2456151
Subdivision Schemes and Refinement Equations with Nonnegative Masks
We consider the two-scale refinement equation f(x)=@?^N"n"="0c"nf(2x-n) with @?"nc"2"n=@?"nc"2"n"+"1=1 where c"0, c"N 0 and the corresponding subdivision scheme. We study the convergence of the subdivision scheme and the cascade algorithm when all c"n>=0. It has long been conjectured that under such an assumption the subdivision algorithm converge, and the cascade algorithm converge uniformly to a continuous function, if and only if only if 00} is 1. We prove the conjecture for a large class of refinement equations.
7385162
On the use of high-order ambiguity function for multi-component polynomial phase signals
Abstract Nonstationary signals appear often in real-life applications and many of them can be modeled as polynomial-phase signals (PPS). High-order ambiguity function (HAF) was first introduced to estimate the parameters of a single-component PPS, but has not been widely used for multi-component PPS because of its nonlinearity. Multi-component PPS arise for example, in Doppler radar applications when multiple objects are tracked simultaneously. In this paper, we show that HAF is virtually additive for multi-component PPS and suggest an algorithm to estimate their parameters. Numerical examples are presented to illustrate the theories.
117639554
Multidimensional two-scale dilation equations
Abstract . This work involves the study of multidimensional scaling functions. These functions satisfy a two-scale dilation equation, just as the 1-D scaling functions which are used to construct 1-D wavelets. Two frameworks are presented for studying these dilation equations. Fourier methods are used to analyze existence, uniqueness and regularity of solutions. Expansions with infinite matrix products are used to derive an iterated function system (IFS) algorithm for generating the scaling function. Application to subdivision schemes for surface generation is presented, as a genuine multidimensional example where scaling functions arise and the IFS algorithm can be applied.
15709234
Sigma–delta quantization errors and the traveling salesman problem
In transmission, storaging and coding of digital signals we frequently perform A/D conversion using quantization. In this paper we study the maximal and mean square errors as a result of quantization. We focus on the sigma–delta modulation quantization scheme in the finite frame expansion setting. We show that this problem is related to the classical Traveling Salesman Problem (TSP) in the Euclidean space. It is known [Benedetto et al., Sigma–delta ($\Sigma\Delta$) quantization and finite frames, IEEE Trans. Inform. Theory 52, 1990–2005 (2006)] that the error bounds from the sigma–delta scheme depends on the ordering of the frame elements. By examining a priori bounds for the Euclidean TSP we show that error bounds in the sigma–delta scheme is superior to those from the pulse code modulation (PCM) scheme in general. We also give a recursive algorithm for finding an ordering of the frame elements that will lead to good maximal error and mean square error.
17444206
The Uniformity of Non-Uniform Gabor Bases
There have been extensive studies on non-uniform Gabor bases and frames in recent years. But interestingly there have not been a single example of a compactly supported orthonormal Gabor basis in which either the frequency set or the translation set is non-uniform. Nor has there been an example in which the modulus of the generating function is not a characteristic function of a set. In this paper, we prove that in the one dimension and if we assume that the generating function g(x) of an orthonormal Gabor basis is supported on an interval, then both the frequency and the translation sets of the Gabor basis must be lattices. In fact, the Gabor basis must be the “trivial” one in the sense that |g(x)|=cχΩ(x) for some fundamental interval of the translation set. We also give examples showing that compactly supported non-uniform orthonormal Gabor bases exist in higher dimensions.
2882341
Effective Criterion Functions for Efficient Agglomerative Clustering on Very Large Networks
As the agglomerative clustering algorithm is widely used in data mining, image processing, bioinformatics and pattern recognition. it has attracted great interests from both academical and industrial communities. However, existing studies neglect the decisive factor of the efficiency of the agglomerative clustering algorithm for large complex networks and usually use criterion functions which lead to inefficiency. In this paper, we propose three effective criterion functions for improving performance of agglomerative clustering algorithm. We note that clustering efficiency is determined by two factors: a) the number of neighbors of two merged clusters in each merge step; b) the number of neighbors shared by the two clusters. Based on these observations, we propose a framework for designing criterion functions in order to efficiently find clusters in very large networks. We devise three criterion functions that can effectively control the number of neighbors of clusters, and they can efficiently produce high-quality clusters. We have implemented our method and compared with existing studies on real networks, and our method outperforms state-of-the-art approaches significantly on large networks.
14757772
Convergence of a Convolution-Filtering-Based Algorithm for Empirical Mode Decomposition
Lin et al. propose the iterative Toeplitz filters algorithm as an alternative iterative algorithm for Empirical Mode Decomposition (EMD). In this alternative algorithm, the average of the upper and lower envelopes is replaced by certain "moving average" obtained through a low-pass filter. Performing the traditional sifting algorithm with such moving averages is equivalent to iterating certain convolution filters (finite length Toeplitz filters). This paper studies the convergence of this algorithm for signals of continuous variables, and proves that the limit function of this iterative algorithm is an ideal high-pass filtering process.
642679
Representing Discovered Patterns Using Attributed Hypergraph
One of the fundamental problems in knowledge discovery in databases and other applications of AI is how to represent knowledge and patterns. Existing representation schemes have various shortcomings. In this paper, we propose a new knowledge representation scheme using attributed hypergraph (AHG), which is simple yet general enough to directly encode different order patterns discovered from large databases. In AHG, both the qualitative and quantitative relations are represented as attributed hyperedges. Such representation is lucid and transparent for visualization. Besides, patterns in AHG are easy to understand. In the discussion, some basic manipulations of AHG for data mining tasks are briefly addressed. The paper ends with examples of pattern representation using AHG.
18413233
Range-Free Localization Using Expected Hop Progress in Wireless Sensor Networks
Localization algorithm continues to be an important and challenging topic in today's wireless sensor networks (WSNs). In this paper, a novel range-free localization algorithm using expected hop progress (LAEP) to predict the location of any sensor in a WSN is proposed. This algorithm is based on an accurate analysis of hop progress in a WSN with randomly deployed sensors and arbitrary node density. By deriving the expected hop progress from a network model for WSNs in terms of network parameters, the distance between any pair of sensors can be accurately computed. Since the distance estimation is a key issue in localization systems for WSNs, the proposed range-free LAEP achieves better performance and less communication overhead as compared to some existent schemes like DV-Hop and RAW. In addition, we study the effect of anchor placement on the algorithm performance by deriving the corresponding mean position error range. Extensive simulations are performed and the results are observed to be in good agreement with the theoretical analysis.
14027651
Optimizing Model of Blasting Parameters Based on Fuzzy Neural Network
Because of the complexity and polytropism of rock and the complexity of blasting proceeding, it is very difficult to obtain better blasting parameters with a certain way. In order to gain perfect blasting effects expected by designers, blasting engineers have been studying the optimizing of blasting parameters all the time. The intelligent optimizing model of blasting parameters based on fuzzy neural network is set up in this paper. The input parameters of the model are rock properties and blasting requirements, and the outputs are the properties of explosive, blasting parameters, initiation means and charging structure. When a new set of parameters are input into the model trained by some successful examples, a good output will be gotten very easily. At last, the optimizing model is applied to a cement mine. From the application, a conclusion can be drawn that it is feasible and reliable to carry out blasting design with the optimizing model based on fuzzy neural network.