Essential Constraints of Edge-Constrained Proximity Graphs

Given a plane forest $F = (V, E)$ of $|V| = n$ points, we find the minimum set $S \subseteq E$ of edges such that the edge-constrained minimum spanning tree over the set $V$ of vertices and the set $S$ of constraints contains $F$. We present an $O(n \log n )$-time algorithm that solves this problem. We generalize this to other proximity graphs in the constraint setting, such as the relative neighbourhood graph, Gabriel graph, $\beta$-skeleton and Delaunay triangulation. We present an algorithm that identifies the minimum set $S\subseteq E$ of edges of a given plane graph $I=(V,E)$ such that $I \subseteq CG_\beta(V, S)$ for $1 \leq \beta \leq 2$, where $CG_\beta(V, S)$ is the constraint $\beta$-skeleton over the set $V$ of vertices and the set $S$ of constraints. The running time of our algorithm is $O(n)$, provided that the constrained Delaunay triangulation of $I$ is given.Comment: 24 pages, 22 figures. A preliminary version of this paper appeared in the Proceedings of 27th International Workshop, IWOCA 2016, Helsinki, Finland. It was published by Springer in the Lecture Notes in Computer Science (LNCS) serie

Spanning Properties of Theta-Theta Graphs

We study the spanning properties of Theta-Theta graphs. Similar in spirit with the Yao-Yao graphs, Theta-Theta graphs partition the space around each vertex into a set of k cones, for some fixed integer k > 1, and select at most one edge per cone. The difference is in the way edges are selected. Yao-Yao graphs select an edge of minimum length, whereas Theta-Theta graphs select an edge of minimum orthogonal projection onto the cone bisector. It has been established that the Yao-Yao graphs with parameter k = 6k' have spanning ratio 11.67, for k' >= 6. In this paper we establish a first spanning ratio of $7.82$ for Theta-Theta graphs, for the same values of $k$. We also extend the class of Theta-Theta spanners with parameter 6k', and establish a spanning ratio of $16.76$ for k' >= 5. We surmise that these stronger results are mainly due to a tighter analysis in this paper, rather than Theta-Theta being superior to Yao-Yao as a spanner. We also show that the spanning ratio of Theta-Theta graphs decreases to 4.64 as k' increases to 8. These are the first results on the spanning properties of Theta-Theta graphs.Comment: 20 pages, 6 figures, 3 table

Gabriel Triangulations and Angle-Monotone Graphs: Local Routing and Recognition

A geometric graph is angle-monotone if every pair of vertices has a path between them that---after some rotation---is $x$- and $y$-monotone. Angle-monotone graphs are $\sqrt 2$-spanners and they are increasing-chord graphs. Dehkordi, Frati, and Gudmundsson introduced angle-monotone graphs in 2014 and proved that Gabriel triangulations are angle-monotone graphs. We give a polynomial time algorithm to recognize angle-monotone geometric graphs. We prove that every point set has a plane geometric graph that is generalized angle-monotone---specifically, we prove that the half-$\theta_6$-graph is generalized angle-monotone. We give a local routing algorithm for Gabriel triangulations that finds a path from any vertex $s$ to any vertex $t$ whose length is within $1 + \sqrt 2$ times the Euclidean distance from $s$ to $t$. Finally, we prove some lower bounds and limits on local routing algorithms on Gabriel triangulations.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Use of intravitreal bevacizumab in a patient with a Von Hippel-Lindau-associated retinal haemangioblastoma of the optic nerve head: a case report

<p>Abstract</p> <p>Introduction</p> <p>The optimum management of a capillary haemangioblastoma affecting the optic nerve head is not clear. A number of treatment modalities have been used to treat the tumours and their consequences. Ocular haemangioblastomas express high levels of vascular endothelial growth factor and levels have been correlated with tumour growth and activity. Treatment with vascular endothelial growth factor inhibitors would therefore seem a logical approach.</p> <p>Case presentation</p> <p>We describe a 23-year-old man with an exophytic capillary haemangioblastoma of the optic nerve head that was treated with intravitreal bevacizumab injections.</p> <p>Conclusion</p> <p>Unfortunately, treatment with intravitreal bevacizumab on three occasions had no effect on either tumour size or exudation in this patient.</p

