ranger: A Fast Implementation of Random Forests for High Dimensional Data in C++ and R

We introduce the C++ application and R package ranger. The software is a fast implementation of random forests for high dimensional data. Ensembles of classification, regression and survival trees are supported. We describe the implementation, provide examples, validate the package with a reference implementation, and compare runtime and memory usage with other implementations. The new software proves to scale best with the number of features, samples, trees, and features tried for splitting. Finally, we show that ranger is the fastest and most memory efficient implementation of random forests to analyze data on the scale of a genome-wide association study

Dimer states in atomic mixtures

A mixture of heavy atoms in a Mott state and light spin-1/2 fermionic atoms is studied in an optical lattice. Inelastic scattering processes between both atomic species excite the heavy atoms and renormalize the tunneling rate as well as the interaction of the light atoms. An effective Hamiltonian for the latter is derived that describes tunneling of single fermions, tunneling of fermionic pairs and an exchange of fermionic spins. Low energy states of this Hamiltonian are a N\'eel state for strong effective repulsion, dimer states for moderate interaction, and a density wave of paired fermions for strong effective attraction.Comment: 10 pages, 3 figure, extended versio

A renormalized Gross-Pitaevskii Theory and vortices in a strongly interacting Bose gas

We consider a strongly interacting Bose-Einstein condensate in a spherical harmonic trap. The system is treated by applying a slave-boson representation for hard-core bosons. A renormalized Gross-Pitaevskii theory is derived for the condensate wave function that describes the dilute regime (like the conventional Gross-Pitaevskii theory) as well as the dense regime. We calculate the condensate density of a rotating condensate for both the vortex-free condensate and the condensate with a single vortex and determine the critical angular velocity for the formation of a stable vortex in a rotating trap.Comment: 13 pages, 5 figures; revision and extension, figure 2 adde

Construction and Analysis of Projected Deformed Products

We introduce a deformed product construction for simple polytopes in terms of lower-triangular block matrix representations. We further show how Gale duality can be employed for the construction and for the analysis of deformed products such that specified faces (e.g. all the k-faces) are ``strictly preserved'' under projection. Thus, starting from an arbitrary neighborly simplicial (d-2)-polytope Q on n-1 vertices we construct a deformed n-cube, whose projection to the last dcoordinates yields a neighborly cubical d-polytope. As an extension of thecubical case, we construct matrix representations of deformed products of(even) polygons (DPPs), which have a projection to d-space that retains the complete (\lfloor \tfrac{d}{2} \rfloor - 1)-skeleton. In both cases the combinatorial structure of the images under projection is completely determined by the neighborly polytope Q: Our analysis provides explicit combinatorial descriptions. This yields a multitude of combinatorially different neighborly cubical polytopes and DPPs. As a special case, we obtain simplified descriptions of the neighborly cubical polytopes of Joswig & Ziegler (2000) as well as of the ``projected deformed products of polygons'' that were announced by Ziegler (2004), a family of 4-polytopes whose ``fatness'' gets arbitrarily close to 9.Comment: 20 pages, 5 figure

Interacting bosons in an optical lattice: Bose-Einstein condensates and Mott insulator

A dense Bose gas with hard-core interaction is considered in an optical lattice. We study the phase diagram in terms of a special mean-field theory that describes a Bose-Einstein condensate and a Mott insulator with a single particle per lattice site for zero as well as for non-zero temperatures. We calculate the densities, the excitation spectrum and the static structure factor for each of these phases.Comment: 17 pages, 5 figures; 1 figure added, typos remove

Online Auction House Liability for the Sale of Trademark Infringing Products

With the rise of the Internet, trademark owners have seen an increase in online trademark infringement. This Comment examines online auction house liability for the sale of trademark infringing products and the methodology used by courts in making this determination. The author outlines contributory trademark jurisprudence in the United States and France and the application of this jurisprudence in Tiffany v. EBay and LVMH v. EBay, respectively. The article then evaluates the implications of the two approaches to determine which approach is more practical and effective. The author concludes that online auction houses should not be liable for trademark infringement unless they have specific knowledge that a third party is infringing a trademark and fail to act to prevent that party from trademark infringement

A Local Cost-sharing Plan for Watersheds Under the Watershed Protection and Flood Prevention Act

Henry N. The “Watershed Protection and Flood Prevention Act” as amended was passed for the purpose of initiating a program to eliminate or reduce flood damages as well as to promote better use of land through better control of water. The multi-responsibility feature of Public Law 566 and the amended portion, Public Law 1018, attempts to coordinate the talents of the Federal and State agencies with that of the local sponsoring group. The latter has a large share of the responsibility of carrying out the successful operation of the project. One of the important features of the law is the Federal and local sharing of costs. Under Public Law 566 the local groups shall assume several non-Federal costs. They must provide monies for acquiring easements and right-of-way of lands as well as all water rights that are necessary for completion of the project. Fees for conducting the bids and letting of contracts are also included. Costs for any purpose other than flood prevention, as stated in the Act, must be shared by the local organization. Another non-Federal cost is the cost of operation and maintenance of the structures

Investigation of ion induced bending mechanism for nanostructures

Ion induced bending is a promising controlled technique for manipulating nanoscale structures. However, the underlying mechanism of the process is not well understood. In this letter, we report a detailed study of the bending mechanism of Si nanowires (NWs) under Ga+ irradiation. The microstructural changes in the NW due to ion beam irradiation are studied and molecular dynamics simulations are used to explore the ion–NW interaction processes. The simulation results are compared with the microstructural studies of the NW. The investigations inform a generic understanding of the bending process in crystalline materials, which we suggest to be feasible as a versatile manipulation and integration technique in nanotechnology

Quantum Monte Carlo study of a nonmagnetic impurity in the two-dimensional Hubbard model

In order to investigate the effects of nonmagnetic impurities in strongly correlated systems, Quantum Monte Carlo (QMC) simulations have been carried out for the doped two-dimensional Hubbard model with one nonmagnetic impurity. Using a bare impurity potential which is onsite and attractive, magnetic and single-particle properties have been calculated. The QMC results show that giant oscillations develop in the Knight shift response around the impurity site due to the short-range antiferromagnetic correlations. These results are useful for interpreting the NMR data on Li and Zn substituted layered cuprates.Comment: 10 pages, 7 figure