Statistical aspects of the fractional stochastic calculus

We apply the techniques of stochastic integration with respect to fractional Brownian motion and the theory of regularity and supremum estimation for stochastic processes to study the maximum likelihood estimator (MLE) for the drift parameter of stochastic processes satisfying stochastic equations driven by a fractional Brownian motion with any level of H\"{o}lder-regularity (any Hurst parameter). We prove existence and strong consistency of the MLE for linear and nonlinear equations. We also prove that a version of the MLE using only discrete observations is still a strongly consistent estimator.Comment: Published at http://dx.doi.org/10.1214/009053606000001541 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Parameter Estimation of Gaussian Stationary Processes using the Generalized Method of Moments

We consider the class of all stationary Gaussian process with explicit parametric spectral density. Under some conditions on the autocovariance function, we defined a GMM estimator that satisfies consistency and asymptotic normality, using the Breuer-Major theorem and previous results on ergodicity. This result is applied to the joint estimation of the three parameters of a stationary Ornstein-Uhlenbeck (fOU) process driven by a fractional Brownian motion. The asymptotic normality of its GMM estimator applies for any H in (0,1) and under some restrictions on the remaining parameters. A numerical study is performed in the fOU case, to illustrate the estimator's practical performance when the number of datapoints is moderate

The Effects of Self-Monitoring, EMG Biofeedback, and Relaxation Tapes in the Treatment of Tension Headaches

Tension headache is an important medical-behavioral disorder because of its high incidence and the personal discomfort and disruption of normal activities that frequently accompany it. Several behavioral strategies have been applied in the treatment of this disorder. Two of the most prominent treatments are EMG biofeedback and Progressive muscle relaxation exercises. Research has shown both of these strategies to be effective treatments of tension headache but much debate still ensues as to which is the more effective treatment. The effects of different self-monitoring procedures have never been compared during EMG biofeedback or Progressive muscle relaxation treatments of tension headache. In the present study, 9 people with tension headaches were used to compare EMG biofeedback and Progressive muscle relaxation tapes in the treatment of tension headache. This study also assessed the contribution of different modes of self-monitoring (daily recording sheets and daily recording sheets plus timers) in the reduction of headache activity. The participants were university students ranging in age from 19 to 25 years. Volunteers included 2 males and 7 females who reported having tension headaches for an average of 41.2 months. Participants were instructed to self-record daily frequency and intensity of headaches plus medication intake, chemical intake and sleeping behavior. After a two week baseline, they were assigned to one of three conditions: EMG, Relaxation tapes, or EMG plus timers. Treatment for each group lasted one week while they continued to fill out their daily self-monitoring sheets and to record their headache activity. Results indicated that each of the nine participants reduced EMG levels with and without feedback given at the conclusion of the treatment phase and that eight of the nine persons also experienced significant reductions in headache frequency. Of these eight, over one-half of them reported decreases in sleep onset and total sleep time with an increase in the amount of restful sleep. While two persons from each group reported decreases in total sleep time and increases in the amount of restful sleep, it was only in the EMG plus timers condition that all three participants reported a decrease in sleep onset. The results of this study indicated that both EMG biofeedback and Relaxation tapes are effective procedures for treating tension headache. Results also suggested that neither home practice nor prior forearm extensor muscle training appeared to be necessary components of success in either treatment modality. Furthermore, although the introduction of timers into the self-monitoring phase of one EMG group did not produce a headache-free condition for those individuals, such an addition may provide a distinct form of cueing which better prepares the headache subject to effectively utilize the biofeedback signal in EMG biofeedback. Additional research was recommended, and limitations of the present data were discussed

Applying a Precautionary Approach to Mobile Contact Tracing for COVID-19: The Value of Reversibility

The COVID-19 pandemic presents unprecedented challenges to public health decision-making. Specifically, the lack of evidence and the urgency with which a response is called for, raise the ethical challenge of assessing how much (and what kind of) evidence is required for the justification of interventions in response to the various threats we face. Here we discuss the intervention of introducing technology that aims to trace and alert contacts of infected persons-contact tracing (CT) technology. Determining whether such an intervention is proportional is complicated by complex trade-offs and feedback loops. We suggest that the resulting uncertainties necessitate a precautionary approach. On the one hand, precautionary reasons support CT technology as a means to contribute to the prevention of harms caused by alternative interventions, or COVID-19 itself. On the other hand, however, both the extent to which such technology itself present risks of serious harm, as well as its effectiveness, remain unclear. We therefore argue that a precautionary approach should put reversibility of CT technology at the forefront. We outline several practical implications

Degradation of Teflon(tm) FEP Following Charged Particle Radiation and Rapid Thermal Cycling

During the Second Servicing Mission (SM2) of the Hubble Space Telescope (HST) severe degradation was observed on the outer layer of the thermal control blankets. Astronaut observations and photographs revealed large cracks in the metallized Teflon' FEP (fluorinated ethylene propylene), the outer layer of the multi-layer insulation (MLI), in many locations around the telescope. In an effort to understand what elements of the space environment might cause such damage, pristine Teflon(registered trademark) FEP was tested for durability to radiation and thermal cycling. Specimens were subjected to electron and proton fluences comparable to those experienced by HST and were subsequently thermal cycled in a custom-built rapid thermal cycle chamber. Tensile tests of the specimens showed that radiation followed by thermal cycling significantly reduced the ultimate strength and elongation of Teflon(registered trademark) FEP

Kilometer-long ordered nanophotonic devices by preform-to-fiber fabrication

Cataloged from PDF version of article.A preform-fo-fiber approach to the fabrication of functional fiber-based devices by thermal drawing in the viscous state is presented. A macroscopic preform rod containing metallic, semiconducting, and insulating constituents in a variety of geometries and close contact produces kilometer-long novel nanostructured fibers and fiber devices. We first review the material selection criteria and then describe metal-semiconductor-metal photosensitive and thermally sensitive fibers. These flexible, lightweight, and low-cost functional fibers may pave the way for new types of fiber sensors, such as thermal sensing fabrics, artificial skin, and large-area optoelectronic screens. Next, the preform-to-fiber approach is used to fabricate spectrally tunable photodetectors that integrate a photosensitive core and a nanostructured photonic crystal structure containing a resonant cavity. An integrated, self-monitoring optical-transmission waveguide is then described that incorporates optical transport and thermal monitoring. This fiber allows one to predict power-transmission failure, which is of paramount importance if high-power optical transmission lines are to be operated safely and reliably in medical, industrial and defense applications. A hybrid electron-photon fiber consisting of a hollow core (for optical transport by means of a photonic bandgap) and metallic wires (for electron transport) is described that may be used for transporting atoms and molecules by radiation pressure. Finally, a solid microstructured fiber fabricated with a highly nonlinear chalcogenide glass enables the generation of supercontinumn light at near-infrared wavelengths