scholarly journals PROTEIN STRUCTURE–STRUCTURE ALIGNMENT WITH DISCRETE FRÉCHET DISTANCE

2008 ◽  
Vol 06 (01) ◽  
pp. 51-64 ◽  
Author(s):  
MINGHUI JIANG ◽  
YING XU ◽  
BINHAI ZHU
Keyword(s):  
Protein Structure ◽  
Structure Prediction ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Distance Measures ◽  
Structure Alignment ◽  
Fréchet Distance ◽  
Frechet Distance ◽  
Polygonal Chains

Matching two geometric objects in two-dimensional (2D) and three-dimensional (3D) spaces is a central problem in computer vision, pattern recognition, and protein structure prediction. In particular, the problem of aligning two polygonal chains under translation and rotation to minimize their distance has been studied using various distance measures. It is well known that the Hausdorff distance is useful for matching two point sets, and that the Fréchet distance is a superior measure for matching two polygonal chains. The discrete Fréchet distance closely approximates the (continuous) Fréchet distance, and is a natural measure for the geometric similarity of the folded 3D structures of biomolecules such as proteins. In this paper, we present new algorithms for matching two polygonal chains in two dimensions to minimize their discrete Fréchet distance under translation and rotation, and an effective heuristic for matching two polygonal chains in three dimensions. We also describe our empirical results on the application of the discrete Fréchet distance to protein structure–structure alignment.

Algorithmic Aspects of Protein Threading

2011 ◽  
pp. 605-619
Author(s):  
Tatsuya Akutsu
Keyword(s):  
Protein Structure ◽  
Protein Structure Prediction ◽  
Structure Prediction ◽  
Three Dimensional ◽  
Structure Alignment ◽  
Protein Structure Alignment ◽  
Amino Acid Residues ◽  
Optimal Solutions ◽  
Score Functions ◽  
Protein Threading

This chapter provides an overview of computational problems and techniques for protein threading. Protein threading is one of the most powerful approaches to protein structure prediction, where protein structure prediction is to infer three-dimensional (3-D) protein structure for a given protein sequence. Protein threading can be modeled as an optimization problem. Optimal solutions can be obtained in polynomial time using simple dynamic programming algorithms if profile type score functions are employed. However, this problem is computationally hard (NP-hard) if score functions include pairwise interaction preferences between amino acid residues. Therefore, various algorithms have been developed for finding optimal or near-optimal solutions. This chapter explains the ideas employed in these algorithms. This chapter also gives brief explanations of related problems: protein threading with constraints, comparison of RNA secondary structures and protein structure alignment.

Algorithmic Aspects of Protein Threading

2011 ◽  
pp. 118-135
Author(s):  
Tatsuya Akutsu
Keyword(s):  
Protein Structure ◽  
Protein Structure Prediction ◽  
Structure Prediction ◽  
Three Dimensional ◽  
Structure Alignment ◽  
Protein Structure Alignment ◽  
Amino Acid Residues ◽  
Optimal Solutions ◽  
Score Functions ◽  
Protein Threading

This chapter provides an overview of computational problems and techniques for protein threading. Protein threading is one of the most powerful approaches to protein structure prediction, where protein structure prediction is to infer three-dimensional (3-D) protein structure for a given protein sequence. Protein threading can be modeled as an optimization problem. Optimal solutions can be obtained in polynomial time using simple dynamic programming algorithms if profile type score functions are employed. However, this problem is computationally hard (NP-hard) if score functions include pairwise interaction preferences between amino acid residues. Therefore, various algorithms have been developed for finding optimal or near-optimal solutions. This chapter explains the ideas employed in these algorithms. This chapter also gives brief explanations of related problems: protein threading with constraints, comparison of RNA secondary structures and protein structure alignment.

scholarly journals VORONOI DIAGRAM OF POLYGONAL CHAINS UNDER THE DISCRETE FRÉCHET DISTANCE

2010 ◽  
Vol 20 (04) ◽  
pp. 471-484
Author(s):  
SERGEY BEREG ◽  
KEVIN BUCHIN ◽  
MAIKE BUCHIN ◽  
MARINA GAVRILOVA ◽  
BINHAI ZHU
Keyword(s):  
Pattern Recognition ◽  
Voronoi Diagram ◽  
Combinatorial Complexity ◽  
Structure Alignment ◽  
Protein Structure Alignment ◽  
Fréchet Distance ◽  
Fundamental Properties ◽  
Frechet Distance ◽  
Polygonal Chains ◽  
First Time

Polygonal chains are fundamental objects in many applications like pattern recognition and protein structure alignment. A well-known measure to characterize the similarity of two polygonal chains is the (continuous/discrete) Fréchet distance. In this paper, for the first time, we consider the Voronoi diagram of polygonal chains in d-dimension under the discrete Fréchet distance. Given a set [Formula: see text] of n polygonal chains in d-dimension, each with at most k vertices, we prove fundamental properties of such a Voronoi diagram [Formula: see text]. Our main results are summarized as follows. • The combinatorial complexity of [Formula: see text] is at most O(ndk+∊). • The combinatorial complexity of [Formula: see text] is at least Ω(ndk) for dimension d = 1, 2; and Ω(nd(k-1)+2) for dimension d > 2.

