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Article
A technique to improve the empirical mode decomposition in the Hilbert-Huang transform
The Hilbert-based time-frequency analysis has promising capacity to reveal the time-variant behaviors of a system. To admit well-behaved Hilbert transforms, component decomposition of signals must be performed...
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Article
Pressure effects on the absorption spectra of Na doped in solid Ar
In this work, the pressure influence on the absorption spectra of Na in solid Ar for various trap** sites is extensively investigated atT=10 K and in the pressure range from 0 to 2.4 GPa by using Monte Carlo me...
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Chapter and Conference Paper
Efficient Computations of Irredundant Triangular Decompositions with the RegularChains Library
We present new functionalities that we have added to the RegularChains library in Maple to efficiently compute irredundant triangular decompositions. We report on the implementation of different strategies. Our e...
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Chapter and Conference Paper
Comprehensive Triangular Decomposition
We introduce the concept of comprehensive triangular decomposition (CTD) for a parametric polynomial system F with coefficients in a field. In broad words, this is a finite partition of the the parameter space in...
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Article
On the verification of polynomial system solvers
We discuss the verification of mathematical software solving polynomial systems symbolically by way of triangular decomposition. Standard verification techniques are highly resource consuming and apply only to...
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Chapter and Conference Paper
Semi-algebraic Description of the Equilibria of Dynamical Systems
We study continuous dynamical systems defined by autonomous ordinary differential equations, themselves given by parametric rational functions. For such systems, we provide semi-algebraic descriptions of their...
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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.
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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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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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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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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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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...
