Hopping on the Bethe lattice: Exact results for densities of states and dynamical mean-field theory

We derive an operator identity which relates tight-binding Hamiltonians with arbitrary hopping on the Bethe lattice to the Hamiltonian with nearest-neighbor hopping. This provides an exact expression for the density of states (DOS) of a non-interacting quantum-mechanical particle for any hopping. We present analytic results for the DOS corresponding to hopping between nearest and next-nearest neighbors, and also for exponentially decreasing hopping amplitudes. Conversely it is possible to construct a hopping Hamiltonian on the Bethe lattice for any given DOS. These methods are based only on the so-called distance regularity of the infinite Bethe lattice, and not on the absence of loops. Results are also obtained for the triangular Husimi cactus, a recursive lattice with loops. Furthermore we derive the exact self-consistency equations arising in the context of dynamical mean-field theory, which serve as a starting point for studies of Hubbard-type models with frustration.Comment: 14 pages, 9 figures; introduction expanded, references added; published versio

Conformal invariance studies of the Baxter-Wu model and a related site-colouring problem

The partition function of the Baxter-Wu model is exactly related to the generating function of a site-colouring problem on a hexagonal lattice. We extend the original Bethe ansatz solution of these models in order to obtain the eigenspectra of their transfer matrices in finite geometries and general toroidal boundary conditions. The operator content of these models are studied by solving numerically the Bethe-ansatz equations and by exploring conformal invariance. Since the eigenspectra are calculated for large lattices, the corrections to finite-size scaling are also calculated.Comment: 12 pages, latex, to appear in J. Phys. A: Gen. Mat

Enumeration of simple random walks and tridiagonal matrices

We present some old and new results in the enumeration of random walks in one dimension, mostly developed in works of enumerative combinatorics. The relation between the trace of the $n$-th power of a tridiagonal matrix and the enumeration of weighted paths of $n$ steps allows an easier combinatorial enumeration of the paths. It also seems promising for the theory of tridiagonal random matrices .Comment: several ref.and comments added, misprints correcte

The stability and melting of aragonite: An experimental and thermodynamic model for carbonated eclogites in the mantle

Subduction of calcium carbonate, sequestered in the oceanic crust by hydrothermal metamorphism and biogenic action, accounts for a significant flux of carbon into the mantle, where it contributes to the genesis of carbonatitic and silica-undersaturated melts. However, the reported phase relations in the system CaCO3, notably the transition boundary from disordered calcite (calcite V, here ccv) to aragonite (ara), vary considerably among different studies. Moreover, the thermodynamic properties of ccv and of liquid CaCO3 (CaCO3L) remain to be determined. In order to address the dearth of experimental data on phase relations, and to determine a set of internally consistent thermodynamic properties for ara, ccv and CaCO3L, multi-anvil experiments were performed at 3\u20136 GPa and 1300\u20131750 \ub0C. By re-evaluating all experimental data, the transformation of ccv-ara fits the equation Tccv-ara = 397.6 + 320.17 7 P and the melting curve Tm = 1578.9 + 139.65 7 P 12 11.646 7 P2, where pressure is in GPa and temperature in K. Thermodynamic properties retrieved for calcite V and liquid CaCO3 are used to compute phase diagrams of relevance for chemical compositions representative of eclogite heterogeneities of the astenospheric mantle, and compared with experimentally derived phase relationships. Aragonite represents a carbonate of major abundance in carbonated eclogites at high temperature, close to the solidus; its ability to fractionate REE and Ba-Sr contributes to the peculiar geochemical signatures of silica undersaturated magmas. The relatively refractory nature of aragonite impacts on our understanding of the deep carbon cycle

Biomarkers of aging in HIV: inflammation and the microbiome

Purpose: HIV-infected subjects present increased levels of inflammatory cytokines and T cell activation in the peripheral blood despite suppressive combination antiretroviral therapy which renders them susceptible to premature aging. The purpose of the present work was to review existing evidence on the ways in which the anatomical and microbiological abnormalities of the gastrointestinal tract can represent a major cause of organ disease in HIV infection. Methods: We conducted a systematic review of the Pubmed database for articles published from 2014 to 2018. We included studies on inflammatory/activation biomarkers associated with cardiovascular and bone disease, neurocognitive impairment and serious non-AIDS events in HIV-infected subjects. We also included researches which linked peripheral inflammation/activation to the anatomical, immune and microbiological alterations of the gastrointestinal tract. Results: Recent literature data confirm the association between non-infectious comorbidities and inflammation in HIV infection which may be driven by gastrointestinal tract abnormalities, specifically microbial translocation and dysbiosis. Furthermore, there is mounting evidence on the possible role of metabolic functions of the microbiota in the pathogenesis of premature aging in the HIV-infected population. Conclusions: Biomarkers need to be validated for their use in the management of HIV infection. Compounds which counteract microbial translocation, inflammation and dysbiosis have been investigated as alternative therapeutic strategies in viro-suppressed HIV-infected individuals, but appear to have limited efficacy, probably due to the multifactorial pathogenesis of non-infectious comorbidities in this setting

Short-Term Repeated-Sprint Training (Straight Sprint vs. Changes of Direction) in Soccer Players

