Mapping and hierarchical self-organizing neural networks for VLSIplacement

We have developed mapping and hierarchical self-organizing neural networks for placement of very large scale integrated (VLST) circuits. In this paper, we introduce MHSO and MHSO2 as two versions of mapping and hierarchical self-organizing network (MHSO) algorithms. By using the MHSO, each module in the placement wins the competition with a probability density function that is defined according to different design styles, e.g., the gate arrays and standard cell circuits. The relation between a placement carrier and movable modules is met by the algorithm's ability to map an input space (somatosensory source) into an output space where the circuit modules are located, MHSO2 is designed for macro cell circuits. In this algorithm, the shape and dimension of each module is simultaneously considered together with the wire length by a hierarchical order. In comparison with other conventional placement approaches, the MHSO algorithms have shown their distinct advantages. The results for benchmark circuits so far obtained are quite comparable to simulated annealing (SA), but the computation time is about eight-ten times faster than with SA.     

基于分层路网的路径规划算法

为了提高路径规划的效率,提出了一种基于分层路网的二叉堆管理开启列表启发搜索算法。首先根据路网分级特点的存在,建立分层地图数据库,然后以启发式A*算法为主搜索方式,结合优先队列二叉堆来管理开启列表,完成路径规划。通过实验对比不同路径规划算法的平均耗时显示：启发式A*算法的效率是盲目式Dijkstra算法的4倍左右,同时在算法中引入二叉堆至少节省5%的规划时间。分层策略使快速路段所占比例达到90%以上,且将路径规划耗时控制在3s以内。实现结果表明,所提算法具有很高的运行效率,同时能满足驾驶者多走快速路段的行车心理。     

Fast surface interpolation using hierarchical basis functions

An alternative to multigrid relaxation that is much easier to implement and more generally applicable is presented. Conjugate gradient descent is used in conjunction with a hierarchical (multiresolution) set of basis functions. The resultant algorithm uses a pyramid to smooth the residual vector before the direction is computed. Simulation results showing the speed of convergence and its dependence on the choice of interpolator, the number of smoothing levels, and other factors are presented. The relationship of this approach to other multiresolution relaxation and representation schemes is also discussed     

一种基于分层道路网的数据准备模型及实现

为了缩短计算中心与车辆之间的数据传送时间，提出并实现了一种TMSCR数据准备模型，即在包含起止点的一个网格集合的外接矩形区域中，提取起点网格内的低层路段、终点网格内的低层路段和所有高层路段的并集，发送给车辆。实验表明，实现该模型的时间代价很小，TMSCR模型与传统的方法相比，可以大大节省通信时间，从而为车辆导航提供优质的服务。     

Formal restructuring functions for hierarchical data bases

Traditionally data restructuring of hierarchical data structures has been illustrated using examples in the context of the expressions of some transformation language. In this paper we define general and exact analysis and restructuring functions for hierarchical data bases. These functions describe restructuring of structural relationships among data structures, i.e. the construction of a target data base from a source data base is defined in detail. In fact, the analysis and restructuring functions define the tasks to be performed by the restructuring software at run time.     

Multiscale approximation with hierarchical radial basis functions networks

An approximating neural model, called hierarchical radial basis function (HRBF) network, is presented here. This is a self-organizing (by growing) multiscale version of a radial basis function (RBF) network. It is constituted of hierarchical layers, each containing a Gaussian grid at a decreasing scale. The grids are not completely filled, but units are inserted only where the local error is over threshold. This guarantees a uniform residual error and the allocation of more units with smaller scales where the data contain higher frequencies. Only local operations, which do not require any iteration on the data, are required; this allows to construct the network in quasi-real time. Through harmonic analysis, it is demonstrated that, although a HRBF cannot be reduced to a traditional wavelet-based multiresolution analysis (MRA), it does employ Riesz bases and enjoys asymptotic approximation properties for a very large class of functions. HRBF networks have been extensively applied to the reconstruction of three-dimensional (3-13) models from noisy range data. The results illustrate their power in denoising the original data, obtaining an effective multiscale reconstruction of better quality than that obtained by MRA.     

