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Article
Open AccessLunar Crater Identification in Digital Images
It is often necessary to identify a pattern of observed craters in a single image of the lunar surface and without any prior knowledge of the camera’s location. This so-called “lost-in-space” crater identifica...
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Article
Open AccessRobust segmentation of lung in chest x-ray: applications in analysis of acute respiratory distress syndrome
This study outlines an image processing algorithm for accurate and consistent lung segmentation in chest radiographs of critically ill adults and children typically obscured by medical equipment. In particular...
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Article
The Gaussian Moments Conjecture and the Jacobian Conjecture
We first propose what we call the Gaussian Moments Conjecture. We then show that the Jacobian Conjecture follows from the Gaussian Moments Conjecture. Note that the the Gaussian Moments Conjecture is a special...
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Article
On the Nuclear Norm and the Singular Value Decomposition of Tensors
Finding the rank of a tensor is a problem that has many applications. Unfortunately, it is often very difficult to determine the rank of a given tensor. Inspired by the heuristics of convex relaxation, we cons...
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Book
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Chapter
Constructive Ideal Theory
In this chapter we provide the basic algorithmic tools which will be used in later chapters. More precisely, we introduce some algorithms of constructive ideal theory, almost all of which are based on Gröbner ...
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Chapter
Invariant Theory of Finite Groups
The invariant theory of finite groups has enjoyed considerable recent interest, as the appearance of the books by Benson [1], Smith [2], Neusel and Smith [3] and Campbell and Wehlau [4] and of numerous article...
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Chapter
Applications of Invariant Theory
In this chapter we give a survey of some applications of invariant theory. The selection of topics is very incomplete, and so are certainly the references given for each topic. For example, we omit application...
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Chapter
Invariant Theory
For convenience, we will assume throughout this chapter that our base field K is algebraically closed, unless stated otherwise. Many results in this chapter remain true for arbitrary fields K as long as all relev...
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Chapter
Invariant Theory of Infinite Groups
Throughout this section G will be a linearly reductive group over an algebraically closed field K and V will be an n-dimensional rational representation. We will present an algorithm for computing generators of t...
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Article
Symmetric and quasi-symmetric functions associated to polymatroids
To every subspace arrangement X we will associate symmetric functions ℘[X] and ℋ[X]. These symmetric functions encode the Hilbert series and the minimal projective resolution of the product ideal associated to th...
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Article
Quivers with potentials and their representations I: Mutations
We study quivers with relations given by noncommutative analogs of Jacobian ideals in the complete path algebra. This framework allows us to give a representation-theoretic interpretation of quiver mutations a...
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Article
A Skolem–Mahler–Lech theorem in positive characteristic and finite automata
Lech proved in 1953 that the set of zeroes of a linear recurrence sequence in a field of characteristic 0 is the union of a finite set and finitely many infinite arithmetic progressions. This result is known a...
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Article
On the Canonical Decomposition of Quiver Representations
Kac introduced the notion of the canonical decomposition for a dimension vector of a quiver. Here we will give an efficient algorithm to compute the canonical decomposition. Our study of the canonical decompos...
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Book
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Chapter
Introduction
Invariant theory is a mathematical discipline with a long tradition, going back at least one hundred and fifty years. Sometimes its has blossomed, sometimes it has lain dormant. But through all phases of its e...
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Chapter
Linear Algebraic Groups
Let us fic an algebraically closed field K. We work in the category of affine varieties over K. The purpose of this section is to give a brief exposition on the basic facts of algebraic groups.
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Chapter
Invariant Theory
For convenience, we will assume throughout this chapter that our base field K is algebraically closed, unless stated otherwise. Many results in this chapter remain true for arbitrary fields K as long as all relev...
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Chapter
Invariant Theory of Reductive Groups
Throughout this section G will be a linearly reductive group over an algebraically closed field K and V will be an n-dimensional rational representation. We will present an algorithm for computing generators of t...
-
Chapter
Constructive Ideal Theory
In this chapter we will provide the basic algorithmic tools which will be used in later chapters. More precisely, we introduce some algorithms of constructive ideal theory, almost all of which are based on Grö...