Physical Data Independence, Constraints and Optimization with Universal Plans

We present an optimization method and al gorithm designed for three objectives: physi cal data independence, semantic optimization, and generalized tableau minimization. The method relies on generalized forms of chase and backchase with constraints (dependen cies). By using dictionaries (finite functions) in physical schemas we can capture with con straints useful access structures such as indexes, materialized views, source capabilities, access support relations, gmaps, etc. The search space for query plans is defined and enumerated in a novel manner: the chase phase rewrites the original query into a universal plan that integrates all the access structures and alternative pathways that are allowed by appli cable constraints. Then, the backchase phase produces optimal plans by eliminating various combinations of redundancies, again according to constraints. This method is applicable (sound) to a large class of queries, physical access structures, and semantic constraints. We prove that it is in fact complete for path-conjunctive queries and views with complex objects, classes and dictio naries, going beyond previous theoretical work on processing queries using materialized views

Graphical Interaction Models for Multivariate Time Series

In this paper we extend the concept of graphical models for multivariate data to multivariate time series. We define a partial correlation graph for time series and use the partial spectral coherence between two components given the remaining components to identify the edges of the graph. As an example we consider multivariate autoregressive processes. The method is applied to air pollution data

Higher-Order Statistics in Visual Object Recognition

In this paper, I develop a higher-order statistical theory of matching models against images. The basic idea is not only to take into account {\em how much} of an object can be seen in the image, but also {\em what parts} of it are jointly present. I show that this additional information can improve the specificity (i.e., reduce the probability of false positive matches) of a recognition algorithm. I demonstrate formally that most commonly used quality of match measures employed by recognition algorithms are based on an independence assumption. Using the Minimum Description Length (MDL) principle and a simple scene-description language as a guide, I show that this independence assumption is not satisfied for common scenes, and propose several important higher-order statistical properties of matches that approximate some aspects of these statistical dependencies. I have implemented a recognition system that takes advantage of this additional statistical information and demonstrate its efficacy in comparisons with a standard recognition system based on bounded error matching. We also observe that the existing use of grouping and segmentation methods has significant effects on the performance of recognition systems that are similar to those resulting from the use of higher-order statistical information. Our analysis provides a statistical framework in which to understand the effects of grouping and segmentation on recognition and suggests ways to take better advantage of such information

Learning Opportunities 1996/1997

MASTER LIST OF APPROVED COURSES - REVISED NOV 9

The independence polynomial of conjugate graph and noncommuting graph of groups of small order

An independent set of a graph is a set of pairwise non-adjacent vertices. The independence polynomial of a graph is defined as a polynomial in which the coefficient is the number of the independent set in the graph. Meanwhile, a graph of a group G is called conjugate graph if the vertices are non-central elements of G and two distinct vertices are adjacent if they are conjugate. The noncommuting graph is defined as a graph whose vertex set is non-central elements in which two vertices are adjacent if and only if they do not commute. In this research, the independence polynomial of the conjugate graph and noncommuting graph are found for three nonabelian groups of order at most eight

Reconstructing Subgraph-Counting Graph Polynomials of Increasing Families of Graphs

A graph polynomial P (G, x) is called reconstructible if it is uniquely determined by the polynomials of the vertex deleted subgraphs of G for every graph G with at least three vertices. In this note it is shown that subgraph-counting graph polynomials of increasing families of graphs are reconstructible if and only if each graph from the corresponding defining family is reconstructible from its polynomial deck. In particular we prove that the cube polynomial is reconstructible. Other reconstructible polynomials are the clique, the path and the independence polynomial. Along the way two new characterizations of hypercubes are obtained