Frobenius Manifolds and Central Invariants for the Drinfeld - Sokolov Bihamiltonian Structures

The Drinfeld - Sokolov construction associates a hierarchy of bihamiltonian integrable systems with every untwisted affine Lie algebra. We compute the complete set of invariants of the related bihamiltonian structures with respect to the group of Miura type transformations.Comment: 73 pages, no figure

Bihamiltonian Cohomologies and Integrable Hierarchies I: A Special Case

We present some general results on properties of the bihamiltonian cohomologies associated to bihamiltonian structures of hydrodynamic type, and compute the third cohomology for the bihamiltonian structure of the dispersionless KdV hierarchy. The result of the computation enables us to prove the existence of bihamiltonian deformations of the dispersionless KdV hierarchy starting from any of its infinitesimal deformations.Comment: 43 pages. V2: the accepted version, to appear in Comm. Math. Phy

Mechanisms of Hybrid Oligomer Formation in the Pathogenesis of Combined Alzheimer's and Parkinson's Diseases

Background: Misfolding and pathological aggregation of neuronal proteins has been proposed to play a critical role in the pathogenesis of neurodegenerative disorders. Alzheimer’s disease (AD) and Parkinson’s disease (PD) are frequent neurodegenerative diseases of the aging population. While progressive accumulation of amyloid b protein (Ab) oligomers has been identified as one of the central toxic events in AD, accumulation of a-synuclein (a-syn) resulting in the formation of oligomers and protofibrils has been linked to PD and Lewy body Disease (LBD). We have recently shown that Ab promotes a-syn aggregation and toxic conversion in vivo, suggesting that abnormal interactions between misfolded proteins might contribute to disease pathogenesis. However the molecular characteristics and consequences of these interactions are not completely clear. Methodology/Principal Findings: In order to understand the molecular mechanisms involved in potential Ab/a-syn interactions, immunoblot, molecular modeling, and in vitro studies with a-syn and Ab were performed. We showed in vivo in the brains of patients with AD/PD and in transgenic mice, Ab and a-synuclein co-immunoprecipitate and form complexes. Molecular modeling and simulations showed that Ab binds a-syn monomers, homodimers, and trimers, forming hybrid ringlike pentamers. Interactions occurred between the N-terminus of Ab and the N-terminus and C-terminus of a-syn. Interacting a-syn and Ab dimers that dock on the membrane incorporated additional a-syn molecules, leading to th

Multiplicity of cerebrospinal fluid functions: New challenges in health and disease

This review integrates eight aspects of cerebrospinal fluid (CSF) circulatory dynamics: formation rate, pressure, flow, volume, turnover rate, composition, recycling and reabsorption. Novel ways to modulate CSF formation emanate from recent analyses of choroid plexus transcription factors (E2F5), ion transporters (NaHCO3 cotransport), transport enzymes (isoforms of carbonic anhydrase), aquaporin 1 regulation, and plasticity of receptors for fluid-regulating neuropeptides. A greater appreciation of CSF pressure (CSFP) is being generated by fresh insights on peptidergic regulatory servomechanisms, the role of dysfunctional ependyma and circumventricular organs in causing congenital hydrocephalus, and the clinical use of algorithms to delineate CSFP waveforms for diagnostic and prognostic utility. Increasing attention focuses on CSF flow: how it impacts cerebral metabolism and hemodynamics, neural stem cell progression in the subventricular zone, and catabolite/peptide clearance from the CNS. The pathophysiological significance of changes in CSF volume is assessed from the respective viewpoints of hemodynamics (choroid plexus blood flow and pulsatility), hydrodynamics (choroidal hypo- and hypersecretion) and neuroendocrine factors (i.e., coordinated regulation by atrial natriuretic peptide, arginine vasopressin and basic fibroblast growth factor). In aging, normal pressure hydrocephalus and Alzheimer's disease, the expanding CSF space reduces the CSF turnover rate, thus compromising the CSF sink action to clear harmful metabolites (e.g., amyloid) from the CNS. Dwindling CSF dynamics greatly harms the interstitial environment of neurons. Accordingly the altered CSF composition in neurodegenerative diseases and senescence, because of adverse effects on neural processes and cognition, needs more effective clinical management. CSF recycling between subarachnoid space, brain and ventricles promotes interstitial fluid (ISF) convection with both trophic and excretory benefits. Finally, CSF reabsorption via multiple pathways (olfactory and spinal arachnoidal bulk flow) is likely complemented by fluid clearance across capillary walls (aquaporin 4) and arachnoid villi when CSFP and fluid retention are markedly elevated. A model is presented that links CSF and ISF homeostasis to coordinated fluxes of water and solutes at both the blood-CSF and blood-brain transport interfaces

QCD and strongly coupled gauge theories : challenges and perspectives

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.Peer reviewe