The Internet Archive has a preservation copy of this work in our general collections.
The file type is `application/pdf`

.

## Filters

##
###
3D shape matching and Teichmüller spaces of pointed Riemann surfaces
[article]

2011
*
arXiv
*
pre-print

*geometry*. ... Shape matching represents a challenging problem in both information engineering and

*computer*science, exhibiting not only a wide spectrum of multimedia applications, but also a deep relation with conformal ... hyperbolic pants

*decomposition*. (4)

*Compute*the Fenchel-Nielsen coordinates. ...

##
###
Preface

2012
*
Journal of symbolic computation
*

There were 70 oral and poster presentations on recent advances in symbolic

doi:10.1016/j.jsc.2011.12.020
fatcat:b32i5tp2bfdpld5v2arslnac64
*computation*, automated reasoning,*computational*topology, and the history of mathematics, among which the following twenty four ... Triangular*Decomposition*of Polynomial Systems: Algorithmic Advances and Remaining Challenges. Dongming Wang. On the Mechanization of*Geometry*: From*Theorem*Proving to Knowledge Management. ...*Theorem*Proving in*Geometry*and Tools for Polynomial System Solving. • Bang-He Li. A Method for Solving Algebraic Equations up to Multiplicities*via*the Ritt-Wu Characteristic Sets. • Hongbo Li. ...##
###
Numerical Local Irreducible Decomposition
[chapter]

2016
*
Lecture Notes in Computer Science
*

Using numerical algebraic

doi:10.1007/978-3-319-32859-1_9
fatcat:cqjc4cqa7jgfrogaq6se7clknq
*geometry*, each irreducible component is represented using a witness set thereby yielding a numerical irreducible*decomposition*of the solution set. ... We define local witness sets and describe a numerical algebraic geometric approach for*computing*a numerical local irreducible*decomposition*for polynomial systems. Several examples are presented. ... The local*parameterization**theorem*is a local version of the Noether Normalization*Theorem*. ...##
###
Geometric Compression Using Riemann Surface Structure

2003
*
Communications in Information and Systems
*

First we

doi:10.4310/cis.2003.v3.n3.a2
fatcat:fkloh43245ervp7gsnv34oed7y
*compute*a global conformal*parameterization*of the surface. ... We present the proofs of the*theorems*and the compression examples. ... The number of zero points is*computed*using Riemann-Roch*theorem*. The*decomposition*structure can be proved using circle-valued Morse*theorem*. Previous Work. ...##
###
Parameterized Complexity of PCA (Invited Talk)

2020
*
Scandinavian Workshop on Algorithm Theory
*

We discuss some recent progress in the study of Principal Component Analysis (PCA) from the perspective of

doi:10.4230/lipics.swat.2020.1
dblp:conf/swat/FominGS20
fatcat:xpthkgfjwnhwvchic4phtdzvdm
*Parameterized*Complexity. ... By the Eckart-Young*theorem*[10] , PCA is efficiently solvable*via*Singular Value*Decomposition*(SVD). ... The proof of the*theorem*requires ideas from kernelization, linear algebra and algebraic*geometry*. Thus Robust PCA is fixed-parameter tractable when*parameterized*by k + d. ...##
###
Rotation Invariant Householder Parameterization for Bayesian PCA
[article]

2019
*
arXiv
*
pre-print

In particular, we avoid the need to

arXiv:1905.04720v1
fatcat:b5qmwoh6anhhbirmwmglqpvtaq
*compute*the Jacobian determinant of the parameter transformation. ... Here, we propose a*parameterization*based on Householder transformations, which remove the rotational symmetry of the posterior. ... be employed at different points. removed*via*singular value*decomposition*(SVD). ...##
###
Decomposing Solution Sets of Polynomial Systems Using Derivatives
[chapter]

2016
*
Lecture Notes in Computer Science
*

A core

doi:10.1007/978-3-319-42432-3_16
fatcat:eugxstgp4bf6nklwk4ia53oeta
*computation*in numerical algebraic*geometry*is the*decomposition*of the solution set of a system of polynomial equations into irreducible components, called the numerical irreducible*decomposition*... We present a new approach which replaces path tracking with local*computations*involving derivatives, called a "local trace test." ... In numerical algebraic*geometry*, irreducible components are represented*via*a witness set with a numerical irreducible*decomposition*consisting of a witness set for each irreducible component. ...##
###
Parameterized Fine-Grained Reductions
[article]

