A unified approach to compute foliations, inertial manifolds, and tracking initial conditions

Several algorithms are presented for the accurate computation of the leaves in the foliation of an ODE near a hyperbolic fixed point. They are variations of a contraction mapping method in [25] to compute inertial manifolds, which represents a particular leaf in the unstable foliation. Such a mapping is combined with one for the leaf in the stable foliation to compute the tracking initial condition for a given solution. The algorithms are demonstrated on the Kuramoto-Sivashinsky equation

Nonstationary Nonlinear Heteroskedasticity in Regression

This paper considers the regression with errors having nonstationary nonlinear heteroskedasticity. For both the usual stationary regression and the nonstationary cointegrating regression, we develop the asymptotic theories for the least squares methods in the presence of conditional heterogeneity given as a nonlinear function of an integrated process. In particular, it is shown that the nonstationarity of volatility in the regression errors may induce spuriousness of the underlying regression. This is true for both the usual stationary regression and the nonstationary cointegrating regression, if excessive nonstationary volatility is present in the errors. Mild nonstationary volatilities do not render the underlying regression spurious. However, their presence makes the least squares estimator asymptotically biased and inefficient and the usual chi-square test invalid. In the paper, we develop an unbiased and efficient method of estimation and a chi-square test applicable for the regression with mild nonstationary volatilities in the errors. We provide some illustrations to demonstrate the empirical relevancy of the model and theory developed in the paper. For this purpose, examined are US consumption function, EURO/USD forward-spot spreads and capital-asset pricing models for some major NYSE stocksvolatility, nonstationary nonlinear heteroskedasticity, regression with heteroskedastic errors, spurious regression, cointegration

Business integration models in the context of web services.

E-commerce development and applications have been bringing the Internet to business and marketing and reforming our current business styles and processes. The rapid development of the Web, in particular, the introduction of the semantic web and web service technologies, enables business processes, modeling and management to enter an entirely new stage. Traditional web based business data and transactions can now be analyzed, extracted and modeled to discover new business rules and to form new business strategies, let alone mining the business data in order to classify customers or products. In this paper, we investigate and analyze the business integration models in the context of web services using a micro-payment system because a micro-payment system is considered to be a service intensive activity, where many payment tasks involve different forms of services, such as payment method selection for buyers, security support software, product price comparison, etc. We will use the micro-payment case to discuss and illustrate how the web services approaches support and transform the business process and integration model.

Scattering of Bunched Fractionally Charged Quasiparticles

The charge of fractionally charged quasiparticles, proposed by Laughlin to explain the fractional quantum Hall effect (FQHE), was recently verified by measurements. Charge q=e/3 and e/5 (e is the electron charge), at filling factors nu=1/3 and 2/5, respectively, were measured. Here we report the unexpected bunching of fractional charges, induced by an extremely weak backscattering potential at exceptionally low electron temperatures (T<10 mK) - deduced from shot noise measurements. Backscattered charges q=nu e, specifically, q=e/3, q=2e/5, and q<3e/7, in the respective filling factors, were measured. For the same settings but at an only slightly higher electron temperature, the measured backscattered charges were q=e/3, q=e/5, and q=e/7. In other words, bunching of backscattered quasiparticles is taking place at sufficiently low temperatures. Moreover, the backscattered current exhibited distinct temperature dependence that was correlated to the backscattered charge and the filling factor. This observation suggests the existence of 'low' and 'high' temperature backscattering states, each with its characteristic charge and characteristic energy.Comment: 4 pages, 3 figure

Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods

In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to page limitations, the overview focuses on a few related methods and is not intended to be comprehensive. We present a general adaptive multiscale model reduction framework, the Generalized Multiscale Finite Element Method. Besides the method's basic outline, we discuss some important ingredients needed for the method's success. We also discuss several applications. The proposed method allows performing local model reduction in the presence of high contrast and no scale separation

An ant colony optimization approach for maximizing the lifetime of heterogeneous wireless sensor networks

Maximizing the lifetime of wireless sensor networks (WSNs) is a challenging problem. Although some methods exist to address the problem in homogeneous WSNs, research on this problem in heterogeneous WSNs have progressed at a slow pace. Inspired by the promising performance of ant colony optimization (ACO) to solve combinatorial problems, this paper proposes an ACO-based approach that can maximize the lifetime of heterogeneous WSNs. The methodology is based on finding the maximum number of disjoint connected covers that satisfy both sensing coverage and network connectivity. A construction graph is designed with each vertex denoting the assignment of a device in a subset. Based on pheromone and heuristic information, the ants seek an optimal path on the construction graph to maximize the number of connected covers. The pheromone serves as a metaphor for the search experiences in building connected covers. The heuristic information is used to reflect the desirability of device assignments. A local search procedure is designed to further improve the search efficiency. The proposed approach has been applied to a variety of heterogeneous WSNs. The results show that the approach is effective and efficient in finding high-quality solutions for maximizing the lifetime of heterogeneous WSNs

Compressed Air Energy Storage-Part I: An Accurate Bi-linear Cavern Model

Compressed air energy storage (CAES) is suitable for large-scale energy storage and can help to increase the penetration of wind power in power systems. A CAES plant consists of compressors, expanders, caverns, and a motor/generator set. Currently used cavern models for CAES are either accurate but highly non-linear or linear but inaccurate. Highly non-linear cavern models cannot be directly utilized in power system optimization problems. In this regard, an accurate bi-linear cavern model for CAES is proposed in this first paper of a two-part series. The charging and discharging processes in a cavern are divided into several virtual states and then the first law of thermodynamics and ideal gas law are used to derive a cavern model, i.e., model for the variation of temperature and pressure in these processes. Thereafter, the heat transfer between the air in the cavern and the cavern wall is considered and integrated into the cavern model. By subsequently eliminating several negligible terms, the cavern model reduces to a bi-linear (linear) model for CAES with multiple (single) time steps. The accuracy of the proposed cavern model is verified via comparison with an accurate non-linear model.Comment: 8 page