Repeated-sprint training (RST) is considered a critical training method in team sports. It is well known that RST effects may depend on several variables such as the duration of the protocol and repeated-sprint methodology. Few studies have evaluated very short-term protocols and compared different RST modalities. The aim of this study was to compare the effectiveness of 2 week RST including straight sprints or changes of direction (CODs) on physical performance in a sample of soccer players. This study used a randomised pre-post parallel group trial design. The participants were assigned to either an RST group using straight sprints (RST-SS = 18 players) or an RST group using CODs (RST-COD = 18 players). The protocols were: 3 sets of 7 x 30 m sprints for the RST-SS and 7 x 20 + 20 m (one COD of 180 degrees) for the RST-COD, with 20 s and 4 min recovery between sprints and sets, respectively. The following evaluations were performed: 10 and 20 m sprint, agility test, repeated sprint test (RSTbest and RSTmean), and Yo-Yo Recovery Level 1. After the training period, the RST-SS did not report any performance variation, while the RST-COD showed improvements in the 10 m sprint and RSTbest (effect size = 0.70 and 0.65, respectively). The between-group analysis did not report any statistical difference between the RST-SS and the RST-COD. In conclusion, this study did not support the utilisation of a very short-term RST protocol with soccer players, however, the RST-COD presented some additional benefits in sprint performance compared to the RST-SS

Magnetic and Combined Field Integral Equations Based on the Quasi-Helmholtz Projectors

Boundary integral equation methods for analyzing electromagnetic scattering phenomena typically suffer from several of the following shortcomings: 1) ill-conditioning when the frequency is low; 2) ill-conditioning when the discretization density is high; 3) ill-conditioning when the structure contains global loops (which are computationally expensive to detect); 4) incorrect solution at low frequencies due to a loss of significant digits; and 5) the presence of spurious resonances. In this article, quasi-Helmholtz projectors are leveraged to obtain magnetic field integral equation (MFIE) that is immune to drawbacks 1)-4). Moreover, when this new MFIE is combined with a regularized electric field integral equation (EFIE), a new quasi-Helmholtz projector-combined field integral equation (CFIE) is obtained that also is immune to 5). The numerical results corroborate the theory and show the practical impact of the newly proposed formulations

Dominant mutations in the cation channel gene transient receptor potential vanilloid 4 cause an unusual spectrum of neuropathies

Hereditary neuropathies form a heterogeneous group of disorders for which over 40 causal genes have been identified to date. Recently, dominant mutations in the transient receptor potential vanilloid 4 gene were found to be associated with three distinct neuromuscular phenotypes: hereditary motor and sensory neuropathy 2C, scapuloperoneal spinal muscular atrophy and congenital distal spinal muscular atrophy. Transient receptor potential vanilloid 4 encodes a cation channel previously implicated in several types of dominantly inherited bone dysplasia syndromes. We performed DNA sequencing of the coding regions of transient receptor potential vanilloid 4 in a cohort of 145 patients with various types of hereditary neuropathy and identified five different heterozygous missense mutations in eight unrelated families. One mutation arose de novo in an isolated patient, and the remainder segregated in families. Two of the mutations were recurrent in unrelated families. Four mutations in transient receptor potential vanilloid 4 targeted conserved arginine residues in the ankyrin repeat domain, which is believed to be important in protein-protein interactions. Striking phenotypic variability between and within families was observed. The majority of patients displayed a predominantly, or pure, motor neuropathy with axonal characteristics observed on electrophysiological testing. The age of onset varied widely, ranging from congenital to late adulthood onset. Various combinations of additional features were present in most patients including vocal fold paralysis, scapular weakness, contractures and hearing loss. We identified six asymptomatic mutation carriers, indicating reduced penetrance of the transient receptor potential vanilloid 4 defects. This finding is relatively unusual in the context of hereditary neuropathies and has important implications for diagnostic testing and genetic counsellin

First Report of Circulating MicroRNAs in Tumour Necrosis Factor Receptor-Associated Periodic Syndrome (TRAPS)

Tumor necrosis factor-receptor associated periodic syndrome (TRAPS) is a rare autosomal dominant autoinflammatory disorder characterized by recurrent episodes of long-lasting fever and inflammation in different regions of the body, such as the musculo-skeletal system, skin, gastrointestinal tract, serosal membranes and eye. Our aims were to evaluate circulating microRNAs (miRNAs) levels in patients with TRAPS, in comparison to controls without inflammatory diseases, and to correlate their levels with parameters of disease activity and/or disease severity. Expression levels of circulating miRNAs were measured by Agilent microarrays in 29 serum samples from 15 TRAPS patients carrying mutations known to be associated with high disease penetrance and from 8 controls without inflammatory diseases. Differentially expressed and clinically relevant miRNAs were detected using GeneSpring GX software. We identified a 6 miRNAs signature able to discriminate TRAPS from controls. Moreover, 4 miRNAs were differentially expressed between patients treated with the interleukin (IL)-1 receptor antagonist, anakinra, and untreated patients. Of these, miR-92a-3p and miR-150-3p expression was found to be significantly reduced in untreated patients, while their expression levels were similar to controls in samples obtained during anakinra treatment. MiR-92b levels were inversely correlated with the number of fever attacks/year during the 1st year from the index attack of TRAPS, while miR-377-5p levels were positively correlated with serum amyloid A (SAA) circulating levels. Our data suggest that serum miRNA levels show a baseline pattern in TRAPS, and may serve as potential markers of response to therapeutic intervention