The sh Lie structure of Poisson brackets in field theory

A general construction of an sh Lie algebra from a homological resolution of a Lie algebra is given. It is applied to the space of local functionals equipped with a Poisson bracket, induced by a bracket for local functions along the lines suggested by Gel'fand, Dickey and Dorfman. In this way, higher order maps are constructed which combine to form an sh Lie algebra on the graded differential algebra of horizontal forms. The same construction applies for graded brackets in field theory such as the Batalin-Fradkin-Vilkovisky bracket of the Hamiltonian BRST theory or the Batalin-Vilkovisky antibracket.Comment: 24 pages Latex fil

Algebra Structures on Hom(C,L)

We consider the space of linear maps from a coassociative coalgebra C into a Lie algebra L. Unless C has a cocommutative coproduct, the usual symmetry properties of the induced bracket on Hom(C,L) fail to hold. We define the concept of twisted domain (TD) algebras in order to recover the symmetries and also construct a modified Chevalley-Eilenberg complex in order to define the cohomology of such algebras

Classical field theory. Advanced mathematical formulation

In contrast with QFT, classical field theory can be formulated in strict mathematical terms of fibre bundles, graded manifolds and jet manifolds. Second Noether theorems provide BRST extension of this classical field theory by means of ghosts and antifields for the purpose of its quantization.Comment: 30 p

Noether's second theorem in a general setting. Reducible gauge theories

We prove Noether's direct and inverse second theorems for Lagrangian systems on fiber bundles in the case of gauge symmetries depending on derivatives of dynamic variables of an arbitrary order. The appropriate notions of reducible gauge symmetries and Noether's identities are formulated, and their equivalence by means of certain intertwining operator is proved.Comment: 20 pages, to be published in J. Phys. A (2005

The KT-BRST complex of a degenerate Lagrangian system

Quantization of a Lagrangian field system essentially depends on its degeneracy and implies its BRST extension defined by sets of non-trivial Noether and higher-stage Noether identities. However, one meets a problem how to select trivial and non-trivial higher-stage Noether identities. We show that, under certain conditions, one can associate to a degenerate Lagrangian L the KT-BRST complex of fields, antifields and ghosts whose boundary and coboundary operators provide all non-trivial Noether identities and gauge symmetries of L. In this case, L can be extended to a proper solution of the master equation.Comment: 15 pages, accepted for publication in Lett. Math. Phy

Lymphatic vasculature mediates macrophage reverse cholesterol transport in mice

Reverse cholesterol transport (RCT) refers to the mobilization of cholesterol on HDL particles (HDL-C) from extravascular tissues to plasma, ultimately for fecal excretion. Little is known about how HDL-C leaves peripheral tissues to reach plasma. We first used 2 models of disrupted lymphatic drainage from skin — 1 surgical and the other genetic — to quantitatively track RCT following injection of [3H]-cholesterol–loaded macrophages upstream of blocked or absent lymphatic vessels. Macrophage RCT was markedly impaired in both models, even at sites with a leaky vasculature. Inhibited RCT was downstream of cholesterol efflux from macrophages, since macrophage efflux of a fluorescent cholesterol analog (BODIPY-cholesterol) was not altered by impaired lymphatic drainage. We next addressed whether RCT was mediated by lymphatic vessels from the aortic wall by loading the aortae of donor atherosclerotic Apoe-deficient mice with [2H]6-labeled cholesterol and surgically transplanting these aortae into recipient Apoe-deficient mice that were treated with anti-VEGFR3 antibody to block lymphatic regrowth or with control antibody to allow such regrowth. [2H]-Cholesterol was retained in aortae of anti–VEGFR3-treated mice. Thus, the lymphatic vessel route is critical for RCT from multiple tissues, including the aortic wall. These results suggest that supporting lymphatic transport function may facilitate cholesterol clearance in therapies aimed at reversing atherosclerosis

Male circumcision and prevalence of genital human papillomavirus infection in men : a multinational study

