Convex recovery of a structured signal from independent random linear measurements

This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. This technique delivers bounds for the sampling complexity that are similar with recent results for standard Gaussian measurements, but the argument applies to a much wider class of measurement ensembles. To demonstrate the power of this approach, the paper presents a short analysis of phase retrieval by trace-norm minimization. The key technical tool is a framework, due to Mendelson and coauthors, for bounding a nonnegative empirical process.Comment: 18 pages, 1 figure. To appear in "Sampling Theory, a Renaissance." v2: minor corrections. v3: updated citations and increased emphasis on Mendelson's contribution

The Viscous Nonlinear Dynamics of Twist and Writhe

Exploiting the "natural" frame of space curves, we formulate an intrinsic dynamics of twisted elastic filaments in viscous fluids. A pair of coupled nonlinear equations describing the temporal evolution of the filament's complex curvature and twist density embodies the dynamic interplay of twist and writhe. These are used to illustrate a novel nonlinear phenomenon: ``geometric untwisting" of open filaments, whereby twisting strains relax through a transient writhing instability without performing axial rotation. This may explain certain experimentally observed motions of fibers of the bacterium B. subtilis [N.H. Mendelson, et al., J. Bacteriol. 177, 7060 (1995)].Comment: 9 pages, 4 figure

Investigation of photoplethysmographs from the anterior fontanelle of neonates

Photoplethysmography (PPG) signals have been investigated at a new anatomical site, the anterior fontanelle (ANTF), on the hypothesis that blood supply at this location is preferentially preserved during cases of poor peripheral circulation which might cause the commercial pulse oximeters to fail to estimate accurately arterial blood oxygen saturation (SpO2). Two custom built reflectance PPG sensors have been developed, one for placement on the fontanelle and one on the periphery (foot). A PPG processing system and software were also developed to process the raw PPG signals and to estimate SpO2. A pilot study on sixteen babies, (9 male, 7 female) with a median age of 15.5 d (interquartile range = 46.8 d) and a median weight of 3.15 kg (SD = 0.93 kg), on a neonatal intensive care unit (NICU) has been carried out. PPG signals from the ANTF were of good quality and high signal-to-noise ratio. The amplitudes of the ANTF PPGs were found to be sensitive to changes in amplitude when amplitudes were observed at the reference PPG site. Bland-Altman analysis of the gold standard blood gas analysis reveals that all three sensors are inaccurate at SaO2 < 85–90 %, but the ANTF sensor shows better mean difference than the commercial device

Estimation in high dimensions: a geometric perspective

This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of asymptotic convex geometry, and demonstrates connections between geometric results and estimation problems. The theory is illustrated with applications to sparse recovery, matrix completion, quantization, linear and logistic regression and generalized linear models.Comment: 56 pages, 9 figures. Multiple minor change

Implementation of an anonymisation tool for clinical trials using a clinical trial processor integrated with an existing trial patient data information system

To present an adapted Clinical Trial Processor (CTP) test set-up for receiving, anonymising and saving Digital Imaging and Communications in Medicine (DICOM) data using external input from the original database of an existing clinical study information system to guide the anonymisation process. Two methods are presented for an adapted CTP test set-up. In the first method, images are pushed from the Picture Archiving and Communication System (PACS) using the DICOM protocol through a local network. In the second method, images are transferred through the internet using the HTTPS protocol. In total 25,000 images from 50 patients were moved from the PACS, anonymised and stored within roughly 2 h using the first method. In the second method, an average of 10 images per minute were transferred and processed over a residential connection. In both methods, no duplicated images were stored when previous images were retransferred. The anonymised images are stored in appropriate directories. The CTP can transfer and process DICOM images correctly in a very easy set-up providing a fast, secure and stable environment. The adapted CTP allows easy integration into an environment in which patient data are already included in an existing information system. Store DICOM images correctly in a very easy set-up in a fast, secure and stable environment Allows adaptation of the software to perform a certain task based on specific needs Allows easy integration into an existing environment Reduce the possibility of inappropriate anonymisation

Lesbian and bisexual women's experiences of sexuality-based discrimination and their appearance concerns

