人类胚胎期小脑组织基因表达的小波多尺度分析

对人类胚胎期小脑组织基因基于时空的表达强度进行小波多尺度5层分解与重构,在常用小波函数中,db2的去噪效果最好,可以用于小脑组织基因表达强度的去噪处理.     

Stock Data Clustering and Multiscale Trend Detection

Generally, trend detection algorithms over the data stream require expert assistance in some form. We present an unsupervised multiscale data stream algorithm which detects trends for evolving time series based on a data driver data stream. The raw stream data clustering algorithm is incremental, space dilating and has linear time complexity. The evolving stream is incrementally explored on a number of windows. Whenever a change occurs, we switch the analysis on this driver data stream in order to detect the new aggregated patterns and the new best selection of window widths among an exponential base set. The window widths are detected using a slightly modified version of an incremental SVD procedure. We apply this clustering algorithm to a free public NYSE stock exchange financial data feed, investigating incrementally the developing trends during the current crisis data from 2007 to 2009. The algorithm detected the changing widths of the trends as well as the trends themselves in the market.     

Efficiency and Vulnerability Analysis for Congested Networks with Random Data

In this note, we combine two theories that have been proposed in the last decade: the theory of vulnerability and efficiency of a congested network, and the theory of stochastic variational inequalities. As a result, we propose a model that describes the performance and vulnerability of a congested network with random traffic demands and where the travel time can be affected by uncertainty. As an application, we investigate in detail the famous Braess’ network.     

Analysis of Multiscale Methods

The heterogeneous multiscale method gives a general framework for the analysis of multiscale methods. In this paper, we demonstrate this by applying this framework to two canonical problems: The elliptic problem with multiscale coefficients and the quasicontinuum method.     

Multiscale Analysis in Many-Body Systems

This paper is an introduction to a multiscale analysis approach to derive mathematical models for systems with finite and infinite degrees of freedom whose fundamental dynamics is stochastic and described by a chemical master equation.     

Insensitive Bandwidth Sharing in Data Networks

We represent a data network as a set of links shared by a dynamic number of competing flows. These flows are generated within sessions and correspond to the transfer of a random volume of data on a pre-defined network route. The evolution of the stochastic process describing the number of flows on all routes, which determines the performance of the data transfers, depends on how link capacity is allocated between competing flows. We use some key properties of Whittle queueing networks to characterize the class of allocations which are insensitive in the sense that the stationary distribution of this stochastic process does not depend on any traffic characteristics (session structure, data volume distribution) except the traffic intensity on each route. We show in particular that this insensitivity property does not hold in general for well-known allocations such as max-min fairness or proportional fairness. These results are ilustrated by several examples on a number of network topologies.     

Financial Optimization Models in Data Networks*

In a competitive market investors in a data network need to give utmost considerations on profitability. They must have clear picture of the size, growth rate and demand for different services. However, the investors’ budget may be limited, and therefore the speed at which the network is rolled out, must be carefully planned to ensure that they can meet profitability targets. We model first the roll out order as combinatorial optimization problems and then extend them as continuous optimization problems. We then implement these models in a practical problem. Numerical studies suggested that the optimization problems have multiple local minima. Therefore, a global optimization technique is used to obtain the global minimum for the continuous variable problem and a combinatorial optimization technique is used to solve the discrete variable problem. Optimal financial indicators are obtained to assess the commercial viability of the network. Finally, we demonstrate that the solution of these optimization problems can provide an investment policy to the investors in data networks. *This network is a combined telephone and data network such as VIP (Voice over Internet Protocol). M. M. Ali: Visitor at the Institute for Mathematics and its Applications, University of Minnesota, USA.     

Multiscale Exploratory Analysis of Regression Quantiles Using Quantile SiZer

The SiZer methodology proposed by Chaudhuri and Marron (1999) is a valuable tool for conducting exploratory data analysis. Since its inception different versions of SiZer have been proposed in the literature. Most of these SiZer variants are targeting the mean structure of the data, and are incapable of providing any information about the quantile composition of the data. To fill this need, this article proposes a quantile version of SiZer for the regression setting. By inspecting the SiZer maps produced by this new SiZer, real quantile structures hidden in a dataset can be more effectively revealed, while at the same time spurious features can be filtered out. The utility of this quantile SiZer is illustrated via applications to both real data and simulated examples. This article has supplementary material online.     

