Stable RNA hairpins in 88 coding regions of human mRNA

RNA hairpins containing UNCG, GNRA, CUUG (N = A, U, C or G, R = G or A) loops are unusually thermodynamic stable and conserved structures. The structural features of these hairpin loops are very special, and they play very important roles in vivo. They are prevalent in rRNA, catalytic RNA and non-coding mRNA. However, the 5' C(UUCG)G 3' hairpin is not found in the folding structure of 88 human mRNA coding regions. It is also different from rRNA in that there is no preference for certain sequences among tetraloops in these 88 mRNA folding structures.

The identification and quantification of highly stable 'common hairpin' in the dynamic process of co-transcriptional mRNA folding

In our studies, 88 human mRNA samples were collected from the Integrated Sequence-Structure database and then the dynamic process in co-transcriptional mRNA folding was simulated using the RNAstructure version 4.1 program. Through statistical analyses of the frequencies of occurrence of hairpins, a group of special folding structures-the 'common hairpins'-were identified. These 'common hairpins' have lower energies and occur in all the subsequent folding units that formed in the dynamic folding process. By applying the formulas (1)-(4) of the 'common hairpins' statistical model, 163 'common hairpins' were found, to make up about 7% of the total of 2286 hairpins. Classified studies further show that the 'common hairpins' that were studied may oscillate in the dynamic folding process. However, the hairpin loops of the 'common hairpins' and stems proximal to those 'common hairpins' loops maintain topologically stable structures, while other loops and stems distal to the 'common hairpins' loops are shown to be alterable structures. Strikingly, further studies indicate that the stable structures of these 'common hairpins' may have unbeknown effects on controlling the formation of protein structures in the translation process (unpublished results). (c) 2005 Elsevier B.V. All rights reserved.

Energy stable and momentum conserving hybrid finite element method for the incompressible Navier-Stokes equations

A hybrid method for the incompressible Navier-Stokes equations is presented. The method inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods when momentum advection becomes significant, equal-order interpolations can be used for the velocity and pressure fields, and mass can be conserved locally. Using continuous Lagrange multiplier spaces to enforce flux continuity across cell facets, the number of global degrees of freedom is the same as for a continuous Galerkin method on the same mesh. Different from our earlier investigations on the approach for the Navier-Stokes equations, the pressure field in this work is discontinuous across cell boundaries. It is shown that this leads to very good local mass conservation and, for an appropriate choice of finite element spaces, momentum conservation. Also, a new form of the momentum transport terms for the method is constructed such that global energy stability is guaranteed, even in the absence of a pointwise solenoidal velocity field. Mass conservation, momentum conservation, and global energy stability are proved for the time-continuous case and for a fully discrete scheme. The presented analysis results are supported by a range of numerical simulations. © 2012 Society for Industrial and Applied Mathematics.

On the stability of a rod adhering to a rigid surface: Shear-induced stable adhesion and the instability of peeling

Using variational methods, we establish conditions for the nonlinear stability of adhesive states between an elastica and a rigid halfspace. The treatment produces coupled criteria for adhesion and buckling instabilities by exploiting classical techniques from Legendre and Jacobi. Three examples that arise in a broad range of engineered systems, from microelectronics to biologically inspired fiber array adhesion, are used to illuminate the stability criteria. The first example illustrates buckling instabilities in adhered rods, while the second shows the instability of a peeling process and the third illustrates the stability of a shear-induced adhesion. The latter examples can also be used to explain how microfiber array adhesives can be activated by shearing and deactivated by peeling. The nonlinear stability criteria developed in this paper are also compared to other treatments. © 2012 Elsevier Ltd. All rights reserved.

Generalization in Adaptation to Stable and Unstable Dynamics

Humans skillfully manipulate objects and tools despite the inherent instability. In order to succeed at these tasks, the sensorimotor control system must build an internal representation of both the force and mechanical impedance. As it is not practical to either learn or store motor commands for every possible future action, the sensorimotor control system generalizes a control strategy for a range of movements based on learning performed over a set of movements. Here, we introduce a computational model for this learning and generalization, which specifies how to learn feedforward muscle activity in a function of the state space. Specifically, by incorporating co-activation as a function of error into the feedback command, we are able to derive an algorithm from a gradient descent minimization of motion error and effort, subject to maintaining a stability margin. This algorithm can be used to learn to coordinate any of a variety of motor primitives such as force fields, muscle synergies, physical models or artificial neural networks. This model for human learning and generalization is able to adapt to both stable and unstable dynamics, and provides a controller for generating efficient adaptive motor behavior in robots. Simulation results exhibit predictions consistent with all experiments on learning of novel dynamics requiring adaptation of force and impedance, and enable us to re-examine some of the previous interpretations of experiments on generalization. © 2012 Kadiallah et al.

