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

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

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

Rationale, application and clinical qualification for NT-proBNP as a surrogate end point in pivotal clinical trials in patients with AL amyloidosis

Amyloid light-chain (LC) amyloidosis (AL amyloidosis) is a rare and fatal disease for which there are no approved therapies. In patients with AL amyloidosis, LC aggregates progressively accumulate in organs, resulting in organ failure that is particularly lethal when the heart is involved. A significant obstacle in the development of treatments for patients with AL amyloidosis, as well as for those with any disease that is rare, severe and heterogeneous, has been satisfying traditional clinical trial end points (for example, overall survival or progression-free survival). It is for this reason that many organizations, including the United States Food and Drug Administration through its Safety and Innovation Act Accelerated Approval pathway, have recognized the need for biomarkers as surrogate end points. The international AL amyloidosis expert community is in agreement that the N-terminal fragment of the pro-brain natriuretic peptide (NT-proBNP) is analytically validated and clinically qualified as a biomarker for use as a surrogate end point for survival in patients with AL amyloidosis. Underlying this consensus is the demonstration that NT-proBNP is an indicator of cardiac response in all interventional studies in which it has been assessed, despite differences in patient population, treatment type and treatment schedule. Furthermore, NT-proBNP expression is directly modulated by amyloidogenic LC-elicited signal transduction pathways in cardiomyocytes. The use of NT-proBNP will greatly facilitate the development of targeted therapies for AL amyloidosis. Here, we review the data supporting the use of NT-proBNP, a biomarker that is analytically validated, clinically qualified, directly modulated by LC and universally accepted by AL amyloidosis specialists, as a surrogate end point for survival.Leukemia advance online publication, 2 August 2016; doi:10.1038/leu.2016.191

Renal apolipoprotein A-I amyloidosis: a rare and usually ignored cause of hereditary tubulointerstitial nephritis

12openopenGregorini G; Izzi C; Obici L; Tardanico R; Röcken C; Viola BF; Capistrano M; Donadei S; Biasi L; Scalvini T; Merlini G; Scolari F.Gregorini, G; Izzi, C; Obici, L; Tardanico, R; Röcken, C; Viola, Bf; Capistrano, M; Donadei, S; Biasi, L; Scalvini, T; Merlini, G; Scolari, Francesc

Critical and off-critical studies of the Baxter-Wu model with general toroidal boundary conditions

The operator content of the Baxter-Wu model with general toroidal boundary conditions is calculated analytically and numerically. These calculations were done by relating the partition function of the model with the generating function of a site-colouring problem in a hexagonal lattice. Extending the original Bethe-ansatz solution of the related colouring problem we are able to calculate the eigenspectra of both models by solving the associated Bethe-ansatz equations. We have also calculated, by exploring the conformal invariance at the critical point, the mass ratios of the underlying massive theory governing the Baxter-Wu model in the vicinity of its critical point.Comment: 32 pages latex, to appear in J. Phys. A: Math. Ge

Extracellular matrix and nuclear abnormalities in skeletal muscle of a patient with Walker–Warburg syndrome caused by POMT1 mutation

AbstractWalker–Warburg syndrome (WWS) is an autosomal recessive disorder characterized by congenital muscular dystrophy, structural eye abnormalities and severe brain malformations. We performed an immunohistochemical and electron microscopy study of a muscle biopsy from a patient affected by WWS carrying a homozygous frameshift mutation in O-mannosyltransferase 1 gene (POMT1). α-Dystroglycan glycosylated epitope was not detected in muscle fibers and intramuscular peripheral nerves. Laminin α2 chain and perlecan were reduced in muscle fibers and well preserved in intramuscular peripheral nerves. The basal lamina in several muscle fibers showed discontinuities and detachment from the plasmalemma. Most nuclei, including myonuclei and satellite cell nuclei, showed detachment or complete absence of peripheral heterochromatin from the nuclear envelope. Apoptotic changes were detected in 3% of muscle fibers. The particular combination of basal lamina and nuclear changes may suggest that a complex pathogenetic mechanism, affecting several subcellular compartments, underlies the degenerative process in WWS muscle

Proteomic and phosphoproteomic analyses reveal that TORC1 is reactivated by pheromone signaling during sexual reproduction in fission yeast.

Starvation, which is associated with inactivation of the growth-promoting TOR complex 1 (TORC1), is a strong environmental signal for cell differentiation. In the fission yeast Schizosaccharomyces pombe, nitrogen starvation has distinct physiological consequences depending on the presence of mating partners. In their absence, cells enter quiescence, and TORC1 inactivation prolongs their life. In presence of compatible mates, TORC1 inactivation is essential for sexual differentiation. Gametes engage in paracrine pheromone signaling, grow towards each other, fuse to form the diploid zygote, and form resistant, haploid spore progenies. To understand the signaling changes in the proteome and phospho-proteome during sexual reproduction, we developed cell synchronization strategies and present (phospho-)proteomic data sets that dissect pheromone from starvation signals over the sexual differentiation and cell-cell fusion processes. Unexpectedly, these data sets reveal phosphorylation of ribosomal protein S6 during sexual development, which we establish requires TORC1 activity. We demonstrate that TORC1 is re-activated by pheromone signaling, in a manner that does not require autophagy. Mutants with low TORC1 re-activation exhibit compromised mating and poorly viable spores. Thus, while inactivated to initiate the mating process, TORC1 is reactivated by pheromone signaling in starved cells to support sexual reproduction

Persistent Dystrophin Protein Restoration 90 Days after a Course of Intraperitoneally Administered Naked 2′OMePS AON and ZM2 NP-AON Complexes in mdx Mice

In Duchenne muscular dystrophy, the exon-skipping approach has obtained proof of concept in animal models, myogenic cell cultures, and following local and systemic administration in Duchenne patients. Indeed, we have previously demonstrated that low doses (7.5 mg/Kg/week) of 2 -O-methyl-phosphorothioate antisense oligoribonucleotides (AONs) adsorbed onto ZM2 nanoparticles provoke widespread dystrophin restoration 7 days after intraperitoneal treatment in mdx mice. In this study, we went on to test whether this dystrophin restoration was still measurable 90 days from the end of the same treatment. Interestingly, we found that both western blot and immunohistochemical analysis (up to 7% positive fibres) were still able to detect dystrophin protein in the skeletal muscles of ZM2-AON-treated mice at this time, and the level of exon-23 skipping could still be assessed by RT real-time PCR (up to 10% of skipping percentage). In contrast, the protein was undetectable by western blot analysis in the skeletal muscles of mdx mice treated with an identical dose of naked AON, and the percentage of dystrophin-positive fibres and exon-23 skipping were reminiscent of those of untreated mdx mice. Our data therefore demonstrate the long-term residual efficacy of this systemic low-dose treatment and confirm the protective effect nanoparticles exert on AON molecules