A Robbins--Monro Sequence That Can Exploit Prior Information For Faster Convergence

We propose a new method to improve the convergence speed of the Robbins-Monro algorithm by introducing prior information about the target point into the Robbins-Monro iteration. We achieve the incorporation of prior information without the need of a -- potentially wrong -- regression model, which would also entail additional constraints. We show that this prior-information Robbins-Monro sequence is convergent for a wide range of prior distributions, even wrong ones, such as Gaussian, weighted sum of Gaussians, e.g., in a kernel density estimate, as well as bounded arbitrary distribution functions greater than zero. We furthermore analyse the sequence numerically to understand its performance and the influence of parameters. The results demonstrate that the prior-information Robbins-Monro sequence converges faster than the standard one, especially during the first steps, which are particularly important for applications where the number of function measurements is limited, and when the noise of observing the underlying function is large. We finally propose a rule to select the parameters of the sequence.Comment: 26 pages, 5 figure

Northern High-Latitude Ecosystems Respond to Climate Change

The northern high latitudes are an area of particular importance to global climate change. As a system dependent on freezing conditions, the top of the planet contains vast amounts of carbon in biomass, soils, and permafrost that have the potential to interact with the atmosphere through the biosphere, hydrosphere, lithosphere, and cryosphere. If released en masse, this carbon would greatly exacerbate the levels of greenhouse gases in the atmosphere. Over the past 2 years, a growing body of research has provided evidence of substantial but idiosyncratic environmental changes, with some surprising aspects, across the region. This article reviews some recent findings and presents a new analysis of northern vegetation photosynthetic and productivity trends tracked from Earth observing satellites

Tailoring Adjuvant Endocrine Therapy for Postmenopausal Breast Cancer: A CYP2D6 Multiple-Genotype-Based Modeling Analysis and Validation

Purpose: Previous studies have suggested that postmenopausal women with breast cancer who present with wild-type CYP2D6 may actually have similar or superior recurrence-free survival outcomes when given tamoxifen in place of aromatase inhibitors (AIs). The present study established a CYP2D6 multiple-genotype-based model to determine the optimal endocrine therapy for patients harboring wild-type CYP2D6. Methods: We created a Markov model to determine whether tamoxifen or AIs maximized 5-year disease-free survival (DFS) for extensive metabolizer (EM) patients using annual hazard ratio (HR) data from the BIG 1-98 trial. We then replicated the model by evaluating 9-year event-free survival (EFS) using HR data from the ATAC trial. In addition, we employed two-way sensitivity analyses to explore the impact of HR of decreased-metabolizer (DM) and its frequency on survival by studying a range of estimates. Results: The 5-year DFS of tamoxifen-treated EM patients was 83.3%, which is similar to that of genotypically unselected patients who received an AI (83.7%). In the validation study, we further demonstrated that the 9-year EFS of tamoxifentreated EM patients was 81.4%, which is higher than that of genotypically unselected patients receiving tamoxifen (78.4%) and similar to that of patients receiving an AI (83.2%). Two-way sensitivity analyses demonstrated the robustness of the results

Ambipolar Electric Field and Potential in the Solar Wind Estimated from Electron Velocity Distribution Functions

The solar wind escapes from the solar corona and is accelerated, over a short distance, to its terminal velocity. The energy balance associated with this acceleration remains poorly understood. To quantify the global electrostatic contribution to the solar wind dynamics, we empirically estimate the ambipolar electric field (E∥) and potential (Φr,∞). We analyze electron velocity distribution functions (VDFs) measured in the near-Sun solar wind between 20.3 RS and 85.3 RS by the Parker Solar Probe. We test the predictions of two different solar wind models. Close to the Sun, the VDFs exhibit a suprathermal electron deficit in the sunward, magnetic-field-aligned part of phase space. We argue that the sunward deficit is a remnant of the electron cutoff predicted by collisionless exospheric models. This cutoff energy is directly linked to Φr,∞. Competing effects of E∥ and Coulomb collisions in the solar wind are addressed by the Steady Electron Runaway Model (SERM). In this model, electron phase space is separated into collisionally overdamped and underdamped regions. We assume that this boundary velocity at small pitch angles coincides with the strahl break-point energy, which allows us to calculate E∥. The obtained Φr,∞ and E∥ agree well with theoretical expectations. They decrease with radial distance as power-law functions with indices αΦ = −0.66 and αE = −1.69. We finally estimate the velocity gained by protons from electrostatic acceleration, which equals 77% calculated from the exospheric models, and 44% from the SERM model

The Radial Dependence of Proton-scale Magnetic Spectral Break in Slow Solar Wind during PSP Encounter 2

International audienceMagnetic field fluctuations in the solar wind are commonly observed to follow a power-law spectrum. Near proton-kinetic scales, a spectral break occurs that is commonly interpreted as a transition to kinetic turbulence. However, this transition is not yet entirely understood. By studying the scaling of the break with various plasma properties, it may be possible to constrain the processes leading to the onset of kinetic turbulence. Using data from the Parker Solar Probe, we measure the proton-scale break over a range of heliocentric distances, enabling a measurement of the transition from inertial to kinetic-scale turbulence under various plasma conditions. We find that the break frequency f(b) increases as the heliocentric distance r decreases in the slow solar wind following a power law of f(b) similar to r(-1.11). We also compare this to the characteristic plasma ion scales to relate the break to the possible physical mechanisms occurring at this scale. The ratio f(b)/f(c) (f(c) for Doppler-shifted ion cyclotron resonance scale) is close to unity and almost independent of plasma beta(p). While f(b)/f(p) (f(p) for Doppler-shifted proton thermal gyroradius) increases with beta(p) approaching to unity at larger beta(p), f(b)/f(d) (f(d) for Doppler-shifted proton inertial length) decreases with beta(p) from unity at small beta(p). Due to the large comparable Alfven and solar wind speeds, we analyze these results using both the standard and modified Taylor hypotheses, demonstrating the robust statistical results