Linear gaussian computations for near-exact Bayesian Monte Carlo inference in skewed alpha-stable time series models

In this paper we study parameter estimation for time series with asymmetric α-stable innovations. The proposed methods use a Poisson sum series representation (PSSR) for the asymmetric α-stable noise to express the process in a conditionally Gaussian framework. That allows us to implement Bayesian parameter estimation using Markov chain Monte Carlo (MCMC) methods. We further enhance the series representation by introducing a novel approximation of the series residual terms in which we are able to characterise the mean and variance of the approximation. Simulations illustrate the proposed framework applied to linear time series, estimating the model parameter values and model order P for an autoregressive (AR(P)) model driven by asymmetric α-stable innovations. © 2012 IEEE.

UV durable colour pigment doped SmA liquid crystal composites for outdoor trans-reflective bi-stable displays

High brightness trans-reflective bi-stable displays based on smectic A (SmA) liquid crystals (LCs) can have nearly perfect transparency in the clear state and very high reflection in the scattered state. Because the LC material in use is stable under UV radiation, this kind of displays can stand for strong day-light and therefore be ideal for outdoor applications from e-books to public signage and advertisement. However, the colour application has been limited because the traditional colourants in use are conventional dyes which are lack of UV stability and that their colours are easily photo bleached. Here we present a colour SmA display demonstrator using pigments as colourant. Mixing pigments with SmA LCs and maintain the desirable optical switching performance is not straightforward. We show here how it can be done, including how to obtain fine sized pigment nano-particles, the effects of particle size and size distribution on the display performance. Our optimized pigments/SmA compositions can be driven by a low frequency waveform (∼101Hz) to a scattered state to exhibit colour while by a high frequency waveform (∼103Hz) to a cleared state showing no colour. Finally, we will present its excellent UV life-time (at least >7.2 years) in comparison with that of dye composition (∼2.4 years). The complex interaction of pigment nano-particles with LC molecules and the resulting effects on the LC electro-optical performances are still to be fully understood. We hope this work will not only demonstrate a new and practical approach for outdoor reflective colour displays but also provide a new material system for fundamental liquid crystal colloid research work. © 2012 SPIE.

Lyapunov functions for stable cascades and applications to global stabilization

This paper generalizes recent Lyapunov constructions for a cascade of two nonlinear systems, one of which is stable rather than asymptotically stable. A new cross-term construction in the Lyapunov function allows us to replace earlier growth conditions by a necessary boundedness condition. This method is instrumental in the global stabilization of feedforward systems, and new stabilization results are derived from the generalized construction.

The stochastic implicit Euler method - A stable coupling scheme for Monte Carlo burnup calculations

Existing Monte Carlo burnup codes use various schemes to solve the coupled criticality and burnup equations. Previous studies have shown that the coupling schemes of the existing Monte Carlo burnup codes can be numerically unstable. Here we develop the Stochastic Implicit Euler method - a stable and efficient new coupling scheme. The implicit solution is obtained by the stochastic approximation at each time step. Our test calculations demonstrate that the Stochastic Implicit Euler method can provide an accurate solution to problems where the methods in the existing Monte Carlo burnup codes fail. © 2013 Elsevier Ltd. All rights reserved.

Stable multivariate rational interpolation for parameter-dependent aerospace models

A multivariate, robust, rational interpolation method for propagating uncertainties in several dimensions is presented. The algorithm for selecting numerator and denominator polynomial orders is based on recent work that uses a singular value decomposition approach. In this paper we extend this algorithm to higher dimensions and demonstrate its efficacy in terms of convergence and accuracy, both as a method for response suface generation and interpolation. To obtain stable approximants for continuous functions, we use an L2 error norm indicator to rank optimal numerator and denominator solutions. For discontinous functions, a second criterion setting an upper limit on the approximant value is employed. Analytical examples demonstrate that, for the same stencil, rational methods can yield more rapid convergence compared to pseudospectral or collocation approaches for certain problems. © 2012 AIAA.

Numerically stable Monte Carlo-burnup-thermal hydraulic coupling schemes

This paper presents stochastic implicit coupling method intended for use in Monte-Carlo (MC) based reactor analysis systems that include burnup and thermal hydraulic (TH) feedbacks. Both feedbacks are essential for accurate modeling of advanced reactor designs and analyses of associated fuel cycles. In particular, we investigate the effect of different burnup-TH coupling schemes on the numerical stability and accuracy of coupled MC calculations. First, we present the beginning of time step method which is the most commonly used. The accuracy of this method depends on the time step length and it is only conditionally stable. This work demonstrates that even for relatively short time steps, this method can be numerically unstable. Namely, the spatial distribution of neutronic and thermal hydraulic parameters, such as nuclide densities and temperatures, exhibit oscillatory behavior. To address the numerical stability issue, new implicit stochastic methods are proposed. The methods solve the depletion and TH problems simultaneously and use under-relaxation to speed up convergence. These methods are numerically stable and accurate even for relatively large time steps and require less computation time than the existing methods. © 2013 Elsevier Ltd. All rights reserved.