Fuzhou Gong

Integrated Sequence-Structure Motifs Suffice to Identify microRNA Precursors

Background Upwards of 1200 miRNA loci have hitherto been annotated in the human genome. The specific features defining a miRNA precursor and deciding its recognition and subsequent processing are not yet exhaustively described and miRNA loci can thus not be computationally identified with sufficient confidence. Results We rendered pre-miRNA and non-pre-miRNA hairpins as strings of integrated sequence-structure information, and used the software Teiresias to identify sequence-structure motifs (ss-motifs) of variable length in these data sets. Using only ss-motifs as features in a Support Vector Machine (SVM) algorithm for pre-miRNA identification achieved 99.2% specificity and 97.6% sensitivity on a human test data set, which is comparable to previously published algorithms employing combinations of sequence-structure and additional features. Further analysis of the ss-motif information contents revealed strongly significant deviations from those of the respective training sets, revealing important potential clues as to how the sequence and structural information of RNA hairpins are utilized by the miRNA processing apparatus. Conclusion Integrated sequence-structure motifs of variable length apparently capture nearly all information required to distinguish miRNA precursors from other stem-loop structures.

ON GROMOV'S THEOREM AND L 2 -HODGE DECOMPOSITION

Using a functional inequality, the essential spectrum and eigenvalues are estimated for Laplace-type operators on Riemannian vector bundles. Consequently, explicit upper bounds are obtained for the dimension of the corresponding L 2-harmonic sections. In particular, some known results concerning Gromovs theorem and the L 2-Hodge decomposition are considerably improved.

Martingale representation and log-Sobolev inequality on loop space

Abstract We obtain a martingale representation theorem for differentiable functions on loop space over a compact Riemannian manifold, which in turn yields a log-Sobolev inequality with a neat and explicit potential depending only on the curvature of the manifold and the Hessian of the heat kernel. Moreover, the potentiel term is L p -integrable for all p ≥ 1.

Ergodicity and asymptotic stability of Feller semigroups on Polish metric spaces

We provide some sharp criteria for studying the ergodicity and asymptotic stability of general Feller semigroups on Polish metric spaces. As an application, the 2D Navier-Stokes equations with degenerate stochastic forcing will be simply revisited.

Stochastic analysis of particle-fluid two-phase flows

This paper is devoted to exploring approaches to understanding the stochastic characteristics of particle-fluid two-phase flow. By quantifying the forces dominating the particle motion and modelling the less important and/or unclear forces as random forces, a stochastic differential equation is proposed to describe the complex behavior of a particle motion. An exploratory simulation has shown satisfactory agreement with phase doppler particle analyzer (PDPA) measurements, which indicates that stochastic analysis is a potential approach for revealing the details of particle-fluid flow phenomena.

RICCI CURVATURE OF MARKOV CHAINS ON POLISH SPACES REVISITED

Recently, Y. Ollivier defined the Ricci curvature of Markov chains on Polish spaces. In this paper, we will discuss further about the spectral gap, entropy decay, and logarithmic Sobolev inequality for the -range gradient operator. As an application, given resistance forms (i.e. symmetric Dirichlet forms with finite effective resistance) on frac- tal sets, we can construct Markov chains with positive Ricci curvature, which yields the Gaussian-then-exponential concentration of invariant probability measures for Lipschitz test functions.

EXPONENTIAL INTEGRABILITY FOR IMAGES OF ORNSTEIN UHLENBECK OPERATORS ACTING ON CYLINDER FUNCTIONS ON LOOP SPACES

Let E be the loop space over a compact connected Riemannian manifold with a torsion skew symmetric (TSS) connection. Let L be the Ornstein–Uhlenbeck (O-U) operator on the loop space E, and f be a cylinder function on E. We first extend the expression of Lf, proved by Enchev and Stroock for the Levi–Civita connection, to a general TSS connection, and then prove that if , e |Lf|2 is exponential integrable for some constant e := e (f)>0.

THE CONDENSATION EXTENSION AND THE MULTIPLE POSITIVE FIXED POINTS OF THE CONDENSING MAPPING

Abstract In the paper the authors present some formulae to the condensation extension and k-set contractive extension of a condensing mapping and a k-set contractive mapping respectively, and obtain the sufficient conditions for a condensing mapping to have two or three fixed points. At last they apply their results to solve the generalized H-equation and two-points boundary value problema.