Concentration Inequalities and Confidence Bands for Needlet Density Estimators on Compact Homogeneous Manifolds

Let $X_1,...,X_n$ be a random sample from some unknown probability density $f$ defined on a compact homogeneous manifold $\mathbf M$ of dimension $d \ge 1$. Consider a 'needlet frame' $\{\phi_{j \eta}\}$ describing a localised projection onto the space of eigenfunctions of the Laplace operator on $\mathbf M$ with corresponding eigenvalues less than $2^{2j}$, as constructed in \cite{GP10}. We prove non-asymptotic concentration inequalities for the uniform deviations of the linear needlet density estimator $f_n(j)$ obtained from an empirical estimate of the needlet projection $\sum_\eta \phi_{j \eta} \int f \phi_{j \eta}$ of $f$. We apply these results to construct risk-adaptive estimators and nonasymptotic confidence bands for the unknown density $f$. The confidence bands are adaptive over classes of differentiable and H\"{older}-continuous functions on $\mathbf M$ that attain their H\"{o}lder exponents.Comment: Probability Theory and Related Fields, to appea

Quantifying Robotic Swarm Coverage

In the field of swarm robotics, the design and implementation of spatial density control laws has received much attention, with less emphasis being placed on performance evaluation. This work fills that gap by introducing an error metric that provides a quantitative measure of coverage for use with any control scheme. The proposed error metric is continuously sensitive to changes in the swarm distribution, unlike commonly used discretization methods. We analyze the theoretical and computational properties of the error metric and propose two benchmarks to which error metric values can be compared. The first uses the realizable extrema of the error metric to compute the relative error of an observed swarm distribution. We also show that the error metric extrema can be used to help choose the swarm size and effective radius of each robot required to achieve a desired level of coverage. The second benchmark compares the observed distribution of error metric values to the probability density function of the error metric when robot positions are randomly sampled from the target distribution. We demonstrate the utility of this benchmark in assessing the performance of stochastic control algorithms. We prove that the error metric obeys a central limit theorem, develop a streamlined method for performing computations, and place the standard statistical tests used here on a firm theoretical footing. We provide rigorous theoretical development, computational methodologies, numerical examples, and MATLAB code for both benchmarks.Comment: To appear in Springer series Lecture Notes in Electrical Engineering (LNEE). This book contribution is an extension of our ICINCO 2018 conference paper arXiv:1806.02488. 27 pages, 8 figures, 2 table

Heterogeneity in the effectiveness of non-pharmaceutical interventions during the first SARS-CoV2 wave in the United States

Background: Attempts to quantify effect sizes of non-pharmaceutical interventions (NPI) to control COVID-19 in the US have not accounted for heterogeneity in social or environmental factors that may influence NPI effectiveness. This study quantifies national and sub-national effect sizes of NPIs during the early months of the pandemic in the US. Methods: Daily county-level COVID-19 cases and deaths during the first wave (January 2020 through phased removal of interventions) were obtained. County-level cases, doubling times, and death rates were compared to four increasingly restrictive NPI levels. Socio-demographic, climate and mobility factors were analyzed to explain and evaluate NPI heterogeneity, with mobility used to approximate NPI compliance. Analyses were conducted separately for the US and for each Census regions (Pacific, Mountain, east/West North Central, East/West South Central, South Atlantic, Middle Atlantic and New England). A stepped-wedge cluster-randomized trial analysis was used, leveraging the phased implementation of policies. Results: Aggressive (level 4) NPIs were associated with slower COVID-19 propagation, particularly in high compliance counties. Longer duration of level 4 NPIs was associated with lower case rates (log beta -0.028, 95% CI -0.04 to -0.02) and longer doubling times (log beta 0.02, 95% CI 0.01–0.03). Effects varied by Census region, for example, level 4 effects on doubling time in Pacific states were opposite to those in Middle Atlantic and New England states. NPI heterogeneity can be explained by differential timing of policy initiation and by variable socio-demographic county characteristics that predict compliance, particularly poverty and racial/ethnic population. Climate exhibits relatively consistent relationships across Census regions, for example, higher minimum temperature and specific humidity were associated with lower doubling times and higher death rates for this period of analysis in South Central, South Atlantic, Middle Atlantic, and New England states. Conclusion and Relevance: Heterogeneity exists in both the effectiveness of NPIs across US Census regions and policy compliance. This county-level variability indicates that control strategies are best designed at community-levelswhere policies can be tuned based on knowledge of local disparities and compliance with public health ordinances.Peer ReviewedPostprint (published version

