Superiorization: An optimization heuristic for medical physics

Purpose: To describe and mathematically validate the superiorization methodology, which is a recently-developed heuristic approach to optimization, and to discuss its applicability to medical physics problem formulations that specify the desired solution (of physically given or otherwise obtained constraints) by an optimization criterion. Methods: The underlying idea is that many iterative algorithms for finding such a solution are perturbation resilient in the sense that, even if certain kinds of changes are made at the end of each iterative step, the algorithm still produces a constraints-compatible solution. This property is exploited by using permitted changes to steer the algorithm to a solution that is not only constraints-compatible, but is also desirable according to a specified optimization criterion. The approach is very general, it is applicable to many iterative procedures and optimization criteria used in medical physics. Results: The main practical contribution is a procedure for automatically producing from any given iterative algorithm its superiorized version, which will supply solutions that are superior according to a given optimization criterion. It is shown that if the original iterative algorithm satisfies certain mathematical conditions, then the output of its superiorized version is guaranteed to be as constraints-compatible as the output of the original algorithm, but it is superior to the latter according to the optimization criterion. This intuitive description is made precise in the paper and the stated claims are rigorously proved. Superiorization is illustrated on simulated computerized tomography data of a head cross-section and, in spite of its generality, superiorization is shown to be competitive to an optimization algorithm that is specifically designed to minimize total variation.Comment: Accepted for publication in: Medical Physic

Feasibility-Seeking and Superiorization Algorithms Applied to Inverse Treatment Planning in Radiation Therapy

We apply the recently proposed superiorization methodology (SM) to the inverse planning problem in radiation therapy. The inverse planning problem is represented here as a constrained minimization problem of the total variation (TV) of the intensity vector over a large system of linear two-sided inequalities. The SM can be viewed conceptually as lying between feasibility-seeking for the constraints and full-fledged constrained minimization of the objective function subject to these constraints. It is based on the discovery that many feasibility-seeking algorithms (of the projection methods variety) are perturbation-resilient, and can be proactively steered toward a feasible solution of the constraints with a reduced, thus superiorized, but not necessarily minimal, objective function value.Comment: Contemporary Mathematics, accepted for publicatio

Convergence and Perturbation Resilience of Dynamic String-Averaging Projection Methods

We consider the convex feasibility problem (CFP) in Hilbert space and concentrate on the study of string-averaging projection (SAP) methods for the CFP, analyzing their convergence and their perturbation resilience. In the past, SAP methods were formulated with a single predetermined set of strings and a single predetermined set of weights. Here we extend the scope of the family of SAP methods to allow iteration-index-dependent variable strings and weights and term such methods dynamic string-averaging projection (DSAP) methods. The bounded perturbation resilience of DSAP methods is relevant and important for their possible use in the framework of the recently developed superiorization heuristic methodology for constrained minimization problems.Comment: Computational Optimization and Applications, accepted for publicatio

Widespread polycistronic gene expression in green algae

Polycistronic gene expression, common in prokaryotes, was thought to be extremely rare in eukaryotes. The development of long-read sequencing of full-length transcript isomers (Iso-Seq) has facilitated a reexamination of that dogma. Using Iso-Seq, we discovered hundreds of examples of polycistronic expression of nuclear genes in two divergent species of green algae: Chlamydomonas reinhardtii and Chromochloris zofingiensis Here, we employ a range of independent approaches to validate that multiple proteins are translated from a common transcript for hundreds of loci. A chromatin immunoprecipitation analysis using trimethylation of lysine 4 on histone H3 marks confirmed that transcription begins exclusively at the upstream gene. Quantification of polyadenylated [poly(A)] tails and poly(A) signal sequences confirmed that transcription ends exclusively after the downstream gene. Coexpression analysis found nearly perfect correlation for open reading frames (ORFs) within polycistronic loci, consistent with expression in a shared transcript. For many polycistronic loci, terminal peptides from both ORFs were identified from proteomics datasets, consistent with independent translation. Synthetic polycistronic gene pairs were transcribed and translated in vitro to recapitulate the production of two distinct proteins from a common transcript. The relative abundance of these two proteins can be modified by altering the Kozak-like sequence of the upstream gene. Replacement of the ORFs with selectable markers or reporters allows production of such heterologous proteins, speaking to utility in synthetic biology approaches. Conservation of a significant number of polycistronic gene pairs between C. reinhardtii, C. zofingiensis, and five other species suggests that this mechanism may be evolutionarily ancient and biologically important in the green algal lineage