Mapping functions and data redistribution for parallel files

Data distribution in memory or on disks is an important factor influencing the performance of parallel applications. On the other hand, programs or systems, like a parallel file system, frequently redistribute data between memory and disks. This paper presents a generalization of previous approaches of the redistribution problem. We introduce algorithms for mapping between two arbitrary distributions of a data set. The algorithms are optimized for multidimensional array partitions. We motivate our approach and present potential utilizations. The paper also presents a case study, the employment of mapping functions, and redistribution algorithms in a parallel file system.

Fuzzy basis functions: comparisons with other basis functions

Fuzzy basis functions (FBF's) which have the capability of combining both numerical data and linguistic information, are compared with other basis functions. Because a FBF network is different from other networks in that it is the only one that can combine numerical and linguistic information, comparisons are made when only numerical data is available. In particular, a FBF network is compared with a radial basis function (RBF) network from the viewpoint of function approximation. Their architectural interrelationships are discussed. Additionally, a RBF network, which is implemented using a regularization technique, is compared with a FBF network from the viewpoint of overcoming ill-posed problems. A FBF network is also compared with Specht's probabilistic neural network and his general regression neural network (GRNN) from an architectural point of view. A FBF network is also compared with a Gaussian sum approximation in which Gaussian functions play a central role. Finally, we summarize the architectural relationships between all the networks discussed in this paper     

A hierarchical modeling approach for clustering probability density functions

The problem of clustering probability density functions is emerging in different scientific domains. The methods proposed for clustering probability density functions are mainly focused on univariate settings and are based on heuristic clustering solutions. New aspects of the problem associated with the multivariate setting and a model-based perspective are investigated. The novel approach relies on a hierarchical mixture modeling of the data. The method is introduced in the univariate context and then extended to multivariate densities by means of a factorial model performing dimension reduction. Model fitting is carried out using an EM-algorithm. The proposed method is illustrated through simulated experiments and applied to two real data sets in order to compare its performance with alternative clustering strategies.     

Mapping of neural network models onto massively parallel hierarchical computer systems

This paper investigates the proposed implementation of neural networks on massively parallel hierarchical computer systems with hypernet topology. The proposed mapping scheme takes advantage of the inherent structure of hypernets to process multiple copies of the neural network in the different subnets, each executing a portion of the training set, and finally combines the weight changes in the subnets to adjust the synaptic weights in all the copies. An expression is derived to estimate the time for all-to-all broadcasting, the principal mode of communication in the parallel implemention of neural networks. This is later used to estimate the time required for executing various execution phases in the neural network algorithm, and thus, to estimate the speedup performance of the proposed implementation.     

Mapping and exploration in a hierarchical heterogeneous multi-robot system using limited capability robots

This paper focusses on the development of a customised mapping and exploration task for a heterogeneous ensemble of mobile robots. Many robots in the team may have limited processing and sensing abilities. This means that each robot may not be able to execute all components of the mapping and exploration task. A hierarchical system is proposed that consists of computationally powerful robots (managers) at the upper level and limited capability robots (workers) at the lower levels. This enables resources (such as processing) to be shared and tasks to be abstracted. The global environment containing scattered obstacles is divided into local environments by the managers for the workers to explore. Worker robots can be assigned planner and/or explorer tasks and are only made aware of information relevant to their assigned tasks.     

An efficient location encoding method for moving objects using hierarchical administrative district and road network

Due to the rapid development in mobile communication technologies, the usage of mobile devices such as cell phone or PDA has increased significantly. As different devices require different applications, various new services are being developed to satisfy the needs. One of the popular services under heavy demand is the location-based service (LBS) that exploits the spatial information of moving objects per temporal changes. In order to support LBS well, in this paper, we investigate how spatio-temporal information of moving objects can be efficiently stored and indexed. In particular, we propose a novel location encoding method based on hierarchical administrative district information. Our proposal is different from conventional approaches where moving objects are often expressed as geometric points in two-dimensional space, (x, y). Instead, in ours, moving objects are encoded as one-dimensional points by both administrative district as well as road information. Our method becomes especially useful for monitoring traffic situation or tracing location of moving objects through approximate spatial queries.     

