On the Absence of Uniform Recovery in Many Real-World Applications of Compressed Sensing and the Restricted Isometry Property and Nullspace Property in Levels

The purpose of this paper is twofold. The first is to point out that the property of uniform recovery, meaning that all sparse vectors are recovered, does not hold in many applications where compressed sensing is successfully used. This includes fields like magnetic resonance imaging (MRI), nuclear magnetic resonance computerized tomography, electron tomography, radio interferometry, helium atom scattering, and fluorescence microscopy. We demonstrate that for natural compressed sensing matrices involving a level based reconstruction basis (e.g., wavelets), the number of measurements required to recover all $s$-sparse signals for reasonable $s$ is excessive. In particular, uniform recovery of all $s$-sparse signals is quite unrealistic. This realization explains why the restricted isometry property (RIP) is insufficient for explaining the success of compressed sensing in various practical applications. The second purpose of the paper is to introduce a new framework based on a generalized RIP and a generalized nullspace property that fit the applications where compressed sensing is used. We demonstrate that the shortcomings previously used to prove that uniform recovery is unreasonable no longer apply if we instead ask for structured recovery that is uniform only within each of the levels. To examine this phenomenon, a new tool, termed the “restricted isometry property in levels” (RIP$_L$) is described and analyzed. Furthermore, we show that with certain conditions on the RIP$_L$, a form of uniform recovery within each level is possible. Fortunately, recent theoretical advances made by Li and Adcock demonstrate the existence of large classes of matrices that satisfy the RIP$_L$. Moreover, such matrices are used extensively in applications such as MRI. Finally, we conclude the paper by providing examples that demonstrate the optimality of the results obtained.The work of the first author was supported by RCUK/Engineering and Physical Science Research Council (EPSRC) grant EP/H023348/1. The work of the second author was supported by EPSRC grant EP/L003457/1 and a Royal Society University research fellowship

Relaxation Dispersion NMR Spectroscopy

Relaxation dispersion nuclear magnetic resonance (NMR) spectroscopy has been developed since the 1950s and has now evolved into a very sensitive and versatile tool to study chemical and conformational exchange processes on the micro- to milliseconds (µs–ms) time scale. While relaxation dispersion NMR was originally designed with small molecules in mind, it has become a very attractive tool to also study the dynamics of biological macromolecules, after major advances had been made in hardware, experimental design and isotope labelling

Generalized Sampling and Infinite-Dimensional Compressed Sensing

© 2015, SFoCM. We introduce and analyze a framework and corresponding method for compressed sensing in infinite dimensions. This extends the existing theory from finite-dimensional vector spaces to the case of separable Hilbert spaces. We explain why such a new theory is necessary by demonstrating that existing finite-dimensional techniques are ill suited for solving a number of key problems. This work stems from recent developments in generalized sampling theorems for classical (Nyquist rate) sampling that allows for reconstructions in arbitrary bases. A conclusion of this paper is that one can extend these ideas to allow for significant subsampling of sparse or compressible signals. Central to this work is the introduction of two novel concepts in sampling theory, the stable sampling rate and the balancing property, which specify how to appropriately discretize an infinite-dimensional problem

Dynamics on the Way to Forming Glass: Bubbles in Space-time

We review a theoretical perspective of the dynamics of glass forming liquids and the glass transition. It is a perspective we have developed with our collaborators during this decade. It is based upon the structure of trajectory space. This structure emerges from spatial correlations of dynamics that appear in disordered systems as they approach non-ergodic or jammed states. It is characterized in terms of dynamical heterogeneity, facilitation and excitation lines. These features are associated with a newly discovered class of non-equilibrium phase transitions. Equilibrium properties have little if anything to do with it. The broken symmetries of these transitions are obscure or absent in spatial structures, but they are vivid in space-time (i.e., trajectory space). In our view, the glass transition is an example of this class of transitions. The basic ideas and principles we review were originally developed through the analysis of idealized and abstract models. Nevertheless, the central ideas are easily illustrated with reference to molecular dynamics of more realistic atomistic models, and we use that illustrative approach here.Comment: 21 pages, 8 figures. Submitted to Annu. Rev. Phys. Che

