Random Bits Regression: a Strong General Predictor for Big Data

To improve accuracy and speed of regressions and classifications, we present a data-based prediction method, Random Bits Regression (RBR). This method first generates a large number of random binary intermediate/derived features based on the original input matrix, and then performs regularized linear/logistic regression on those intermediate/derived features to predict the outcome. Benchmark analyses on a simulated dataset, UCI machine learning repository datasets and a GWAS dataset showed that RBR outperforms other popular methods in accuracy and robustness. RBR (available on https://sourceforge.net/projects/rbr/) is very fast and requires reasonable memories, therefore, provides a strong, robust and fast predictor in the big data era.Comment: 20 pages,1 figure, 2 tables, research articl

Local curvature estimates for the Laplacian flow

In this paper we give local curvature estimates for the Laplacian flow on closed G_2-structures under the condition that the Ricci curvature is bounded along the flow. The main ingredient consists of the idea of Kotschwar-Munteanu-Wang who gave local curvature estimates for the Ricci flow on complete manifolds and then provided a new elementary proof of Sesum's result, and the particular structure of the Laplacian flow on closed G_2-structures. As an immediate consequence, this estimates give a new proof of Lotay-Wei's result which is an analogue of Sesum's theorem. The second result is about an interesting evolution equation for the scalar curvature of the Laplacian flow of closed G_2-structures. Roughly speaking, we can prove that the time derivative of the scalar curvature R_t is equal to the Laplacian of R_t, plus an extra term which can be written as the difference of two nonnegative quantities.Comment: Correct the statement of Theorem 1.3, where we cannot extend it to complete and noncompact setting. Thus, in this paper we give alternative proof of Lotay-Wei's result. Thanks Yao and Kotschwa

On Deformations of Generalized Complex Structures: the Generalized Calabi-Yau Case

We prove an analog of the Tian-Todorov theorem for twisted generalized Calabi-Yau manifolds; namely, we show that the moduli space of generalized complex structures on a compact twisted generalized Calabi-Yau manifold is unobstructed and smooth. We also construct the extended moduli space and study its Frobenius structure. The physical implications are also discussed.Comment: 28 pages; typos corrected; Lemma 2 slightly generalized and one appendix adde

Generalized Ricci flow I: Higher derivatives estimates for compact manifolds

We consider a generalized Ricci flow with a given (not necessarily closed) three-form and establish the higher derivatives estimates for compact manifolds. As an application, we prove the compactness theorem for this generalized Ricci flow. The similar results still hold for a more generalized Ricci flow.Comment: 28 pages; Analysis & PDE, 5(2012), no. 4, 747-77

On an extention of the H^k mean curvature flow of closed convex hypersurfaces

In this paper we prove that the H^k (k is odd and larger than 2) mean curvature flow of a closed convex hypersurface can be extended over the maximal time provided that the total L^p integral of the mean curvature is finite for some pComment: 8 pages. Geometriae Didicata, 201

Exact results for itinerant ferromagnetism in a t2gt_{2g} orbital system on cubic and square lattices

We study itinerant ferromagnetism in a $t_{2g}$ multi-orbital Hubbard system in the cubic lattice, which consists of three planar oriented orbital bands of $d_{xy}$, $d_{yz}$, and $d_{zx}$. Electrons in each orbital band can only move within a two-dimensional plane in the three-dimensional lattice parallel to the corresponding orbital orientation. Electrons of different orbitals interact through the on-site multi-orbital interactions including Hund's coupling. The strong coupling limit is considered in which there are no doubly occupied orbitals but multiple on-site occupations are allowed. We show that, in the case in which there is one and only one hole for each orbital band in each layer parallel to the orbital orientation, the ground state is a fully spin-polarized itinerant ferromagnetic state, which is unique apart from the trivial spin degeneracy. When the lattice is reduced into a single two-dimensional layer, the $d_{zx}$ and $d_{yz}$ bands become quasi-one-dimensional while the $d_{xy}$ band remains two-dimensional. The ground state ferromagnetism also appears in the strong-coupling limit as a generalization of the double exchange mechanism. Possible applications to the systems of SrRuO$_3$ and LaAlO$_3$/SrTiO$_3$ interface are discussed

Some results of Marino-Vafa formula

In this paper we derive some new Hodge integral identities by taking limits of the Marino-Vafa formula. These identities include the formula of lambda_{1}lambda_{g}-integral on M_{g,1}, the vanishing result of lambda_{g}ch_{2l}(E)-integral on M_{g,1} for l taking value between 1 and g-3. Finally, we give another simple proof of lambda_{g} conjecture and some examples of low genus integral.Comment: 13 pages, LaTe

Harnack inequality for the negative power Gaussian curvature flow

In this paper, we study the power of Gaussian curvature flow of a compact convex hypersurface and establish its Harnack inequality when the power is negative. In the Harnack inequality, we require that the absolute value of the power is strictly positive and strictly less than the inverse of the dimension of the hypersurface.Comment: 12 pages; Proc. Amer. Math. Soc., 139(2011), no. 10, 3707-371

Mabuchi and Aubin-Yau functionals over complex surfaces

In this note we construct Mabuchi $\mathcal{L}^{{\rm M}}_{\omega}$ functional and Aubin-Yau functionals $\mathcal{I}^{{\rm AY}}_{\omega}, \mathcal{J}^{{\rm AY}}_{\omega}$ on any compact complex surfaces, and establish a number of properties. Our construction coincides with the original one in the K\"ahler case.Comment: 16 pages; rewrite Theorem 1.

Isolation of Flow and Nonflow by Two- and Multi-Particle Cumulant Measurements of vnv_n in sNN=200\sqrt{s_{NN}} = 200 GeV Au+Au Collisions by STAR

We apply a data-driven method to STAR Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV to isolate $\Delta\eta$-dependent and $\Delta\eta$-independent correlations by using two- and four-particle Q-cumulant $v_{n}$ measurements. The $\Delta\eta$-independent part, dominated by flow, is found to be $\eta$-independent within the STAR TPC of $\pm1$ unit of pseudo-rapidity. The $\Delta\eta$-dependent part may be associated to nonflow, and is responsible for the $\Delta\eta$ drop in the measured two-particle $v_{2}$ cumulant. We combine our result to four- and six-particle cumulants to gain further insights on the nature of flow fluctuations.Comment: 4 pages, 4 figures, submitted to Quark Matter 2012 proceeding