Cross Helicity Reversals in Magnetic Switchbacks

International audienceWe consider 2D joint distributions of normalized residual energy, sigma(r)(s, t), and cross helicity, sigma(c)(s, t), during one day of Parker Solar Probe's (PSP's) first encounter as a function of wavelet scale s. The broad features of the distributions are similar to previous observations made by Helios in slow solar wind, namely well-correlated and fairly Alfvenic wind, except for a population with negative cross helicity that is seen at shorter wavelet scales. We show that this population is due to the presence of magnetic switchbacks, or brief periods where the magnetic field polarity reverses. Such switchbacks have been observed before, both in Helios data and in Ulysses data in the polar solar wind. Their abundance and short timescales as seen by PSP in its first encounter is a new observation, and their precise origin is still unknown. By analyzing these MHD invariants as a function of the wavelet scale, we show that magnetohydrodynamic (MHD) waves do indeed follow the local mean magnetic field through switchbacks, with a net Elsasser flux propagating inward during the field reversal and that they, therefore, must be local kinks in the magnetic field and not due to small regions of opposite polarity on the surface of the Sun. Such observations are important to keep in mind as computing cross helicity without taking into account the effect of switchbacks may result in spurious underestimation of sigma(c) as PSP gets closer to the Sun in later orbits

de Sitter Thick Brane Solution in Weyl Geometry

In this paper, we consider a de Sitter thick brane model in a pure geometric Weyl integrable five-dimensional space-time, which is a generalization of Riemann geometry and is invariant under a so-called Weyl rescaling. We find a solution of this model via performing a conformal transformation to map the Weylian structure into a familiar Riemannian one with a conformal metric. The metric perturbations of the model are discussed. For gravitational perturbation, we get the effective modified P$\ddot{\text{o}}$schl-Teller potential in corresponding Schr$\ddot{\text{o}}$dinger equation for Kaluza-Klein (KK) modes of the graviton. There is only one bound state, which is a normalizable massless zero mode and represents a stable 4-dimensional graviton. Furthermore, there exists a mass gap between the massless mode and continuous KK modes. We also find that the model is stable under the scalar perturbation in the metric. The correction to the Newtonian potential on the brane is proportional to $e^{-3 r \beta/2}/r^2$, where $\beta$ is the de Sitter parameter of the brane. This is very different from the correction caused by a volcano-like effective potential.Comment: 24 pages, 13 figures, published versio

Magnetic connectivity of the ecliptic plane within 0.5 AU : PFSS modeling of the first PSP encounter

We compare magnetic field measurements taken by the FIELDS instrument on Parker Solar Probe (PSP) during its first solar encounter to predictions obtained by Potential Field Source Surface (PFSS) modeling. Ballistic propagation is used to connect the spacecraft to the source surface. Despite the simplicity of the model, our results show striking agreement with PSPs first observations of the heliospheric magnetic field from 0.5 AU (107.5 Rs) down to 0.16 AU (35.7 Rs). Further, we show the robustness of the agreement is improved both by allowing the photospheric input to the model to vary in time, and by advecting the field from PSP down to the PFSS model domain using in situ PSP/SWEAP measurements of the solar wind speed instead of assuming it to be constant with longitude and latitude. We also explore the source surface height parameter (RSS) to the PFSS model finding that an extraordinarily low source surface height (1.3-1.5Rs) predicts observed small scale polarity inversions which are otherwise washed out with regular modeling parameters. Finally, we extract field line traces from these models. By overlaying these on EUV images we observe magnetic connectivity to various equatorial and mid-latitude coronal holes indicating plausible magnetic footpoints and offering context for future discussions of sources of the solar wind measured by PSP

Constraining Ion-Scale Heating and Spectral Energy Transfer in Observations of Plasma Turbulence

International audienceWe perform a statistical study of the turbulent power spectrum at inertial and kinetic scales observed during the first perihelion encounter of the Parker Solar Probe. We find that often there is an extremely steep scaling range of the power spectrum just above the ion-kinetic scales, similar to prior observations at 1 A.U., with a power-law index of around −4. Based on our measurements, we demonstrate that either a significant (>50%) fraction of the total turbulent energy flux is dissipated in this range of scales, or the characteristic nonlinear interaction time of the turbulence decreases dramatically from the expectation based solely on the dispersive nature of nonlinearly interacting kinetic Alfvén waves

Sharp Alfvenic impulses in the near-Sun solar wind

Measurements of the near-Sun solar wind by Parker Solar Probe have revealed the presence of largenumbers of discrete Alfv ́enic impulses with an anti-Sunward sense of propagation. These are similarto those previously observed near 1 AU, in high speed streams over the Sun’s poles and at 60 solarradii. At 35 solar radii, however, they are typically shorter and sharper than seen elsewhere. Inaddition, these spikes occur in “patches” and there are also clear periods within the same stream whenthey do not occur; the timescale of these patches might be related to the rate at which the spacecraftmagnetic footpoint tracks across the coronal hole from which the plasma originated. While the velocityfluctuations associated with these spikes are typically under 100 km/s, due to the rather low Alfv ́enspeeds in the streams observed by the spacecraft to date, these are still associated with large angulardeflections of the magnetic field - and these deflections are not isotropic. These deflections do notappear to be related to the recently reported large scale, pro-rotation solar wind flow. Estimates ofthe size and shape of the spikes reveal high aspect ratio flow-aligned structures with a transverse scaleof≈104km. These events might be signatures of near-Sun impulsive reconnection events