23 Result(s)
within
Chapter
**angbo Chen
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Chapter and Conference Paper
Comparison of Simplified SE-ResNet and SE-DenseNet for Micro-Expression Classification
Micro-expressions are rapid and subtle facial movements that can reflect the most real emotional state hidden in the human heart. Classifying different micro-expressions is still challenging because of their s...
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Chapter and Conference Paper
Chordality Preserving Incremental Triangular Decomposition and Its Implementation
In this paper, we first prove that the incremental algorithm for computing triangular decompositions proposed by Chen and Moreno Maza in ISSAC’ 2011 in its original form preserves chordality, which is an impo...
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Chapter and Conference Paper
Variable Ordering Selection for Cylindrical Algebraic Decomposition with Artificial Neural Networks
Cylindrical algebraic decomposition (CAD) is a fundamental tool in computational real algebraic geometry. Previous studies have shown that machine learning (ML) based approaches may outperform traditional heu...
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Chapter and Conference Paper
Revealing Bistability in Neurological Disorder Models By Solving Parametric Polynomial Systems Geometrically
Understanding the mechanisms of the brain is a common theme for both computational neuroscience and artificial intelligence. Machine learning technique, like artificial neural network, has been benefiting from...
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Chapter and Conference Paper
A Continuation Method for Visualizing Planar Real Algebraic Curves with Singularities
We present a new method for visualizing planar real algebraic curves inside a bounding box based on numerical continuation and critical point methods. Since the topology of the curve near a singular point is n...
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Chapter and Conference Paper
Penalty Function Based Critical Point Approach to Compute Real Witness Solution Points of Polynomial Systems
We present a critical point method based on a penalty function for finding certain solution (witness) points on real solutions components of general real polynomial systems. Unlike other existing numerical met...
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Chapter and Conference Paper
Full Rank Representation of Real Algebraic Sets and Applications
We introduce the notion of the full rank representation of a real algebraic set, which represents it as the projection of a union of real algebraic manifolds ...
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Chapter and Conference Paper
A Numerical Method for Computing Border Curves of Bi-parametric Real Polynomial Systems and Applications
For a bi-parametric real polynomial system with parameter values restricted to a finite rectangular region, under certain assumptions, we introduce the notion of border curve. We propose a numerical method to ...
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Chapter and Conference Paper
Regular Chains under Linear Changes of Coordinates and Applications
Given a regular chain, we are interested in questions like computing the limit points of its quasi-component, or equivalently, computing the variety of its saturated ideal. We propose techniques relying on lin...
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Chapter and Conference Paper
Simplification of Cylindrical Algebraic Formulas
For a set S of cells in a cylindrical algebraic decomposition of ℝ n , we introduce the notion of generalized cylindrical algebraic formula (GCAF) associated with S. We propose a...
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Chapter and Conference Paper
Solving Parametric Polynomial Systems by RealComprehensiveTriangularize
In the authors’ previous work, the concept of comprehensive triangular decomposition of parametric semi-algebraic systems (RCTD for short) was introduced. For a given parametric semi-algebraic system, say S, a...
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Chapter and Conference Paper
The Basic Polynomial Algebra Subprograms
The Basic Polynomial Algebra Subprograms (BPAS) provides arithmetic operations (multiplication, division, root isolation, etc.) for univariate and multivariate polynomials over prime fields or with integer coeffi...
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Chapter and Conference Paper
Cylindrical Algebraic Decomposition in the RegularChains Library
Cylindrical algebraic decomposition (CAD) is a fundamental tool in computational real algebraic geometry and has been implemented in several software. While existing implementations are all based on Collins’ p...
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Chapter and Conference Paper
Doing Algebraic Geometry with the RegularChains Library
Traditionally, Groebner bases and cylindrical algebraic decomposition are the fundamental tools of computational algebraic geometry. Recent progress in the theory of regular chains has exhibited efficient algo...
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Chapter and Conference Paper
Real Quantifier Elimination in the RegularChains Library
Quantifier elimination (QE) over real closed fields has found numerous applications. Cylindrical algebraic decomposition (CAD) is one of the main tools for handling quantifier elimination of nonlinear input fo...
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Chapter and Conference Paper
Truth Table Invariant Cylindrical Algebraic Decomposition by Regular Chains
A new algorithm to compute cylindrical algebraic decompositions (CADs) is presented, building on two recent advances. Firstly, the output is truth table invariant (a TTICAD) meaning given formulae have constan...
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Chapter and Conference Paper
Real Root Isolation of Regular Chains
We present an algorithm RealRootIsolate for isolating the real roots of a polynomial system given by a zerodimensional squarefree regular chain. The output of the algorithm is guaranteed in the sense that all rea...
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Chapter and Conference Paper
An Incremental Algorithm for Computing Cylindrical Algebraic Decompositions
In this paper, we propose an incremental algorithm for computing cylindrical algebraic decompositions. The algorithm consists of two parts: computing a complex cylindrical tree and refining this complex tree i...
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Chapter and Conference Paper
Problem Formulation for Truth-Table Invariant Cylindrical Algebraic Decomposition by Incremental Triangular Decomposition
Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advances: truth-table invariance, ...
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Chapter and Conference Paper
Computing the Limit Points of the Quasi-component of a Regular Chain in Dimension One
For a regular chain R in dimension one, we propose an algorithm which computes the (non-trivial) limit points of the quasi-component of R, that is, the set ...
