Classifying genes according to predefined patterns by controlling false discovery rate

Classifying genes with time-course expression data into one of the several predefined patterns is viewed as a multiple significance testing problem. The proposed approach calculates the p-value of test statistic using the Monte Carlo method and classifies genes by controlling the overall false discovery rate. We also estimate the positive false discovery rate of each pattern. The proposed procedure was applied to a real data set and some numerical experiments using synthetic data are performed.     

On the linear span of the p -ary cascaded GMW sequences

In this paper, a recursion is derived to compute the linear span of the p-ary cascaded GMW sequences. It is the first time to determine the linear span of the p-ary cascaded GMW sequence without any restriction on the parameters completely. Whereas, the known result on the p-ary cascaded GMW sequence with the specific parameters in the literature could be viewed as a special case of the new result. Supported by the National Natural Science Foundation of China (Grant No. 60302015), the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200341), and Sichuan Youth Science Foundation (Grant No. 04ZQ026-048)     

Improved inference on a scalar fixed effect of interest in nonlinear mixed-effects models

Likelihood-based inference on a scalar fixed effect of interest in nonlinear mixed-effects models usually relies on first-order approximations. If the sample size is small, tests and confidence intervals derived from first-order solutions can be inaccurate. An improved test statistic based on a modification of the signed likelihood ratio statistic is presented which was recently suggested by Skovgaard [1996. An explicit large-deviation approximation to one-parameter tests. Bernoulli 2, 145-165]. The finite sample behaviour of this statistic is investigated through a set of simulation studies. The results show that its finite-sample null distribution is better approximated by the standard normal than it is for its first-order counterpart. The R code used to run the simulations is freely available.     

Minimum ℓ1, ℓ2, and ℓ∞ Norm Approximate Solutions to an Overdetermined System of Linear Equations

Cadzow, J. A., Minimum ℓ₁, ℓ₂, and ℓ_∞ Norm Approximate Solutions to an Overdetermined System of Linear Equations, Digital Signal Processing12 (2002) 524–560Many practical problems encountered in digital signal processing and other quantitative oriented disciplines entail finding a best approximate solution to an overdetermined system of linear equations. Invariably, the least squares error approximate solution (i.e., minimum ℓ₂ norm) is chosen for this task due primarily to the existence of a convenient closed expression for its determination. It should be noted, however, that in many applications a minimum ℓ₁ or ℓ_∞ norm approximate solution is preferable. For example, in cases where the data being analyzed contain a few data outliers a minimum ℓ₁ approximate solution is preferable since it tends to ignore bad data points. In other applications one may wish to determine an approximate solution whose largest error magnitude is the smallest possible (i.e., a minimum ℓ_∞ norm approximate solution). Unfortunately, there do not exist convenient closed form expressions for either the minimum ℓ₁ or the minimum ℓ_∞ norm approximate solution and one must resort to nonlinear programming methods for their determination. Effective algorithms for determining these two solutions are herein presented (see Cadzow, J. A., Data Analysis and Signal Processing: Theory and Applications).     

Flow regularity and optimality conditions with controls inL p

In this paper we study theC ^p regularity of the flow of a nonlinear nonautonomous control system with respect to control maps belonging toL ^p withp≥r. The results obtained are applied to get first- and second-order optimality conditions when the control space isL ^p . The problem which we consider is in the Mayer form and includes endpoint constraints. We present first-order necessary conditions for a wide class of control systems. Moreover, we show that the usual second-order sufficient conditions are effective only if the mapf that defines the control system is a polynomial of degree two in the control variable and the controls belong toL ².     

The Leader–Follower Location Model

This paper summarizes some results for the leader–follower location model on networks in several scenarios. Discretization results are considered and differences derived from the inelastic and elastic demand assumptions, as well as from the customer’s choice rule, are emphasized. Finally, some issues for future lines of investigation are suggested.     

Increasing the power: A practical approach to goodness-of-fit test for logistic regression models with continuous predictors

When continuous predictors are present, classical Pearson and deviance goodness-of-fit tests to assess logistic model fit break down. The Hosmer-Lemeshow test can be used in these situations. While simple to perform and widely used, it does not have desirable power in many cases and provides no further information on the source of any detectable lack of fit. Tsiatis proposed a score statistic to test for covariate regional effects. While conceptually elegant, its lack of a general rule for how to partition the covariate space has, to a certain degree, limited its popularity. We propose a new method for goodness-of-fit testing that uses a very general partitioning strategy (clustering) in the covariate space and either a Pearson statistic or a score statistic. Properties of the proposed statistics are discussed, and a simulation study demonstrates increased power to detect model misspecification in a variety of settings. An application of these different methods on data from a clinical trial illustrates their use. Discussions on further improvement of the proposed tests and extending this new method to other data situations, such as ordinal response regression models are also included.     

