Nuclear Modification to Parton Distribution Functions and Parton Saturation

We introduce a generalized definition of parton distribution functions (PDFs) for a more consistent all-order treatment of power corrections. We present a new set of modified DGLAP evolution equations for nuclear PDFs, and show that the resummed $\alpha_s A^{1/3}/Q^2$-type of leading nuclear size enhanced power corrections significantly slow down the growth of gluon density at small-$x$. We discuss the relation between the calculated power corrections and the saturation phenomena.Comment: 4 pages, to appear in the proceedings of QM200

Top-N Recommendation on Graphs

Recommender systems play an increasingly important role in online applications to help users find what they need or prefer. Collaborative filtering algorithms that generate predictions by analyzing the user-item rating matrix perform poorly when the matrix is sparse. To alleviate this problem, this paper proposes a simple recommendation algorithm that fully exploits the similarity information among users and items and intrinsic structural information of the user-item matrix. The proposed method constructs a new representation which preserves affinity and structure information in the user-item rating matrix and then performs recommendation task. To capture proximity information about users and items, two graphs are constructed. Manifold learning idea is used to constrain the new representation to be smooth on these graphs, so as to enforce users and item proximities. Our model is formulated as a convex optimization problem, for which we need to solve the well-known Sylvester equation only. We carry out extensive empirical evaluations on six benchmark datasets to show the effectiveness of this approach.Comment: CIKM 201

Multipole Gravitational Lensing and High-order Perturbations on the Quadrupole Lens

An arbitrary surface mass density of gravitational lens can be decomposed into multipole components. We simulate the ray-tracing for the multipolar mass distribution of generalized SIS (Singular Isothermal Sphere) model, based on the deflection angles which are analytically calculated. The magnification patterns in the source plane are then derived from inverse shooting technique. As have been found, the caustics of odd mode lenses are composed of two overlapping layers for some lens models. When a point source traverses such kind of overlapping caustics, the image numbers change by \pm 4, rather than \pm 2. There are two kinds of images for the caustics. One is the critical curve and the other is the transition locus. It is found that the image number of the fold is exactly the average value of image numbers on two sides of the fold, while the image number of the cusp is equal to the smaller one. We also focus on the magnification patterns of the quadrupole (m = 2) lenses under the perturbations of m = 3, 4 and 5 mode components, and found that one, two, and three butterfly or swallowtail singularities can be produced respectively. With the increasing intensity of the high-order perturbations, the singularities grow up to bring sixfold image regions. If these perturbations are large enough to let two or three of the butterflies or swallowtails contact, eightfold or tenfold image regions can be produced as well. The possible astronomical applications are discussed.Comment: 24 pages, 6 figure

Origins of the Isospin Violation of Dark Matter Interactions

Light dark matter (DM) with a large DM-nucleon spin-independent cross section and furthermore proper isospin violation (ISV) $f_n/f_p\approx-0.7$ may provide a way to understand the confusing DM direct detection results. Combing with the stringent astrophysical and collider constraints, we systematically investigate the origin of ISV first via general operator analyses and further via specifying three kinds of (single) mediators: A light $Z'$ from chiral $U(1)_X$, an approximate spectator Higgs doublet (It can explain the $W+jj$ anomaly simultaneously) and color triplets. In addition, although $Z'$ from an exotic $U(1)_X$ mixing with $U(1)_Y$ generating $f_n=0$, we can combine it with the conventional Higgs to achieve proper ISV. As a concrete example, we propose the $U(1)_X$ model where the $U(1)_X$ charged light sneutrino is the inelastic DM, which dominantly annihilates to light dark states such as $Z'$ with sub-GeV mass. This model can address the recent GoGeNT annual modulation consistent with other DM direct detection results and free of exclusions.Comment: References added and English greatly improve