Geometry of integrable dynamical systems on 2-dimensional surfaces

This paper is devoted to the problem of classification, up to smooth isomorphisms or up to orbital equivalence, of smooth integrable vector fields on 2-dimensional surfaces, under some nondegeneracy conditions. The main continuous invariants involved in this classification are the left equivalence classes of period or monodromy functions, and the cohomology classes of period cocycles, which can be expressed in terms of Puiseux series. We also study the problem of Hamiltonianization of these integrable vector fields by a compatible symplectic or Poisson structure.Comment: 31 pages, 12 figures, submitted to a special issue of Acta Mathematica Vietnamic

The effects of high-intensity interval training on glucose metabolism, cardiorespiratory fitness and weight control in subjects with diabetes: systematic review a meta-analysis

Aim: The objective of this meta-analysis was to explore the effects of high-intensity interval training (HIIT) compared with control conditions (CON) or moderate intensity continuous training (MICT) on glycemic parameters in diabetes subjects. Methods: Pubmed, Embase and Google Scholar databases were searched for HIIT interventions that were carried out in diabetic subjects and exploring fasting glucose, glycated haemoglobin (HbA1c), fasting insulin and/or HOMA-IR. Results: This systematic review retrieved a total of 1741 studies of which 32 articles fulfilled the eligibility criteria. Nineteen trials were included in the meta-analysis since they compared HIIT intervention with CON or MICT group. There was a significantly reduction of fasting glucose of 13.3 mg/dL (p < 0.001), Hb1Ac -0.34% (p < 0.001), insulin -2.27 UI/L (p = 0.003), HOMA-IR -0.88 (p = 0.005) in the HIIT-group compared with CON-group. Nevertheless, this reduction was not significantly different when comparing HIIT with MICT (p = 0.140, p = 0.315, p = 0.520 and p = 0.389). Besides, there was a significant increase of absolute VO2max of 0.21 L/min (p < 0.001) and relative VO2max of 2.94 ml/kg/min (p < 0.001) in the HIIT-group compared with the CON-group and the MICT-group (0.22 L/min, p = 0.025) and (0.97 ml/kg/min, p = 0.045). Conclusions: These findings revealed that HIIT intervention led to significant improvement in glycemic control and insulin resistance in subjects with diabetes compared with CON-group

Cost-effectiveness of exercise referral schemes enhanced by self-management strategies to battle sedentary behaviour in older adults: Protocol for an economic evaluation alongside the SITLESS three-armed pragmatic randomised controlled trial