An optimized TOPS+ comparison method for enhanced TOPS models

This article has been made available through the Brunel Open Access Publishing Fund.Background Although methods based on highly abstract descriptions of protein structures, such as VAST and TOPS, can perform very fast protein structure comparison, the results can lack a high degree of biological significance. Previously we have discussed the basic mechanisms of our novel method for structure comparison based on our TOPS+ model (Topological descriptions of Protein Structures Enhanced with Ligand Information). In this paper we show how these results can be significantly improved using parameter optimization, and we call the resulting optimised TOPS+ method as advanced TOPS+ comparison method i.e. advTOPS+. Results We have developed a TOPS+ string model as an improvement to the TOPS [1-3] graph model by considering loops as secondary structure elements (SSEs) in addition to helices and strands, representing ligands as first class objects, and describing interactions between SSEs, and SSEs and ligands, by incoming and outgoing arcs, annotating SSEs with the interaction direction and type. Benchmarking results of an all-against-all pairwise comparison using a large dataset of 2,620 non-redundant structures from the PDB40 dataset [4] demonstrate the biological significance, in terms of SCOP classification at the superfamily level, of our TOPS+ comparison method. Conclusions Our advanced TOPS+ comparison shows better performance on the PDB40 dataset [4] compared to our basic TOPS+ method, giving 90 percent accuracy for SCOP alpha+beta; a 6 percent increase in accuracy compared to the TOPS and basic TOPS+ methods. It also outperforms the TOPS, basic TOPS+ and SSAP comparison methods on the Chew-Kedem dataset [5], achieving 98 percent accuracy. Software Availability: The TOPS+ comparison server is available at http://balabio.dcs.gla.ac.uk/mallika/WebTOPS/.This article is available through the Brunel Open Access Publishing Fun

Gliders2d: Source Code Base for RoboCup 2D Soccer Simulation League

We describe Gliders2d, a base code release for Gliders, a soccer simulation team which won the RoboCup Soccer 2D Simulation League in 2016. We trace six evolutionary steps, each of which is encapsulated in a sequential change of the released code, from v1.1 to v1.6, starting from agent2d-3.1.1 (set as the baseline v1.0). These changes improve performance by adjusting the agents' stamina management, their pressing behaviour and the action-selection mechanism, as well as their positional choice in both attack and defense, and enabling riskier passes. The resultant behaviour, which is sufficiently generic to be applicable to physical robot teams, increases the players' mobility and achieves a better control of the field. The last presented version, Gliders2d-v1.6, approaches the strength of Gliders2013, and outperforms agent2d-3.1.1 by four goals per game on average. The sequential improvements demonstrate how the methodology of human-based evolutionary computation can markedly boost the overall performance with even a small number of controlled steps.Comment: 12 pages, 1 figure, Gliders2d code releas

Multiple structure alignment and consensus identification for proteins

<p>Abstract</p> <p>Background</p> <p>An algorithm is presented to compute a multiple structure alignment for a set of proteins and to generate a consensus (pseudo) protein which captures common substructures present in the given proteins. The algorithm represents each protein as a sequence of triples of coordinates of the alpha-carbon atoms along the backbone. It then computes iteratively a sequence of transformation matrices (i.e., translations and rotations) to align the proteins in space and generate the consensus. The algorithm is a heuristic in that it computes an approximation to the optimal alignment that minimizes the sum of the pairwise distances between the consensus and the transformed proteins.</p> <p>Results</p> <p>Experimental results show that the algorithm converges quite rapidly and generates consensus structures that are visually similar to the input proteins. A comparison with other coordinate-based alignment algorithms (MAMMOTH and MATT) shows that the proposed algorithm is competitive in terms of speed and the sizes of the conserved regions discovered in an extensive benchmark dataset derived from the HOMSTRAD and SABmark databases.</p> <p>The algorithm has been implemented in C++ and can be downloaded from the project's web page. Alternatively, the algorithm can be used via a web server which makes it possible to align protein structures by uploading files from local disk or by downloading protein data from the RCSB Protein Data Bank.</p> <p>Conclusions</p> <p>An algorithm is presented to compute a multiple structure alignment for a set of proteins, together with their consensus structure. Experimental results show its effectiveness in terms of the quality of the alignment and computational cost.</p

An enhanced partial order curve comparison algorithm and its application to analyzing protein folding trajectories

