Minimum-weight triangulation is NP-hard

A triangulation of a planar point set S is a maximal plane straight-line graph with vertex set S. In the minimum-weight triangulation (MWT) problem, we are looking for a triangulation of a given point set that minimizes the sum of the edge lengths. We prove that the decision version of this problem is NP-hard. We use a reduction from PLANAR-1-IN-3-SAT. The correct working of the gadgets is established with computer assistance, using dynamic programming on polygonal faces, as well as the beta-skeleton heuristic to certify that certain edges belong to the minimum-weight triangulation.Comment: 45 pages (including a technical appendix of 13 pages), 28 figures. This revision contains a few improvements in the expositio

Shelling the Voronoi interface of protein-protein complexes predicts residue activity and conservation

The accurate description of protein-protein interfaces remains a challenging task. Traditional criteria, based on atomic contacts or changes in solvent accessibility, tend to over or underpredict the interface itself and cannot discriminate active from less relevant parts. A recent simulation study by Mihalek and co-authors (2007, JMB 369, 584-95) concluded that active residues tend to be `dry', that is, insulated from water fluctuations. We show that patterns of `dry' residues can, to a large extent, be predicted by a fast, parameter-free and purely geometric analysis of protein interfaces. We introduce the shelling order of Voronoi facets as a straightforward quantitative measure of an atom's depth inside an interface. We analyze the correlation between Voronoi shelling order, dryness, and conservation on a set of 54 protein-protein complexes. Residues with high shelling order tend to be dry; evolutionary conservation also correlates with dryness and shelling order but, perhaps not surprisingly, is a much less accurate predictor of either property. Voronoi shelling order thus seems a meaningful and efficient descriptor of protein interfaces. Moreover, the strong correlation with dryness suggests that water dynamics within protein interfaces may, in first approximation, be described by simple diffusion models

Extending the Advanced Data Extraction Infrastructure : Research on HTML5 usage, server monitoring tool, support for multidimensional datasets

The Advanced Data Extraction Infrastructure (ADEI) project functions as a bridge between the control systems that collect the measurements of various subsystems controlling the flow of data acquisition from experiments, and scientists analysing the flow of experiments and evaluating the collected data. The project is still in development and new features are added constantly. During the thesis the current version of the ADEI was extended by implementing a new data reader module to deal with Round Robin Database files that are used to monitor the status of the computers operating as part of control and data acquisition subsystems of the ADEI. The future development of the ADEI was also researched. The current server-side graphing approach has significant limitations in scalability and requires a rather high bandwidth between the server and clients. The use of HTML5 markup language was investigated. The investigation focused on the usage of canvas along the JavaScript drawing library RGraph to implement the ADEI’s graph drawing features on the client side of the application to lessen the need for high bandwidth. The test was successful and it is recommended to use the RGraph library as the platform for a new ADEI frontend. The current version of the ADEI can only present simple time series data while many experiments generate multidimensional time series data. To achieve the visualization of multidimensional data, a prototype module handling several new types of data that could not be presented with the current ADEI was created to provide a foundation for the further development of these features.ADEI projektin kehittämä web-pohjainen sovellus toimii linkkinä erilaisten mittaustuloksia keräävien laitteistojen ja tuloksia analysoivien tutkijoiden välillä. Projektia kehitetään ja uusia ominaisuuksia lisätään jatkuvasti. Osana opinnäytetyötä tutkittiin HTML5 merkkauskielen mahdollista käyttöä ADEIn jatkokehittämisessä keskittyen tarkastelemaan uutta canvas elementtiä ja piirtämiseen tarkoitetun RGraph JavaScript kirjaston käyttöä toteuttamaan ADEIn nykyiset kuvaajien piirto-ominaisuudet asiakaslaitteen puolella. Näin pystytään vähentämään palvelimen ja asiakaslaitteiden välisen korkean kaistanleveyden tarvetta. Testi onnistui ja suosittelen Rgraphia käytettäväksi ADEIn uuden käyttöliittymän kehityksessä. Lisäksi kehitettiin nykyiseen ADEI versioon uusi lukurajapinnan laajennus käsittelemään Round Robin Database tiedostoja jota tultaisiin käyttämään ADEI palvelimien suorituskyvyn tarkkailuun. Moniulotteisen datan, jota ei pystytä esittämään selkeästi nykyisten piirto-ominaisuuksien avulla, esittämistä varten kehitettiin kokeellinen moduuli. joka muodostaa pohjan näiden ominaisuuksien tulevalle jatkokehittämiselle

On the design of a multiagent user interface for Next Generation Geographic Information System

In this thesis, a multiagent user interface architecture is designed for the Next Generation Geographic Information System(NGGIS) which supports the following advanced features: multiple users, multiple views, direct manipulation, distribution, and intelligence. In this architecture, agent is a basic functional unit. Agents cooperate with each other by exchanging messages. The User is just a special agent who communicates with any other agents. The ShowCase and its cooperative agents are specialized to present the geographic objects in different views. The WorkShop and its cooperative agents provide a complete interface to allow the user to manipulate the GIS objects directly. The Monitor is specialized to enforce the semantic constrains and control the system consistency. The Interaction Expert interprets multimedia user input and generates multimedia output by driving other agents. The Selector is a cooperative agent of both WorkShop and ShowCase which allows users to select geographic objects with specific constraints

A Data-Analysis and Sensitivity-Optimization Framework for the KATRIN Experiment

Presently under construction, the Karlsruhe TRitium Neutrino (KATRIN) experiment is the next generation tritium beta-decay experiment to perform a direct kinematical measurement of the electron neutrino mass with an unprecedented sensitivity of 200 meV (90% C.L.). This thesis describes the implementation of a consistent data analysis framework, addressing technical aspects of the data taking process and statistical challenges of a neutrino mass estimation from the beta-decay electron spectrum