A novel feature selection for RNA-seq analysis

RNA-seq data are challenging existing omics data analytics for its volume and complexity. Although quite a few computational models were proposed from different standing points to conduct differential expression (D.E.) analysis, almost all these methods do not provide a rigorous feature selection for high-dimensional RNA-seq count data. Instead, most or even all genes are invited into differential calls no matter they have real contributions to data variations or not. Thus, it would inevitably affect the robustness of D.E. analysis and lead to the increase of false positive ratios.In this study, we presented a novel feature selection method: nonnegative singular value approximation (NSVA) to enhance RNA-seq differential expression analysis by taking advantage of RNA-seq count data's non-negativity. As a variance-based feature selection method, it selects genes according to its contribution to the first singular value direction of input data in a data-driven approach. It demonstrates robustness to depth bias and gene length bias in feature selection in comparison with its five peer methods. Combining with state-of-the-art RNA-seq differential expression analysis, it contributes to enhancing differential expression analysis by lowering false discovery rates caused by the biases. Furthermore, we demonstrated the effectiveness of the proposed feature selection by proposing a data-driven differential expression analysis: NSVA-seq, besides conducting network marker discovery.     

Recovery of Immersions from Their Metric Tensors and Nonlinear Korn Inequalities: A Brief Survey

The authors discuss the existence and uniqueness up to isometries of Enof immersions φ : Ω  R~n→ E~n with prescribed metric tensor field(g ij) : Ω→ S~n, and discuss the continuity of the mapping(gij) →φ defined in this fashion with respect to various topologies. In particular, the case where the function spaces have little regularity is considered. How, in some cases, the continuity of the mapping(gij) →φ can be obtained by means of nonlinear Korn inequalities is shown.     

Time Discrete Approximation of Weak Solutions to Stochastic Equations of Geophysical Fluid Dynamics and Applications

As a first step towards the numerical analysis of the stochastic primitive equations of the atmosphere and the oceans,the time discretization of these equations by an implicit Euler scheme is studied.From the deterministic point of view,the 3D primitive equations are studied in their full form on a general domain and with physically realistic boundary conditions.From the probabilistic viewpoint,this paper deals with a wide class of nonlinear,state dependent,white noise forcings which may be interpreted in either the It6 or the Stratonovich sense.The proof of convergence of the Euler scheme,which is carried out within an abstract framework,covers the equations for the oceans,the atmosphere,the coupled oceanic-atmospheric system as well as other related geophysical equations.The authors obtain the existence of solutions which are weak in both the PDE and probabilistic sense,a result which is new by itself to the best of our knowledge.     

Some gradient estimates and Harnack inequalities for nonlinear parabolic equations on Riemannian manifolds

In this paper, by the method of J. F. Li and X. J. Xu (Differential Harnack inequalities on Riemannian manifolds I: Linear heat equation, Adv. in Math., 226 (2011), 4456–4491 ), we shall consider the nonlinear parabolic equation on Riemannian manifolds with , . First of all, we shall derive the corresponding Li–Xu type gradient estimates of the positive solutions for . As applications, we deduce Liouville type theorem and Harnack inequality for some special cases. Besides, when , our results are different from Li and Yau's results. We also extend the results of J. F. Li and X. J. Xu, and the results of Y. Yang.     

Generalized Method of Separation of Variables on the Nonlinear Elastic-Plastic Wave Motion

The method of separation of variables is developed in addition to the Karman method and the method of characteristics for the wave motion of uniaxial stress in rods. Rate-independent theory is considered and it is shown that the plastic wave speed is independent of the constant n in the stress-strain law. Stresses are determined in explicit forms for two cases.     

Nonlinear Dynamics and Stability of a Two D.O.F. Elastic/Elasto-Plastic Model System

The local and global nonlinear dynamics of a two-degree-of-freedom model system is studied. The undeflected model consists of an inverted T formed by three rigid bars, with the tips of the two horizontal bars supported on springs. The springs exhibit an elasto-plastic response, including the Bauschinger effect. The vertical rigid bar is subjected to a conservative (dead) or non-conservative (follower) force having static and periodic components. First, the method of multiple scales is used for the analysis of the local dynamics of the system with elastic springs. The attention is focused at modal interaction phenomena in weak excitation at primary resonance and in hard sub-harmonic excitation. Three different asymptotic expansions are utilised to get a structural response for typical ranges of excitation parameters. Numerical integration of the governing equations is then performed to validate results of asymptotic analysis in each case. A full global nonlinear dynamics analysis of the elasto-plastic system is performed to reveal the role of plastic deformations in the stability of this system. Static 'force-displacement' curves are plotted and the role of plastic deformations in the destabilisation of the system is discussed. Large-amplitude non-linear oscillations of the elasto-plastic system are studied, including the influence of material hardening and of static and sinusoidal components of the applied force. A practical method is proposed for the study of a non-conservative elasto-plastic system as a non-conservative elastic system with an 'equivalent' viscous damping. This revised version was published online in July 2006 with corrections to the Cover Date.     

Stability of Relative Equilibria. Part I: Comparison of Four Methods

In this first part of the paper, we review methods for the investigation of stability of relative equilibria of symmetric Hamiltonian systems and explain them by means of the model problem of a rotating pendulum. For this example the modern approaches, known as energy momentum methods are compared with stability assessment by linearization and by the classical method of Routh.