2019
*
arXiv
*
pre-print

During recent years the field of fine-grained complexity has bloomed to produce a plethora of results, with both applied and theoretical impact on the

arXiv:1902.05529v1
fatcat:b2migtkxfvgajevtpkja7az75q
*computer*science community. ... We provide a*parameterized*viewpoint of these reductions (PFGR) in order to further analyze the structure of improvable problems and set the foundations of a unified methodology for extending algorithmic ...*Geometry*). ...##
###
Computational information geometry: theory and practice
[article]

2012
*
arXiv
*
pre-print

In so doing, it extends information

arXiv:1209.1988v1
fatcat:y47sva2hyvdzbmlgjt7nzaolqu
*geometry*from a manifold based approach to one where the simplex is the fundamental geometrical object, thereby allowing applications to models which do not have a fixed ... Finally, it starts to build a*computational*framework which will act as a proxy for the 'space of all distributions' that can be used, in particular, to investigate model selection and model uncertainty ... The*decomposition*presented in part (b) of the*theorem*shows that these subsets are, in fact, contained in -1-affine subspaces.*Theorem*2.1. ...##
###
On the treewidth of triangulated 3-manifolds

2019
*
Journal of Computational Geometry
*

such as pathwidth or treewidth for graphs, or the concept of thin position for 3-manifolds, play an important role when studying algorithmic problems; in particular, there is a variety of problems in

doi:10.20382/jogc.v10i2a5
dblp:journals/jocg/HuszarSW19
fatcat:fxkmg2nkkbewvepedijgdr3rwi
*computational*... topology of a 3-manifold M on the one hand and width-type parameters of the dual graphs of triangulations of M on the other hand, answering a question that had been raised repeatedly by researchers in*computational*... We are grateful to Arnaud de Mesmay and Saul Schleimer for noticing a gap in an earlier proof of*Theorem*4 and for pointing us towards key ingredients of the current proof. ...##
###
Computational Information Geometry in Statistics: Foundations
[chapter]

2013
*
Lecture Notes in Computer Science
*

*Computational*information

*geometry*explicitly uses the information

*geometry*of ∆ k to numerically

*compute*statistically important features of M. ... For more details of the

*geometry*of the observed face see the paper [3] .

*Theorem*3. ...

##
###
Multivariate Analysis of Orthogonal Range Searching and Graph Distances

2019
*
International Symposium on Parameterized and Exact Computation
*

ACM Subject Classification Theory of

doi:10.4230/lipics.ipec.2018.4
dblp:conf/iwpec/BringmannHM18
fatcat:xx3ermqaqfho7d7k2ndpmcvydm
*computation*→ Shortest paths, Theory of*computation*→*Parameterized*complexity and exact algorithms, Theory of*computation*→*Computational**geometry*, Mathematics of ... We also investigate the same problems*parameterized*by vertex cover number:*Theorem*4. ... the dependency on k as well as the time required for*computing*a tree*decomposition*. ...##
###
Book Review: Toric varieties

2013
*
Bulletin of the American Mathematical Society
*

This second notion of a toric variety

doi:10.1090/s0273-0979-2013-01441-1
fatcat:duzkjpdybzgclisic6xttl5rvm
*via*monomial*parameterization*is distinct from the first notion of toric varieties associated to fans in Z n . ... For example, consider the following*decomposition*of the 3 × 3 square in Z 2 . ...##
###
Floor decompositions of tropical curves : the planar case
[article]

2019
*
arXiv
*
pre-print

We give here detailed proofs in the tropical

arXiv:0812.3354v3
fatcat:akbk5hnrafejdlunmkndtiuslq
*geometry*framework, in the case when the ambient variety is a complex surface, and give some examples of*computations*using floor diagrams. ... In a previous paper, we announced a formula to*compute*Gromov-Witten and Welschinger invariants of some toric varieties, in terms of combinatorial objects called floor diagrams. ... This paper is devoted to explain how floor diagrams can be used to*compute*the numbers N (∆, g) and W (∆, r) (*Theorems*3.6 and 3.9), and to give some examples of concrete*computations*(section 6). ...##
###
Parametric shortest-path algorithms via tropical geometry
[article]

2021
*
arXiv
*
pre-print

We study

arXiv:1904.01082v4
fatcat:mwt4xy4dkfd6lcmao7mf4hmun4
*parameterized*versions of classical algorithms for*computing*shortest-path trees. This is most easily expressed in terms of tropical*geometry*. ... With the same conditions as in*Theorem*4, and if k is considered a fixed constant, all*parameterized*shortest paths can be*computed*in O(n 3 ) time, if they exist. Remark 6. ... Floyd and Warshall's algorithm reduces the complexity of*computing*D * to O(n 3 )*via*dynamic programming. ...
« Previous

*Showing results 1 — 15 out of 15,876 results*