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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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Article
Open AccessBell’s Nonlocality Can be Detected by the Violation of Einstein-Podolsky-Rosen Steering Inequality
Recently quantum nonlocality has been classified into three distinct types: quantum entanglement, Einstein-Podolsky-Rosen steering, and Bell’s nonlocality. Among which, Bell’s nonlocality is the strongest type...
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Article
Diverse bacterial symbionts of insect-pathogentic fungi and possible impact on the maintenance of virulence during infection
Bacterial-fungal interactions (BFIs) which have important ramifications for the biology of the interacting partners have been demonstrated extensively. Here we show for the first time that diverse bacterial sy...
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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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Article
Open AccessMiscibility and ordered structures of MgO-ZnO alloys under high pressure
The MgxZn1−xO alloy system may provide an optically tunable family of wide band gap materials that can be used in various UV luminescences, absorption, lighting and display applications. A systematic investigatio...
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Article
Open AccessNitrogen concentration driving the hardness of rhenium nitrides
The structures and properties of rhenium nitrides are studied with density function based first principle method. New candidate ground states or high-pressure phases at Re:N ratios of 3:2, 1:3 and 1:4 are iden...
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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 ...
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Article
Hsp90 stress potentiates rapid cellular adaptation through induction of aneuploidy
Aneuploidy is shown to be induced by pleiotropic stress conditions (especially Hsp90 inhbition) in yeast, leading to stress adaptation.
