arXiv subjects

Jie Wang

Publications and source records attributed to Jie Wang.

At least 667 records · Page 37Linked to original sources

arXiv2013

A Safe Screening Rule for Sparse Logistic Regression

The l1-regularized logistic regression (or sparse logistic regression) is a widely used method for simultaneous classification and feature selection. Although many recent efforts have been devoted to its efficient implementation, its application to high dimensional data still poses significant challenges. In this paper, we present a fast and effective sparse logistic regression screening rule (Slores) to identify the 0 components in the solution vector, which may lead to a substantial reduction in the number of features to be entered to the optimization. An appealing feature of Slores is that the data set needs to be scanned only once to run the screening and its computational cost is negligible compared to that of solving the sparse logistic regression problem. Moreover, Slores is independent of solvers for sparse logistic regression, thus Slores can be integrated with any existing solver to improve the efficiency. We have evaluated Slores using high-dimensional data sets from different applications. Extensive experimental results demonstrate that Slores outperforms the existing state-of-the-art screening rules and the efficiency of solving sparse logistic regression is improved by one magnitude in general.

cs.LG↗

arXiv2013

Efficient Mixed-Norm Regularization: Algorithms and Safe Screening Methods

Sparse learning has recently received increasing attention in many areas including machine learning, statistics, and applied mathematics. The mixed-norm regularization based on the l1q norm with q>1 is attractive in many applications of regression and classification in that it facilitates group sparsity in the model. The resulting optimization problem is, however, challenging to solve due to the inherent structure of the mixed-norm regularization. Existing work deals with special cases with q=1, 2, infinity, and they cannot be easily extended to the general case. In this paper, we propose an efficient algorithm based on the accelerated gradient method for solving the general l1q-regularized problem. One key building block of the proposed algorithm is the l1q-regularized Euclidean projection (EP_1q). Our theoretical analysis reveals the key properties of EP_1q and illustrates why EP_1q for the general q is significantly more challenging to solve than the special cases. Based on our theoretical analysis, we develop an efficient algorithm for EP_1q by solving two zero finding problems. To further improve the efficiency of solving large dimensional mixed-norm regularized problems, we propose a screening method which is able to quickly identify the inactive groups, i.e., groups that have 0 components in the solution. This may lead to substantial reduction in the number of groups to be entered to the optimization. An appealing feature of our screening method is that the data set needs to be scanned only once to run the screening. Compared to that of solving the mixed-norm regularized problems, the computational cost of our screening test is negligible. The key of the proposed screening method is an accurate sensitivity analysis of the dual optimal solution when the regularization parameter varies. Experimental results demonstrate the efficiency of the proposed algorithm.

cs.LG↗

arXiv2013

Hard X-ray optics simulation using the coherent mode decomposition of Gaussian Schell model

The propagation of hard X ray beam from partially coherent synchrotron source is simulated by using the novel method based on the coherent mode decomposition of Gaussian Schell model and wave front propagation. We investigate how the coherency properties and intensity distributions of the beam are changed by propagation through optical elements. Here, we simulate and analyze the propagation of the partially coherent radiation transmitted through an ideal slit. We present the first simulations for focusing partially coherent synchrotron hard X ray beams using this novel method. And when compared with the traditional method which assumes the source is a totally coherent point source or completely incoherent, this method is proved to be more reasonable and can also demonstrate the coherence properties of the focusing beam. We also simulate the double slit experiment and the simulated results validate the academic analysis.

