自适应小波算法用于近红外光谱的多元校正

实现了一种构建自适应小波滤波器的方法,并将其用于近红外光谱数据的多元校正。该方法根据一定的目标函数,针对信号的特性自适应地构造小波滤波器。用该法构建的滤波器对烟草样品的近红外光谱进行压缩,并将压缩后的数据采用偏最小二乘法建模,实现了烟草样品常规组分的定量分析。     

Adaptive umbrella sampling of the potential energy: modified updating procedure of the umbrella potential and application to peptide folding

Adaptive umbrella sampling of the potential energy is used as a search method to determine the structures and thermodynamics of peptides in solution. It leads to uniform sampling of the potential energy, so as to combine sampling of low-energy conformations that dominate the properties of the system at room temperature with sampling of high-energy conformations that are important for transitions between different minima. A modification of the procedure for updating the umbrella potential is introduced to increase the number of transitions between folded and unfolded conformations. The method does not depend on assumptions about the geometry of the native state. Two peptides with 12 and 13 residues, respectively, are studied using the CHARMM polar-hydrogen energy function and the analytical continuum solvent potential for treatment of solvation. In the original adaptive umbrella sampling simulations of the two peptides, two and six transitions occur between folded and unfolded conformations, respectively, over a simulation time of 10 ns. The modification increases the number of transitions to 6 and 12, respectively, in the same simulation time. The precision of estimates of the average effective energy of the system as a function of temperature and of the contributions to the average effective energy of folded conformations obtained with the adaptive methods is discussed. Received: 11 July 1998 / Accepted: 22 September 1998 / Published online: 17 December 1998     

Global error estimation based on the tolerance proportionality for some adaptive Runge–Kutta codes

Modern codes for the numerical solution of Initial Value Problems (IVPs) in ODEs are based in adaptive methods that, for a user supplied tolerance δ$\delta$, attempt to advance the integration selecting the size of each step so that some measure of the local error is ?δ$?\delta$. Although this policy does not ensure that the global errors are under the prescribed tolerance, after the early studies of Stetter [Considerations concerning a theory for ODE-solvers, in: R. Burlisch, R.D. Grigorieff, J. Schröder (Eds.), Numerical Treatment of Differential Equations, Proceedings of Oberwolfach, 1976, Lecture Notes in Mathematics, vol. 631, Springer, Berlin, 1978, pp. 188–200; Tolerance proportionality in ODE codes, in: R. März (Ed.), Proceedings of the Second Conference on Numerical Treatment of Ordinary Differential Equations, Humbold University, Berlin, 1980, pp. 109–123] and the extensions of Higham [Global error versus tolerance for explicit Runge–Kutta methods, IMA J. Numer. Anal. 11 (1991) 457–480; The tolerance proportionality of adaptive ODE solvers, J. Comput. Appl. Math. 45 (1993) 227–236; The reliability of standard local error control algorithms for initial value ordinary differential equations, in: Proceedings: The Quality of Numerical Software: Assessment and Enhancement, IFIP Series, Springer, Berlin, 1997], it has been proved that in many existing explicit Runge–Kutta codes the global errors behave asymptotically as some rational power of δ$\delta$. This step-size policy, for a given IVP, determines at each grid point _tn$t_n$ a new step-size _hn+1=h(_tn;δ)$h_{n+1}=h(t_n;\delta )$ so that h(t;δ)$h(t;\delta )$ is a continuous function of t$t$.     

The completion of locally refined simplicial partitions created by bisection

Recently, in [Found. Comput. Math., 7(2) (2007), 245-269], we proved that an adaptive finite element method based on newest vertex bisection in two space dimensions for solving elliptic equations, which is essentially the method from [SINUM, 38 (2000), 466-488] by Morin, Nochetto, and Siebert, converges with the optimal rate.The number of triangles in the output partition of such a method is generally larger than the number of triangles that in all intermediate partitions have been marked for bisection, because additional bisections are needed to retain conforming meshes.A key ingredient to our proof was a result from [Numer. Math., 97(2004), 219-268] by Binev, Dahmen and DeVore saying that for some absolute constant , where is the number of triangles from the initial partition that have never been bisected. In this paper, we extend this result to bisection algorithms of -simplices, with that generalizing the result concerning optimality of the adaptive finite element method to general space dimensions.