GH 2 control for uncertain discrete-time-delay fuzzy systems based on a switching fuzzy model and piecewise Lyapunov function

Generalized H2 （GH2） stability analysis and controller design of the uncertain discrete-time Takagi-Sugeno （T-S） fuzzy systems with state delay are studied based on a switching fuzzy model and piecewise Lyapunov function. GH2 stability sufficient conditions are derived in terms of linear matrix inequalities （LMIs）. The interactions among the fuzzy subsystems are considered. Therefore, the proposed conditions are less conservative than the previous results. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. To illustrate the validity of the proposed method, a design example is provided.     

Universal stabilization of a class of nonlinear systems with homogeneous vector fields

Under relative-degree-one and minimum-phase assumptions, it is well known that the class of finite-dimensional, linear, single-input (u), single-output (y) systems (A,b,c) is universally stabilized by the feedback strategy u = Λ(λ)y, λ = y², where Λ is a function of Nussbaum type (the terminology “universal stabilization” being used in the sense of rendering /s(0/s) a global attractor for each member of the underlying class whilst assuring boundedness of the function λ(·)). A natural generalization of this result to a class ^k of nonlinear control systems (a,b,c), with positively homogeneous (of degree k 1) drift vector field a, is described. Specifically, under the relative-degree-one (cb ≠ 0) and minimum-phase hypotheses (the latter being interpreted as that of asymptotic stability of the equilibrium of the “zero dynamics”), it is shown that the strategy u = Λ(λ)/vby/vb^k−1y, assures ^k-universal stabilization. More generally, the strategy u = Λ(λ)exp(/vby/vb)y, assures -universal stabilization, where = _{k 1} ^k.     

Soft -ideals of soft BCI-algebras

Molodtsov [D. Molodtsov, Soft set theory–First results, Comput. Math. Appl. 37 (1999) 19–31] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. Jun [Y. B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl. 56 (2008) 1408–1413] applied first the notion of soft sets by Molodtsov to the theory of BCK/BCI-algebras. In this paper we introduce the notion of soft p-ideals and p-idealistic soft BCI-algebras, and then investigate their basic properties. Using soft sets, we give characterizations of (fuzzy) p-ideals in BCI-algebras. We provide relations between fuzzy p-ideals and p-idealistic soft BCI-algebras.     

Dynamic Analysis of Stochastic Recurrent Neural Networks

This paper addresses the issue of pth moment exponential stability of stochastic recurrent neural networks (SRNN) with time-varying interconnections and delays. With the help of the Dini derivative of the expectation of V(t, X(t)) “along” the solution X(t) of the model and the technique of Halanay-type inequality, some novel sufficient conditions on pth moment exponential stability of the trivial solution has been established. Conclusions of the development as presented in this paper have gone beyond some published results and are helpful to design stability of networks when stochastic noise is taken into consideration. An example is also given to illustrate the effectiveness of our results.     

Reliable Location and Regression Estimates with Application to Range Image Segmentation

Range images provide important sources of information in many three-dimensional robot vision problems such as navigation and object recognition. Many physical factors, however, introduce noise to the discrete measurements in range images, identifying the need to reassess the error distribution in samples taken from real range images. This paper suggests the use of the L _p norms to yield reliable estimates of location and regression coefficients. This particular approach is compared against two commonly used approaches: Equally Weighted Least Squares, which minimizes the L₂ norm; and the Chebychev approximation, which minimizes the L ₁ norm. The problem is a weighted least squares case where the weights are derived from the chosen parameter, p, and its ability to yield a variety of location estimates spanning from the sample mean to the sample median. These two estimates have a wide application in image processing that includes noise removal. This paper will show the problems associated with these two techniques, and suggest experimental solutions to minimize them. A specific operating range is determined in which the L _p norms perform well and a regression module is used in conjunction with a region-growing segmentation algorithm to provide a reliable partition of range images.     

An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations

The tanh-function method for finding explicit travelling solitary wave solutions to non-linear evolution equations is described. The method is usually extremely tedious to use by hand. We present a Mathematica package ATFM that deals with the tedious algebra and outputs directly the required solutions. The use of the package is illustrated by applying it to a variety of equations; not only are previously known solutions recovered but in some cases more general forms of solution are obtained.     

