Gauge-invariant implementation of the Abelian Higgs model on optical lattices

We present a gauge-invariant effective action for the Abelian Higgs model (scalar electrodynamics) with a chemical potential $\mu$ on a 1+1 dimensional lattice. This formulation provides an expansion in the hopping parameter $\kappa$ which we test with Monte Carlo simulations for a broad range of the inverse gauge coupling $\beta_{pl}$ and small values of the scalar self-coupling $\lambda$. In the opposite limit of infinitely large $\lambda$, the partition function can be written as a traced product of local tensors which allows us to write exact blocking formulas. Their numerical implementation requires truncations but there is no sign problem for arbitrary values of $\mu$. We show that the time continuum limit of the blocked transfer matrix can be obtained numerically and, in the limit of infinite $\beta_{pl}$ and with a spin-1 truncation, the small volume energy spectrum is identical to the low energy spectrum of a two-species Bose-Hubbard model in the limit of large onsite repulsion. We extend this procedure for finite $\beta_{pl}$ and derive a spin-1 approximation of the Hamiltonian. It involves new terms corresponding to transitions among the two species in the Bose-Hubbard model. We propose an optical lattice implementation involving a ladder structure.Comment: 10 pages, 9 figure

Tumor Classification Using High-Order Gene Expression Profiles Based on Multilinear ICA

Motivation. Independent Components Analysis (ICA) maximizes the statistical independence of the representational components of a training gene expression profiles (GEP) ensemble, but it cannot distinguish relations between the different factors, or different modes, and it is not available to high-order GEP Data Mining. In order to generalize ICA, we introduce Multilinear-ICA and apply it to tumor classification using high order GEP. Firstly, we introduce the basis conceptions and operations of tensor and recommend Support Vector Machine (SVM) classifier and Multilinear-ICA. Secondly, the higher score genes of original high order GEP are selected by using t-statistics and tabulate tensors. Thirdly, the tensors are performed by Multilinear-ICA. Finally, the SVM is used to classify the tumor subtypes. Results. To show the validity of the proposed method, we apply it to tumor classification using high order GEP. Though we only use three datasets, the experimental results show that the method is effective and feasible. Through this survey, we hope to gain some insight into the problem of high order GEP tumor classification, in aid of further developing more effective tumor classification algorithms

3-Hydr­oxy-3-phenyl­isoindolin-1-one 0.33-hydrate

The asymmetric unit of the title compound, C14H11NO2·0.33H2O, contains three 3-hydr­oxy-3-phenyl­isoindolin-1-one (HPIO) mol­ecules and one water mol­ecule. The three independent HPIO mol­ecules differ in the orientations of hydr­oxy and phenyl groups substituted at the 3-position with respect to the planar [r.m.s. deviations of 0.0173, 0.0170 and 0.0102 Å] dihydro­isoindolin-1-one ring system. In the crystal structure, mol­ecules are linked into a three-dimensional network by O—H⋯O, N—H⋯O and C—H⋯O hydrogen bonds