Relative Convex Hull Determination from Convex Hulls in the Plane

A new algorithm for the determination of the relative convex hull in the plane of a simple polygon A with respect to another simple polygon B which contains A, is proposed. The relative convex hull is also known as geodesic convex hull, and the problem of its determination in the plane is equivalent to find the shortest curve among all Jordan curves lying in the difference set of B and A and encircling A. Algorithms solving this problem known from Computational Geometry are based on the triangulation or similar decomposition of that difference set. The algorithm presented here does not use such decomposition, but it supposes that A and B are given as ordered sequences of vertices. The algorithm is based on convex hull calculations of A and B and of smaller polygons and polylines, it produces the output list of vertices of the relative convex hull from the sequence of vertices of the convex hull of A.Comment: 15 pages, 4 figures, Conference paper published. We corrected two typing errors in Definition 2: $I_S$ has to be defined based on $O_S$, and $I_E$ has to be defined based on $O_E$ (not just using $O$). These errors appeared in the text of the original conference paper, which also contained the pseudocode of an algorithm where $I_S$ and $I_E$ appeared as correctly define

Classifying the Arithmetical Complexity of Teaching Models

This paper classifies the complexity of various teaching models by their position in the arithmetical hierarchy. In particular, we determine the arithmetical complexity of the index sets of the following classes: (1) the class of uniformly r.e. families with finite teaching dimension, and (2) the class of uniformly r.e. families with finite positive recursive teaching dimension witnessed by a uniformly r.e. teaching sequence. We also derive the arithmetical complexity of several other decision problems in teaching, such as the problem of deciding, given an effective coding $\{\mathcal L_0,\mathcal L_1,\mathcal L_2,\ldots\}$ of all uniformly r.e. families, any $e$ such that $\mathcal L_e = \{L^e_0,L^e_1,\ldots,\}$, any $i$ and $d$, whether or not the teaching dimension of $L^e_i$ with respect to $\mathcal L_e$ is upper bounded by $d$.Comment: 15 pages in International Conference on Algorithmic Learning Theory, 201

PCA-based lung motion model

Organ motion induced by respiration may cause clinically significant targeting errors and greatly degrade the effectiveness of conformal radiotherapy. It is therefore crucial to be able to model respiratory motion accurately. A recently proposed lung motion model based on principal component analysis (PCA) has been shown to be promising on a few patients. However, there is still a need to understand the underlying reason why it works. In this paper, we present a much deeper and detailed analysis of the PCA-based lung motion model. We provide the theoretical justification of the effectiveness of PCA in modeling lung motion. We also prove that under certain conditions, the PCA motion model is equivalent to 5D motion model, which is based on physiology and anatomy of the lung. The modeling power of PCA model was tested on clinical data and the average 3D error was found to be below 1 mm.Comment: 4 pages, 1 figure. submitted to International Conference on the use of Computers in Radiation Therapy 201

Preconditioning 2D integer data for fast convex hull computations

In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s ? n, which also contains the same hull. We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p × q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q) ? n the algorithm executes in time within O(n); second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n) time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q) ? n holds; the smaller the ratio min(p, q)/n is in the dataset, the greater the speedup factor achieved

A COMPARISON BETWEEN 1.5µm PHOTOLUMINESCENCE FROM Er-DOPED Si-RICH SiO2 FILMS AND (Er,Ge) CO-DOPED SiO2 FILMS

photoluminescence, nanoclusters, erbium, Transmission electron microscopyWe have studied the 1.5 µm photoluminescence (PL) from Er ions after annealing two different sample sets in the temperature range 500 °C to 1100 °C. The different sample sets were made by magnetron sputtering from composite targets of Si+SiO2+Er and Ge+SiO2+Er respectively for the different sample sets. The annealing induces Si - and Ge-nanoclusters respectively in the different film sets. The PL peak reaches its maximum intensity after annealing at 700 °C for samples with Ge nanoclusters and after annealing at 800 °C for samples with Si. No luminescence from nanoclusters was detected in neither sample sets. This is interpreted as an energy transfer from the nanocluster to Er atoms. Transmission electron microscopy shows that after annealing to the respective temperature yielding the maximum PL intensity both the Ge and Si clusters are non-crystalline. Here we mainly compare the spectral shape of Er luminescence emitted in these different nanostructured matrixes. The PL spectral shapes are clearly different and witness a different local environment for the Er ions

Evaluating the Impacts of Subsidies on Innovation Activities in Germany

Innovations are a key factor to ensure the competitiveness of establishments as well as to enhance the growth and wealth of nations. But more than any other economic activity, decisions about innovations are plagued by failures of the market mechanism. As a response, public instruments have been implemented to stimulate private innovation activities. The effectiveness of these measures, however, is ambiguous and calls for an empirical evaluation. In this paper we make use of the IAB Establishment Panel and apply various microeconometric methods to estimate the effect of public measures on innovation activities of German establishments. We find that neglecting sample selection due to observable as well as to unobservable characteristics leads to an overestimation of the treatment effect and that there are considerable differences with regard to size class and betweenWest and East German establishments

Theory and practice in Finnish teacher education : a rhetorical analysis of changing values from the 1960s to the present day

Our aim in this article is to examine the relationship between theory and practice in Finnish teacher education from the 1960s to the present. We identify four different periods to represent this relationship based on our analysis of national committee and evaluation reports. Theory and practice gradually converged, culminating in a research-based agenda that reflects the current situation. This relationship between theory and practice also reflects the ideal teacher of different times and what a teacher's working orientation should be. We use rhetorical analysis and the concept of a 'philosophical pair' introduced by Perelman and Olbrechts-Tyteca to interpret this development.Peer reviewe