Berge Sorting

In 1966, Claude Berge proposed the following sorting problem. Given a string of $n$ alternating white and black pegs on a one-dimensional board consisting of an unlimited number of empty holes, rearrange the pegs into a string consisting of $\lceil\frac{n}{2}\rceil$ white pegs followed immediately by $\lfloor\frac{n}{2}\rfloor$ black pegs (or vice versa) using only moves which take 2 adjacent pegs to 2 vacant adjacent holes. Avis and Deza proved that the alternating string can be sorted in $\lceil\frac{n}{2}\rceil$ such {\em Berge 2-moves} for $n\geq 5$. Extending Berge's original problem, we consider the same sorting problem using {\em Berge $k$-moves}, i.e., moves which take $k$ adjacent pegs to $k$ vacant adjacent holes. We prove that the alternating string can be sorted in $\lceil\frac{n}{2}\rceil$ Berge 3-moves for $n\not\equiv 0\pmod{4}$ and in $\lceil\frac{n}{2}\rceil+1$ Berge 3-moves for $n\equiv 0\pmod{4}$, for $n\geq 5$. In general, we conjecture that, for any $k$ and large enough $n$, the alternating string can be sorted in $\lceil\frac{n}{2}\rceil$ Berge $k$-moves. This estimate is tight as $\lceil\frac{n}{2}\rceil$ is a lower bound for the minimum number of required Berge $k$-moves for $k\geq 2$ and $n\geq 5$.Comment: 10 pages, 2 figure

Fitting 3D Morphable Models using Local Features

In this paper, we propose a novel fitting method that uses local image features to fit a 3D Morphable Model to 2D images. To overcome the obstacle of optimising a cost function that contains a non-differentiable feature extraction operator, we use a learning-based cascaded regression method that learns the gradient direction from data. The method allows to simultaneously solve for shape and pose parameters. Our method is thoroughly evaluated on Morphable Model generated data and first results on real data are presented. Compared to traditional fitting methods, which use simple raw features like pixel colour or edge maps, local features have been shown to be much more robust against variations in imaging conditions. Our approach is unique in that we are the first to use local features to fit a Morphable Model. Because of the speed of our method, it is applicable for realtime applications. Our cascaded regression framework is available as an open source library (https://github.com/patrikhuber).Comment: Submitted to ICIP 2015; 4 pages, 4 figure

Band structures of II-VI semiconductors using Gaussian basis functions with separable ab initio pseudopotentials: Application to prediction of band offsets

We describe the implementation of a separable pseudopotential into the dual space approach for ab initio density-functional calculations using Gaussian basis functions. We apply this Gaussian dual space method (GDS/DFT) to the study of II-VI semiconductors (II=Zn, Cd, Hg; VI=S, Se, Te, Po). The results compare well with experimental data and demonstrate the general transferability of the separable pseudopotential. We also introduce a band-consistent tight-binding (BC-TB) model for calculating the bulk contributions to the valence-band offsets (VBO’s). This BC-TB approach yields good agreement with all-electron ab initio GDS/DFT results. Comparisons between BC-TB results of VBO obtained with and without p-d coupling demonstrate quantitatively the importance of d electrons and cation-d–anion-p coupling in II-VI systems. Agreement between ab initio results and experimental results is excellent

First principles studies of band offsets at heterojunctions and of surface reconstruction using Gaussian dual-space density functional theory

The use of localized Gaussian basis functions for large scale first principles density functional calculations with periodic boundary conditions (PBC) in 2 dimensions and 3 dimensions has been made possible by using a dual space approach. This new method is applied to the study of electronic properties of II–VI (II=Zn, Cd, Hg; VI=S, Se, Te, Po) and III–V (III=Al, Ga; V=As, N) semiconductors. Valence band offsets of heterojunctions are calculated including both bulk contributions and interfacial contributions. The results agree very well with available experimental data. The p(2 × 1) cation terminated surface reconstructions of CdTe and HgTe (100) are calculated using the local density approximation (LDA) with two-dimensional PBC and also using the ab initio Hartree–Fock (HF) method with a finite cluster. The LDA and HF results do not agree very well

FACTORS THAT IMPACT UNSYSTEMATIC RISK IN THE U.S. RESTAURANT INDUSTRY

The purpose of this research is to explore the relationship between restaurant management factors and the unsystematic risk portion of restaurant stock returns. The riskiness of the restaurant business has been brought to the forefront of popular culture through a number of reality television shows. Although the riskiness of the business overall has been exaggerated, these shows highlight the importance of the ability of the ownermanager. We examine three critical areas of restaurant management, including financial management, operations management, and firm size, and find that all are significantly related to a firm’s unsystematic risk