Benchmarking the variational cluster approach by means of the one-dimensional Bose-Hubbard model

Convergence properties of the variational cluster approach with respect to the variational parameter space, cluster size, and boundary conditions of the reference system are investigated and discussed for bosonic many-body systems. Specifically, the variational cluster approach is applied to the one-dimensional Bose-Hubbard model, which exhibits a quantum phase transition from Mott to superfluid phase. In order to benchmark the variational cluster approach, results for the phase boundary delimiting the first Mott lobe are compared with essentially exact density matrix renormalization group data. Furthermore, static quantities, such as the ground state energy and the one-particle density matrix are compared with high-order strong coupling perturbation theory results. For reference systems with open boundary conditions the variational parameter space is extended by an additional variational parameter which allows for a more uniform particle density on the reference system and thus drastically improves the results. It turns out that the variational cluster approach yields accurate results with relatively low computational effort for both spectral as well as static properties of the one-dimensional Bose-Hubbard model, even at the tip of the first Mott lobe where correlation effects are most pronounced.Comment: 12 pages, 16 figures, minor changes, version as publishe

Budgeting for Growth and Prosperity: A Long-Term Plan to Balance the Budget, Grow the Economy, and Strengthen the Middle Class

Proposes reducing the deficit by investing in education, infrastructure, and technology; spending more efficiently; bolstering the social safety net; containing healthcare costs; simplifying the tax code; and raising gas and financial transaction taxes

Statistical methods for tissue array images - algorithmic scoring and co-training

Recent advances in tissue microarray technology have allowed immunohistochemistry to become a powerful medium-to-high throughput analysis tool, particularly for the validation of diagnostic and prognostic biomarkers. However, as study size grows, the manual evaluation of these assays becomes a prohibitive limitation; it vastly reduces throughput and greatly increases variability and expense. We propose an algorithm - Tissue Array Co-Occurrence Matrix Analysis (TACOMA) - for quantifying cellular phenotypes based on textural regularity summarized by local inter-pixel relationships. The algorithm can be easily trained for any staining pattern, is absent of sensitive tuning parameters and has the ability to report salient pixels in an image that contribute to its score. Pathologists' input via informative training patches is an important aspect of the algorithm that allows the training for any specific marker or cell type. With co-training, the error rate of TACOMA can be reduced substantially for a very small training sample (e.g., with size 30). We give theoretical insights into the success of co-training via thinning of the feature set in a high-dimensional setting when there is "sufficient" redundancy among the features. TACOMA is flexible, transparent and provides a scoring process that can be evaluated with clarity and confidence. In a study based on an estrogen receptor (ER) marker, we show that TACOMA is comparable to, or outperforms, pathologists' performance in terms of accuracy and repeatability.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS543 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Spectral properties of coupled cavity arrays in one dimension

Spectral properties of coupled cavity arrays in one dimension are investigated by means of the variational cluster approach. Coupled cavity arrays consist of two distinct "particles," namely, photons and atomiclike excitations. Spectral functions are evaluated and discussed for both particle types. In addition, densities of states, momentum distributions and spatial correlation functions are presented. Based on this information, polariton "quasiparticles" are introduced as appropriate, wave vector and filling dependent linear combinations of photon and atomiclike particles. Spectral functions and densities of states are evaluated for the polariton quasiparticles, and the weights of their components are analyzed.Comment: 17 pages, 16 figures, version as publishe

Excitations in disordered bosonic optical lattices

Spectral excitations of ultracold gases of bosonic atoms trapped in one dimensional optical lattices with disorder are investigated by means of the variational cluster approach applied to the Bose-Hubbard model. In particular, qualitatively different disorder distributions typically employed in experiments are considered. The computed spectra exhibit a strong dependence on both the shape of the disorder distribution and the disorder strength. We compare alternative results for the Mott gap obtained from its formal definition and from the minimum peak distance, which is the quantity available from experiments.Comment: 8 pages, 7 figures, version as publishe