Discrete Curves in  and the Toda Lattice

Hoffmann, Tim; Kutz, Nadja

doi:10.1111/j.1467-9590.2004.01493.x

Cited by 21 publications

(20 citation statements)

References 17 publications

(38 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The CAROL system [81][82][83]59] reduces the search space of the alignment method with a local search strategy based on the extended history of the Delaunay Net. False matches are removed through consistency checks between subsets.…”

Section: Feature Based Methods (Spot Matching)mentioning

confidence: 99%

See 1 more Smart Citation

The role of bioinformatics in two‐dimensional gel electrophoresis

2003

View full text Add to dashboard Cite

Over the last two decades, two-dimensional electrophoresis (2-DE) gel has established itself as the de facto approach to separating proteins from cell and tissue samples. Due to the sheer volume of data and its experimental geometric and expression uncertainties, quantitative analysis of these data with image processing and modelling has become an actively pursued research topic. The results of these analyses include accurate protein quantification, isoelectric point and relative molecular mass estimation, and the detection of differential expression between samples run on different gels. Systematic errors such as current leakage and regional expression inhomogeneities are corrected for, followed by each protein spot in the gel being segmented and modelled for quantification. To assess differential expression of protein spots in different samples run on a series of two-dimensional gels, a number of image registration techniques for correcting geometric distortion have been proposed. This paper provides a comprehensive review of the computation techniques used in the analysis of 2-DE gels, together with a discussion of current and future trends in large scale analysis. We examine the pitfalls of existing techniques and highlight some of the key areas that need to be developed in the coming years, especially those related to statistical approaches based on multiple gel runs and image mining techniques through the use of parallel processing based on cluster computing and the grid technology.

show abstract

Section: Feature Based Methods (Spot Matching)mentioning

confidence: 99%

“…The alignment method is only used in the local matching phase as only rigid transformations can be accounted for [81]. The 12 points are annotated with a discrete intensity score between 0 and 10.…”

Section: Feature Based Methods (Spot Matching)mentioning

confidence: 99%

The role of bioinformatics in two‐dimensional gel electrophoresis

2003

View full text Add to dashboard Cite

show abstract

“…A more pedestrian approach based on local coordinate computations can be found in Refs. . Definition A discrete curve

γ : Z \to {double-struckR}^{2}, n \mapsto γ_{n} = false(x_{n}, u_{n} false)

is said to be regular if any three successive points

γ_{n - 1}

γ_{n}

γ_{n + 1}

are different for all

n \in Z

.…”

Section: Invariant Discrete Flowsmentioning

confidence: 99%

“…In Ref. , discrete curves flows in

C^{2}

C P^{1}

, and

double-struckC

were investigated and the differential‐difference mKdV was obtained as the evolution equation of the curvature under the arc length preserving tangent flow of discrete planar curves. Last, in Ref.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Invariant discrete flows

Benson

Valiquette

2019

Stud Appl Math

View full text Add to dashboard Cite

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group SE(2), the special linear group SL(2), and the semidirect group R⋉double-struckR2, we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.

show abstract

Synthesis of poly(glycerol methacrylate) and its application to dimensional stabilization of wood

Soulounganga¹,

Marion²,

Huber³

et al. 2003

J of Applied Polymer Sci

View full text Add to dashboard Cite

ABSTRACT:The dimensional stabilization of wood is investigated using poly(glycerol methacrylate) (PGMA) prepared from polyglycerol and glycidyl methacrylate instead of the well-known poly(ethylene glycol). PGMA allows waterborne treatment of wood, which after polymerization leads to the formation of a wood polymer composite with improved dimensional stability. Microscopic observations and a picture analysis permit the location of PGMA in the wood cell walls and explains the dimensional stabilization by its bulking effect.

show abstract

Discrete Curves in and the Toda Lattice

Abstract: In this paper, we investigate flows on discrete curves in C 2 , CP 1 , and C. A novel interpretation of the one-dimensional Toda lattice hierarchy and reductions thereof as flows on discrete curves are given.

Cited by 21 publications

References 17 publications

The role of bioinformatics in two‐dimensional gel electrophoresis

The role of bioinformatics in two‐dimensional gel electrophoresis

Invariant discrete flows

Synthesis of poly(glycerol methacrylate) and its application to dimensional stabilization of wood

Contact Info

Product

Resources

About