A Numerical Investigation of High-Order Finite Elements for Problems of Elastoplasticity

A high order finite element approach is applied to elastoplastic problems in two as well as in three dimensions. The element formulations are based on quadrilaterals and hexahedrals, taking advantage of the blending function method in order to accurately represent the geometry. A comparison of h- and p-extensions is drawn and it is shown that thin-walled structures commonly being analysed by dimensionally reduced elements may be consistently discretized by high order hexahedral elements leading to reliable and efficient computations even in case of physically nonlinear problems.     

Initialization strategies to enhancing the performance of genetic algorithms for the p-median problem

Finding solutions to the p-median problem is an important research topic in location science. A number of meta-heuristic methods have been developed in the literature to find optimal or near optimal solutions to large-scale p-median problems within an acceptable computational time. Among these methods, the recent literature has demonstrated the effectiveness of genetic algorithms (GAs) and hybrid GAs. In this paper, we focus on the strategies of generating the initial population of a genetic algorithm and examine the impact of such strategies on the overall GA performance in terms of solution quality and computational time. Our initialization approach first produces a near optimal solution with low computational complexity, and then uses this solution as a seed to generate a set of solutions as the initial GA population, which is then used in an existing hybrid GA to test the performance of the proposed approach. Experiments based on the forty p-median problems in the OR Library are conducted. Results demonstrate that the proposed approach can significantly reduce computational time without compromising the quality of resulting solutions in almost all cases, and the excellence of the proposed approach increases with the problem scale. Furthermore, a geo-referenced dataset is also tested and the resulting solution maps visualize and validate the principle of the proposed approach.     

The Use of Curved Elements in the Finite Element Approximation of Thin Plates by High Order p and hp Methods

In this article we focus on the approximation of the Reissner–Mindlin (R–M) plate model by high-order p and hp versions of the Finite Element Method (FEM), in the case when the mesh includes curved elements; this is of particular interest when plates with smooth boundary are considered. Our main goal is to verify that an appropriately defined Mixed Interpolated Tensorial Components (MITC) FEM performs well, in the presence of curved elements, when the energy norm is used as an error measure, as well as when quantities of engineering interest are computed. Comments on the performance of the standard FEM formulation are also made     

Simultaneous Lp-stabilization and internal stabilization of linear systems subject to input saturation — state feedback case

We consider the problem of simultaneous finite gain L_p-stabilization and internal stabilization of linear systems subject to input saturation via linear static state feedback. We show that bounded input finite-gain L_p-stabilization and local asymptotic stabilization can always be achieved simultaneously no matter where the poles of the open-loop system are, and the locations of these poles play a role only when bounded input finite gain L_p-stabilization and global or semi-global stabilization are required simultaneously.     

High-dimensional pseudo-logistic regression and classification with applications to gene expression data

High dimension low sample size data, like the microarray gene expression levels, pose numerous challenges to conventional statistical methods. In the particular case of binary classification, some classification methods, such as the support vector machine (SVM), can efficiently deal with high-dimensional predictors, but lacks the accuracy in estimating the probability of membership of a class. In contrast, the traditional logistic regression (TLR) effectively estimates the probability of class membership for data with low-dimensional inputs, but does not handle high-dimensional cases. The study bridges the gap between SVM and TLR by their loss functions. Based on the proposed new loss function, a pseudo-logistic regression and classification approach which simultaneously combines the strengths of both SVM and TLR is also proposed. Simulation evaluations and real data applications demonstrate that for low-dimensional data, the proposed method produces regression estimates comparable to those of TLR and penalized logistic regression, and that for high-dimensional data, the new method possesses higher classification accuracy than SVM and, in the meanwhile, enjoys enhanced computational convergence and stability.     

An exploratory study into whether to or not to include users in the development of industrial hypermedia applications

While there is agreement among both information system (IS) practitioners and IS researchers as to the value of user participation in IS development, the correlation between user participation and actual use or user satisfaction (surrogate measures of IS success) has been equivocal. A possible reason for the contradictory findings could be that user participation is being utilised, regardless of the levels of complexity of either the system or the task. This paper describes two exploratory case studies to test this hypothesis. Industrial hypermedia applications (IHA) were developed and qualitative data collected, through usability trials, to see the effect of user participation on user perception (extrinsic motivations of use) of the system, rather than IS success. The findings show that users should participate in the development when both the IS and the task are complex. On the other hand, when both the system and the task are not complex, user participation can be kept to a minimum. Furthermore, it is recommended that user participation should not be evaluated against IS success, but against system features.