physics.acc-ph↗

arXiv2013

Detection of the large scale alignment of massive galaxies at z~0.6

We report on the detection of the alignment between galaxies and large-scale structure at z~0.6 based on the CMASS galaxy sample from the Baryon Oscillation Spectroscopy Survey data release 9. We use two statistics to quantify the alignment signal: 1) the alignment two-point correlation function which probes the dependence of galaxy clustering at a given separation in redshift space on the projected angle (theta_p) between the orientation of galaxies and the line connecting to other galaxies, and 2) the cos(2theta)-statistic which estimates the average of cos(2theta_p) for all correlated pairs at given separation. We find significant alignment signal out to about 70 Mpc/h in both statistics. Applications of the same statistics to dark matter halos of mass above 10^12 M_sun/h in a large cosmological simulation show similar scale-dependent alignment signals to the observation, but with higher amplitudes at all scales probed. We show that this discrepancy may be partially explained by a misalignment angle between central galaxies and their host halos, though detailed modeling is needed in order to better understand the link between the orientations of galaxies and host halos. In addition, we find systematic trends of the alignment statistics with the stellar mass of the CMASS galaxies, in the sense that more massive galaxies are more strongly aligned with the large-scale structure.

astro-ph.CO↗

arXiv2013

The birational geometry of moduli space of sheaves on the projective plane

We describe a close relation between wall crossings in the birational geometry of moduli space of Gieseker stable sheaves $M_H(v)$ on $\bb{P}^2$ and mini-wall crossings in the stability manifold $Stab(D^b(\bb{P}^2))$.

math.AG↗

arXiv2012

The Spatial Distribution of Galactic Satellites in the LCDM Cosmology

We investigate the spatial distribution of galactic satellites in high resolution simulations of structure formation in the LCDM model: the Aquarius dark matter simulations of individual halos and the Millennium II simulation of a large cosmological volume. To relate the simulations to observations of the Milky Way we use two alternative models to populate dark halos with "visible" galaxies: a semi-analytic model of galaxy formation and an abundance matching technique. We find that the radial density profile of massive satellites roughly follows that of the dark matter halo (unlike the distribution of dark matter subhalos). Furthermore, our two galaxy formation models give results consistent with the observed profile of the 11 classical satellites of the Milky Way. Our simulations predict that larger, fainter samples of satellites should still retain this profile at least up to samples of 100 satellites. The angular distribution of the classical satellites of the Milky Way is known to be highly anisotropic. Depending on the exact measure of flattening, 5--10 per cent of satellite systems in our simulations are as flat as the Milky Way's and this fraction does not change when we correct for possible obscuration of satellites by the Galactic disk. A moderate flattening of satellite systems is a general property of LCDM, best understood as the consequence of preferential accretion along filaments of the cosmic web. Accretion of a single rich group of satellites can enhance the flattening due to such anisotropic accretion. We verify that a typical Milky Way-mass CDM halo does not acquire its 11 most massive satellites from a small number of rich groups. Single--group accretion becomes more likely for less massive satellites. Our model predictions should be testable with forthcoming studies of satellite systems in other galaxies and surveys of fainter satellites in the Milky Way.

astro-ph.GA↗

arXiv2012

Anisotropy in the matter distribution beyond the baryonic acoustic oscillation scale

Tracing the cosmic evolution of the Baryonic Acoustic Oscillation (BAO) scale with galaxy two point correlation functions is currently the most promising approach to detect dark energy at early times. A number of ongoing and future experiments will measure the BAO peak with unprecedented accuracy. We show based on a set of N-Body simulations that the matter distribution is anisotropic out to ~150 Mpc/h, far beyond the BAO scale of ~100M pc/h, and discuss implications for the measurement of the BAO. To that purpose we use alignment correlation functions, i.e., cross correlation functions between high density peaks and the overall matter distribution measured along the orientation of the peaks and perpendicular to it. The correlation function measured along (perpendicular to) the orientation of high density peaks is enhanced (reduced) by a factor of ~2 compared to the conventional correlation function and the location of the BAO peak shifts towards smaller (larger) scales if measured along (perpendicular to) the orientation of the high density peaks. Similar effects are expected to shape observed galaxy correlation functions at BAO scales.