Lesbian and bisexual women frequently experience sexuality-based discrimination, which is often based on others' judgements about their appearance. This short article aims to explore whether there is a relationship between lesbian and bisexual women's experiences of sexuality-based discrimination and their satisfaction with the way that they look. Findings from an online survey suggest that discrimination is negatively related to appearance satisfaction for lesbian women, but not for bisexual women. It is argued that this difference exists because lesbian appearance norms are more recognisable and distinctive than bisexual women's appearance norms

Hydrodynamic Synchronisation of Model Microswimmers

We define a model microswimmer with a variable cycle time, thus allowing the possibility of phase locking driven by hydrodynamic interactions between swimmers. We find that, for extensile or contractile swimmers, phase locking does occur, with the relative phase of the two swimmers being, in general, close to 0 or pi, depending on their relative position and orientation. We show that, as expected on grounds of symmetry, self T-dual swimmers, which are time-reversal covariant, do not phase-lock. We also discuss the phase behaviour of a line of tethered swimmers, or pumps. These show oscillations in their relative phases reminiscent of the metachronal waves of cilia.Comment: 17 pages, 8 figure

Gravitational Microlensing Evidence for a Planet Orbiting a Binary Star System

The study of extra-solar planetary systems has emerged as a new discipline of observational astronomy in the past few years with the discovery of a number of extra-solar planets. The properties of most of these extra-solar planets were not anticipated by theoretical work on the formation of planetary systems. Here we report observations and light curve modeling of gravitational microlensing event MACHO-97-BLG-41, which indicates that the lens system consists of a planet orbiting a binary star system. According to this model, the mass ratio of the binary star system is 3.8:1 and the stars are most likely to be a late K dwarf and an M dwarf with a separation of about 1.8 AU. A planet of about 3 Jupiter masses orbits this system at a distance of about 7 AU. If our interpretation of this light curve is correct, it represents the first discovery of a planet orbiting a binary star system and the first detection of a Jovian planet via the gravitational microlensing technique. It suggests that giant planets may be common in short period binary star systems.Comment: 11 pages, with 1 color and 2 b/w Figures included (published version

Photoplethysmographic measurements from central nervous system tissue

A new system for measuring the oxygen saturation of blood within tissue has been developed, for a number of potential patient monitoring applications. This proof of concept project aims to address the unmet need of real-time measurement of oxygen saturation in the central nervous system (CNS) for patients recovering from neurosurgery or trauma, by developing a fibre optic signal acquisition system for internal placement through small apertures. The development and testing of a two-wavelength optical fibre reflectance photoplethysmography (PPG) system is described together with measurements in rats and preliminary results from a clinical trial of the system in patients undergoing neurosurgery. It was found that good quality red and near-infrared PPG signals could be consistently obtained from the rat spinal cord (n=6) and human cerebral cortex (n=4) using the fibre optic probe. These findings justify further development and clinical evaluation of this fibre optic system

Possible origins of macroscopic left-right asymmetry in organisms

I consider the microscopic mechanisms by which a particular left-right (L/R) asymmetry is generated at the organism level from the microscopic handedness of cytoskeletal molecules. In light of a fundamental symmetry principle, the typical pattern-formation mechanisms of diffusion plus regulation cannot implement the "right-hand rule"; at the microscopic level, the cell's cytoskeleton of chiral filaments seems always to be involved, usually in collective states driven by polymerization forces or molecular motors. It seems particularly easy for handedness to emerge in a shear or rotation in the background of an effectively two-dimensional system, such as the cell membrane or a layer of cells, as this requires no pre-existing axis apart from the layer normal. I detail a scenario involving actin/myosin layers in snails and in C. elegans, and also one about the microtubule layer in plant cells. I also survey the other examples that I am aware of, such as the emergence of handedness such as the emergence of handedness in neurons, in eukaryote cell motility, and in non-flagellated bacteria.Comment: 42 pages, 6 figures, resubmitted to J. Stat. Phys. special issue. Major rewrite, rearranged sections/subsections, new Fig 3 + 6, new physics in Sec 2.4 and 3.4.1, added Sec 5 and subsections of Sec