A separated vortex ring underlies the flight of the dandelion

Wind-dispersed plants have evolved ingenious ways to lift their seeds1,2. The common dandelion uses a bundle of drag-enhancing bristles (the pappus) that helps to keep their seeds aloft. This passive flight mechanism is highly effective, enabling seed dispersal over formidable distances3,4; however, the physics underpinning pappus-mediated flight remains unresolved. Here we visualized the flow around dandelion seeds, uncovering an extraordinary type of vortex. This vortex is a ring of recirculating fluid, which is detached owing to the flow passing through the pappus. We hypothesized that the circular disk-like geometry and the porosity of the pappus are the key design features that enable the formation of the separated vortex ring. The porosity gradient was surveyed using microfabricated disks, and a disk with a similar porosity was found to be able to recapitulate the flow behaviour of the pappus. The porosity of the dandelion pappus appears to be tuned precisely to stabilize the vortex, while maximizing aerodynamic loading and minimizing material requirements. The discovery of the separated vortex ring provides evidence of the existence of a new class of fluid behaviour around fluid-immersed bodies that may underlie locomotion, weight reduction and particle retention in biological and manmade structures

Conceptual design report for the LUXE experiment

This Conceptual Design Report describes LUXE (Laser Und XFEL Experiment), an experimental campaign that aims to combine the high-quality and high-energy electron beam of the European XFEL with a powerful laser to explore the uncharted terrain of quantum electrodynamics characterised by both high energy and high intensity. We will reach this hitherto inaccessible regime of quantum physics by analysing high-energy electron-photon and photon-photon interactions in the extreme environment provided by an intense laser focus. The physics background and its relevance are presented in the science case which in turn leads to, and justifies, the ensuing plan for all aspects of the experiment: Our choice of experimental parameters allows (i) field strengths to be probed where the coupling to charges becomes non-perturbative and (ii) a precision to be achieved that permits a detailed comparison of the measured data with calculations. In addition, the high photon flux predicted will enable a sensitive search for new physics beyond the Standard Model. The initial phase of the experiment will employ an existing 40 TW laser, whereas the second phase will utilise an upgraded laser power of 350 TW. All expectations regarding the performance of the experimental set-up as well as the expected physics results are based on detailed numerical simulations throughout

Massage Therapy for Osteoarthritis of the Knee: A Randomized Dose-Finding Trial

In a previous trial of massage for osteoarthritis (OA) of the knee, we demonstrated feasibility, safety and possible efficacy, with benefits that persisted at least 8 weeks beyond treatment termination.We performed a RCT to identify the optimal dose of massage within an 8-week treatment regimen and to further examine durability of response. Participants were 125 adults with OA of the knee, randomized to one of four 8-week regimens of a standardized Swedish massage regimen (30 or 60 min weekly or biweekly) or to a Usual Care control. Outcomes included the Western Ontario and McMaster Universities Arthritis Index (WOMAC), visual analog pain scale, range of motion, and time to walk 50 feet, assessed at baseline, 8-, 16-, and 24-weeks.WOMAC Global scores improved significantly (24.0 points, 95% CI ranged from 15.3-32.7) in the 60-minute massage groups compared to Usual Care (6.3 points, 95% CI 0.1-12.8) at the primary endpoint of 8-weeks. WOMAC subscales of pain and functionality, as well as the visual analog pain scale also demonstrated significant improvements in the 60-minute doses compared to usual care. No significant differences were seen in range of motion at 8-weeks, and no significant effects were seen in any outcome measure at 24-weeks compared to usual care. A dose-response curve based on WOMAC Global scores shows increasing effect with greater total time of massage, but with a plateau at the 60-minute/week dose.Given the superior convenience of a once-weekly protocol, cost savings, and consistency with a typical real-world massage protocol, the 60-minute once weekly dose was determined to be optimal, establishing a standard for future trials.ClinicalTrials.gov NCT00970008