     

Survival criterion for a population subject to selection and mutations; Application to temporally piecewise constant environments

We study a parabolic Lotka–Volterra type equation that describes the evolution of a population structured by a phenotypic trait, under the effects of mutations and competition for resources modelled by a nonlocal feedback. The limit of small mutations is characterized by a Hamilton–Jacobi equation with constraint that describes the concentration of the population on some traits. This result was already established in Barles and Perthame (2008); Barles et al. (2009); Lorz et al. (2011) in a time-homogeneous environment, when the asymptotic persistence of the population was ensured by assumptions on either the growth rate or the initial data. Here, we relax these assumptions to extend the study to situations where the population may go extinct at the limit. For that purpose, we provide conditions on the initial data for the asymptotic fate of the population. Finally, we show how this study for a time-homogeneous environment allows to consider temporally piecewise constant environments.     

MEXIT: Maximal un-coupling times for stochastic processes

Classical coupling constructions arrange for copies of the same Markov process started at two different initial states to become equal as soon as possible. In this paper, we consider an alternative coupling framework in which one seeks to arrange for two different Markov (or other stochastic) processes to remain equal for as long as possible, when started in the same state. We refer to this “un-coupling” or “maximal agreement” construction as MEXIT, standing for “maximal exit”. After highlighting the importance of un-coupling arguments in a few key statistical and probabilistic settings, we develop an explicit MEXIT construction for stochastic processes in discrete time with countable state-space. This construction is generalized to random processes on general state-space running in continuous time, and then exemplified by discussion of MEXIT for Brownian motions with two different constant drifts.     

ADAPTIVE QUADRILATERAL AND HEXAHEDRAL FINITE ELEMENT METHODS WITH HANGING NODES AND CONVERGENCE ANALYSIS

In this paper we study the convergence of adaptive finite element methods for the gen- eral non-attine equivalent quadrilateral and hexahedral elements on 1-irregular meshes with hanging nodes. Based on several basic ingredients, such as quasi-orthogonality, estimator reduction and D6fler marking strategy, convergence of the adaptive finite element methods for the general second-order elliptic partial equations is proved. Our analysis is effective for all conforming Qm elements which covers both the two- and three-dimensional cases in a unified fashion.     

A nonmonotone adaptive trust region method for unconstrained optimization based on conic model

In this paper, we present a nonmonotone adaptive trust region method for unconstrained optimization based on conic model. The new method combines nonmonotone technique and a new way to determine trust region radius at each iteration. The local and global convergence properties are proved under reasonable assumptions. Numerical experiments show that our algorithm is effective.     

Further results on adaptive full-order and reduced-order observers for Lur’e differential inclusions

This paper is concerned with the adaptive observer design of Lur’e differential inclusions with unknown parameters. Under a relaxed assumption on nonlinear perturbation functions, a sufficient condition for the existence of an adaptive full-order observer is established. Comparing with results in the literature, the present conditions are complemented with a numerically reliable computational approach, which can be checked by means of linear matrix inequalities. Furthermore, it is shown that, under the sufficient condition, the existence of a reduced-order observer is guaranteed. Also, the reduced-order observer is designed. The effectiveness of the proposed design is illustrated via a simulation example.     

A fourth-order approximate projection method for the incompressible Navier–Stokes equations on locally-refined periodic domains

In this follow-up of our previous work [30], the author proposes a high-order semi-implicit method for numerically solving the incompressible Navier–Stokes equations on locally-refined periodic domains. Fourth-order finite-volume stencils are employed for spatially discretizing various operators in the context of structured adaptive mesh refinement (AMR). Time integration adopts a fourth-order, semi-implicit, additive Runge–Kutta method to treat the non-stiff convection term explicitly and the stiff diffusion term implicitly. The divergence-free condition is fulfilled by an approximate projection operator. Altogether, these components yield a simple algorithm for simulating incompressible viscous flows on periodic domains with fourth-order accuracies both in time and in space. Results of numerical tests show that the proposed method is superior to previous second-order methods in terms of accuracy and efficiency. A major contribution of this work is the analysis of a fourth-order approximate projection operator.