Convergence rates of general regularization methods for statistical inverse problems and applications

During the past the convergence analysis for linear statistical inverse problems has mainly focused on spectral cut-off and Tikhonov type estimators. Spectral cut-off estimators achieve minimax rates for a broad range of smoothness classes and operators, but their practical usefulness is limited by the fact that they require a complete spectral decomposition of the operator. Tikhonov estimators are simpler to compute, but still involve the inversion of an operator and achieve minimax rates only in restricted smoothness classes. In this paper we introduce a unifying technique to study the mean square error of a large class of regularization methods (spectral methods) including the aforementioned estimators as well as many iterative methods, such as í-methods and the Landweber iteration. The latter estimators converge at the same rate as spectral cut-off, but only require matrixvector products. Our results are applied to various problems, in particular we obtain precise convergence rates for satellite gradiometry, L2-boosting, and errors in variable problems. --Statistical inverse problems,iterative regularization methods,Tikhonov regularization,nonparametric regression,minimax convergence rates,satellite gradiometry,Hilbert scales,boosting,errors in variable

M\"{o}bius deconvolution on the hyperbolic plane with application to impedance density estimation

In this paper we consider a novel statistical inverse problem on the Poincar\'{e}, or Lobachevsky, upper (complex) half plane. Here the Riemannian structure is hyperbolic and a transitive group action comes from the space of $2\times2$ real matrices of determinant one via M\"{o}bius transformations. Our approach is based on a deconvolution technique which relies on the Helgason--Fourier calculus adapted to this hyperbolic space. This gives a minimax nonparametric density estimator of a hyperbolic density that is corrupted by a random M\"{o}bius transform. A motivation for this work comes from the reconstruction of impedances of capacitors where the above scenario on the Poincar\'{e} plane exactly describes the physical system that is of statistical interest.Comment: Published in at http://dx.doi.org/10.1214/09-AOS783 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Kolmogorov Similarity Hypotheses for Scalar Fields: Sampling Intermittent Turbulent Mixing in the Ocean and Galaxy

Kolmogorov's three universal similarity hypotheses are extrapolated to describe scalar fields like temperature mixed by turbulence. By the analogous Kolmogorov third hypothesis for scalars, temperature dissipation rates chi averaged over lengths r > L_K should be lognormally distributed with intermittency factors I that increase with increasing turbulence energy length scales L_O as I_chi-r = m_T ln(L_O/r). Tests of Kolmogorovian velocity and scalar universal similarity hypotheses for very large ranges of turbulence length and time scales are provided by data from the ocean and the Galactic interstellar medium. The universal constant for turbulent mixing intermittency m_T is estimated from oceanic data to be 0.44+-0.01, which is remarkably close to estimates for Kolmogorov's turbulence intermittency constant m_u of 0.45+-0.05 from Galactic as well as atmospheric data. Extreme intermittency complicates the oceanic sampling problem, and may lead to quantitative and qualitative undersampling errors in estimates of mean oceanic dissipation rates and fluxes. Intermittency of turbulence and mixing in the interstellar medium may be a factor in the formation of stars.Comment: 23 pages original of Proc. Roy. Soc. article, 8 figures; in "Turbulence and Stochastic Processes: Kolmogorov's ideas 50 years on", London The Royal Society, 1991, J.C.R. Hunt, O.M. Phillips, D. Williams Eds., pages 1-240, vol. 434 (no. 1890) Proc. Roy. Soc. Lond. A, PDF fil

Design, theory, and measurement of a polarization insensitive absorber for terahertz imaging

We present the theory, design, and realization of a polarization-insensitive metamaterial absorber for terahertz frequencies. We derive geometrical-independent conditions for effective medium absorbers in general, and for resonant metamaterials specically. Our fabricated design reaches and absorptivity of 78% at 1.145 ThzComment: 6 Pages, 5 figures; figures update

A gain-loss framework based on ensemble flow forecasts to switch the urban drainage-wastewater system management towards energy optimization during dry periods

Precipitation is the cause of major perturbation to the flow in urban drainage and wastewater systems. Flow forecasts, generated by coupling rainfall predictions with a hydrologic runoff model, can potentially be used to optimize the operation of integrated urban drainage–wastewater systems (IUDWSs) during both wet and dry weather periods. Numerical weather prediction (NWP) models have significantly improved in recent years, having increased their spatial and temporal resolution. Finer resolution NWP are suitable for urban-catchment-scale applications, providing longer lead time than radar extrapolation. However, forecasts are inevitably uncertain, and fine resolution is especially challenging for NWP. This uncertainty is commonly addressed in meteorology with ensemble prediction systems (EPSs). Handling uncertainty is challenging for decision makers and hence tools are necessary to provide insight on ensemble forecast usage and to support the rationality of decisions (i.e. forecasts are uncertain and therefore errors will be made; decision makers need tools to justify their choices, demonstrating that these choices are beneficial in the long run). <br><br> This study presents an economic framework to support the decision-making process by providing information on when acting on the forecast is beneficial and how to handle the EPS. The relative economic value (REV) approach associates economic values with the potential outcomes and determines the preferential use of the EPS forecast. The envelope curve of the REV diagram combines the results from each probability forecast to provide the highest relative economic value for a given gain–loss ratio. This approach is traditionally used at larger scales to assess mitigation measures for adverse events (i.e. the actions are taken when events are forecast). The specificity of this study is to optimize the energy consumption in IUDWS during low-flow periods by exploiting the electrical smart grid market (i.e. the actions are taken when no events are forecast). Furthermore, the results demonstrate the benefit of NWP neighbourhood post-processing methods to enhance the forecast skill and increase the range of beneficial uses