Multiscale kernels

This paper reconstructs multivariate functions from scattered data by a new multiscale technique. The reconstruction uses standard methods of interpolation by positive definite reproducing kernels in Hilbert spaces. But it adopts techniques from wavelet theory and shift-invariant spaces to construct a new class of kernels as multiscale superpositions of shifts and scales of a single compactly supported function φ. This means that the advantages of scaled regular grids are used to construct the kernels, while the advantages of unrestricted scattered data interpolation are maintained after the kernels are constructed. Using such a multiscale kernel, the reconstruction method interpolates at given scattered data. No manipulations of the data (e.g., thinning or separation into subsets of certain scales) are needed. Then, the multiscale structure of the kernel allows to represent the interpolant on regular grids on all scales involved, with cheap evaluation due to the compact support of the function φ, and with a recursive evaluation technique if φ is chosen to be refinable. There also is a wavelet-like data reduction effect, if a suitable thresholding strategy is applied to the coefficients of the interpolant when represented over a scaled grid. Various numerical examples are presented, illustrating the multiresolution and data compression effects.     

利用贝叶斯网络分析基因表达数据

利用基因表达数据提出一种新的网络模型—贝叶斯网络,发现基因的互作.一个贝叶斯网络是多变量联合概率分布的有向图模型,表示变量间的条件独立属性.首先我们阐明贝叶斯网络如何表示基因间的互作,然后介绍从基因芯片数据学习贝叶斯网络的方法.     

Institutional Logics from the Aggregation of Organizational Networks: Operational Procedures for the Analysis of Counted Data

We address some problems of network aggregation that are central to organizational studies. We show that concepts of network equivalence (including generalizations and special cases of structural equivalence) are relevant to the modeling of the aggregation of social categories in cross-classification tables portraying relations within an organizational field (analogous to one-mode networks). We extend our results to model the dual aggregation of social identities and organizational practices (an example of a two-mode network). We present an algorithm to accomplish such dual aggregation. Within the formal and quantitative framework that we present, we emphasize a unified treatment of (a) aggregation on the basis of structural equivalence (invariance of actors within equivalence sets), (b) the study of variation in relations between structurally equivalent sets, and (c) the close connections between aggregation within organizational networks and multi-dimensional modeling of organizational fields.     

Harmonic Analysis of Neural Networks

It is known that superpositions of ridge functions (single hidden-layer feedforward neural networks) may give good approximations to certain kinds of multivariate functions. It remains unclear, however, how to effectively obtain such approximations. In this paper, we use ideas from harmonic analysis to attack this question. We introduce a special admissibility condition for neural activation functions. The new condition is not satisfied by the sigmoid activation in current use by the neural networks community; instead, our condition requires that the neural activation function be oscillatory. Using an admissible neuron we construct linear transforms which represent quite general functionsfas a superposition of ridge functions. We develop

• • • a continuous transform which satisfies a Parseval-like relation;
• • • a discrete transform which satisfies frame bounds.

Both transforms representfin a stable and effective way. The discrete transform is more challenging to construct and involves an interesting new discretization of time–frequency–direction space in order to obtain frame bounds for functions inL²(A) whereAis a compact set of Rⁿ. Ideas underlying these representations are related to Littlewood–Paley theory, wavelet analysis, and group representation theory.     

A Comparison of Data Envelopment Analysis and Artificial Neural Networks as Tools for Assessing the Efficiency of Decision Making Units

This paper is concerned with the comparison of two popular non-parametric methodologies—data envelopment analysis and artificial neural networks—as tools for assessing performance. Data envelopment analysis has been established since 1978 as a superior alternative to traditional parametric methodologies, such as regression analysis, for assessing performance. Neural networks have recently been proposed as a method for assessing performance. In this paper, we use a simulated production technology of two inputs and one output for testing the success of the two methods for assessing efficiency. The two methods are also compared on their practical use as performance measurement tools on a set of bank branches, having multiple input and output criteria. The results demonstrate that, despite their differences, both methods offer a useful range of information regarding the assessment of performance.     