<p>Abstract</p> <p>Background</p> <p>Understanding how proteins fold is essential to our quest in discovering how life works at the molecular level. Current computation power enables researchers to produce a huge amount of folding simulation data. Hence there is a pressing need to be able to interpret and identify novel folding features from them.</p> <p>Results</p> <p>In this paper, we model each folding trajectory as a multi-dimensional curve. We then develop an effective multiple curve comparison (MCC) algorithm, called the <it>enhanced partial order (EPO) </it>algorithm, to extract features from a set of diverse folding trajectories, including both successful and unsuccessful simulation runs. The EPO algorithm addresses several new challenges presented by comparing high dimensional curves coming from folding trajectories. A detailed case study on miniprotein Trp-cage <abbrgrp><abbr bid="B1">1</abbr></abbrgrp> demonstrates that our algorithm can detect similarities at rather low level, and extract biologically meaningful folding events.</p> <p>Conclusion</p> <p>The EPO algorithm is general and applicable to a wide range of applications. We demonstrate its generality and effectiveness by applying it to aligning multiple protein structures with low similarities. For user's convenience, we provide a web server for the algorithm at <url>http://db.cse.ohio-state.edu/EPO</url>.</p

The present status of childhood cancer therapy in Korea.

We have studied the incidence pattern of childhood cancers in Korea. Although the incidence of many tumors in Korea is similar to that in other countries, the incidence of acute myelogenous leukemia, non-Hodgkin's lymphoma and hepatoma is greater in Korean children. Yonsei Cancer Center commenced a study of multi-modality treatment of childhood cancers in July 1974. The most striking improvement of survival rate was seen in patients with acute lymphocytic leukemia (50% at 5 years), Wilms' tumor (65% at 5 years), neuroblastoma (45% at 2 years), osteogenic sarcoma (55% at 2 years) and malignant histiocytosis (20% at 5 years). This study is an attempt to create a basic framework providing the best possible treatment of childhood cancer in Korea. The data obtained in Korea are briefly compared with those in Japan and the United States.</p

Comparison study on k-word statistical measures for protein: From sequence to 'sequence space'

<p>Abstract</p> <p>Background</p> <p>Many proposed statistical measures can efficiently compare protein sequence to further infer protein structure, function and evolutionary information. They share the same idea of using <it>k</it>-word frequencies of protein sequences. Given a protein sequence, the information on its related protein sequences hasn't been used for protein sequence comparison until now. This paper proposed a scheme to construct protein 'sequence space' which was associated with protein sequences related to the given protein, and the performances of statistical measures were compared when they explored the information on protein 'sequence space' or not. This paper also presented two statistical measures for protein: <it>gre.k </it>(generalized relative entropy) and <it>gsm.k </it>(gapped similarity measure).</p> <p>Results</p> <p>We tested statistical measures based on protein 'sequence space' or not with three data sets. This not only offers the systematic and quantitative experimental assessment of these statistical measures, but also naturally complements the available comparison of statistical measures based on protein sequence. Moreover, we compared our statistical measures with alignment-based measures and the existing statistical measures. The experiments were grouped into two sets. The first one, performed via ROC (Receiver Operating Curve) analysis, aims at assessing the intrinsic ability of the statistical measures to discriminate and classify protein sequences. The second set of the experiments aims at assessing how well our measure does in phylogenetic analysis. Based on the experiments, several conclusions can be drawn and, from them, novel valuable guidelines for the use of protein 'sequence space' and statistical measures were obtained.</p> <p>Conclusion</p> <p>Alignment-based measures have a clear advantage when the data is high redundant. The more efficient statistical measure is the novel <it>gsm.k </it>introduced by this article, the <it>cos.k </it>followed. When the data becomes less redundant, <it>gre.k </it>proposed by us achieves a better performance, but all the other measures perform poorly on classification tasks. Almost all the statistical measures achieve improvement by exploring the information on 'sequence space' as word's length increases, especially for less redundant data. The reasonable results of phylogenetic analysis confirm that <it>Gdis.k </it>based on 'sequence space' is a reliable measure for phylogenetic analysis. In summary, our quantitative analysis verifies that exploring the information on 'sequence space' is a promising way to improve the abilities of statistical measures for protein comparison.</p