Search

The possibility of an Earth-Sun analog beyond our solar system is one of the most longstanding questions in science. At present, answering this question embodies an extremely difficult measurement problem that requires multiple coordinated advances in astronomical telescopes, fiber optics, precision spectrographs, large format detector arrays, and advanced data processing. Taken together, addressing this challenge will require the measurement and calibration of shifts in stellar spectra at the 10^-10 level over multi-year periods. The potential for such precision has recently been advanced by the introduction of laser frequency combs (LFCs) to the field of precision astronomical spectroscopy. However, the expense, complexity and lack of full spectral coverage of LFCs has limited their widespread use and ultimate impact. To address this issue, we explore simple and robust white-light-illuminated Fabry-Perot (FP) etalons as spectral calibrators for precise radial velocity measurements. We track the frequencies of up to 13,000 etalon modes of the installed FPs from two state-of-the-art astronomical spectrographs. Combining these measurements with modeling, we trace unexpected chromatic variations of the FP modes to sub-picometer changes in the dielectric layers of the broad bandwidth FP mirrors. This yields the determination of the frequencies of the FP modes with precision approaching 10^-11/day, equivalent to a radial velocity (RV) Doppler shift of 3 mm/s/day. These results represent critical progress in precision RV measurements on two fronts: first, they make FP etalons a more powerful stand-alone calibration tool, and second, they demonstrate the capability of LFCs to extend cm/s level RV measurement precision over periods approaching a year. Together, these advances highlight a path to achieving spectroscopic calibration at levels that will be critical for finding earths like our own., Comment: 12 pages, 4 figures

We prove path-by-path uniqueness of solution to hyperbolic stochastic partial differential equations when the drift coefficient is the difference of two componentwise monotone Borel measurable functions of spatial linear growth. The Yamada-Watanabe principle for SDE driven by Brownian sheet then allows to derive strong uniqueness for such equation and thus extending the results in [Bogso, Dieye and Menoukeu Pamen, Elect. J. Probab., 27:1-26, 2022] and [Nualart and Tindel, Potential Anal., 7(3):661--680, 1997]. Assuming that the drift is globally bounded, we show that the unique strong solution is Malliavin differentiable. The case of spatial linear growth drift coefficient is also studied., Comment: 25 pages. arXiv admin note: text overlap with arXiv:2112.00393

We develop regularity theory for elliptic Kolmogorov operator with divergence-free drift in a large class (or, more generally, drift having singular divergence). A key step in our proofs is "Caccioppoli's iterations", used in addition to the classical De Giorgi's iterations and Moser's method.

For near-critical, transient Markov chains on the non-negative integers in the Lamperti regime, where the mean drift at $x$ decays as $1/x$ as $x \to \infty$, we quantify degree of transience via existence of moments for conditional return times and for last exit times, assuming increments are uniformly bounded. Our proof uses a Doob $h$-transform, for the transient process conditioned to return, and we show that the conditioned process is also of Lamperti type with appropriately transformed parameters. To do so, we obtain an asymptotic expansion for the ratio of two return probabilities, evaluated at two nearby starting points; a consequence of this is that the return probability for the transient Lamperti process is a regularly-varying function of the starting point., Comment: 26 pages; v2: minor revisions, expanded discussion

We consider in this work the convergence of a split-step Euler type scheme (SSM) for the numerical simulation of interacting particle Stochastic Differential Equation (SDE) systems and McKean-Vlasov Stochastic Differential Equations (MV-SDEs) with full super-linear growth in the spatial and the interaction component in the drift, and non-constant Lipschitz diffusion coefficient. The super-linear growth in the interaction (or measure) component stems from convolution operations with super-linear growth functions allowing in particular application to the granular media equation with multi-well confining potentials. From a methodological point of view, we avoid altogether functional inequality arguments (as we allow for non-constant non-bounded diffusion maps). The scheme attains, in stepsize, a near-optimal classical (path-space) root mean-square error rate of $1/2-\varepsilon$ for $\varepsilon>0$ and an optimal rate $1/2$ in the non-path-space mean-square error metric. Numerical examples illustrate all findings. In particular, the testing raises doubts if taming is a suitable methodology for this type of problem (with convolution terms and non-constant diffusion coefficients)., Comment: 40 pages, 3 figures; Final author accepted version (to appear in IMA J. of Num. Analysis)

