1536242
Substitution Delone Sets 

Abstract. Substitution Delone set families are families of Delone sets X =(X1, . . ., Xn) which satisfy the inflation functional equation
 X_i = \bigvee_{j=1}^m ( \mbox{\phvr A} (X_j) + {\cal D}_$ij$ ) , \qquad 1 \le i \le m, 
 in which A is an expanding matrix, i.e., all of the eigenvalues of A fall outside the unit circle. Here the Dij are finite sets of vectors in Rd and V denotes union that counts multiplicity. This paper characterizes families X=(X1, . . ., Xn) that satisfy an inflation functional equation, in which each Xi is a multiset (set with multiplicity) whose underlying set is discrete. It then studies the subclass of Delone set solutions, and gives necessary conditions on the coefficients of the inflation functional equation for such solutions X to exist. It relates Delone set solutions to a narrower subclass of solutions, called self-replicating multi-tiling sets, which arise as tiling sets for self-replicating multi-tilings.

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.
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.
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.
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.
14649490
Generation of finite tight frames by Householder transformations
Finite tight frames are widely used for many applications. An important problem is to construct finite frames with prescribed norm for each vector in the tight frame. In this paper we provide a fast and simple algorithm for such a purpose. Our algorithm employs the Householder transformations. For a finite tight frame consisting of m vectors in ℝn or ℂn only O(nm) operations are needed. In addition, we also study the following question: Given a set of vectors in ℝn or ℂn, how many additional vectors, possibly with constraints, does one need to add in order to obtain a tight frame?
1235699
High resolution tracking of non-rigid 3D motion of densely sampled data using harmonic maps
We present a novel fully automatic method for high resolution, nonrigid dense 3D point tracking. High quality dense point clouds of nonrigid geometry moving at video speeds are acquired using a phase-shifting structured light ranging technique. To use such data for the temporal study of subtle motions such as those seen in facial expressions, an efficient nonrigid 3D motion tracking algorithm is needed to establish inter-frame correspondences. The novelty of this paper is the development of an algorithmic framework for 3D tracking that unifies tracking of intensity and geometric features, using harmonic maps with added feature correspondence constraints. While the previous uses of harmonic maps provided only global alignment, the proposed introduction of interior feature constraints guarantees that nonrigid deformations are accurately tracked as well. The harmonic map between two topological disks is a diffeomorphism with minimal stretching energy and bounded angle distortion. The map is stable, insensitive to resolution changes and is robust to noise. Due to the strong implicit and explicit smoothness constraints imposed by the algorithm and the high-resolution data, the resulting registration/deformation field is smooth, continuous and gives dense one-to-one inter-frame correspondences. Our method is validated through a series of experiments demonstrating its accuracy and efficiency.
10246554
An Overview of Associative Classifiers
Associative classification is a new classification approach integrating association mining and classification. It becomes a significant tool for knowledge discovery and data mining. This paper presents a critical overview of certain aspects on modelling associative classifiers including event association mining, computational complexity in mining associations, methods of constructing associative classifiers based on the association patterns discovered, some similarities and differences among the reported associative classification systems, and experimental comparisons of these associative classifiers with the conventional classification system such as C4.5.
13987121
A Unified Framework for Segmentation-Assisted Image Registration
This paper presents a unified variational framework for seamlessly integrating prior segmentation information into non-rigid registration procedures. Under this framework, in addition to the forces arise from the similarity measure in seeking for detailed correspondence, another set of forces generated by the prior segmentation contours can provide an extra guidance in assisting the alignment process towards a more meaningful, stable and noise-tolerant procedure. Local correlation (LC) is being used as the underlying similarity measures to handle intensity variations. We present several 2D/3D examples on synthetic and real data.
21082976
Real-time machine learning in embedded software and hardware platforms
This paper describes on-going research work into real-time machine learning using embedded software and reconfigurable hardware. The main focus of the work is to develop real-time incremental learning methods particularly targeted at demonstration in mobile robot environments. Three main areas are described. The first represents reactive robot navigation knowledge using a novel frequency table technique whose memory requirement is known a priori. The second area investigates a Genetic Algorithm (GA) method that combines planning and reactive approaches to allow navigation to proceed even in the face of time constraints. In the third area we are developing novel hardware-based machine learning systems suitable for implementation in reconfigurable platforms.
17540624
Asymptotic White noise Hypothesis for PCM quantization
For a signal distributed in Rd with an arbitrary density we find the limit distribution as the cell size goes to zero of the quantization noise in the case of a redundant system and the pulse-code modulation scheme. The dimension the support of the limiting distribution equals the largest number of non-comeasurable vectors in the frame and the limit distribution is uniform over its support. This gives the necessary and sufficient conditions for the asymptotic form of the white noise hypothesis.