Noether's theorem and gauge transformations. Application to the bosonic string and CP(2,n-1) model

New results on the theory of constrained systems are applied to characterize the generators of Noethers symmetry transformations. As a byproduct, an algorithm to construct gauge transformations in Hamiltonian formalism is derived. This is illustrated with two relevant examples.

Lee HWA Chung theorem for presympectic manifolds. Canonical transformations for constrained systems

We generalize the analogous of Lee Hwa Chungs theorem to the case of presymplectic manifolds. As an application, we study the canonical transformations of a canonical system (M, S, O). The role of Dirac brackets as a test of canonicity is clarified.

World-line condition and the noninteraction theorem

A 6N-dimensional alternative formulation is proposed for constrained Hamiltonian systems. In this context the noninteraction theorem is derived from the world-line conditions. A model of two interacting particles is exhibited where physical coordinates are canonical.

Test of the fluctuation theorem for stochastic entropy production in a nonequilibrium steady state

We derive a simple closed analytical expression for the total entropy production along a single stochastic trajectory of a Brownian particle diffusing on a periodic potential under an external constant force. By numerical simulations we compute the probability distribution functions of the entropy and satisfactorily test many of the predictions based on Seiferts integral fluctuation theorem. The results presented for this simple model clearly illustrate the practical features and implications derived from such a result of nonequilibrium statistical mechanics.

Lee HWA Chung theorem for presympectic manifolds. Canonical transformations for constrained systems

We generalize the analogous of Lee Hwa Chungs theorem to the case of presymplectic manifolds. As an application, we study the canonical transformations of a canonical system (M, S, O). The role of Dirac brackets as a test of canonicity is clarified.

Realizations of Poincar group induced by second order differential systems. Non interaction theorem

A generalization of the predictive relativistic mechanics is studied where the initial conditions are taken on a general hypersurface of M4. The induced realizations of the Poincar group are obtained. The same procedure is used for the Galileo group. Noninteraction theorems are derived for both groups.

Arenavirus envelope glycoproteins mimic autoprocessing sites of the cellular proprotein convertase subtilisin kexin isozyme-1/site-1 protease.

A crucial step in the arenavirus life cycle is the proteolytic processing of the viral envelope glycoprotein precursor (GPC) by the cellular proprotein convertase (PC) subtilisin kexin isozyme-1 (SKI-1)/site-1 protease (S1P). Here we conducted a systematic and quantitative analysis of SKI-1/S1P processing of peptides derived from the recognition sites of GPCs of different Old World and New World arenaviruses. We found that SKI-1/S1P showed a strong preference for arenaviral sequences resembling its autoprocessing sites, which are recurrent motifs in arenaviral GPCs. The African arenaviruses Lassa, Mobala, and Mopeia resemble the SKI-1/S1P autoprocessing C-site, whereas sequences derived from Clade B New World viruses Junin and Tacaribe have similarities to the autoprocessing B-site. In contrast, analogous peptides derived from cellular SKI-1/S1P substrates were remarkably poor substrates. The data suggest that arenavirus GPCs evolved to mimic SKI-1/S1P autoprocessing sites, likely ensuring efficient cleavage and perhaps avoiding competition with SKI-1/S1P's cellular substrates.

Approximation and support theorem for a wave equation in two space dimensions

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise. For some particular classes of coefficients, approximation in the Lp-norm for p¿1 is also proved.

Constructive micritic envelope developed in the vadose continental environment in the Pleistocene eoliantes of Mallorca (Spain)

In this study we analyze and explain the formation of the constructive micrite envelope in the vadose continental environment. This constructive micrite envelope shows a wide variety of textural components. The principal textural components are: microorganisms, micritic and microspar LMC cement, whisker crystals, microfibres and aggregates of LMC acicular crystals. The main microorganisms are hyphae fungi, although actynomicetes and bacteries also occur. The constructive micrite envelope is due to the action of calcified filaments (hyphae fungi) which collapse and coalesce forming an intertwined mesh as well as due to the precipitation of micritic and microspar cement. The whisker crystals, microfibres and aggregates of LMC acicular crystals are secondary microtextures. Constructive micrite envelopes does not indicate a specific diagenetic environment. The constructive micrite envelopes present irregularities or bumps at the outer surface of the grains, and the destructive micrite envelopes present irregularities towards the grain interior. This morphologic criterion is useful to differenciate the micrite envelope origin, constructive or destructive, in the fossil record.

