Risk hull method and regularization by projections of ill-posed inverse problems

We study a standard method of regularization by projections of the linear inverse problem $Y=Af+\epsilon$, where $\epsilon$ is a white Gaussian noise, and $A$ is a known compact operator with singular values converging to zero with polynomial decay. The unknown function $f$ is recovered by a projection method using the singular value decomposition of $A$. The bandwidth choice of this projection regularization is governed by a data-driven procedure which is based on the principle of risk hull minimization. We provide nonasymptotic upper bounds for the mean square risk of this method and we show, in particular, that in numerical simulations this approach may substantially improve the classical method of unbiased risk estimation.Comment: Published at http://dx.doi.org/10.1214/009053606000000542 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Regularization of statistical inverse problems and the Bakushinskii veto

In the deterministic context Bakushinskii's theorem excludes the existence of purely data driven convergent regularization for ill-posed problems. We will prove in the present work that in the statistical setting we can either construct a counter example or develop an equivalent formulation depending on the considered class of probability distributions. Hence, Bakushinskii's theorem does not generalize to the statistical context, although this has often been assumed in the past. To arrive at this conclusion, we will deduce from the classic theory new concepts for a general study of statistical inverse problems and perform a systematic clarification of the key ideas of statistical regularization.Comment: 20 page

Minimax estimation of the Wigner function in quantum homodyne tomography with ideal detectors

We estimate the quantum state of a light beam from results of quantum homodyne measurements performed on identically prepared pulses. The state is represented through the Wigner function, a ``quasi-probability density'' on $\mathbb{R}^{2}$ which may take negative values and must respect intrinsic positivity constraints imposed by quantum physics. The data consists of $n$ i.i.d. observations from a probability density equal to the Radon transform of the Wigner function. We construct an estimator for the Wigner function, and prove that it is minimax efficient for the pointwise risk over a class of infinitely differentiable functions. A similar result was previously derived by Cavalier in the context of positron emission tomography. Our work extends this result to the space of smooth Wigner functions, which is the relevant parameter space for quantum homodyne tomography.Comment: 15 page

Analyses of Groundwater for Trace Levels of Pesticides

Agricultural production is a major source of revenue in Arkansas. In order to increase productivity, it has been necessary to rely increasingly on the use of pesticides and irrigation water. In the last 15 years several states have reported finding pesticides in groundwater as a result of normal agricultural practices. Since almost half of the population also relies on groundwater as their source of drinking water, it is necessary to conduct research as to ascertain the presence or absence of commonly used pesticides in groundwater. Multi residue analytical techniques were developed for the analysis of acifluorfen, alachlor, atrazine, cyanazine, diuron, fluometuron, linuron, metolachlor and propanil from groundwater, by either GLC or HPLC. Analytical sensitivities ranged from 1 to 5 ppb. Groundwater samples were collected from three areas of southeastern Arkansas that are under heavy agricultural production. Samples were collected directly from irrigation wells just prior to and during the peak of the irrigation season and will be compared to determine whether any temporal differences exist. To-date, over 500 samples have been analyzed. No positive finding for any pesticide has been shown

Reconstruction of source location in a network of gravitational wave interferometric detectors

This paper deals with the reconstruction of the direction of a gravitational wave source using the detection made by a network of interferometric detectors, mainly the LIGO and Virgo detectors. We suppose that an event has been seen in coincidence using a filter applied on the three detector data streams. Using the arrival time (and its associated error) of the gravitational signal in each detector, the direction of the source in the sky is computed using a chi^2 minimization technique. For reasonably large signals (SNR>4.5 in all detectors), the mean angular error between the real location and the reconstructed one is about 1 degree. We also investigate the effect of the network geometry assuming the same angular response for all interferometric detectors. It appears that the reconstruction quality is not uniform over the sky and is degraded when the source approaches the plane defined by the three detectors. Adding at least one other detector to the LIGO-Virgo network reduces the blind regions and in the case of 6 detectors, a precision less than 1 degree on the source direction can be reached for 99% of the sky.Comment: Accepted in Phys. Rev.

