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

The effectiveness of the Penn Resiliency Programme (PRP) and its adapted versions in reducing depression and anxiety and improving explanatory style: A systematic review and meta-analysis

Mental health promotion in schools is a key priority for national governments. The aim of this meta-aggregation is to synthesise the findings from universal, depression and/or anxiety, Cognitive-Behavioural Therapy (CBT) and/or Interpersonal Therapy (IPT)-based, programmes implemented in schools, which are focused on reducing depression and anxiety in student populations aged 8-17 years. Electronic databases were searched for published original qualitative studies which assess students’ perceptions and experiences from participating in universal, school-based, depression and/or anxiety, prevention programmes. Extraction and synthesis of findings was assisted by NVivo qualitative data analysis software. The Joanna Briggs Institute-Qualitative Assessment and Review Instrument (JBI-QARI) Critical Appraisal Checklist for Interpretative and Critical Research was used for assessing methodological quality of the included studies. The confidence of synthesised qualitative findings (ConQual) approach was followed for assessing the confidence in the estimates of syntheses output. Five studies from Australia, Sweden, and UK met the inclusion criteria. Modification in the structure and mode of implementation of universal prevention programmes is required in order to enhance programmes’ applicability and impact. The study provides key practical recommendations to stakeholders and policy makers about the content, delivery, and implementation of school-based, universal, prevention programmes

The role of carotid plaque echogenicity in baroreflex sensitivity

ObjectiveThe baroreflex sensitivity is impaired in patients with carotid atherosclerosis. The purpose of our study was to assess the impact of carotid plaque echogenicity on the baroreflex function in patients with significant carotid atherosclerosis, who have not undergone carotid surgery.MethodSpontaneous baroreflex sensitivity (sBRS) was estimated in 45 patients with at least a severe carotid stenosis (70%-99%). sBRS calculation was performed noninvasively, with the spontaneous sequence method, based on indirectly estimated central blood pressures from radial recordings. This method failed in three patients due to poor-quality recordings, and eventually 42 patients were evaluated. After carotid duplex examination, carotid plaque echogenicity was graded from 1 to 4 according to Gray-Weale classification and the patients were divided into two groups: the echolucent group (grades 1 and 2) and the echogenic group (grades 3 and 4).ResultsSixteen patients (38%) and 26 patients (62%) were included in the echolucent and echogenic group, respectively. Diabetes mellitus was observed more frequently among echolucent plaques (χ2 = 8.0; P < .004), while those plaques were also more commonly symptomatic compared with echogenic atheromas (χ2 = 8.5; P < .003). Systolic arterial pressure, diastolic arterial pressure, and heart rate were similar in the two groups. Nevertheless, the mean value of baroreflex sensitivity was found to be significantly lower in the echogenic group (2.96 ms/mm Hg) compared with the echolucent one (5.0 ms/mm Hg), (F [1, 42] = 10.1; P < .003).ConclusionsThese findings suggest that echogenic plaques are associated with reduced baroreflex function compared with echolucent ones. Further investigation is warranted to define whether such an sBRS impairment could be responsible for cardiovascular morbidity associated with echogenic plaques

Cooperative cell motility during tandem locomotion of amoeboid cells.

Streams of migratory cells are initiated by the formation of tandem pairs of cells connected head to tail to which other cells subsequently adhere. The mechanisms regulating the transition from single to streaming cell migration remain elusive, although several molecules have been suggested to be involved. In this work, we investigate the mechanics of the locomotion ofDictyosteliumtandem pairs by analyzing the spatiotemporal evolution of their traction adhesions (TAs). We find that in migrating wild-type tandem pairs, each cell exerts traction forces on stationary sites (∼80% of the time), and the trailing cell reuses the location of the TAs of the leading cell. Both leading and trailing cells form contractile dipoles and synchronize the formation of new frontal TAs with ∼54-s time delay. Cells not expressing the lectin discoidin I or moving on discoidin I-coated substrata form fewer tandems, but the trailing cell still reuses the locations of the TAs of the leading cell, suggesting that discoidin I is not responsible for a possible chemically driven synchronization process. The migration dynamics of the tandems indicate that their TAs' reuse results from the mechanical synchronization of the leading and trailing cells' protrusions and retractions (motility cycles) aided by the cell-cell adhesions

Three-Dimensional Quantification of Cellular Traction Forces and Mechanosensing of Thin Substrata by Fourier Traction Force Microscopy

We introduce a novel three-dimensional (3D) traction force microscopy (TFM) method motivated by the recent discovery that cells adhering on plane surfaces exert both in-plane and out-of-plane traction stresses. We measure the 3D deformation of the substratum on a thin layer near its surface, and input this information into an exact analytical solution of the elastic equilibrium equation. These operations are performed in the Fourier domain with high computational efficiency, allowing to obtain the 3D traction stresses from raw microscopy images virtually in real time. We also characterize the error of previous two-dimensional (2D) TFM methods that neglect the out-of-plane component of the traction stresses. This analysis reveals that, under certain combinations of experimental parameters (\ie cell size, substratums' thickness and Poisson's ratio), the accuracy of 2D TFM methods is minimally affected by neglecting the out-of-plane component of the traction stresses. Finally, we consider the cell's mechanosensing of substratum thickness by 3D traction stresses, finding that, when cells adhere on thin substrata, their out-of-plane traction stresses can reach four times deeper into the substratum than their in-plane traction stresses. It is also found that the substratum stiffness sensed by applying out-of-plane traction stresses may be up to 10 times larger than the stiffness sensed by applying in-plane traction stresses