Background: Accumulated evidence from epidemiological studies and more recently from randomized controlled trials suggests that male circumcision (MC) may substantially protect against genital HPV infection in men. The purpose of this study was to assess the association between MC and genital HPV infection in men in a large multinational study. Methods: A total of 4072 healthy men ages 18-70 years were enrolled in a study conducted in Brazil, Mexico, and the United States. Enrollment samples combining exfoliated cells from the coronal sulcus, glans penis, shaft, and scrotum were analyzed for the presence and genotyping of HPV DNA by PCR and linear array methods. Prevalence ratios (PR) were used to estimate associations between MC and HPV detection adjusting for potential confounders. Results: MC was not associated with overall prevalence of any HPV, oncogenic HPV types or unclassified HPV types. However, MC was negatively associated with non-oncogenic HPV infections (PR 0.85, 95% confident interval: 0.76-0.95), in particular for HPV types 11, 40, 61, 71, and 81. HPV 16, 51, 62, and 84 were the most frequently identified genotypes regardless of MC status. Conclusions: This study shows no overall association between MC and genital HPV infections in men, except for certain non-oncogenic HPV types for which a weak association was found. However, the lack of association with MC might be due to the lack of anatomic site specific HPV data, for example the glans penis, the area expected to be most likely protected by MC

Homological evolutionary vector fields in Korteweg-de Vries, Liouville, Maxwell, and several other models

We review the construction of homological evolutionary vector fields on infinite jet spaces and partial differential equations. We describe the applications of this concept in three tightly inter-related domains: the variational Poisson formalism (e.g., for equations of Korteweg-de Vries type), geometry of Liouville-type hyperbolic systems (including the 2D Toda chains), and Euler-Lagrange gauge theories (such as the Yang-Mills theories, gravity, or the Poisson sigma-models). Also, we formulate several open problems.Comment: Proc. 7th International Workshop "Quantum Theory and Symmetries-7" (August 7-13, 2011; CVUT Prague, Czech Republic), 20 page

Mutations in the nuclear localization sequence of the Aristaless related homeobox; sequestration of mutant ARX with IPO13 disrupts normal subcellular distribution of the transcription factor and retards cell division

The electronic version of this article is the complete one and can be found online at: http://www.pathogeneticsjournal.com/content/3/1/1Background: Aristaless related homeobox (ARX) is a paired-type homeobox gene. ARX function is frequently affected by naturally occurring mutations. Nonsense mutations, polyalanine tract expansions and missense mutations in ARX cause a range of intellectual disability and epilepsy phenotypes with or without additional features including hand dystonia, lissencephaly, autism or dysarthria. Severe malformation phenotypes, such as X-linked lissencephaly with ambiguous genitalia (XLAG), are frequently observed in individuals with protein truncating or missense mutations clustered in the highly conserved paired-type homeodomain. Results: We have identified two novel point mutations in the R379 residue of the ARX homeodomain; c.1135C>A, p.R379S in a patient with infantile spasms and intellectual disability and c.1136G>T, p.R379L in a patient with XLAG. We investigated these and other missense mutations (R332P, R332H, R332C, T333N: associated with XLAG and Proud syndrome) predicted to affect the nuclear localisation sequences (NLS) flanking either end of the ARX homeodomain. The NLS regions are required for correct nuclear import facilitated by Importin 13 (IPO13). We demonstrate that missense mutations in either the N- or C-terminal NLS regions of the homeodomain cause significant disruption to nuclear localisation of the ARX protein in vitro. Surprisingly, none of these mutations abolished the binding of ARX to IPO13. This was confirmed by co-immunoprecipitation and immmuno fluorescence studies. Instead, tagged and endogenous IPO13 remained bound to the mutant ARX proteins, even in the RanGTP rich nuclear environment. We also identify the microtubule protein TUBA1A as a novel interacting protein for ARX and show cells expressing mutant ARX protein accumulate in mitosis, indicating normal cell division may be disrupted. Conclusions: We show that the most likely, common pathogenic mechanism of the missense mutations in NLS regions of the ARX homeodomain is inadequate accumulation and distribution of the ARX transcription factor within the nucleus due to sequestration of ARX with IPO13.Cheryl Shoubridge, May Huey Tan, Tod Fullston, Desiree Cloosterman, David Coman, George McGillivray, Grazia M Mancini, Tjitske Kleefstra and Jozef Géc