Equation of motion approach to the Hubbard model in infinite dimensions

We consider the Hubbard model on the infinite-dimensional Bethe lattice and construct a systematic series of self-consistent approximations to the one-particle Green's function, $G^{(n)}(\omega),\ n=2,3,\dots\$ . The first $n-1$ equations of motion are exactly fullfilled by $G^{(n)}(\omega)$ and the $n$'th equation of motion is decoupled following a simple set of decoupling rules. $G^{(2)}(\omega)$ corresponds to the Hubbard-III approximation. We present analytic and numerical results for the Mott-Hubbard transition at half filling for $n=2,3,4$.Comment: 10pager, REVTEX, 8-figures not available in postscript, manuscript may be understood without figure

Integrative DNA methylome analysis of pan-cancer biomarkers in cancer discordant monozygotic twin-pairs

BACKGROUND: A key focus in cancer research is the discovery of biomarkers that accurately diagnose early lesions in non-invasive tissues. Several studies have identified malignancy-associated DNA methylation changes in blood, yet no general cancer biomarker has been identified to date. Here, we explore the potential of blood DNA methylation as a biomarker of pan-cancer (cancer of multiple different origins) in 41 female cancer discordant monozygotic (MZ) twin-pairs sampled before or after diagnosis using the Illumina HumanMethylation450 BeadChip. RESULTS: We analysed epigenome-wide DNA methylation profiles in 41 cancer discordant MZ twin-pairs with affected individuals diagnosed with tumours at different single primary sites: the breast, cervix, colon, endometrium, thyroid gland, skin (melanoma), ovary, and pancreas. No significant global differences in whole blood DNA methylation profiles were observed. Epigenome-wide analyses identified one novel pan-cancer differentially methylated position at false discovery rate (FDR) threshold of 10 % (cg02444695, P = 1.8 × 10(-7)) in an intergenic region 70 kb upstream of the SASH1 tumour suppressor gene, and three suggestive signals in COL11A2, AXL, and LINC00340. Replication of the four top-ranked signals in an independent sample of nine cancer-discordant MZ twin-pairs showed a similar direction of association at COL11A2, AXL, and LINC00340, and significantly greater methylation discordance at AXL compared to 480 healthy concordant MZ twin-pairs. The effects at cg02444695 (near SASH1), COL11A2, and LINC00340 were the most promising in biomarker potential because the DNA methylation differences were found to pre-exist in samples obtained prior to diagnosis and were limited to a 5-year period before diagnosis. Gene expression follow-up at the top-ranked signals in 283 healthy individuals showed correlation between blood methylation and gene expression in lymphoblastoid cell lines at PRL, and in the skin tissue at AXL. A significant enrichment of differential DNA methylation was observed in enhancer regions (P = 0.03). CONCLUSIONS: We identified DNA methylation signatures in blood associated with pan-cancer, at or near SASH1, COL11A2, AXL, and LINC00340. Three of these signals were present up to 5 years prior to cancer diagnosis, highlighting the potential clinical utility of whole blood DNA methylation analysis in cancer surveillance

Charge-density-wave order parameter of the Falicov-Kimball model in infinite dimensions

In the large-U limit, the Falicov-Kimball model maps onto an effective Ising model, with an order parameter described by a BCS-like mean-field theory in infinite dimensions. In the small-U limit, van Dongen and Vollhardt showed that the order parameter assumes a strange non-BCS-like shape with a sharp reduction near T approx T_c/2. Here we numerically investigate the crossover between these two regimes and qualitatively determine the order parameter for a variety of different values of U. We find the overall behavior of the order parameter as a function of temperature to be quite anomalous.Comment: (5 pages, 3 figures, typeset with ReVTeX4

Initial spare parts assortment decision making for rolling stock maintenance: a structured approach

Design for maintenance and maintenance operations become increasingly important in recent years. In the capital-intensive industry, maintenance expenditures can add up to several times the initial investment. In order to be competitive in their business, owners and users of these capital goods have to take into account the total life cycle cost at investment (the lifespan of a train is about 30 years), the renewal decisions for their installations and the logistic management of the spare parts. Erroneous or unstructured initial spare parts assortment decision-making part of the logistic management can lead to undesired downtime and increases the risk of obsolete or unavailable components. Decision making is further complicated by non- existent data in the early design phase and several information management problems. Based on a case study at NedTrain (the largest maintainer of rolling stock in the Netherlands) and literature review a Decision Support Model to structure and to improve the initial spare part assortment for the rolling stock maintenance is proposed

Orbital-selective Mott transitions in the anisotropic two-band Hubbard model at finite temperatures

The anisotropic degenerate two-orbital Hubbard model is studied within dynamical mean-field theory at low temperatures. High-precision calculations on the basis of a refined quantum Monte Carlo (QMC) method reveal that two distinct orbital-selective Mott transitions occur for a bandwidth ratio of 2 even in the absence of spin-flip contributions to the Hund exchange. The second transition -- not seen in earlier studies using QMC, iterative perturbation theory, and exact diagonalization -- is clearly exposed in a low-frequency analysis of the self-energy and in local spectra.Comment: 4 pages, 5 figure

Renormalisation-theoretic analysis of non-equilibrium phase transitions II: The effect of perturbations on rate coefficients in the Becker-Doring equations

We study in detail the application of renormalisation theory to models of cluster aggregation and fragmentation of relevance to nucleation and growth processes. In particular, we investigate the Becker-Doring (BD) equations, originally formulated to describe and analyse non-equilibrium phase transitions, but more recently generalised to describe a wide range of physicochemical problems. We consider here rate coefficients which depend on the cluster size in a power-law fashion, but now perturbed by small amplitude random noise. Power-law rate coefficients arise naturally in the theory of surface-controlled nucleation and growth processes. The noisy perturbations on these rates reflect the effect of microscopic variations in such mean-field coefficients, thermal fluctuations and/or experimental uncertainties. In the present paper we generalise our earlier work that identified the nine classes into which all dynamical behaviour must fall by investigating how random perturbations of the rate coefficients influence the steady-state and kinetic behaviour of the coarse-grained, renormalised system. We are hence able to confirm the existence of a set of up to nine universality classes for such BD systems.Comment: 30 pages, to appear in J Phys A Math Ge

Metal--Insulator Transitions in the Falicov--Kimball Model with Disorder

The ground state phase diagrams of the Falicov--Kimball model with local disorder is derived within the dynamical mean--field theory and using the geometrically averaged (''typical'') local density of states. Correlated metal, Mott insulator and Anderson insulator phases are identified. The metal--insulator transitions are found to be continuous. The interaction and disorder compete with each other stabilizing the metallic phase against occurring one of the insulators. The Mott and Anderson insulators are found to be continuously connected.Comment: 6 pages, 7 figure