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Problem Formulation for Truth-Table Invariant Cylindrical Algebraic Decomposition by Incremental Triangular Decomposition [chapter]

Matthew England, Russell Bradford, Changbo Chen, James H. Davenport, Marc Moreno Maza, David Wilson
2014 Lecture Notes in Computer Science  
Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond.  ...  CAD construction by regular chains technology, where first a complex decomposition is constructed by refining a tree incrementally by constraint.  ...  Use Heuristic 3 for a mixed approach, for example if a low cell count is required but the problem size makes Heuristic 2 infeasible.  ... 
doi:10.1007/978-3-319-08434-3_5 fatcat:t7stb6nxiva4nj7rrqsebln54y

Choosing a Variable Ordering for Truth-Table Invariant Cylindrical Algebraic Decomposition by Incremental Triangular Decomposition [chapter]

Matthew England, Russell Bradford, James H. Davenport, David Wilson
2014 Lecture Notes in Computer Science  
Cylindrical algebraic decomposition (CAD) is a key tool for solving problems in real algebraic geometry and beyond.  ...  We consider the latest variant of this which builds the complex decomposition incrementally by polynomial and produces CADs on whose cells a sequence of formulae are truth-invariant.  ...  Acknowledgements This work was supported by EPSRC grant EP/J003247/1. RC-TTICAD was developed by Changbo Chen, Marc Moreno Maza and the present authors.  ... 
doi:10.1007/978-3-662-44199-2_68 fatcat:gj5u2g4osncwfp46e3er34plby

Truth Table Invariant Cylindrical Algebraic Decomposition by Regular Chains [chapter]

Russell Bradford, Changbo Chen, James H. Davenport, Matthew England, Marc Moreno Maza, David Wilson
2014 Lecture Notes in Computer Science  
Firstly, the output is truth table invariant (a TTICAD) meaning given formulae have constant truth value on each cell of the decomposition.  ...  Secondly, the computation uses regular chains theory to first build a cylindrical decomposition of complex space (CCD) incrementally by polynomial.  ...  Acknowledgements Supported by the CSTC (grant cstc2013jjys0002), the EPSRC (grant EP/J003247/1) and the NSFC (grant 11301524).  ... 
doi:10.1007/978-3-319-10515-4_4 fatcat:rev7pskrhbbvrhyms7td7crlie

Recent Advances in Real Geometric Reasoning [chapter]

James H. Davenport, Matthew England
2015 Lecture Notes in Computer Science  
the recent major advances in Collins method: such as an alternative approach based on passing via the complexes, and advances which come closer to "solving the question asked" rather than "solving all problems  ...  Acknowledgements This work was supported by the EPSRC (grant number EP/J003247/1). The  ...  Cylindrical Algebraic Decomposition by Projection and Lifting [Col75] constructs a sampled 2 Cylindrical Algebraic Decomposition (CAD) of R n which is sign-invariant for the p i , where these words are  ... 
doi:10.1007/978-3-319-21362-0_3 fatcat:kyr53ossuzccrcdffp5ipmucfa

Optimising Problem Formulation for Cylindrical Algebraic Decomposition [chapter]

Russell Bradford, James H. Davenport, Matthew England, David Wilson
2013 Lecture Notes in Computer Science  
This leads to new heuristics for choosing: the variable ordering for a CAD problem, a designated equational constraint, and formulations for truth-table invariant CADs (TTICADs).  ...  Cylindrical algebraic decomposition (CAD) is an important tool for the study of real algebraic geometry with many applications both within mathematics and elsewhere.  ...  Acknowledgements This work was supported by the EPSRC grant: EP/J003247/1.  ... 
doi:10.1007/978-3-642-39320-4_2 fatcat:aoyt7b6jn5eb5mtobsrgn6tfve

Using the Distribution of Cells by Dimension in a Cylindrical Algebraic Decomposition

David Wilson, Matthew England, Russell Bradford, James H. Davenport
2014 2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing  
We investigate the distribution of cells by dimension in cylindrical algebraic decompositions (CADs).  ...  Since constructing only full-dimensional cells is relatively inexpensive (involving no costly algebraic number calculations) this leads to heuristics for helping with various questions of problem formulation  ...  ACKNOWLEDGEMENTS This work was supported by EPSRC grant: EP/J003247/1.  ... 
doi:10.1109/synasc.2014.15 dblp:conf/synasc/WilsonEBD14 fatcat:euhwsbmfnnb7lltm3kbops7xgu

Cylindrical Algebraic Sub-Decompositions

D. J. Wilson, R. J. Bradford, J. H. Davenport, M. England
2014 Mathematics in Computer Science  
In this paper we introduce cylindrical algebraic sub-decompositions (sub-CADs), which are subsets of CADs containing all the information needed to specify a solution for a given problem.  ...  Cylindrical algebraic decompositions (CADs) are a key tool in real algebraic geometry, used primarily for eliminating quantifiers over the reals and studying semi-algebraic sets.  ...  Acknowledgements This work was supported by the EPSRC grant: EP/J003247/1.  ... 
doi:10.1007/s11786-014-0191-z fatcat:ju3yinoah5giplhwdkkwucyr54