Serum Lp(a) Lipoprotein Levels in Patients with Atherosclerotic Occlusive Disease of the Lower Extremities

AbstractObjective to evaluate the association between Lp(a) lipoprotein levels, other serum lipids and the presence of lower limb atherosclerotic occlusive disease. Materials and methods angiographic findings in 36 patients were related to serum Lp(a). Total cholesterol, triglycerides, LDL-cholesterol, HDL-cholesterol and Lp(a) levels were compared with those of 73 age- and sex-matched healthy controls. Results atheromatous lesions were localised in the femoropopliteal (≈60%) and aortoiliac (≈40%) segments. The number of stenosed arteries was ≥2 and the range of stenosis severity was between 40% and 100%. There was a significant increase in serum Lp(a) (p= 0.000001) and a decrease in serum HDL (p= 0.000009) levels in patients compared to controls. No difference was observed in total cholesterol, LDL-cholesterol or triglyceride. However, the ratio of total cholesterol/HDL-cholesterol was significantly higher (p= 0.005) in patients. Conclusion a dyslipidaemic serum profile, characterised by increased Lp(a) levels and decreased HDL-cholesterol levels, is associated with atherosclerotic occlusive disease of the lower extremities

On fundamental computational barriers in the mathematics of information

This thesis is about computational theory in the setting of the mathematics of information. The first goal is to demonstrate that many commonly considered problems in optimisation theory cannot be solved with an algorithm if the input data is only known up to an arbitrarily small error (modelling the fact that most real numbers are not expressible to infinite precision with a floating point based computational device). This includes computing the minimisers to basis pursuit, linear programming, lasso and image deblurring as well as finding an optimal neural network given training data. These results are somewhat paradoxical given the success that existing algorithms exhibit when tackling these problems with real world datasets and a substantial portion of this thesis is dedicated to explaining the apparent disparity, particularly in the context of compressed sensing. To do so requires the introduction of a variety of new concepts, including that of a breakdown epsilon, which may have broader applicability to computational problems outside of the ones central to this thesis. We conclude with a discussion on future research directions opened up by this work.This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/H023348/1 for the University of Cambridge Centre for Doctoral Training, the Cambridge Centre for Analysis

Testing the validity of a novel, conceptual, strength-based model in predicting resilient functioning in an UK-based, adolescent, student population: a prospective evaluation

Introduction: Mental health problems in adolescence can be precursors of psychosocial problems in adulthood, increasing the likelihood for engaging in health-risk behaviours. Given that most of mental health problems remain untreated for years with subsequent repercussions for society and economy, governments have stressed the need to implement universal, resilience interventions early in adolescence. Adolescence is a pivotal developmental period, favouring the large-scale roll-out of universal, resilience interventions. Due to the inconsistent effects of these interventions in decreasing mental health problems and promoting resilience, their content and structure should be reconsidered. As such, it is vital to investigate the underpinning pathways between stress and resilient functioning. Aim: This study aims to test the validity of a novel, conceptual, strength-based model in predicting resilient functioning in an UK-based, adolescent population. Methods: A prospective, questionnaire-based, cohort study with a baseline and 6-month follow-up assessments was conducted. Overall, 561 adolescents aged 11-16 were enrolled and participated in this study. Measures: Seven validated questionnaires were used, namely: i) the Perceived Stress Scale (PSS), ii) the Self-Efficacy Questionnaire for Children (SEQ-C), iii) Emotion Regulation Questionnaire for Children and Adolescents (ERQ-CA), iv) the Warwick-Edinburgh Mental Well-being Scale (WEMWBS), v) the Revised Children’s Manifest Anxiety Scale (RCMAS), vi) Positive & Negative Affect Scale (PANAS), and viii) the Strengths and Difficulties Questionnaire (SDQ). Analysis: A panel, moderated-mediation, path model was analysed. The proposed model consisted of a predictor variable (PSS), a mediator variable (SEQ-C), a moderator variable (ERQ-CA), and four outcome variables (WEMWBS, RCMAS, PANAS, & SDQ). Results: Perceived self-efficacy was found to be a significant mediator between: stress perceptions and anxiety symptoms (0.13, 95%CI = 0.06, 0.21, p≤0.001), stress perceptions and socio-emotional disturbances (0.18, 95%CI = 0.14, 0.24, p≤0.001), stress perceptions and positive emotions (-0.42, 95%CI = -0.52, -0.32, p≤0.001), and stress perceptions and mental well-being (-0.49, 95%CI = -0.59, -0.39, p≤0.001) while emotion regulation was found to significantly moderate the relationship between stress perceptions and perceived self-efficacy. Discussion: Perceived self-efficacy and emotion regulation were found to counterbalance stress levels and increase resilient functioning. Future interventions will benefit from following a strength-based approach