Real-space renormalization group study of the Hubbard model on a non-bipartite lattice

We present the real-space block renormalization group equations for fermion systems described by a Hubbard Hamiltonian on a triangular lattice with hexagonal blocks. The conditions that keep the equations from proliferation of the couplings are derived. Computational results are presented including the occurrence of a first-order metal-insulator transition at the critical value of $U/t \approx 12.5$

Integral Human Pose Regression

State-of-the-art human pose estimation methods are based on heat map representation. In spite of the good performance, the representation has a few issues in nature, such as not differentiable and quantization error. This work shows that a simple integral operation relates and unifies the heat map representation and joint regression, thus avoiding the above issues. It is differentiable, efficient, and compatible with any heat map based methods. Its effectiveness is convincingly validated via comprehensive ablation experiments under various settings, specifically on 3D pose estimation, for the first time

High-order density-matrix perturbation theory

We present a simple formalism for the calculation of the derivatives of the electronic density matrix at any order, within density functional theory. Our approach, contrary to previous ones, is not based on the perturbative expansion of the Kohn-Sham wavefunctions. It has the following advantages: (i) it allows a simple derivation for the expression for the high order derivatives of the density matrix; (ii) in extended insulators, the treatment of uniform-electric-field perturbations and of the polarization derivatives is straightforward.Comment: 4 page

Embryonic Pattern Scaling Achieved by Oppositely Directed Morphogen Gradients

Morphogens are proteins, often produced in a localised region, whose concentrations spatially demarcate regions of differing gene expression in developing embryos. The boundaries of expression must be set accurately and in proportion to the size of the one-dimensional developing field; this cannot be accomplished by a single gradient. Here, we show how a pair of morphogens produced at opposite ends of a developing field can solve the pattern-scaling problem. In the most promising scenario, the morphogens effectively interact according to the annihilation reaction $A+B\to\emptyset$ and the switch occurs according to the absolute concentration of $A$ or $B$. In this case embryonic markers across the entire developing field scale approximately with system size; this cannot be achieved with a pair of non-interacting gradients that combinatorially regulate downstream genes. This scaling occurs in a window of developing-field sizes centred at a few times the morphogen decay length.Comment: 24 pages; 11 figures; uses iopar

Ariel - Volume 9 Number 6

Executive Editor Seth B. Paul Associate Editor Warren J. Ventriglia Business Manager Fredric Jay Matlin University News John Patrick Welch World News George Robert Coar Editorials Editor Steve Levine Features Mark Rubin Sports Editor Eli Saleeby Photo Editor Ken Buckwalter Circulation Victor Onufreiczuk Lee Wugofski Graphics and Art Steve Hulkower Commons Editor Brenda Peterso

Determination of Mercury in an Assortment of Dietary Supplements Using an Inexpensive Combustion Atomic Absorption Spectrometry Technique

The concentrations of mercury in forty, commercially available dietary supplements, were determined using a new, inexpensive analysis technique. The method involves thermal decomposition, amalgamation, and detection of mercury by atomic absorption spectrometry with an analysis time of approximately six minutes per sample. The primary cost savings from this approach is that labor-intensive sample digestion is not required prior to analysis, further automating the analytical procedure. As a result, manufacturers and regulatory agencies concerned with monitoring lot-to-lot product quality may find this approach an attractive alternative to the more classical acid-decomposition, cold vapor atomic absorption methodology. Dietary supplement samples analyzed included astragalus, calcium, chromium picolinate, echinacea, ephedra, fish oil, ginger, ginkgo biloba, ginseng, goldenseal, guggul, senna, St John's wort, and yohimbe products. Quality control samples analyzed with the dietary supplements indicated a high level of method accuracy and precision. Ten replicate preparations of a standard reference material (NIST 1573a, tomato leaves) were analyzed, and the average mercury recovery was 109% (2.0% RSD). The method quantitation limit was 0.3 ng, which corresponded to 1.5 ng/g sample. The highest found mercury concentration (123 ng/g) was measured in a concentrated salmon oil sample. When taken as directed by an adult, this product would result in an approximate mercury ingestion of 7 μg per week