Characterization of Microlensing Planets with Moderately Wide Separations

In future high-cadence microlensing surveys, planets can be detected through a new channel of an independent event produced by the planet itself. The two populations of planets to be detected through this channel are wide-separation planets and free-floating planets. Although they appear as similar short time-scale events, the two populations of planets are widely different in nature and thus distinguishing them is important. In this paper, we investigate the lensing properties of events produced by planets with moderately wide separations from host stars. We find that the lensing behavior of these events is well described by the Chang-Refsdal lensing and the shear caused by the primary not only produces a caustic but also makes the magnification contour elongated along the primary-planet axis. The elongated magnification contour implies that the light curves of these planetary events are generally asymmetric and thus the asymmetry can be used to distinguish the events from those produced by free-floating planets. The asymmetry can be noticed from the overall shape of the light curve and thus can hardly be missed unlike the very short-duration central perturbation caused by the caustic. In addition, the asymmetry occurs regardless of the event magnification and thus the bound nature of the planet can be identified for majority of these events. The close approximation of the lensing light curve to that of the Chang-Refsdal lensing implies that the analysis of the light curve yields only the information about the projected separation between the host star and the planet.Comment: 4 pages, 2 figure

Pairs of Frequency-based Nonhomogeneous Dual Wavelet Frames in the Distribution Space

In this paper, we study nonhomogeneous wavelet systems which have close relations to the fast wavelet transform and homogeneous wavelet systems. We introduce and characterize a pair of frequency-based nonhomogeneous dual wavelet frames in the distribution space; the proposed notion enables us to completely separate the perfect reconstruction property of a wavelet system from its stability property in function spaces. The results in this paper lead to a natural explanation for the oblique extension principle, which has been widely used to construct dual wavelet frames from refinable functions, without any a priori condition on the generating wavelet functions and refinable functions. A nonhomogeneous wavelet system, which is not necessarily derived from refinable functions via a multiresolution analysis, not only has a natural multiresolution-like structure that is closely linked to the fast wavelet transform, but also plays a basic role in understanding many aspects of wavelet theory. To illustrate the flexibility and generality of the approach in this paper, we further extend our results to nonstationary wavelets with real dilation factors and to nonstationary wavelet filter banks having the perfect reconstruction property

Magnetic structure of our Galaxy: A review of observations

The magnetic structure in the Galactic disk, the Galactic center and the Galactic halo can be delineated more clearly than ever before. In the Galactic disk, the magnetic structure has been revealed by starlight polarization within 2 or 3 kpc of the Solar vicinity, by the distribution of the Zeeman splitting of OH masers in two or three nearby spiral arms, and by pulsar dispersion measures and rotation measures in nearly half of the disk. The polarized thermal dust emission of clouds at infrared, mm and submm wavelengths and the diffuse synchrotron emission are also related to the large-scale magnetic field in the disk. The rotation measures of extragalactic radio sources at low Galactic latitudes can be modeled by electron distributions and large-scale magnetic fields. The statistical properties of the magnetized interstellar medium at various scales have been studied using rotation measure data and polarization data. In the Galactic center, the non-thermal filaments indicate poloidal fields. There is no consensus on the field strength, maybe mG, maybe tens of uG. The polarized dust emission and much enhanced rotation measures of background radio sources are probably related to toroidal fields. In the Galactic halo, the antisymmetric RM sky reveals large-scale toroidal fields with reversed directions above and below the Galactic plane. Magnetic fields from all parts of our Galaxy are connected to form a global field structure. More observations are needed to explore the untouched regions and delineate how fields in different parts are connected.Comment: 10+1 pages. Invited Review for IAU Symp.259: Cosmic Magnetic Fields: From Planets, to Stars and Galaxies (Tenerife, Spain. Nov.3-7, 2009). K.G. Strassmeier, A.G. Kosovichev & J.E. Beckman (eds.

High Dimensional Semiparametric Scale-Invariant Principal Component Analysis

We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the distributions are multivariate Gaussian. COCA improves upon PCA and sparse PCA in three aspects: (i) It is robust to modeling assumptions; (ii) It is robust to outliers and data contamination; (iii) It is scale-invariant and yields more interpretable results. We prove that the COCA estimators obtain fast estimation rates and are feature selection consistent when the dimension is nearly exponentially large relative to the sample size. Careful experiments confirm that COCA outperforms sparse PCA on both synthetic and real-world datasets.Comment: Accepted in IEEE Transactions on Pattern Analysis and Machine Intelligence (TPMAI

ECA: High Dimensional Elliptical Component Analysis in non-Gaussian Distributions