\noindent Consider an infinite collection of particles on the real line moving according to independent Brownian motions and such that the $i$-th particle from the left gets the drift $g_{i-1}$. The case where $g_0=1$ and $g_{i}=0$ for all $i \in \mathbb{N}$ corresponds to the well studied infinite Atlas model. Under conditions on the drift vector $\boldsymbol{g} = (g_0, g_1, \ldots)'$ it is known that the Markov process corresponding to the gap sequence of the associated ranked particles has a continuum of product form stationary distributions $\{\pi_a^{\boldsymbol{g}}, a \in S^{\boldsymbol{g}}\}$ where $S^{\boldsymbol{g}}$ is a semi-infinite interval of the real line. In this work we show that all of these stationary distributions are extremal and ergodic. We also prove that any product form stationary distribution of this Markov process that satisfies a mild integrability condition must be $\pi_a^{\boldsymbol{g}}$ for some $a \in S^{\boldsymbol{g}}$. These results are new even for the infinite Atlas model. The work makes progress on the open problem of characterizing all the invariant distributions of general competing Brownian particle systems interacting through their relative ranks. Proofs rely on synchronous and mirror coupling of Brownian particles and properties of the intersection local times of the various particles in the infinite system., Comment: 29 pages. To appear in Probability Theory and Related Fields

We consider parabolic PDEs associated with fractional type operators drifted by non-linear singular first order terms. When the drift enjoys some boundedness properties in appropriate Lebesgue and Besov spaces, we establish by exploiting a priori Besov-type estimates, the H{\"o}lder continuity of the solutions. In particular, we handle the almost critical case in whole generality.

We study stochastic differential equations(SDEs) with a small perturbation parameter. Under the dissipative condition on the drift coefficient and the local Lipschitz condition on the drift and diffusion coefficients we prove the existence and uniqueness result for the perturbed SDE, also the convergence result for the solution of the perturbed system to the solution of the unperturbed system when the perturbation parameter approaches zero.We consider the application of the above-mentioned results to the Cauchy problem and the transport equations.

In-situ, two-dimensional (2D) Langmuir probe measurements across a large part of the TCV divertor are reported in L-mode discharges with and without divertor baffles. This provides detailed insights into time averaged profiles, particle fluxes, and fluctuations behavior in different divertor regimes. The presence of the baffles is shown to substantially increase the divertor neutral pressure for a given upstream density and to facilitate the access to detachment, an effect that increases with plasma current. The detailed, 2D probe measurements allow for a divertor particle balance, including ion flux contributions from parallel flows and ExB drifts. The poloidal flux contribution from the latter is often comparable or even larger than the former, such that the divertor parallel flow direction reverses in some conditions, pointing away from the target. In most conditions, the integrated particle flux at the outer target can be predominantly ascribed to ionization along the outer divertor leg, consistent with a closed-box approximation of the divertor. The exception is a strongly detached divertor, achieved here only with baffles, where the total poloidal ion flux even decreases towards the outer target, indicative of significant plasma recombination. The most striking observation from relative density fluctuation measurements along the outer divertor leg is the transition from poloidally uniform fluctuation levels in attached conditions to fluctuations strongly peaking near the X-point when approaching detachment., Comment: Added reference

Multiple medical institutions collaboratively training a model using federated learning (FL) has become a promising solution for maximizing the potential of data-driven models, yet the non-independent and identically distributed (non-iid) data in medical images is still an outstanding challenge in real-world practice. The feature heterogeneity caused by diverse scanners or protocols introduces a drift in the learning process, in both local (client) and global (server) optimizations, which harms the convergence as well as model performance. Many previous works have attempted to address the non-iid issue by tackling the drift locally or globally, but how to jointly solve the two essentially coupled drifts is still unclear. In this work, we concentrate on handling both local and global drifts and introduce a new harmonizing framework called HarmoFL. First, we propose to mitigate the local update drift by normalizing amplitudes of images transformed into the frequency domain to mimic a unified imaging setting, in order to generate a harmonized feature space across local clients. Second, based on harmonized features, we design a client weight perturbation guiding each local model to reach a flat optimum, where a neighborhood area of the local optimal solution has a uniformly low loss. Without any extra communication cost, the perturbation assists the global model to optimize towards a converged optimal solution by aggregating several local flat optima. We have theoretically analyzed the proposed method and empirically conducted extensive experiments on three medical image classification and segmentation tasks, showing that HarmoFL outperforms a set of recent state-of-the-art methods with promising convergence behavior. Code is available at https://github.com/med-air/HarmoFL., Comment: Accepted at AAAI 2022