Occurrence of testicular microlithiasis in androgen insensitive hypogonadal mice

<b>Background</b>: Testicular microliths are calcifications found within the seminiferous tubules. In humans, testicular microlithiasis (TM) has an unknown etiology but may be significantly associated with testicular germ cell tumors. Factors inducing microlith development may also, therefore, act as susceptibility factors for malignant testicular conditions. Studies to identify the mechanisms of microlith development have been hampered by the lack of suitable animal models for TM.<BR/> <b>Methods</b>: This was an observational study of the testicular phenotype of different mouse models. The mouse models were: cryptorchid mice, mice lacking androgen receptors (ARs) on the Sertoli cells (SCARKO), mice with a ubiquitous loss of androgen ARs (ARKO), hypogonadal (hpg) mice which lack circulating gonadotrophins, and hpg mice crossed with SCARKO (hpg.SCARKO) and ARKO (hpg.ARKO) mice.<BR/> <b>Results</b>: Microscopic TM was seen in 94% of hpg.ARKO mice (n=16) and the mean number of microliths per testis was 81 +/- 54. Occasional small microliths were seen in 36% (n=11) of hpg testes (mean 2 +/- 0.5 per testis) and 30% (n=10) of hpg.SCARKO testes (mean 8 +/- 6 per testis). No microliths were seen in cryptorchid, ARKO or SCARKO mice. There was no significant effect of FSH or androgen on TM in hpg.ARKO mice.<BR/> <b>Conclusions</b>: We have identified a mouse model of TM and show that lack of endocrine stimulation is a cause of TM. Importantly, this model will provide a means with which to identify the mechanisms of TM development and the underlying changes in protein and gene expression

Removal of ecotoxicity of 17α-ethinylestradiol using TAML/peroxide water treatment

17α -ethinylestradiol (EE2), a synthetic oestrogen in oral contraceptives, is one of many pharmaceuticals found in inland waterways worldwide as a result of human consumption and excretion into wastewater treatment systems. At low parts per trillion (ppt), EE2 induces feminisation of male fish, diminishing reproductive success and causing fish population collapse. Intended water quality standards for EE2 set a much needed global precedent. Ozone and activated carbon provide effective wastewater treatments, but their energy intensities and capital/operating costs are formidable barriers to adoption. Here we describe the technical and environmental performance of a fast- developing contender for mitigation of EE2 contamination of wastewater based upon smallmolecule, full-functional peroxidase enzyme replicas called “TAML activators”. From neutral to basic pH, TAML activators with H2O2 efficiently degrade EE2 in pure lab water, municipal effluents and EE2-spiked synthetic urine. TAML/H2O2 treatment curtails estrogenicity in vitro and substantially diminishes fish feminization in vivo. Our results provide a starting point for a future process in which tens of thousands of tonnes of wastewater could be treated per kilogram of catalyst. We suggest TAML/H2O2 is a worthy candidate for exploration as an environmentally compatible, versatile, method for removing EE2 and other pharmaceuticals from municipal wastewaters.Heinz Endowments, the Swiss National Science Foundation, the Steinbrenner Institute for a Steinbrenner Doctoral Fellowship. NMR instrumentation at CMU was partially supported by NSF (CHE-0130903 and CHE-1039870)

Developing a digital intervention for cancer survivors: an evidence-, theory- and person-based approach

This paper illustrates a rigorous approach to developing digital interventions using an evidence-, theory- and person-based approach. Intervention planning included a rapid scoping review which identified cancer survivors’ needs, including barriers and facilitators to intervention success. Review evidence (N=49 papers) informed the intervention’s Guiding Principles, theory-based behavioural analysis and logic model. The intervention was optimised based on feedback on a prototype intervention through interviews (N=96) with cancer survivors and focus groups with NHS staff and cancer charity workers (N=31). Interviews with cancer survivors highlighted barriers to engagement, such as concerns about physical activity worsening fatigue. Focus groups highlighted concerns about support appointment length and how to support distressed participants. Feedback informed intervention modifications, to maximise acceptability, feasibility and likelihood of behaviour change. Our systematic method for understanding user views enabled us to anticipate and address important barriers to engagement. This methodology may be useful to others developing digital interventions

Quality of treatment plans and accuracy of in vivo portal dosimetry in hybrid intensity-modulated radiation therapy and volumetric modulated arc therapy for prostate cancer.