astro-ph.CO↗

arXiv2012

The Missing Massive Satellites of the Milky Way

Recent studies suggest that only three of the twelve brightest satellites of the Milky Way (MW) inhabit dark matter halos with maximum circular velocity, V_max, exceeding 30km/s. This is in apparent contradiction with the LCDM simulations of the Aquarius Project, which suggest that MW-sized halos should have at least 8 subhalos with V_max>30km/s. The absence of luminous satellites in such massive subhalos is thus puzzling and may present a challenge to the LCDM paradigm. We note, however, that the number of massive subhalos depends sensitively on the (poorly-known) virial mass of the Milky Way, and that their scarcity makes estimates of their abundance from a small simulation set like Aquarius uncertain. We use the Millennium Simulation series and the invariance of the scaled subhalo velocity function (i.e., the number of subhalos as a function of ν, the ratio of subhalo V_max to host halo virial velocity, V_200) to secure improved estimates of the abundance of rare massive subsystems. In the range 0.1<ν<0.5, N_sub(>ν) is approximately Poisson-distributed about an average given by =10.2x(ν/0.15)^(-3.11). This is slightly lower than in Aquarius halos, but consistent with recent results from the Phoenix Project. The probability that a LCDM halo has 3 or fewer subhalos with V_max above some threshold value, V_th, is then straightforward to compute. It decreases steeply both with decreasing V_th and with increasing halo mass. For V_th=30km/s, ~40% of M_halo=10^12 M_sun halos pass the test; fewer than 5% do so for M_halo>= 2x10^12 M_sun; and the probability effectively vanishes for M_halo>= 3x 10^12 M_sun. Rather than a failure of LCDM, the absence of massive subhalos might simply indicate that the Milky Way is less massive than is commonly thought.

astro-ph.GA↗

arXiv2012

Determination of the forms of calcium present in coal chars by Ca K-edge XANES with Synchrotron Radiation

This work is concerned with the Ca transformations during the pyrolysis of Ca(OH)2 or CaCO3-added coals. Ca K-edge X-ray absorption near edge structure (XANES) spectroscopy was applied to determine the forms of Ca in chars prepared from the pyrolysis of Ca-added coal. Results showed that Ca(OH)2 and CaSO4 existed in both the Ca(OH)2-added chars and the CaCO3-added chars, while CaS and CaO only existed in the chars prepared from the Ca(OH)2-added coal. Moreover, it was found that carboxyl Ca was formed during pyrolysis for either the Ca(OH)2-added coal or the CaCO3-added coals.

physics.chem-ph↗

arXiv2012

The haloes of bright satellite galaxies in a warm dark matter universe

High resolution N-body simulations of galactic cold dark matter haloes indicate that we should expect to find a few satellite galaxies around the Milky Way whose haloes have a maximum circular velocity in excess of 40 kms. Yet, with the exception of the Magellanic Clouds and the Sagittarius dwarf, which likely reside in subhaloes with significantly larger velocities than this, the bright satellites of the Milky Way all appear to reside in subhaloes with maximum circular velocities below 40 kms. As recently highlighted by Boylan-Kolchin et al., this discrepancy implies that the majority of the most massive subhaloes within a cold dark matter galactic halo are much too concentrated to be consistent with the kinematic data for the bright Milky Way satellites. Here we show that no such discrepancy exists if haloes are made of warm, rather than cold dark matter because these haloes are less concentrated on account of their typically later formation epochs. Warm dark matter is one of several possible explanations for the observed kinematics of the satellites.

astro-ph.CO↗

arXiv2011

Tuning Optical Orbital Angular Momentum in Optical Superlattice under Electro-optic Effect

We introduce a new method to generate and tune the optical orbital angular momentum of a focused Gaussian beam passing through the optical superlattice under the electro-optic effect. The orbital angular momentum (OAM) arises from the curl of polarization in our calculation. We see that adjusting the external electric field, the beam waist radius and the crystal length provides dramatic variation of OAM of light across the transverse section. It is believed that this invention will find its application in optical manipulation area.

