Sparsity Order Estimation from a Single Compressed Observation Vector

We investigate the problem of estimating the unknown degree of sparsity from compressive measurements without the need to carry out a sparse recovery step. While the sparsity order can be directly inferred from the effective rank of the observation matrix in the multiple snapshot case, this appears to be impossible in the more challenging single snapshot case. We show that specially designed measurement matrices allow to rearrange the measurement vector into a matrix such that its effective rank coincides with the effective sparsity order. In fact, we prove that matrices which are composed of a Khatri-Rao product of smaller matrices generate measurements that allow to infer the sparsity order. Moreover, if some samples are used more than once, one of the matrices needs to be Vandermonde. These structural constraints reduce the degrees of freedom in choosing the measurement matrix which may incur in a degradation in the achievable coherence. We thus also address suitable choices of the measurement matrices. In particular, we analyze Khatri-Rao and Vandermonde matrices in terms of their coherence and provide a new design for Vandermonde matrices that achieves a low coherence

Offenders’ perceptions of the UK prison smoking ban

Purpose Despite overall reductions in levels of smoking in the UK, rates of offender smoking remain high. In 2016, it was announced that prisons in England and Wales would gradually introduce a smoking ban. The purpose of this paper is to explore offenders’ perceptions around the upcoming smoking ban. Design/methodology/approach A total of eight focus groups were conducted in four prisons across the North of England. Both smoking and non-smoking offenders participated in the focus groups, and thematic analysis was used to explore the findings. Findings Themes generated from the data were “freedom and rights”, “the prison environment” and “guiding support”. Participants discussed how the smoking ban was viewed as a punishment and restricted their freedom, with perceptions as to why the ban was being implemented centring around others trying to control them. Participants expressed concerns around the financial implications of the smoking ban on already stretched prison resources. Participants also recommended improving the nicotine replacement therapy on offer, and increasing the range of leisure activities within the prison to prepare for the smoking ban. Originality/value Overall, it was apparent that participants’ awareness of the smoking ban was generally poor. It is recommended that offenders need to be made more aware of the smoking cessation support they will receive and given the opportunity to ask questions about the smoking ban. Increasing offenders’ awareness of the ban may reduce stress associated with a perceived lack of choice around their smoking behaviours

Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation

When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating each component weight during the nonlinear propagation stage an approximation of the true pdf can be successfully reconstructed. Particle filtering (PF) methods have gained popularity recently for solving nonlinear estimation problems due to their straightforward approach and the processing capabilities mentioned above. The basic concept behind PF is to represent any pdf as a set of random samples. As the number of samples increases, they will theoretically converge to the exact, equivalent representation of the desired pdf. When the estimated qth moment is needed, the samples are used for its construction allowing further analysis of the pdf characteristics. However, filter performance deteriorates as the dimension of the state vector increases. To overcome this problem Ref. [5] applies a marginalization technique for PF methods, decreasing complexity of the system to one linear and another nonlinear state estimation problem. The marginalization theory was originally developed by Rao and Blackwell independently. According to Ref. [6] it improves any given estimator under every convex loss function. The improvement comes from calculating a conditional expected value, often involving integrating out a supportive statistic. In other words, Rao-Blackwellization allows for smaller but separate computations to be carried out while reaching the main objective of the estimator. In the case of improving an estimator's variance, any supporting statistic can be removed and its variance determined. Next, any other information that dependents on the supporting statistic is found along with its respective variance. A new approach is developed here by utilizing the strengths of the adaptive Gaussian sum propagation in Ref. [2] and a marginalization approach used for PF methods found in Ref. [7]. In the following sections a modified filtering approach is presented based on a special state-space model within nonlinear systems to reduce the dimensionality of the optimization problem in Ref. [2]. First, the adaptive Gaussian sum propagation is explained and then the new marginalized adaptive Gaussian sum propagation is derived. Finally, an example simulation is presented

A walking stick in one hand and a chainsaw in the other: Patients’ perspectives of living with multimorbidity

AIMS: Multimorbidity is common, yet there are major gaps in research, particularly among younger and indigenous populations. This research aimed to understand patients’ perspectives of living with multimorbidity. METHODS: A qualitative study of 61 people living with multimorbidity, 27 of whom were Māori and a third aged under 65, from urban and rural regions in New Zealand. Six focus groups and 14 interviews were conducted, recorded, transcribed and analysed. RESULTS: For many participants, living with multimorbidity disrupted their ‘normal’ lives, posing challenges in everyday activities such as eating and toileting, working and managing medications. Dealing with the health system posed challenges such as accessing appointments and having enough time in consultations. Cultural competency, good communication and continuity of care from healthcare providers were all valued. Participants had many recommendations to improve management, including a professional single point of contact to coordinate all specialist care. CONCLUSIONS: Living with multimorbidity is often challenging requiring people to manage their conditions while continuing to live their lives. This research suggests changes are needed in the health system in New Zealand and elsewhere to better manage multimorbidity thus improving patient’s lives and reducing costs to the health sector and wider society

Head Coverings in the Courtroom: A Question of Respect for the Judge or of Judicial Tolerance?