A Multiscale Multilevel Monte Carlo Method for Multiscale Elliptic PDEs with Random Coefficients

We propose a multiscale multilevel Monte Carlo(MsMLMC)method to solve multiscale elliptic PDEs with random coefficients in the multi-query setting.Our method consists of offline and online stages.In the offline stage,we construct a small number of reduced basis functions within each coarse grid block,which can then be used to approximate the multiscale finite element basis functions.In the online stage,we can obtain the multiscale finite element basis very efficiently on a coarse grid by using the pre-computed multiscale basis.The MsMLMC method can be applied to multiscale RPDE starting with a relatively coarse grid,without requiring the coarsest grid to resolve the smallestscale of the solution.We have performed complexity analysis and shown that the MsMLMC offers considerable savings in solving multiscale elliptic PDEs with random coefficients.Moreover,we provide convergence analysis of the proposed method.Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for several multiscale stochastic problems without scale separation.     

A Model-Based Approach and Analysis for Multi-Period Networks

The aim of this contribution is to address a general class of network problems, very common in process systems engineering, where spoilage on arcs and storage in nodes are inevitable as time changes. Having a set of capacities, so-called horizon capacity which limits the total flow passing arcs over all periods, the min-cost flow problem in the discrete-time model with time-varying network parameters is investigated. While assuming a possibility of storage or and spoilage, we propose some approaches employing polyhedrals to obtain optimal solutions for a pre-specified planning horizon. Our methods describe some reformulations based on polyhedrals that lead to LP problems comprising a set of sparse subproblems with exceptional structures. Considering the sparsity and repeating structure of the polyhedrals, algorithmic approaches based on decomposition techniques of block-angular and block-staircase cases are proposed to handle the global problem aiming to reduce the computational resources required.     

Stability of Nonlinear Subdivision and Multiscale Transforms

Extending upon the work of Cohen, Dyn, and Matei (Appl. Comput. Harmon. Anal. 15:89–116, 2003) and of Amat and Liandrat (Appl. Comput. Harmon. Anal. 18:198–206, 2005), we present a new general sufficient condition for the Lipschitz stability of nonlinear subdivision schemes and multiscale transforms in the univariate case. It covers the special cases (weighted essentially nonoscillatory scheme, piecewise polynomial harmonic transform) considered so far but also implies the stability in some new cases (median interpolating transform, power-p schemes, etc.). Although the investigation concentrates on multiscale transforms $\bigl\{v^0,d^1,\ldots,d^J\bigr\}\longmapsto v^J,\quad J\ge1,$ in ? _∞(?) given by a stationary recursion of the form $v^{j}=Sv^{j-1}+d^{j},\quad j\ge1,$ involving a nonlinear subdivision operator S acting on ? _∞(?), the approach is extendable to other nonlinear multiscale transforms and norms, as well.     

An Ergodic Algorithm for the Power-Control Games for CDMA Data Networks

In this paper, we consider power control for the uplink of a direct-sequence code-division multiple-access data network. In the uplink, the purpose of power control is for each user to transmit enough power so that it can achieve the required quality of service without causing unnecessary interference to other users in the system. One method that has been very successful in solving this purpose for power control is the game-theoretic approach. The problem for power control is modified as a Nash equilibrium problem in which each user can choose its transmit power in order to maximize its own utility, and a Nash equilibrium is an ideal solution of the power-control game. We present a noncooperative power-control game in which each user can choose the transmit power in a way that it gets the sufficient signal-to-interference-plus-noise ratio and maximizes its own utility. To ensure the existence of a solution, we also propose the variational inequality problem which is connected with the proposed game. On a linear receiver, we deal with the matched filter receiver. Next we present a new ergodic algorithm for the proposed power control because the existing iterative algorithms can not be applied effectively to the proposed power control. We also present convergence analysis for the proposed algorithm. In addition, applying the proposed algorithm to the proposed power control, we provide numerical examples for the transmit power, the signal-to-interference-plus-noise ratio and so on. Numerical results for the proposed algorithm shall show that as compared with the existing power-control game and its method, all users in the network can enjoy the sufficient signal-to-interference-plus-noise ratio and achieve the required quality of service.      

Analysis of a Prototypical Multiscale Method Coupling Atomistic and Continuum Mechanics： the Convex Case

In order to describe a solid which deforms smoothly in some region,but non smoothly in someother region,many multiscale methods have been recently proposed that aim at coupling an atomistic model(discrete mechanics) with a macroscopic model (continuum mechanics).We provide here a theoretical basis forsuch a coupling in a one-dimensional setting,in the case of convex energy.