Convergence rates of general regularization methods for statistical inverse problems and applications

During the past the convergence analysis for linear statistical inverse problems has mainly focused on spectral cut-off and Tikhonov type estimators. Spectral cut-off estimators achieve minimax rates for a broad range of smoothness classes and operators, but their practical usefulness is limited by the fact that they require a complete spectral decomposition of the operator. Tikhonov estimators are simpler to compute, but still involve the inversion of an operator and achieve minimax rates only in restricted smoothness classes. In this paper we introduce a unifying technique to study the mean square error of a large class of regularization methods (spectral methods) including the aforementioned estimators as well as many iterative methods, such as í-methods and the Landweber iteration. The latter estimators converge at the same rate as spectral cut-off, but only require matrixvector products. Our results are applied to various problems, in particular we obtain precise convergence rates for satellite gradiometry, L2-boosting, and errors in variable problems

Identifying Inconsistencies and Reporting Deficits in Therapeutic Massage and Bodywork (TMB) Case Reports Authored by TMB Practitioners: a TMB-Adapted CAse REport (CARE) Guidelines Audit Through 2014

INTRODUCTION: Case reports are a fundamental tool through which therapeutic massage and bodywork (TMB) practitioners can inform research and impact their field by detailing the presentation, treatment, and follow-up of a single individual encountered in practice. Inconsistencies in case reporting limit their impact as fundamental sources of clinical evidence. Using the TMB-adapted CAse REport (CARE) guidelines, the current study sought to provide a rich description regarding the reporting quality of TMB practitioner authored TMB case reports in the literature. METHODS: 1) Systematic identification of published, peer-reviewed TMB case reports authored by TMB practitioners following PRISMA recommendations; 2) audit development based on TMB-adapted CARE guidelines; 3) audit implementation; and 4) descriptive analysis of audit scores. RESULTS: Our search identified 977 articles and 35 met study inclusion criteria. On average, TMB case reports included approximately 58% of the total items identified as necessary by the TMB-adapted CARE guidelines. Introduction sections of case reports had the best item reporting (80% on average), while Case Presentation (54%) and Results (52%) sections scored moderately overall, with only 20% of necessary Practitioner Description items included on average. Audit scores revealed inconsistent abstract reporting and few audited case reports including client race (20%), perspective (26%), and occupation/activities (40%); practitioner practice setting (12%), training (12%), scope-of-practice (29%), and credentialing (20%); adverse events or lack thereof (17%); and some aspect of informed consent (34%). Treatment descriptor item reporting varied from high to low. Various implications of concern are discussed. CONCLUSION: The current audit and descriptive analysis highlight several reporting inconsistencies in TMB case reports prior to 2015. Reporting guidelines for case reports are important if standards for, and impact of, TMB case reports are desired. Adherence to reporting specifications outlined by the TMB-adapted CARE guidelines could improve the impact and usability of TMB case reports in research, education, and practice

Transverse fluctuations of grafted polymers

We study the statistical mechanics of grafted polymers of arbitrary stiffness in a two-dimensional embedding space with Monte Carlo simulations. The probability distribution function of the free end is found to be highly anisotropic and non-Gaussian for typical semiflexible polymers. The reduced distribution in the transverse direction, a Gaussian in the stiff and flexible limits, shows a double peak structure at intermediate stiffnesses. We also explore the response to a transverse force applied at the polymer free end. We identify F-Actin as an ideal benchmark for the effects discussed.Comment: 10 pages, 4 figures, submitted to Physical Review

Policing virtual spaces: public and private online challenges in a legal perspective

The chapter concerns public and private policing of online platforms and the current challenges in terms of legislation, policing practices and the Dark Web

MSL Entry, Descent, and Landing Instrumentation: Return on Investment

On Aug 5, 2012 the Mars Science Laboratory (MSL) Entry, Descent, and Landing Instrumentation (MEDLI) suite on MSL entry vehicle heatshield suc-cessfully returned surface pressure and in-depth temperature data.1,2 The MEDLI data has given scientists and engineers an unprecedented ability to reconstruct entry environment, atmospheric density, and flight trajectory, and flight validation of predic-tions vehicle aerodynamics and thermal protection system (TPS) performance. This presentation will dis-cuss key findings from MEDLI, some of which are being applied to improve definition of aerothermal environment and TPS sizing margins for existing NASA entry missions. The postflight analysis has shown that a significant thermal protection mass saving upon redesign is possible for an MSL-class vehicle. The success of MEDLI has also demonstrated and qualified robust flight instrumentation technologies at very low risk to the mission. The potential benefits of MEDLI to planetary exploration and sample return missions, as well as to exploration class missions to Mars will be presented