The one-round Voronoi game replayed

We consider the one-round Voronoi game, where player one (``White'', called ``Wilma'') places a set of n points in a rectangular area of aspect ratio r <=1, followed by the second player (``Black'', called ``Barney''), who places the same number of points. Each player wins the fraction of the board closest to one of his points, and the goal is to win more than half of the total area. This problem has been studied by Cheong et al., who showed that for large enough $n$ and r=1, Barney has a strategy that guarantees a fraction of 1/2+a, for some small fixed a. We resolve a number of open problems raised by that paper. In particular, we give a precise characterization of the outcome of the game for optimal play: We show that Barney has a winning strategy for n>2 and r>sqrt{2}/n, and for n=2 and r>sqrt{3}/2. Wilma wins in all remaining cases, i.e., for n>=3 and r<=sqrt{2}/n, for n=2 and r<=sqrt{3}/2, and for n=1. We also discuss complexity aspects of the game on more general boards, by proving that for a polygon with holes, it is NP-hard to maximize the area Barney can win against a given set of points by Wilma.Comment: 14 pages, 6 figures, Latex; revised for journal version, to appear in Computational Geometry: Theory and Applications. Extended abstract version appeared in Workshop on Algorithms and Data Structures, Springer Lecture Notes in Computer Science, vol.2748, 2003, pp. 150-16

Correlation effects on the electronic structure of TiOCl: a NMTO+DMFT study

Using the recently developed N-th order muffin-tin orbital-based downfolding technique in combination with the Dynamical Mean Field theory, we investigate the electronic properties of the much discussed Mott insulator TiOCl in the undimerized phase. Inclusion of correlation effects through this approach provides a description of the spectral function into an upper and a lower Hubbard band with broad valence states formed out of the orbitally polarized, lower Hubbard band. We find that these results are in good agreement with recent photo-emission spectra.Comment: 4 pages, 3 figure

Mott transition and suppression of orbital fluctuations in orthorhombic 3d1d^{1} perovskites

Using $t_{2g}$ Wannier-functions, a low-energy Hamiltonian is derived for orthorhombic $3d^{1}$ transition-metal oxides. Electronic correlations are treated with a new implementation of dynamical mean-field theory for non-cubic systems. Good agreement with photoemission data is obtained. The interplay of correlation effects and cation covalency (GdFeO$_{3}$-type distortions) is found to suppress orbital fluctuations in LaTiO$_{3},$ and even more in YTiO$_{3}$, and to favor the transition to the insulating state.Comment: 4 pages, 3 figures; revised manuscrip

Trends and guidelines in online privacy policy

Online privacy policies (OPP) are important mechanisms for informing online consumers about the level of information privacy protection afforded when visiting web sites. To date, societal mechanisms and technologies have been the focus of attempts to improve the quality and effectiveness of OPPs. We present findings from a longitudinal, empirical study of online privacy policies. Our research found that although online privacy policies have improved in quality and effectiveness since 2000, they still fall well short of the level of privacy assurance desired by consumers. This study analyses trends in OPPs over the two years of the study, identifying areas of deficiency and improvements, and offering a solution in the form of a detailed set of guidelines for organisational online privacy policy. Our study adds to existing theory in this area and, more immediately, will assist businesses concerned about the effect of privacy issues on consumer web usage.<br /

Effective online privacy policies

Online privacy policies are important mechanisms for informing web site users about the level of information privacy protection afforded when visiting web sites. To date, societal mechanisms and technologies have been the focus of attempts to improve the quality and effectiveness of online privacy policies. Little attention, however, has been given to the development and use of organisational measures for this purpose. In this paper we present findings from an empirical study of online privacy policies, resulting in a set of organisational guidelines for effective online privacy policies, which extend the research base in this area and, more immediately, will assist companies concerned about the impact of privacy concerns on consumer web usage

Adding value to online privacy for consumers: remedying deficiences in online privacy policies with an holistic approach

We present findings from a longitudinal, empirical study of online privacy policies. Our research found that although online privacy policies have improved in quality and effectiveness since 2000, they still fall well short of the level of privacy assurance desired by consumers. This study has identified broad areas of deficiency in existing online privacy policies, and offers a solution in the form of an holistic framework for the development, factors and content of online privacy policies for organizations. Our study adds to existing theory in this area and, more immediately, will assist businesses concerned about the effect of privacy issues on consumer Web usage.<br /

On the mechanism for orbital-ordering in KCuF3

The Mott insulating perovskite KCuF3 is considered the archetype of an orbitally-ordered system. By using the LDA+dynamical mean-field theory (DMFT) method, we investigate the mechanism for orbital-ordering (OO) in this material. We show that the purely electronic Kugel-Khomskii super-exchange mechanism (KK) alone leads to a remarkably large transition temperature of T_KK about 350 K. However, orbital-order is experimentally believed to persist to at least 800 K. Thus Jahn-Teller distortions are essential for stabilizing orbital-order at such high temperatures.Comment: 4 pages, 5 figure

Local magnetic moments in iron and nickel at ambient and Earth's core conditions

Some Bravais lattices have a particular geometry that can slow down the motion of Bloch electrons by pre-localization due to the band-structure properties. Another known source of electronic localization in solids is the Coulomb repulsion in partially filled d- or f-orbitals, which leads to the formation of local magnetic moments. The combination of these two effects is usually considered of little relevance to strongly correlated materials. Here we show that it represents, instead, the underlying physical mechanism in two of the most important ferromagnets: nickel and iron. In nickel, the van Hove singularity has an unexpected impact on the magnetism. As a result, the electron-electron scattering rate is linear in temperature, in violation of the conventional Landau theory of metals. This is true even at Earth's core pressures, at which iron is instead a good Fermi liquid. The importance of nickel in models of geomagnetism may have therefore to be reconsidered.Comment: Supplementary Information available at https://www.nature.com/articles/ncomms16062#supplementary-informatio

Functional renormalization group study of an eight-band model for the iron arsenides

We investigate the superconducting pairing instabilities of eight-band models for the iron arsenides. Using a functional renormalization group treatment, we determine how the critical energy scale for superconductivity depends on the electronic band structure. Most importantly, if we vary the parameters from values corresponding to LaFeAsO to SmFeAsO, the pairing scale is strongly enhanced, in accordance with the experimental observation. We analyze the reasons for this trend and compare the results of the eight-band approach to those found using five-band models.Comment: 11 pages, 10 figure