The Human Rights Centre at Ghent University (the HRC) first initiated the present research while preparing an amicus curiae brief in the Lachiri v. Belgium case before the European Court of Human Rights (ECtHR). The applicant in Lachiri, who was a civil party in legal proceedings concerning the murder of her brother, was denied access to a Brussels courtroom after refusing to remove her Islamic headscarf . Ms. Lachiri’s admission was refused in reliance on Article 759 of the Belgian Judicial Code (Gerechtelijk Wetboek/ Code Judiciaire), which provides that “[t]he audience will attend the sessions with their heads uncovered, respectfully and silently; whatever the judge commands for the maintenance of order will be punctually and immediately executed.” In its third-party intervention, the HRC sought to supply the ECtHR with additional information concerning three points: the debate on the wearing of Islamic headscarves in Belgium, the history, object and purpose of Article 759 of the Belgian Judicial Code, and the scope of the State margin of appreciation in prohibiting religious items of clothing

A numerical study of interannual variability in the North Icelandic Irminger Current

Author Posting. © American Geophysical Union, 2018. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research-Oceans 123(12), (2018): 8994-9009, doi:10.1029/2018JC013800.The North Icelandic Irminger Current (NIIC) is an important component of the Atlantic Water (AW) inflow to the Nordic Seas. In this study, both observations and a high‐resolution (1/12°) numerical model are used to investigate the seasonal to interannual variability of the NIIC and its forcing mechanisms. The model‐simulated velocity and hydrographic fields compare well with the available observations. The water mass over the entire north Icelandic shelf exhibits strong seasonal variations in both temperature and salinity, and such variations are closely tied to the AW seasonality in the NIIC. In addition to seasonal variability, there is considerable variation on interannual time scales, including a prominent event in 2003 when the AW volume transport increased by about 0.5 Sv. To identify and examine key forcing mechanisms for this event, we analyzed outputs from two additional numerical experiments: using only the seasonal climatology for buoyancy flux (the momentum case) and using only the seasonal climatology for wind stress (the buoyancy case). It is found that changes in the wind stress are predominantly responsible for the interannual variations in the AW volume transport, AW fraction in the NIIC water, and salinity. Temperature changes on the shelf, however, are equally attributable to the buoyancy flux and wind forcing. Correlational analyses indicate that the AW volume transport is most sensitive to the wind stress southwest of Iceland.This work is supported by the U.S. National Science Foundation (NSF) under grants OCE‐1634886 (J. Zhao and J. Yang) and OCE‐1558742 (R. Pickart), and by the Bergen Research Foundation grant BFS2016REK01 (K. Våge and S. Semper). We thank Xiaobiao Xu at Florida State University for providing the initial model configuration. Comments from anonymous reviewers help to improve the manuscript. The altimeter products are produced and distributed by the Copernicus Marine and Environment Monitoring Service (CMEMS, http://www.marine.copernicus.eu). The hydrographic maps along the Hornbanki section are available at http://www.hafro.is/Sjora/.2019-04-1

Risk, colon cancer & physical activity: a qualitative exploration in older adults

Rationale and Objectives There is convincing evidence that physical activity (PA) reduces risk of colon cancer (CC) and may improve survival after cancer, although few older adults achieve recommended PA guidelines. Numerous barriers to participation exist, though few studies focus on socio-cultural influences. This study explores barriers specific to individuals at elevated risk of CC following screening colonoscopy, as well as how health professionals or a ‘diagnosis’ may provide additional motivation to change. Methods Interviews were conducted with colonic polyp patients and CC survivors over 60 years old, selectively sampled from a feasibility study for a randomised controlled PA intervention. Narrative accounts enabled discussion of influences on health behaviour throughout participants’ lifetimes, the impact of their recent ‘diagnosis’, and attitudes towards PA. Interviews and focus groups were conducted with health professionals to triangulate data collection. All interviews were transcribed verbatim and a constructivist grounded theory approach to data analysis was followed. Findings Despite not meeting current PA guidelines, participants perceived a lifetime of ‘natural’ PA. CC survivors were more inclined to initiate PA engagement to improve their health; conversely, elevated risk individuals were often not aware of their change in health status, leading them to conclude that no lifestyle change was necessary. Professionals confirmed that no PA guidance is currently offered to screening patients, but believed that there may be scope to implement health promotion advice. Barriers towards this however, are complex and numerous. Conclusions The ‘meaning of PA’ is situated and understandings may differ. Despite reporting perceptions of high PA, this study sample did not seem to understand what constitutes sufficient PA to elicit a positive health response. Risk status awareness and the benefits of PA is lacking in elevated risk individuals. For the screening setting to be utilised, questions around ‘why’, ‘when’ ‘who’ and ‘how’ health promotion should be delivered, need to be addressed