Mapping Boolean functions with neural networks having binaryweights and zero thresholds

In this paper, the ability of a binary neural-network comprising only neurons with zero thresholds and binary weights to map given samples of a Boolean function is studied. A mathematical model describing a network with such restrictions is developed. It is shown that this model is quite amenable to algebraic manipulation. A key feature of the model is that it replaces the two input and output variables with a single "normalized" variable. The model is then used to provide a priori criteria, stated in terms of the new variable, that a given Boolean function must satisfy in order to be mapped by a network having one or two layers. These criteria provide necessary, and in the case of a one-layer network, sufficient conditions for samples of a Boolean function to be mapped by a binary neural network with zero thresholds. It is shown that the necessary conditions imposed by the two-layer network are, in some sense, minimal.     

An adaptive hierarchical approximation method on the sphere using axisymmetric locally supported basis functions

The paper discusses the approximation of scattered data on the sphere which is one of the major tasks in geomathematics. Starting from the discretization of singular integrals on the sphere the authors devise a simple approximation method that employs locally supported spherical polynomials and does not require equidistributed grids. It is the basis for a hierarchical approximation algorithm using differently scaled basis functions, adaptivity and error control. The method is applied to two examples one of which is a digital terrain model of Australia.     

具有任意形状隶属函数的分层模糊系统逼近性能研究

首先证明了对任意给定的矩阵A和正数c, 一定存在向量b, 使得方程Ax=b有非负解, 且b和解的范数均小于c. 在此基础上证明了具有任意形状隶属函数的分层模糊系统对紧集上连续函数的逼近性质, 为使用分层模糊系统进行辨识或控制以避免模糊规则数目随系统变量个数呈指数增长提供了理论依据.     

Multi-objective design of hierarchical consensus functions for clustering ensembles via genetic programming

This paper investigates a genetic programming (GP) approach aimed at the multi-objective design of hierarchical consensus functions for clustering ensembles. By this means, data partitions obtained via different clustering techniques can be continuously refined (via selection and merging) by a population of fusion hierarchies having complementary validation indices as objective functions. To assess the potential of the novel framework in terms of efficiency and effectiveness, a series of systematic experiments, involving eleven variants of the proposed GP-based algorithm and a comparison with basic as well as advanced clustering methods (of which some are clustering ensembles and/or multi-objective in nature), have been conducted on a number of artificial, benchmark and bioinformatics datasets. Overall, the results corroborate the perspective that having fusion hierarchies operating on well-chosen subsets of data partitions is a fine strategy that may yield significant gains in terms of clustering robustness.     

Multiple Lyapunov functions and other analysis tools for switchedand hybrid systems

We introduce some analysis tools for switched and hybrid systems. We first present work on stability analysis. We introduce multiple Lyapunov functions as a tool for analyzing Lyapunov stability and use iterated function systems theory as a tool for Lagrange stability. We also discuss the case where the switched systems are indexed by an arbitrary compact set. Finally, we extend Bendixson's theorem to the case of Lipschitz continuous vector fields, allowing limit cycle analysis of a class of “continuous switched” systems     

Mapping from parametric characteristics to generalized frequency response functions of non-linear systems

Based on the parametric characteristic of the nth-order generalized frequency response function (GFRF) for non-linear systems described by a non-linear differential equation (NDE) model, a mapping function from the parametric characteristics to the GFRFs is established, by which the nth-order GFRF can be directly written into a more straightforward and meaningful form in terms of the first order GFRF, i.e., an n-degree polynomial function of the first order GFRF. The new expression has no recursive relationship between different order GFRFs, and demonstrates some new properties of the GFRFs which can explicitly unveil the linear and non-linear factors included in the GFRFs, and reveal clearly the relationship between the nth-order GFRF and its parametric characteristic, as well as the relationship between the nth-order GFRF and the first order GFRF. The new results provide a novel and useful insight into the frequency domain analysis and design of non-linear systems based on the GFRFs. Several examples are given to illustrate the theoretical results.