Topological mass in seven dimensions and dualities in four dimensions

The massive topologically and self dual theories en seven dimensions are considered. The local duality between these theories is established and the dimensional reduction lead to the different dualities for massive antisymmetric fields in four dimensions.Comment: 7 page

A new case of autosomal recessive agammaglobulinaemia with impaired pre-B cell differentiation due to a large deletion of the IGH locus

Males with X-linked agammaglobulinaemia (XLA) due to mutations in the Bruton tyrosine kinase gene constitute the major group of congenital hypogammaglobulinaemia with absence of peripheral B cells. In these cases, blockages between the pro-B and pre-B cell stage in the bone marrow are found. The remaining male and female cases clinically similar to XLA represent a genotypically heterogeneous group of diseases. In these patients, various autosomal recessive disorders have been identified such as mutations affecting IGHM, CD79A, IGLL1 genes involved in the composition of the pre-B cell receptor (pre-BCR) or the BLNK gene implicated in pre-BCR signal transduction. In this paper, we report on a young female patient characterised by a severe non-XLA agammaglobulinaemia that represents a new case of Igmu defect. We show that the B cell blockage at the pro-B to pre-B cell transition is due to a large homologous deletion in the IGH locus encompassing the IGHM gene leading to the inability to form a functional pre-BCR. The deletion extends from the beginning of the diversity (D) region to the IGHG2 gene, with all JH segments and IGHM, IGHD, IGHG3 and IGHG1 genes missing. CONCLUSION: alteration in Igmu expression seems to be relatively frequent and could account for most of the reported cases of autosomal recessive agammaglobulinaemia

Deriving amino acid contact potentials from their frequencies of occurence in proteins: a lattice model study

The possibility of deriving the contact potentials between amino acids from their frequencies of occurence in proteins is discussed in evolutionary terms. This approach allows the use of traditional thermodynamics to describe such frequencies and, consequently, to develop a strategy to include in the calculations correlations due to the spatial proximity of the amino acids and to their overall tendency of being conserved in proteins. Making use of a lattice model to describe protein chains and defining a "true" potential, we test these strategies by selecting a database of folding model sequences, deriving the contact potentials from such sequences and comparing them with the "true" potential. Taking into account correlations allows for a markedly better prediction of the interaction potentials

Thermodynamics of protein folding: a random matrix formulation

The process of protein folding from an unfolded state to a biologically active, folded conformation is governed by many parameters e.g the sequence of amino acids, intermolecular interactions, the solvent, temperature and chaperon molecules. Our study, based on random matrix modeling of the interactions, shows however that the evolution of the statistical measures e.g Gibbs free energy, heat capacity, entropy is single parametric. The information can explain the selection of specific folding pathways from an infinite number of possible ways as well as other folding characteristics observed in computer simulation studies.Comment: 21 Pages, no figure

Bernstein-Sato functional equations, VV-filtrations, and multiplier ideals of direct summands

This paper investigates the existence and properties of a Bernstein-Sato functional equation in nonregular settings. In particular, we construct $D$-modules in which such formal equations can be studied. The existence of the Bernstein-Sato polynomial for a direct summand of a polynomial over a field is proved in this context. It is observed that this polynomial can have zero as a root, or even positive roots. Moreover, a theory of $V$-filtrations is introduced for nonregular rings, and the existence of these objects is established for what we call differentially extensible summands. This family of rings includes toric, determinantal, and other invariant rings. This new theory is applied to the study of multiplier ideals and Hodge ideals of singular varieties. Finally, we extend known relations among the objects of interest in the smooth case to the setting of singular direct summands of polynomial rings.Comment: 42 pages. A new section on Hodge ideals is included. Comments welcom

Bernstein's inequality and holonomicity for certain singular rings

In this manuscript we prove the Bernstein inequality and develop the theory of holonomic D-modules for rings of invariants of finite groups in characteristic zero, and for strongly F-regular finitely generated graded algebras with FFRT in prime characteristic. In each of these cases, the ring itself, its localizations, and its local cohomology modules are holonomic. We also show that holonomic D-modules, in this context, have finite length. We obtain these results using a more general version of Bernstein filtrations.Comment: 34 pages. Comments welcom