Some recent developments in quantization of fractal measures

We give an overview on the quantization problem for fractal measures, including some related results and methods which have been developed in the last decades. Based on the work of Graf and Luschgy, we propose a three-step procedure to estimate the quantization errors. We survey some recent progress, which makes use of this procedure, including the quantization for self-affine measures, Markov-type measures on graph-directed fractals, and product measures on multiscale Moran sets. Several open problems are mentioned.Comment: 13 page

On the convergence of autonomous agent communities

This is the post-print version of the final published paper that is available from the link below. Copyright @ 2010 IOS Press and the authors.Community is a common phenomenon in natural ecosystems, human societies as well as artificial multi-agent systems such as those in web and Internet based applications. In many self-organizing systems, communities are formed evolutionarily in a decentralized way through agents' autonomous behavior. This paper systematically investigates the properties of a variety of the self-organizing agent community systems by a formal qualitative approach and a quantitative experimental approach. The qualitative formal study by applying formal specification in SLABS and Scenario Calculus has proven that mature and optimal communities always form and become stable when agents behave based on the collective knowledge of the communities, whereas community formation does not always reach maturity and optimality if agents behave solely based on individual knowledge, and the communities are not always stable even if such a formation is achieved. The quantitative experimental study by simulation has shown that the convergence time of agent communities depends on several parameters of the system in certain complicated patterns, including the number of agents, the number of community organizers, the number of knowledge categories, and the size of the knowledge in each category

Compactly supported radial basis functions: how and why?

The use of radial basis functions have attracted increasing attention in recent years as an elegant scheme for high-dimensional scattered data approximation, an accepted method for machine learning, one of the foundations of mesh-free methods, an alternative way to construct higher order methods for solving partial differential equations (PDEs), an emerging method for solving PDEs on surfaces, a novel method for mesh repair and so on. All these applications share one mathematical foundation: high dimensional approximation/interpolation. This paper explains why radial basis functions are preferred to multi-variate polynomials for scattered data approximation in high-dimensional space; and gives a brief description on how to construct the most commonly used compactly supported radial basis functions. Without sophisticated mathematics, one can construct a compactly supported (radial) basis function with required smoothness according to procedures described here. Short programs and tables for compactly supported radial basis functions are supplied

Air-Coupled Surface Wave Transmission Measurement Across A Partially Closed Surface-Breaking Crack In Concrete

Previous researchers have demonstrated that the transmission of surface waves is effective to estimate the depth of a surface-breaking crack in solids. However, most of the results were obtained using a well-defined crack (or notch) in laboratory. In fact, there is a critical gap to apply the theory to surface-breaking cracks in concrete structures subjected to external loadings where the cracks are generally ill-defined, and partially closed. In this study, the authors investigated transmission coefficients of surface waves across a partially closed surface-breaking crack in concrete subjected to monotonically increasing compressive loadings. First, a concrete beam (0.5 X 0.154 X 2.1 m(3)) having two surface-breaking cracks with various crack widths was prepared in laboratory. Second, transmission coefficients of impact-induced surface waves were measured across a surface-breaking crack in the concrete beam with increasing compressive loadings from 0 to 140kN (10% of the ultimate compressive strength of the concrete beam). External post-tensioning was used to apply the compression. For comparison purpose, sensitivity of surface wave velocity to compressive loading was also investigated. As a result, observations in this study reveal that transmission coefficient is a more sensitive acoustic parameter than phase velocity to evaluate a surface-breaking cracking in concrete subjected to compressive loadings.Civil, Architectural, and Environmental Engineerin

Joint Dynamic Radio Resource Allocation and Mobility Load Balancing in 3GPP LTE Multi-Cell Network

Load imbalance, together with inefficient utilization of system resource, constitute major factors responsible for poor overall performance in Long Term Evolution (LTE) network. In this paper, a novel scheme of joint dynamic resource allocation and load balancing is proposed to achieve a balanced performance improvement in 3rd Generation Partnership Project (3GPP) LTE Self-Organizing Networks (SON). The new method which aims at maximizing network resource efficiency subject to inter-cell interference and intra-cell resource constraints is implemented in two steps. In the first step, an efficient resource allocation, including user scheduling and power assignment, is conducted in a distributed manner to serve as many users in the whole network as possible. In the second step, based on the resource allocation scheme, the optimization objective namely network resource efficiency can be calculated and load balancing is implemented by switching the user that can maximize the objective function. Lagrange Multipliers method and heuristic algorithm are used to resolve the formulated optimization problem. Simulation results show that our algorithm achieves better performance in terms of user throughput, fairness, load balancing index and unsatisfied user number compared with the traditional approach which takes resource allocation and load balancing into account, respectively

Local Quasiparticle States around an Anderson Impurity in a d-Wave Superconductor: Kondo Effects

The Kondo effects of an Anderson impurity embedded into a d-wave superconductor is studied. Within the slave-boson mean-field approach, the derived Bogoliubov-de Gennes equations are solved via exact diagonalization. We show that a critical coupling strength, above which the Kondo effect takes place, exists regardless of whether the band particle-hole symmetry is present or not. The resonant quasiparticle peaks are found in the local density of states (LDOS) both directly at the impurity and around its neighbors, which is in sharp contrast to the case of nonmagnetic unitary impurities, where the LDOS vanishes on the impurity site.Comment: To appear in Physical Review B as a Rapid Communication (January 1, 2001