2,205 research outputs found
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
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 Ć-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
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
Design and analysis of three-arm trials with negative binomially distributed endpoints.
A three-arm clinical trial design with an experimental treatment, an active control, and a placebo control, commonly referred to as the gold standard design, enables testing of non-inferiority or superiority of the experimental treatment compared with the active control. In this paper, we propose methods for designing and analyzing three-arm trials with negative binomially distributed endpoints. In particular, we develop a Wald-type test with a restricted maximum-likelihood variance estimator for testing non-inferiority or superiority. For this test, sample size and power formulas as well as optimal sample size allocations will be derived. The performance of the proposed test will be assessed in an extensive simulation study with regard to type I error rate, power, sample size, and sample size allocation. For the purpose of comparison, Wald-type statistics with a sample variance estimator and an unrestricted maximum-likelihood estimator are included in the simulation study. We found that the proposed Wald-type test with a restricted variance estimator performed well across the considered scenarios and is therefore recommended for application in clinical trials. The methods proposed are motivated and illustrated by a recent clinical trial in multiple sclerosis. The R package Three Armed Trials, which implements the methods discussed in this paper, is available on CRAN
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Multi-Physics Bi-directional Evolutionary Topology Optimization on GPU-architecture
Topology optimization has proven to be viable for use in the preliminary phases of real world design problems. Ultimately, the restricting factor is the computational expense since a multitude of designs need to be considered. This is especially imperative in such fields as aerospace, automotive and biomedical, where the problems involve multiple physical models, typically fluids and structures, requiring excessive computational calculations. One possible solution to this is to implement codes on massively parallel computer architectures, such as graphics processing units (GPUs). The present work investigates the feasibility of a GPU-implemented lattice Boltzmann method for multi-physics topology optimization for the first time. Noticeable differences between the GPU implementation and a central processing unit (CPU) version of the code are observed and the challenges associated with finding feasible solutions in a computational efficient manner are discussed and solved here, for the first time on a multi-physics topology optimization problem. The main goal of this paper is to speed up the topology optimization process for multi-physics problems without restricting the design domain, or sacrificing considerable performance in the objectives. Examples are compared with both standard CPU and various levels of numerical precision GPU codes to better illustrate the advantages and disadvantages of this implementation. A structural and fluid objective topology optimization problem is solved to vary the dependence of the algorithm on the GPU, extending on the previous literature that has only considered structural objectives of non-design dependent load problems. The results of this work indicate some discrepancies between GPU and CPU implementations that have not been seen before in the literature and are imperative to the speed-up of multi-physics topology optimization algorithms using GPUs.D. J. Munk thanks the Australian government for their financial support through the Endeavour Fellowship scheme. The authors would like to acknowledge the UK Consortium on Mesoscale Engineering
Sciences (UKCOMES) EPSRC grant No EP/L00030X/1 for providing the HPC capabilities used in this article
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 Ī½-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.
AMS subject classifications: 62G05, 62J05, 62P35, 65J10, 35R3
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
An Unbiased Test for the Bioequivalence Problem
It is shown that the standard two one-sided tests procedure for bioequivalence is a biased test. Better tests exist. In this paper, an unbiased Ī±-level test and other tests which are uniformly more powerful than the two one-sided tests procedure are constructed. Its power can be noticeably larger than that of the Ī±-level two one-sided tests procedure
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
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 drainageāwastewater 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).
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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 gaināloss 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
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