Background and purpose Delivering selected parts of volumetric modulated arc therapy (VMAT) plans using step-and-shoot intensity modulated radiotherapy (IMRT) beams has the potential to increase plan quality by allowing specific aperture positioning. This study investigates the quality of treatment plans and the accuracy of in vivo portal dosimetry in such a hybrid approach for the case of prostate radiotherapy.Material and methods Conformal and limited-modulation VMAT plans were produced, together with five hybrid IMRT/VMAT plans, in which 0%, 25%, 50%, 75% or 100% of the segments were sequenced for IMRT, while the remainder were sequenced for VMAT. Integrated portal images were predicted for the plans. The plans were then delivered as a single hybrid beam using an Elekta Synergy accelerator with Agility head to a water-equivalent phantom and treatment time, isocentric dose and portal images were measured.Results Increasing the IMRT percentage improves dose uniformity to the planning target volume (p<0.01 for 50% IMRT or more), substantially reduces the volume of rectum irradiated to 65Gy (p=0.02 for 25% IMRT) and increases the monitor units (p<0.001). Delivery time also increases substantially. All plans show accurate delivery of dose and reliable prediction of portal images.Conclusions Hybrid IMRT/VMAT can be efficiently planned and delivered as a single beam sequence. Beyond 25% IMRT, the delivery time becomes unacceptably long, with increased risk of intrafraction motion, but 25% IMRT is an attractive compromise. Integrated portal images can be used to perform in vivo dosimetry for this technique

A Repeated Measures Experiment of Green Exercise to Improve Self-Esteem in UK School Children

Exercising in natural, green environments creates greater improvements in adult's self-esteem than exercise undertaken in urban or indoor settings. No comparable data are available for children. The aim of this study was to determine whether so called 'green exercise' affected changes in self-esteem; enjoyment and perceived exertion in children differently to urban exercise. We assessed cardiorespiratory fitness (20 m shuttle-run) and self-reported physical activity (PAQ-A) in 11 and 12 year olds (n = 75). Each pupil completed two 1.5 mile timed runs, one in an urban and another in a rural environment. Trials were completed one week apart during scheduled physical education lessons allocated using a repeated measures design. Self-esteem was measured before and after each trial, ratings of perceived exertion (RPE) and enjoyment were assessed after completing each trial. We found a significant main effect (F (1,74), = 12.2, p<0.001), for the increase in self-esteem following exercise but there was no condition by exercise interaction (F (1,74), = 0.13, p = 0.72). There were no significant differences in perceived exertion or enjoyment between conditions. There was a negative correlation (r = -0.26, p = 0.04) between habitual physical activity and RPE during the control condition, which was not evident in the green exercise condition (r = -0.07, p = 0.55). Contrary to previous studies in adults, green exercise did not produce significantly greater increases in self-esteem than the urban exercise condition. Green exercise was enjoyed more equally by children with differing levels of habitual physical activity and has the potential to engage less active children in exercise. © 2013 Reed et al

When counting cattle is not enough: multiple perspectives in agricultural and veterinary research

A traditional approach in agricultural and veterinary research is focussing on the biological perspective where large cattle-databases are used to analyse the dairy herd. This approach has yielded valuable insights. However, recent research indicates that this knowledge-base can be further increased by examining agricultural and veterinary challenges from other perspectives. In this paper we suggest three perspectives that may supplement the biological perspective in agricultural and veterinary research; the economic-, the managerial-, and the social perspective. We review recent studies applying or combining these perspectives and discuss how multiple perspectives may improve our understanding and ability to handle cattle-health challenges