physics.optics↗

arXiv2011

The population of Milky Way satellites in the LambdaCDM cosmology

We present a model for the satellites of the Milky Way in which galaxy formation is followed using semi-analytic techniques applied to the six high-resolution N-body simulations of galactic halos of the Aquarius project. The model, calculated using the Galform code, incorporates improved treatments of the relevant physics in the LambdaCDM cosmogony, particularly a self-consistent calculation of reionization by UV photons emitted by the forming galaxy population, including the progenitors of the central galaxy. Along the merger tree of each halo, the model calculates gas cooling (by Compton scattering off cosmic microwave background photons, molecular hydrogen and atomic processes), gas heating (from hydrogen photoionization and supernova energy), star formation and evolution. The evolution of the intergalactic medium is followed simultaneously with that of the galaxies. Star formation in the more massive progenitor subhalos is suppressed primarily by supernova feedback, while for smaller subhalos it is suppressed primarily by photoionization due to external and internal sources. The model is constrained to match a wide range of properties of the present day galaxy population as a whole, but at high redshift it requires an escape fraction of UV photons near unity in order completely to reionize the universe by redshift z ~ 8. In the most successful model the local sources photoionize the pre-galactic region completely by z ~ 10. In addition to the luminosity function of Milky Way satellites, the model matches their observed luminosity-metallicity relation, their radial distribution and the inferred values of the mass within 300 pc, which in the models increase slowly but significantly with luminosity. There is a large variation in satellite properties from halo to halo, with the luminosity function, for example, varying by a factor of ~ 2 among the six simulations.

astro-ph.GA↗

arXiv2010

Assembly History and Structure of Galactic Cold Dark Matter Halos

We use the Aquarius simulation series to study the imprint of assembly history on the structure of Galaxy-mass cold dark matter halos. Our results confirm earlier work regarding the influence of mergers on the mass density profile and the inside-out growth of halos. The inner regions that contain the visible galaxies are stable since early times and are significantly affected only by major mergers. Particles accreted diffusely or in minor mergers are found predominantly in the outskirts of halos. Our analysis reveals trends that run counter to current perceptions of hierarchical halo assembly. For example, major mergers (i.e. those with progenitor mass ratios greater than 1:10) contribute little to the total mass growth of a halo, on average less than 20 per cent for our six Aquarius halos. The bulk is contributed roughly equally by minor mergers and by "diffuse" material which is not resolved into individual objects. This is consistent with modeling based on excursion-set theory which suggests that about half of this diffuse material should not be part of a halo of any scale. Interestingly, the simulations themselves suggest that a significantly fraction is not truly diffuse, since it was ejected from earlier halos by mergers prior to their joining the main system. The Aquarius simulations resolve halos to much lower mass scales than are expected to retain gas or form stars. These results thus confirm that most of the baryons from which visible galaxies form are accreted diffusely, rather than through mergers, and they suggest that only relatively rare major mergers will affect galaxy structure at later times.

astro-ph.CO↗

arXiv2010

Deformations of pairs (X,L) when X is singular

We give an elementary construction of the tangent-obstruction theory of the deformations of the pair $(X,L)$ with $X$ a reduced local complete intersection scheme and $L$ a line bundle on $X$. This generalizes the classical deformation theory of pairs in case $X$ is smooth. A criteria for sections of $L$ to extend is also given.

math.AG↗

arXiv2010

On the Maximal Rank Conjecture for Line Bundles of Extremal Degree

We propose a new method, using deformation theory, to study the maximal rank conjecture. For line bundles of extremal degree, which can be viewed as the first case to test the conjecture, we prove that maximal rank conjecture holds by our new method.

math.AG↗

arXiv2010

Secondary Infall and the Pseudo-Phase-Space Density Profiles of Cold Dark Matter Halos