Adoção do IFRS no Brasil: um terreno fértil para pesquisa sobre gerenciamento de resultados

We highlight aspects of the Brazilian operating and reporting environment that have led to ample opportunities for researchers to examine the topic of earnings management in financial reporting. In particular, we discuss the potential for research since Brazil has adopted a financial reporting system (IFRS) to replace its tax compliance system. Within that framework, we consider the role of other aspects of Brazil’s environment, including the recent influx of foreign investment, the ability to choose corporate structure, and the implications of inflation on the incentives and opportunities for earnings management. As a guideline to researchers in Brazil, we have also provided a discussion of the applicability of testing those earnings properties most often tested in relation to earnings management, paying particular attention to issues that would be of interest beyond Brazil’s borders.Esta pesquisa investiga aspectos do ambiente econômico em que são elaborados relatórios financeiros e contábeis, favoráveis ao estudo do gerenciamento de resultados. Em particular, o estudo discute o potencial de investigação acadêmica desse tópico no Brasil, país que adotou recentemente o IFRS, sistema internacional de relatórios financeiros, para substituir seu atual modelo de cumprimento das obrigações fiscais. Dentro desse quadro, foi considerado o papel de outras características do ambiente econômico brasileiro, como a atratividade recente de investimentos estrangeiros, a capacidade de escolha da estrutura societária e as implicações da inflação sobre os incentivos e sobre as oportunidades para o gerenciamento de resultados. Como orientação para pesquisadores no Brasil, este estudo discute a aplicabilidade do teste das propriedades do gerenciamento e dos ganhos vinculados a essa prática, com especial atenção para as questões de interesse para além das fronteiras do Brasil

Nitrogen deprivation induces triacylglycerol accumulation, drug tolerance and hypervirulence in mycobacteria.

Mycobacteria share with other actinomycetes the ability to produce large quantities of triacylglycerol (TAG), which accumulate as intracytoplasmic lipid inclusions (ILI) also known as lipid droplets (LD). Mycobacterium tuberculosis (M. tb), the etiologic agent of tuberculosis, acquires fatty acids from the human host which are utilized to synthesize TAG, subsequently stored in the form of ILI to meet the carbon and nutrient requirements of the bacterium during long periods of persistence. However, environmental factors governing mycobacterial ILI formation and degradation remain poorly understood. Herein, we demonstrated that in the absence of host cells, carbon excess and nitrogen starvation promote TAG accumulation in the form of ILI in M. smegmatis and M. abscessus, used as surrogate species of M. tb. Based on these findings, we developed a simple and reversible in vitro model to regulate ILI biosynthesis and hydrolysis in mycobacteria. We also showed that TAG formation is tgs1 dependent and that lipolytic enzymes mediate TAG breakdown. Moreover, we confirmed that the nitrogen-deprived and ILI-rich phenotype was associated with an increased tolerance towards several drugs used for treating mycobacterial infections. Importantly, we showed that the presence of ILI substantially enhanced the bacterial burden and granuloma abundance in zebrafish embryos infected with lipid-rich M. abscessus as compared to embryos infected with lipid-poor M. abscessus, suggesting that ILI are actively contributing to mycobacterial virulence and pathogenesis

Benefits of joint LIGO -- Virgo coincidence searches for burst and inspiral signals

We examine the benefits of performing a joint LIGO--Virgo search for transient signals. We do this by adding burst and inspiral signals to 24 hours of simulated detector data. We find significant advantages to performing a joint coincidence analysis, above either a LIGO only or Virgo only search. These include an increased detection efficiency, at a fixed false alarm rate, to both burst and inspiral events and an ability to reconstruct the sky location of a signal.Comment: 11 pages 8 figures, Amaldi 6 proceeding

EROS Variable Stars : Discovery of Beat Cepheids in the Small Magellanic Cloud and the effect of metallicity on pulsation

We report the discovery of eleven beat Cepheids in the Small Magellanic Cloud, using data obtained by the EROS microlensing survey. Four stars are beating in the fundamental and first overtone mode (F/1OT), seven are beating in the first and second overtone (1OT/2OT). The SMC F/1OT ratio is systematically higher than the LMC F/1OT, while the 1OT/2OT period ratio in the SMC Cepheids is the same as the LMC one.Comment: 4 pages, Latex file with 4 .ps figures. accepted for publication in A A Letter

The effect of metallicity on the Cepheid distance scale and its implications for the Hubble constant (H0H_0) determination

Recent HST determinations of the expansion's rate of the Universe (the Hubble constant, H_0) assumed that the Cepheid Period-Luminosity relation at V and I are independent of metallicity (Freedman, et al., 1996, Saha et al., 1996, Tanvir et al., 1995). The three groups obtain different vales for H_0. We note that most of this discrepancy stems from the asumption (by both groups) that the Period-Luminosity relation is independent of metallicity. We come to this conclusion as a result of our study of the Period-Luminosity relation of 481 Cepheids with 3 millions two colour measurements in the Large Magellanic Cloud and the Small Magellanic Cloud obtained as a by-product of the EROS microlensing survey. We find that the derived interstellar absorption corrections are particularly sensitive to the metallicity and when our result is applied to recent estimates based on HST Cepheids observations it makes the low-H_0 values higher and the high-H_0 value lower, bringing those discrepant estimates into agrement around $H_0 \approx 70 km/s Mpc^{-1}$.Comment: 4 pages, Latex, with 2 .ps accepted for publication astronomy and astrophysics Letter