The factorization method, first developed by Tomasi and Kanade, recovers both the shape of an object and its motion from a sequence of images, using many images and tracking many feature points to obtain highly redundant feature position information. The method robustly processes the feature

This paper generalizes many-sorted algebra (hereafter, MSA) to order-sorted algebra (hereafter, OSA) by allowing a partial ordering relation on the set of sorts. This supports abstract data types with multiple inheritance (in roughly the sense of object-oriented programming), several forms

Abstract. Large numeric matrices and multidimensional data arrays appear in many science domains, as well as in applications of financial and business warehousing. Common applications include eigenvalue deter-mination of large matrices, which decompose into a set of linear algebra operations

The Turing degree spectrum of a countable structure A is the set of all Turing degrees of isomorphic copies of A. The Turing degree of the isomorphism type of A, if it exists, is the least Turing degree in its degree spectrum. We show that there are elements with isomorphism types of arbitrary Turing degrees in each of the following classes: countable fields, rings, and torsion-free Abelian groups of any finite rank. We also show that there are structures in each of these classes the isomorphism types of which do not have Turing degrees. The case of torsion-free Abelian groups of finite rank settles a question left open by Knight, Downey and Jockusch

Abstract. In the acyclic case, we establish a one-to-one correspondence between the tilting objects of the cluster category and the clusters of the associated cluster algebra. This correspondence enables us to solve conjectures on cluster algebras. We prove a multiplicativity theorem, a denominator

spatially inhomogeneous objects. We suppose that observations are contaminated by white noise and that the object is an unknown element of a Besov space. We prove that nonlinear WVD shrinkage can be tuned to attain the minimax rate of convergence, for L 2 loss, over the entire Besov scale. The important

This article describes a new approach to the unit testing of object-oriented programs, a set of tools based on this approach, and two case studies. In this approach, each test case consists of a tuple of sequences of messages, along with tags indicating whether these sequences should put objects

This is an introduction for algebraists to the theory of algebras and Hopf algebras in braided categories. Such objects generalise super-algebras and super-Hopf algebras, as well as colour-Lie algebras. Basic facts about braided categories C are recalled, the modules and comodules of Hopf algebras

This paper surveys our current state of knowledge (and ignorance) on the use of hidden sorted algebra as a foundation for the object paradigm. Our main goal is to support equational reasoning about properties of concurrent systems of objects, because of its simple and ecient mechanisation. We

, statistics, machine learning, control theory, and numerous other areas. The set of solutions to a system of polynomial equations is an algebraic variety, the basic object of algebraic geometry. The algorithmic study of algebraic varieties is the central theme of computational algebraic geometry. Exciting