Cylindrical algebraic decompositions for boolean combinations

Russell Bradford, James H. Davenport, Matthew England, Scott McCallum, David Wilson
2013 Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation - ISSAC '13  
This motivates our definition of a Truth Table Invariant CAD (TTICAD).  ...  This article makes the key observation that when using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is not always the signs of those polynomials  ...  This work was supported by the EPSRC grant: EP/J003247/1.  ... 
doi:10.1145/2465506.2465516 dblp:conf/issac/BradfordDEMW13 fatcat:zhezrhqv5retdml2xllhwy4ihi

Truth table invariant cylindrical algebraic decomposition

Russell Bradford, James H. Davenport, Matthew England, Scott McCallum, David Wilson
2016 Journal of symbolic computation  
When using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is likely not the signs of those polynomials that are of paramount importance but rather  ...  This observation motivates our article and definition of a Truth Table Invariant CAD (TTICAD).  ...  We also thank the rest of the Triangular Sets seminar at Bath (A. Locatelli, G. Sankaran and N. Vorobjov) for their  ... 
doi:10.1016/j.jsc.2015.11.002 fatcat:ugizbf4sz5cjdgq5hmoglztfyy

On Incremental Structure-from-Motion using Lines [article]

André Mateus, Omar Tahri, A. Pedro Aguiar, Pedro U. Lima, Pedro Miraldo
2021 arXiv   pre-print
We start by presenting a model that uses spherical coordinates for representing the line's moment vector.  ...  In this paper, we present solutions for SfM using lines, namely, incremental SfM. These approaches consist of designing state observers for a camera's dynamical visual system looking at a 3D line.  ...  of an innovative, autonomous mobile robot for retail stores".  ... 
arXiv:2105.11196v1 fatcat:hxwkeginzfekpd2ryehwbcuria

The annual meeting in Pittsburgh

R. D. Schafer, J. W. Green
1955 Bulletin of the American Mathematical Society  
The necessity of the modular law may be shown by applying the theorem to a triangular circuit.  ...  By Schur's Lemma we need only consider triangular matrices. For such we give nasc. that CÇzQ n for arbitrary n in terms of a quadratic form associated with C. (Received November 12, 1954.) 197. E.  ... 
doi:10.1090/s0002-9904-1955-09897-5 fatcat:fgaeb7kifnd3tndgo7eecdeoju

Learning Equivariant Representations [article]

Carlos Esteves
2020 arXiv   pre-print
We propose equivariant models for different transformations defined by groups of symmetries.  ...  By sliding a filter over the input, when the input shifts, the response shifts by the same amount, exploiting the structure of natural images where semantic content is independent of absolute pixel positions  ...  and incrementally steering for the remaining subgroups.  ... 
arXiv:2012.02771v1 fatcat:al6pkept5nhupgrvqwkhxycyne

Geometrodynamics: Spacetime or Space ? [article]

E. Anderson
2004 arXiv   pre-print
B) GR Initial value problem (IVP) methods, the badness of timelike splits of the EFE's and studying braneworlds under guidance from GR IVP and Cauchy problem methods.  ...  In our view a good way of achieving this is via the (n, 0) IVP, followed where possible by the heavily-protected (n, 0; -1) CP.  ...  3 (n, 0; -1) methods with thin matter sheets 3 .1 Hierarchy of problems and their difficulties We are here concerned with the study of (n + 1)-d GR models with thin matter sheets using only well-studied  ... 
arXiv:gr-qc/0409123v1 fatcat:33iyppdpajephmxepkuewq2mvi

Modeling of Ground Excavation with the Particle Finite-Element Method

Josep Maria Carbonell, Eugenio Oñate, Benjamín Suárez
2010 Journal of engineering mechanics  
The formulation provides a foundation in the updated lagrangian formulation for solids. The dynamic problem is integrated using an implicit scheme.  ...  PFEM is presented as a very suitable tool for the treatment of excavation problem. The method gives solution for the analysis of all processes that derive from it.  ...  For the formulation of the boundary value problem a solid with a rigid surface is considered.  ... 
doi:10.1061/(asce)em.1943-7889.0000086 fatcat:ftiaghzppjbrpi6lhrnfiipfjm

Cognitive Constructivism and the Epistemic Significance of Sharp Statistical Hypotheses in Natural Sciences [article]

J.M. Stern
2020 arXiv   pre-print
The basic metaphor presented in this text, as a foundation for cognitive constructivism, is that of an eigen-solution, and the verification of its objective epistemic status.  ...  We believe that this alternative perspective, complementary to the one ofered by decision theory, can provide powerful insights and make pertinent contributions in the context of scientific research.  ...  High level decomposition strategies replace the original large or complex problem by several hierarchically interconnected small or simple optimization problems, see for example Geoffrion (1972 ), Lasdon  ... 
arXiv:1006.5471v8 fatcat:v375ybolz5bkbe6ordmjnnulhi
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