The human epidermal differentiation complex: cornified envelope precursors, S100 proteins and the 'fused genes' family.

  The skin is essential for survival and protects our body against biological attacks, physical stress, chemical injury, water loss, ultraviolet radiation and immunological impairment. The epidermal barrier constitutes the primordial frontline of this defense established during terminal differentiation. During this complex process proliferating basal keratinocytes become suprabasally mitotically inactive and move through four epidermal layers (basal, spinous, granular and layer, stratum corneum) constantly adapting to the needs of the respective cell layer. As a result, squamous keratinocytes contain polymerized keratin intermediate filament bundles and a water-retaining matrix surrounded by the cross-linked cornified cell envelope (CE) with ceramide lipids attached on the outer surface. These cells are concomitantly insulated by intercellular lipid lamellae and hold together by corneodesmosmes. Many proteins essential for epidermal differentiation are encoded by genes clustered on chromosomal human region 1q21. These genes constitute the 'epidermal differentiation complex' (EDC), which is divided on the basis of common gene and protein structures, in three gene families: (i) CE precursors, (ii) S100A and (iii) S100 fused genes. EDC protein expression is regulated in a gene and tissue-specific manner by a pool of transcription factors. Among them, Klf4, Grhl3 and Arnt are essential, and their deletion in mice is lethal. The importance of the EDC is further reflected by human diseases: FLG mutations are the strongest risk factor for atopic dermatitis (AD) and for AD-associated asthma, and faulty CE formation caused by TG1 deficiency causes life-threatening lamellar ichthyosis. Here, we review the EDC genes and the progress in this field.

Uniform estimates in the Poincare-Aronszajn theorem on the separation of singularities of analytic functions

We study the possibility of splitting any bounded analytic function $f$ with singularities in a closed set $E\cup F$ as a sum of two bounded analytic functions with singularities in $E$ and $F$ respectively. We obtain some results under geometric restrictions on the sets $E$ and $F$ and we provide some examples showing the sharpness of the positive results.

Molecular characterization of the processing of arenavirus envelope glycoprotein precursors by subtilisin kexin isozyme-1/site-1 protease.

A crucial step in the life cycle of arenaviruses is the biosynthesis of the mature fusion-active viral envelope glycoprotein (GP) that is essential for virus-host cell attachment and entry. The maturation of the arenavirus GP precursor (GPC) critically depends on proteolytic processing by the cellular proprotein convertase (PC) subtilisin kexin isozyme-1 (SKI-1)/site-1 protease (S1P). Here we undertook a molecular characterization of the SKI-1/S1P processing of the GPCs of the prototypic arenavirus lymphocytic choriomeningitis virus (LCMV) and the pathogenic Lassa virus (LASV). Previous studies showed that the GPC of LASV undergoes processing in the endoplasmic reticulum (ER)/cis-Golgi compartment, whereas the LCMV GPC is cleaved in a late Golgi compartment. Herein we confirm these findings and provide evidence that the SKI-1/S1P recognition site RRLL, present in the SKI-1/S1P prodomain and LASV GPC, but not in the LCMV GPC, is crucial for the processing of the LASV GPC in the ER/cis-Golgi compartment. Our structure-function analysis revealed that the cleavage of arenavirus GPCs, but not cellular substrates, critically depends on the autoprocessing of SKI-1/S1P, suggesting differences in the processing of cellular and viral substrates. Deletion mutagenesis showed that the transmembrane and intracellular domains of SKI-1/S1P are dispensable for arenavirus GPC processing. The expression of a soluble form of the protease in SKI-I/S1P-deficient cells resulted in the efficient processing of arenavirus GPCs and rescued productive virus infection. However, exogenous soluble SKI-1/S1P was unable to process LCMV and LASV GPCs displayed at the surface of SKI-I/S1P-deficient cells, indicating that GPC processing occurs in an intracellular compartment. In sum, our study reveals important differences in the SKI-1/S1P processing of viral and cellular substrates.