We use N-body simulations to investigate the radial dependence of the density and velocity dispersion in cold dark matter (CDM) halos. In particular, we explore how closely Q rho/sigma^3, a surrogate measure of the phase-space density, follows a power-law in radius. Our study extends earlier work by considering, in addition to spherically-averaged profiles, local Q-estimates for individual particles, Q_i; profiles based on the ellipsoidal radius dictated by the triaxial structure of the halo, Q_i(r'); and by carefully removing substructures in order to focus on the profile of the smooth halo, Q^s. The resulting Q_i^s(r') profiles follow closely a power law near the center, but show a clear upturn from this trend near the virial radius, r_{200}. The location and magnitude of the deviations are in excellent agreement with the predictions from Bertschinger's spherical secondary-infall similarity solution. In this model, Q \propto r^{-1.875} in the inner, virialized regions, but departures from a power-law occur near r_{200} because of the proximity of this radius to the location of the first shell crossing - the shock radius in the case of a collisional fluid. Particles there have not yet fully virialized, and so Q departs from the inner power-law profile. Our results imply that the power-law nature of $Q$ profiles only applies to the inner regions and cannot be used to predict accurately the structure of CDM halos beyond their characteristic scale radius.

astro-ph.CO↗

arXiv2009

The Diversity and Similarity of Simulated Cold Dark Matter Halos

We study the mass, velocity dispersion, and anisotropy profiles of $Λ$CDM halos using a suite of N-body simulations of unprecedented numerical resolution (the {\it Aquarius Project}). Our analysis confirms a number of results claimed by earlier work, and clarifies a few issues where conflicting claims may be found in the recent literature. The spherically-averaged density profile becomes progressively shallower inwards and, at the innermost resolved radius, the logarithmic slope is $γ\equiv -$d$\lnρ/$d$\ln r \simlt 1$. Asymptotic inner slopes as steep as the recently claimed $ρ\propto r^{-1.2}$ are clearly ruled out. The radial dependence of $γ$ is well approximated by a power-law, $γ\propto r^α$ (the Einasto profile). The shape parameter, $α$, varies slightly but significantly from halo to halo, implying that the mass profiles of $Λ$CDM halos are not strictly universal: different halos cannot, in general, be rescaled to look identical. Departures from similarity are also seen in velocity dispersion profiles and correlate with those in density profiles so as to preserve a power-law form for the spherically averaged pseudo-phase-space density, $ρ/σ^3\propto r^{-1.875}$. Our conclusions are reliable down to radii below 0.4% of the virial radius, providing well-defined predictions for halo structure when baryonic effects are neglected, and thus an instructive theoretical template against which the modifications induced by the baryonic components of real galaxies can be judged.

astro-ph↗

arXiv2009

Alignment between galaxies and large-scale structure

Based on the Sloan Digital Sky Survey DR6 (SDSS) and Millennium Simulation (MS) we investigate the alignment between galaxies and large-scale structure. For this purpose we develop two new statistical tools, namely the alignment correlation function and the cos(2theta)-statistic. The former is a two-dimensional extension of the traditional two-point correlation function and the latter is related to the ellipticity correlation function used for cosmic shear measurements. Both are based on the cross correlation between a sample of galaxies with orientations and a reference sample which represents the large-scale structure. Applied to the SDSS galaxy catalog the alignment correlation function reveals an overabundance of reference galaxies along the major axes of red, luminous (L > L*) galaxies out to projected separations of 60 Mpc/h. No alignment signal is detected for blue galaxies. The cos(2θ)-statistic yields very similar results. Starting from a MS semi-analytic galaxy catalog we assign an orientation to each red, luminous and central galaxy, based on the central region of the host halo. Alternatively, we use the orientation of the host halo itself. We find a mean projected misalignment between a halo and its central region of ~25 deg. Agreement with the SDSS results is good if the central orientations are used. Using the halo orientations overestimates the observed alignment by more than a factor of 2. The large volume of the MS allows to generate two-dimensional maps of the alignment correlation function which show the reference galaxy distribution to be flattened parallel to the orientations of red luminous galaxies with axis ratios of ~0.5 and ~0.75 for halo and central orientations,respectively. These ratios are almost independent of scale out to 60 Mpc/h.

astro-ph↗