Discrete Tomography of Penrose Model Sets

Various theoretical and algorithmic aspects of inverse problems in discrete tomography of planar Penrose model sets are discussed. These are motivated by the demand of materials science for the reconstruction of quasicrystalline structures from a small number of images produced by quantitative high resolution transmission electron microscopy.Comment: 7 pages, 1 figure; paper presented at Aperiodic 2006 (Zao, Japan

Magic numbers in the discrete tomography of cyclotomic model sets

We report recent progress in the problem of distinguishing convex subsets of cyclotomic model sets $\varLambda$ by (discrete parallel) X-rays in prescribed $\varLambda$-directions. It turns out that for any of these model sets $\varLambda$ there exists a `magic number' $m_{\varLambda}$ such that any two convex subsets of $\varLambda$ can be distinguished by their X-rays in any set of $m_{\varLambda}$ prescribed $\varLambda$-directions. In particular, for pentagonal, octagonal, decagonal and dodecagonal model sets, the least possible numbers are in that very order 11, 9, 11 and 13.Comment: 6 pages, 1 figure; based on the results of arXiv:1101.4149 [math.MG]; presented at Aperiodic 2012 (Cairns, Australia

Comparison of two sampling protocols and four home-range estimators using radio-tracking data from urban badgers Meles meles

Radio-telemetry is often the method of choice for studies of species whose behaviour is difficult to observe directly. However, considerable debate has ensued about the best way of deriving home-range estimates. In recent years, kernel estimators have become the most widely used method, together with the oldest and simplest method, the minimum convex polygon (MCP). More recently, it has been suggested that the local convex hull (LCH) might be more appropriate than kernel methods in cases where an animal’s home range includes a priori inaccessible areas. Yet another method, the Brownian bridge (BB), explicitly uses autocorrelated data to determine movement paths and, ultimately, home ranges or migration routes of animals. Whereas several studies have used simulation techniques to compare these different methods, few have used data from real animals. We used radio-telemetric data from urban badgers Meles meles to compare two sampling protocols (10-minute vs at least 30-minute inter-fix intervals) and four home-range estimators (MCP, fixed kernels (FK), LCH and BB). We used a multi-response permutation procedure and randomisation tests to compare overall patterns of fixes and degree of overlap of home ranges estimated using data from different sampling protocols, and a general linear model to compare the influence of sampling protocols and home-range estimator on the size of habitat patches. The shape of the estimated home ranges was influenced by sampling protocol in some cases. By contrast, the sizes and proportions of different habitats within home ranges were influenced by estimator type but not by sampling protocol. LCH performed consistently better than FK, and is especially appropriate for patchy study areas containing frequent no-go zones. However, we recommend using LCH in combination with other methods to estimate total range size, because LCH tended to produce smaller estimates than any other method. Results relating to BB are preliminary but suggest that this method is unsuitable for species in which range size is small compared to average travel speed.Marie-Curie Intra-European Fellowship (BSSUB - 24007); Defra WSC contract WM0304; Wildlife Biology granted the permit to upload the article to this repositor

Local Control: An Educational Model of Private Enforcement of Public Rules

We study a society of agents where individual incentives conflict with collective ones and thus individual utility maximization leads to inefficient outcomes. We assume that there is no functioning central institution which can control individual behavior. Instead, we analyze a system of what we call local control (LC), where the enforcement of punishment lies in the hands of individuals in the society rather than in the hand of a central institution. The mechanism that governs the spread of control is the educational impact on an agent being controlled by some other agent, where we distinguish between executed and threatened punishment. Agents maximize their payoffs and underlie a constant drift towards not controlling others anymore. Our main results show that LC can survive if the educational impact of control is strong enough relative to the drift. If the educational impact of control is too weak LC breaks down. Moreover, there exists a non{monotonic punishment effect that sets a trap for standard legal policy advices.cooperation;prisoner's dilemma;social control;punishment;institutional change

The East End, the West End, and King's Cross: On Clustering in the Four-Player Hotelling Game

We study experimentally a standard four-player Hotelling game, with a uniform density of consumers and inelastic demand. The pure strategy Nash equilibrium configuration consists of two firms located at one quarter of the ``linear city'', and the other two at three quarters. We do not observe convergence to such an equilibrium. In our experimental data we find three clusters. Besides the direct proximity of the two equilibrium locations this concerns the focal mid-point. Moreover, we observe that whereas this mid-point appears to become more notable over time, other focal points fade away. We explain how these observations are related to best-response dynamics, and to the fact that the players rely on best-responses in particular when they are close to the equilibrium configuration.Location model, Nonconvergence, Focal point, Best-response dynamics

A note on 5-cycle double covers

The strong cycle double cover conjecture states that for every circuit $C$ of a bridgeless cubic graph $G$, there is a cycle double cover of $G$ which contains $C$. We conjecture that there is even a 5-cycle double cover $S$ of $G$ which contains $C$, i.e. $C$ is a subgraph of one of the five 2-regular subgraphs of $S$. We prove a necessary and sufficient condition for a 2-regular subgraph to be contained in a 5-cycle double cover of $G$

Proceedings of the Second International Mobile Satellite Conference (IMSC 1990)

Presented here are the proceedings of the Second International Mobile Satellite Conference (IMSC), held June 17-20, 1990 in Ottawa, Canada. Topics covered include future mobile satellite communications concepts, aeronautical applications, modulation and coding, propagation and experimental systems, mobile terminal equipment, network architecture and control, regulatory and policy considerations, vehicle antennas, and speech compression

Local Control:An Educational Model of Private Enforcement of Public Rules

We study a society of agents where individual incentives conflict with collective ones and thus individual utility maximization leads to inefficient outcomes. We assume that there is no functioning central institution which can control individual behavior. Instead, we analyze a system of what we call local control (LC), where the enforcement of punishment lies in the hands of individuals in the society rather than in the hand of a central institution. The mechanism that governs the spread of control is the educational impact on an agent being controlled by some other agent, where we distinguish between executed and threatened punishment. Agents maximize their payoffs and underlie a constant drift towards not controlling others anymore. Our main results show that LC can survive if the educational impact of control is strong enough relative to the drift. If the educational impact of control is too weak LC breaks down. Moreover, there exists a non{monotonic punishment effect that sets a trap for standard legal policy advices.