Intermediate Wakimoto modules for Affine sl(n+1)

We construct certain boson type realizations of affine sl(n+1) that depend on a parameter r. When r=0 we get a Fock space realization of Imaginary Verma modules appearing in the work of the first author and when r=n they are the Wakimoto modules described in the work of Feigin and Frenkel

Virasoro action on Imaginary Verma modules and the operator form of the KZ-equation

We define the Virasoro algebra action on imaginary Verma modules for affine sl(2) and construct the analogs of Knizhnik-Zamolodchikov equation in the operator form. Both these results are based on a free field realization of imaginary Verma modules

Models of competitive learning: complex dynamics, intermittent conversions and oscillatory coarsening

We present two models of competitive learning, which are respectively interfacial and cooperative learning. This learning is outcome-related, so that spatially and temporally local environments influence the conversion of a given site between one of two different types. We focus here on the behavior of the models at coexistence, which yields new critical behavior and the existence of a phase involving a novel type of coarsening which is oscillatory in nature.Comment: 23 pages, 11 figures. To appear in Phys. Rev.

Decrease in Myelin-Associated Lipids Precedes Neuronal Loss and Glial Activation in the CNS of the Sandhoff Mouse as Determined by Metabolomics

Sandhoff disease (SD) is a lysosomal disease caused by mutations in the gene coding for the β subunit of β-hexosaminidase, leading to deficiency in the enzymes β-hexosaminidase (HEX) A and B. SD is characterised by an accumulation of gangliosides and related glycolipids, mainly in the central nervous system, and progressive neurodegeneration. The underlying cellular mecha-nisms leading to neurodegeneration and the contribution of inflammation in SD remain unde-fined. The aim of the present study was to measure global changes in metabolism over time that might reveal novel molecular pathways of disease. We used liquid chromatography-mass spec-trometry and 1H Nuclear Magnetic Resonance spectroscopy to profile intact lipids and aqueous metabolites, respectively. We examined spinal cord and cerebrum from healthy and Hexb -/- mice, a mouse model of SD, at ages one, two, three and four months. We report decreased concentrations in lipids typical of the myelin sheath, galactosylceramides and plasmalogen-phosphatidylethanolamines, suggesting that reduced synthesis of myelin lipids is an early event in the development of disease pathology. Reduction in neuronal density is pro-gressive, as demonstrated by decreased concentrations of N-acetylaspartate and amino acid neurotransmitters. Finally, microglial activation, indicated by increased amounts of myo-inositol correlates closely with the late symptomatic phases of the disease

Asymptotic expansion for reversible A + B <-> C reaction-diffusion process

We study long-time properties of reversible reaction-diffusion systems of type A + B C by means of perturbation expansion in powers of 1/t (inverse of time). For the case of equal diffusion coefficients we present exact formulas for the asymptotic forms of reactant concentrations and a complete, recursive expression for an arbitrary term of the expansions. Taking an appropriate limit we show that by studying reversible reactions one can obtain "singular" solutions typical of irreversible reactions.Comment: 6 pages, no figures, to appear in PR

Majority versus minority dynamics: Phase transition in an interacting two-state spin system

We introduce a simple model of opinion dynamics in which binary-state agents evolve due to the influence of agents in a local neighborhood. In a single update step, a fixed-size group is defined and all agents in the group adopt the state of the local majority with probability p or that of the local minority with probability 1-p. For group size G=3, there is a phase transition at p_c=2/3 in all spatial dimensions. For p>p_c, the global majority quickly predominates, while for p<p_c, the system is driven to a mixed state in which the densities of agents in each state are equal. For p=p_c, the average magnetization (the difference in the density of agents in the two states) is conserved and the system obeys classical voter model dynamics. In one dimension and within a Kirkwood decoupling scheme, the final magnetization in a finite-length system has a non-trivial dependence on the initial magnetization for all p.ne.p_c, in agreement with numerical results. At p_c, the exact 2-spin correlation functions decay algebraically toward the value 1 and the system coarsens as in the classical voter model.Comment: 11 pages, 3 figures, revtex4 2-column format; minor revisions for publication in PR

The role of transglutaminase in the rat subtotal nephrectomy model of renal fibrosis

Tissue transglutaminase is a calcium-dependent enzyme that catalyzes the cross-linking of polypeptide chains, including those of extracellular matrix (ECM) proteins, through the formation of epsilon-(gamma-glutamyl) lysine bonds. This crosslinking leads to the formation of protein polymers that are highly resistant to degradation. As a consequence, the enzyme has been implicated in the deposition of ECM protein in fibrotic diseases such as pulmonary fibrosis and atherosclerosis. In this study, we have investigated the involvement of tissue transglutaminase in the development of kidney fibrosis in adult male Wistar rats submitted to subtotal nephrectomy (SNx). Groups of six rats were killed on days 7, 30, 90, and 120 after SNx. As previously described, these rats developed progressive glomerulosclerosis and tubulo-interstitial fibrosis. The tissue level of epsilon-(gamma-glutamyl) lysine cross-link (as determined by exhaustive proteolytic digestion followed by cation exchange chromatography) increased from 3.47+/- 0.94 (mean+/-SEM) in controls to 13.24+/-1.43 nmol/g protein 90 d after SNx, P </= 0.01. Levels of epsilon-(gamma-glutamyl) lysine cross-link correlated well with the renal fibrosis score throughout the 120 observation days (r = 0.78, P </= 0.01). Tissue homogenates showed no significant change in overall transglutaminase activity (14C putrescine incorporation assay) unless adjusted for the loss of viable tubule cells, when an increase from 5.77+/-0.35 to 13.93+/-4.21 U/mg DNA in cytosolic tissue transglutaminase activity was seen. This increase was supported by Western blot analysis, showing a parallel increase in renal tissue transglutaminase content. Immunohistochemistry demonstrated that this large increase in epsilon-(gamma-glutamyl) lysine cross-link and tissue transglutaminase took place predominantly in the cytoplasm of tubular cells, while immunofluorescence also showed low levels of the epsilon-(gamma-glutamyl) lysine cross-link in the extracellular renal interstitial space. The number of cells showing increases in tissue transglutaminase and its cross-link product, epsilon-(gamma-glutamyl) lysine appeared greater than those showing signs of typical apoptosis as determined by in situ end-labeling. This observed association between tissue transglutaminase, epsilon-(gamma-glutamyl) lysine cross-link, and renal tubulointerstitial scarring in rats submitted to SNx suggests that tissue transglutaminase may play an important role in the development of experimental renal fibrosis and the associated loss of tubule integrity