to assist with the anticipated changes to the research guidelines and their implementation as the COVID-19 conditions dictate

Teaching Queer Trauma: Applying Meditation as a Pedagogy of Compassion

Mindfulness practices can help greatly when teaching potentially triggering courses on queerness and trauma. Meditation allows students to learn how to manage triggers, enhancing their distress tolerance and their ability to fully engage with course material. It also has practical benefits for applied courses, as students will learn how mindfulness practices can help when working with queer and traumatized clients in, for example, a social services setting. This original teaching activity describes a course I taught called \u27Queer Trauma and Resilience: Canadian Perspectives,\u27 and outlines several meditations that were taught progressively throughout the course. Debriefing methods are included as well as reflective assessments used in the course