Algorithmic Aspects of Protein Threading

2008 ◽  
pp. 103-118
Author(s):  
Tatsuya Akutsu
Keyword(s):  
Protein Structure ◽  
Protein Structure Prediction ◽  
Structure Prediction ◽  
Three Dimensional ◽  
Structure Alignment ◽  
Protein Structure Alignment ◽  
Amino Acid Residues ◽  
Optimal Solutions ◽  
Score Functions ◽  
Protein Threading

This chapter provides an overview of computational problems and techniques for protein threading. Protein threading is one of the most powerful approaches to protein structure prediction, where protein structure prediction is to infer three-dimensional (3-D) protein structure for a given protein sequence. Protein threading can be modeled as an optimization problem. Optimal solutions can be obtained in polynomial time using simple dynamic programming algorithms if profile type score functions are employed. However, this problem is computationally hard (NP-hard) if score functions include pairwise interaction preferences between amino acid residues. Therefore, various algorithms have been developed for finding optimal or near-optimal solutions. This chapter explains the ideas employed in these algorithms. This chapter also gives brief explanations of related problems: protein threading with constraints, comparison of RNA secondary structures and protein structure alignment.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates

2012 ◽  
Vol 696 ◽  
pp. 228-262 ◽  
Author(s):  
A. Kourmatzis ◽  
J. S. Shrimpton
Keyword(s):  
Spatial Data ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Energy Budgets ◽  
Turbulent Regime ◽  
Scalar Flux ◽  
Wide Range ◽  
Scalar Variance

AbstractThe fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (${\mathit{Re}}_{E} = 1$) and high electric Reynolds numbers (up to ${\mathit{Re}}_{E} = 120$). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field ${ E}_{i}^{\ensuremath{\prime} } $ in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that ${ E}_{i}^{\ensuremath{\prime} } $ is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.

scholarly journals On the forces that cable webs under tension can support and how to design cable webs to channel stresses

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180781 ◽  
Author(s):  
Guy Bouchitté ◽  
Ornella Mattei ◽  
Graeme W. Milton ◽  
Pierre Seppecher
Keyword(s):  
Linear Programming ◽  
Convex Hull ◽  
Structural Engineering ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Finite Dimensional ◽  
Necessary And Sufficient

In many applications of structural engineering, the following question arises: given a set of forces f 1 ,  f 2 , …,  f N applied at prescribed points x 1 ,  x 2 , …,  x N , under what constraints on the forces does there exist a truss structure (or wire web) with all elements under tension that supports these forces? Here we provide answer to such a question for any configuration of the terminal points x 1 ,  x 2 , …,  x N in the two- and three-dimensional cases. Specifically, the existence of a web is guaranteed by a necessary and sufficient condition on the loading which corresponds to a finite dimensional linear programming problem. In two dimensions, we show that any such web can be replaced by one in which there are at most P elementary loops, where elementary means that the loop cannot be subdivided into subloops, and where P is the number of forces f 1 ,  f 2 , …,  f N applied at points strictly within the convex hull of x 1 ,  x 2 , …,  x N . In three dimensions, we show that, by slightly perturbing f 1 ,  f 2 , …,  f N , there exists a uniloadable web supporting this loading. Uniloadable means it supports this loading and all positive multiples of it, but not any other loading. Uniloadable webs provide a mechanism for channelling stress in desired ways.

APL: An angle probability list to improve knowledge-based metaheuristics for the three-dimensional protein structure prediction

2015 ◽  
Vol 59 ◽  
pp. 142-157 ◽  
Author(s):  
Bruno Borguesan ◽  
Mariel Barbachan e Silva ◽  
Bruno Grisci ◽  
Mario Inostroza-Ponta ◽  
Márcio Dorn
Keyword(s):  
Protein Structure ◽  
Protein Structure Prediction ◽  
Structure Prediction ◽  
Three Dimensional ◽  
Knowledge Based

Simplifying 3D Polygonal Chains Under the Discrete Fréchet Distance

2008 ◽  
pp. 630-641 ◽  
Author(s):  
Sergey Bereg ◽  
Minghui Jiang ◽  
Wencheng Wang ◽  
Boting Yang ◽  
Binhai Zhu
Keyword(s):  
Fréchet Distance ◽  
Frechet Distance ◽  
Polygonal Chains
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