We present a robust alternative to principal component analysis (PCA) --- called elliptical component analysis (ECA) --- for analyzing high dimensional, elliptically distributed data. ECA estimates the eigenspace of the covariance matrix of the elliptical data. To cope with heavy-tailed elliptical distributions, a multivariate rank statistic is exploited. At the model-level, we consider two settings: either that the leading eigenvectors of the covariance matrix are non-sparse or that they are sparse. Methodologically, we propose ECA procedures for both non-sparse and sparse settings. Theoretically, we provide both non-asymptotic and asymptotic analyses quantifying the theoretical performances of ECA. In the non-sparse setting, we show that ECA's performance is highly related to the effective rank of the covariance matrix. In the sparse setting, the results are twofold: (i) We show that the sparse ECA estimator based on a combinatoric program attains the optimal rate of convergence; (ii) Based on some recent developments in estimating sparse leading eigenvectors, we show that a computationally efficient sparse ECA estimator attains the optimal rate of convergence under a suboptimal scaling.Comment: to appear in JASA (T&M

Magnetic fields of our Galaxy on large and small scales

Magnetic fields have been observed on all scales in our Galaxy, from AU to kpc. With pulsar dispersion measures and rotation measures, we can directly measure the magnetic fields in a very large region of the Galactic disk. The results show that the large-scale magnetic fields are aligned with the spiral arms but reverse their directions many times from the inner-most arm (Norma) to the outer arm (Perseus). The Zeeman splitting measurements of masers in HII regions or star-formation regions not only show the structured fields inside clouds, but also have a clear pattern in the global Galactic distribution of all measured clouds which indicates the possible connection of the large-scale and small-scale magnetic fields.Comment: 9 pages. Invited Talk at IAU Symp.242, 'Astrophysical Masers and their Environments', Proceedings edited by J. M. Chapman & W. A. Baa

Seasonal Variability of the Labrador Current and Shelf Circulation off Newfoundland

Three-dimensional finite element models were established for the Newfoundland and Labrador Shelf to investigate climatological monthly mean wind- and density-driven circulation. The model was forced using wind stresses from the National Center for Environmental Prediction-National Center for Atmospheric Research reanalysis data prescribed at the sea surface, large-scale remote forcing determined from a North Atlantic model, monthly mean temperature and salinity climatology, and M2 tide on the open boundary. The model results were examined against various in situ observations (moored current meter, tide gauge, and vessel-mounted acoustic Doppler current profiler data) and satellite drift measurements and discussed together with literature information. The seasonal mean circulation solutions were investigated in terms of relative importance of wind to density forcing for the Labrador Current. The model results indicate significant seasonal and spatial variations, consistent generally with previous study results and in approximate agreement with observations for the major currents. The region is dominated by the equatorward flowing Labrador Current along the shelf edge and along the Labrador and Newfoundland coasts. The Labrador Current is strong in the fall/winter and weak in the spring/summer. The mean transport of the shelf edge Labrador Current is 7.5 Sv at the Seat Island transect and 5.5 Sv through the Flemish Pass. The seasonal ranges are 4.5 and 5.2 Sv at the two sections, respectively. Density- and wind-driven components are both important in the inshore Labrador Current. The density-driven component dominates the mean component of the shelf edge Labrador Current while the large-scale wind-forcing contributes significantly to its seasonal variability

A Direct Estimation of High Dimensional Stationary Vector Autoregressions

The vector autoregressive (VAR) model is a powerful tool in modeling complex time series and has been exploited in many fields. However, fitting high dimensional VAR model poses some unique challenges: On one hand, the dimensionality, caused by modeling a large number of time series and higher order autoregressive processes, is usually much higher than the time series length; On the other hand, the temporal dependence structure in the VAR model gives rise to extra theoretical challenges. In high dimensions, one popular approach is to assume the transition matrix is sparse and fit the VAR model using the "least squares" method with a lasso-type penalty. In this manuscript, we propose an alternative way in estimating the VAR model. The main idea is, via exploiting the temporal dependence structure, to formulate the estimating problem into a linear program. There is instant advantage for the proposed approach over the lasso-type estimators: The estimation equation can be decomposed into multiple sub-equations and accordingly can be efficiently solved in a parallel fashion. In addition, our method brings new theoretical insights into the VAR model analysis. So far the theoretical results developed in high dimensions (e.g., Song and Bickel (2011) and Kock and Callot (2012)) mainly pose assumptions on the design matrix of the formulated regression problems. Such conditions are indirect about the transition matrices and not transparent. In contrast, our results show that the operator norm of the transition matrices plays an important role in estimation accuracy. We provide explicit rates of convergence for both estimation and prediction. In addition, we provide thorough experiments on both synthetic and real-world equity data to show that there are empirical advantages of our method over the lasso-type estimators in both parameter estimation and forecasting.Comment: 36 pages, 3 figur