Introduction: Promoting physical activity (PA) and reducing sedentary behaviour (SB) may exert beneficial effects on the older adult population, improving behavioural, functional, health and psychosocial outcomes in addition to reducing health, social care and personal costs. This paper describes the planned economic evaluation of SITLESS, a multicountry three-armed pragmatic randomised controlled trial (RCT) which aims to assess the short-term and long-term effectiveness and cost-effectiveness of a complex intervention on SB and PA in community-dwelling older adults, based on exercise referral schemes enhanced by a group intervention providing self-management strategies to encourage lifestyle change. Methods and analysis: A within-trial economic evaluation and long-term model from both a National Health Service/personal social services perspective and a broader societal perspective will be undertaken alongside the SITLESS multinational RCT. Healthcare costs (hospitalisations, accident and emergency visits, appointment with health professionals) and social care costs (eg, community care) will be included in the economic evaluation. For the cost-utility analysis, quality-adjusted life-years will be measured using the EQ-5D-5L and capability well-being measured using the ICEpop CAPability measure for Older people (ICECAP-O) questionnaire. Other effectiveness outcomes (health related, behavioural, functional) will be incorporated into a cost-effectiveness analysis and cost-consequence analysis. The multinational nature of this RCT implies a hierarchical structure of the data and unobserved heterogeneity between clusters that needs to be adequately modelled with appropriate statistical and econometric techniques. In addition, a long-term population health economic model will be developed and will synthesise and extrapolate within-trial data with additional data extracted from the literature linking PA and SB outcomes with longer term health states. Methods guidance for population health economic evaluation will be adopted including the use of a long-time horizon, 1.5% discount rate for costs and benefits, cost consequence analysis framework and a multisector perspective. Ethics and dissemination: The study design was approved by the ethics and research committee of each intervention site: the Ethics and Research Committee of Ramon Llull University (reference number: 1314001P) (Fundació Blanquerna, Spain), the Regional Committees on Health Research Ethics for Southern Denmark (reference number: S-20150186) (University of Southern Denmark, Denmark), Office for Research Ethics Committees in Northern Ireland (ORECNI reference number: 16/NI/0185) (Queen’s University of Belfast) and the Ethical Review Board of Ulm University (reference number: 354/15) (Ulm, Germany). Participation is voluntary and all participants will be asked to sign informed consent before the start of the study. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement number 634 270. This article reflects only the authors' view and the Commission is not responsible for any use that may be made of the information it contains. The findings of the study will be disseminated to different target groups (academia, policymakers, end users) through different means following the national ethical guidelines and the dissemination regulation of the Horizon 2020 funding agency. Use of the EuroQol was registered with the EuroQol Group in 2016. Use of the ICECAP-O was registered with the University of Birmingham in March 2017. Trial registration number: NCT02629666; Pre-results

A regularity class for the roots of nonnegative functions

We investigate the regularity of the positive roots of a non-negative function of one-variable. A modified H\"older space $\mathcal{F}^\beta$ is introduced such that if $f\in \mathcal{F}^\beta$ then $f^\alpha \in C^{\alpha \beta}$. This provides sufficient conditions to overcome the usual limitation in the square root case ($\alpha = 1/2$) for H\"older functions that $f^{1/2}$ need be no more than $C^1$ in general. We also derive bounds on the wavelet coefficients of $f^\alpha$, which provide a finer understanding of its local regularity.Comment: 12 page

Intravascular Large B-Cell Lymphoma Genomic Profile Is Characterized by Alterations in Genes Regulating NF-κB and Immune Checkpoints.

Intravascular large B-cell lymphoma (IVLBCL) is an uncommon lymphoma with an aggressive clinical course characterized by selective growth of tumor cells within the vessels. Its pathogenesis is still uncertain and there is little information on the underlying genomic alterations. In this study, we performed a clinicopathologic and next-generation sequencing analysis of 15 cases of IVLBCL using a custom panel for the detection of alterations in 68 recurrently mutated genes in B-cell lymphomagenesis. Six patients had evidence of hemophagocytic syndrome. Four patients presented concomitantly a solid malignancy. Tumor cells outside the vessels were observed in 7 cases, 2 with an overt diffuse large B-cell cell lymphoma. In 4 samples, tumor cells infiltrated lymphatic vessel in addition to blood capillaries. Programmed death-ligand 1 (PD-L1) was positive in tumor cells in 4 of 11 evaluable samples and in macrophages intermingled with tumor cells in 8. PD-L1 copy number gains were identified in a higher proportion of cases expressing PD-L1 than in negative tumors. The most frequently mutated gene was PIM1 (9/15, 60%), followed by MYD88L265P and CD79B (8/15, 53% each). In 6 cases, MYD88L265P and CD79B mutations were detected concomitantly. We also identified recurrent mutations in IRF4 , TMEM30A , BTG2 , and ETV6 loci (4/15, 27% each) and novel driver mutations in NOTCH2 , CCND3 , and GNA13 , and an IRF4 translocation in 1 case each. The mutational profile was similar in patients with and without evidence of hemophagocytic syndrome and in cases with or without dissemination of tumor cells outside the vessels. Our results confirm the relevance of mutations in B-cell receptor/nuclear factor-κB signaling and immune escape pathways in IVLBCL and identify novel driver alterations. The similar mutational profile in tumors with extravascular dissemination suggests that these cases may also be considered in the spectrum of IVLBCL