Canonical Lévy process and Malliavin calculus

A suitable canonical Lévy process is constructed in order to study a Malliavin calculus based on a chaotic representation property of Lévy processes proved by Itô using multiple two-parameter integrals. In this setup, the two-parameter derivative _Dt,x$D_{t,x}$ is studied, depending on whether x=0$x=0$ or x≠0$x\ne 0$; in the first case, we prove a chain rule; in the second case, a formula by trajectories.     

Characterization of the core-shell nanoparticles formed as soluble hydrogen-bonding interpolymer complexes at low pH

The formation of soluble hydrogen-bonding interpolymer complexes between poly(acrylic acid) (PAA) and poly(acrylic acid-co-2-acrylamido-2-methyl-1-propane sulfonic acid)-graft-poly(N,N-dimethylacrylamide) (P(AA-co-AMPSA)-g-PDMAM) at pH=2.0 was studied. A viscometric study showed that in semidilute solution a physical gel is formed due to the interconnection of the anionic P(AA-co-AMPSA) backbone of the graft copolymer, in a transient network, by means of the complexes formed between the PDMAM side chains of the graft copolymer and PAA. Dynamic and static light scattering measurements, in conjunction with small-angle neutron scattering measurements, suggest the formation of core-shell colloidal nanoparticles in dilute solution, comprised by an insoluble PAA/PDMAM core surrounded by an anionic P(AA-co-AMPSA) corona. Even if larger clusters are formed in semidilute solution, the size of the insoluble core remains practically stable. Atomic force microscopy performed under ambient conditions reveal that the particles collapse and flatten upon deposition on a substrate, with dimensions close to the ones of the dry hydrophobic core.     

Highly fluorinated thermotropic liquid crystals: an update

Fluorine is used in liquid crystal materials in order to give them particular properties as compared to their hydrocarbon homologues. This leads to use of the new compounds as materials mainly in display devices such as Twisted Nematic Liquid Crystals Display (TNLCD) or for the development of Surface Stabilized Ferroelectric smectic C* display (SSFLCDs). In this paper, we describe recent studies and research effort concerning the liquid crystalline behavior of compounds incorporating a highly fluorinated part with more than one fluoromethylene units. We examine some of their mesophase properties and the impact of molecular shape on the resulting liquid crystal behavior.     

Considerations on the spring analogy

This paper presents an investigation on the spring analogy. The spring analogy serves for deformation in a moving boundary problem. First, two different kinds of springs are discussed: the vertex springs and the segment springs. The vertex spring analogy is originally used for smoothing a mesh after mesh generation or refinement. The segment spring analogy is used for deformation of the mesh in a moving boundary problem. The difference between the two methods lies in the equilibrium length of the springs. By means of an analogy to molecular theory, the two theories are generalized into a single theory that covers both. The usual choice of the stiffness of the spring is clarified by the mathematical analysis of a representative one‐dimensional configuration. The analysis shows that node collision is prevented when the stiffness is chosen as the inverse of the segment length. The observed similarity between elliptic grid generation and the spring analogy is also investigated. This investigation shows that both methods update the grid point position by a weighted average of the surrounding points in an iterative manner. The weighting functions enforce regularity of the mesh. Based on these considerations, several improvements on the spring analogy are developed. The principle of Saint Venant is circumvented by a boundary correction. The prevention of inversion of triangular elements is improved by semi‐torsional springs. The numerical results show the superiority of the segment spring analogy over the vertex one for a small rotation of an NACA0012 mesh. The boundary correction allows for large deformation of the mesh, where the standard spring analogy fails. The final test is performed on a Navier–Stokes mesh. This mesh contains high aspect ratio mesh cells near the boundary. Large deformation of this mesh shows that the semi‐torsional spring improvement is imperative to retain the validity of this mesh. Copyright © 2000 John Wiley & Sons, Ltd.     

On the b-Coloring of Cographs and <Emphasis Type="Italic">P</Emphasis><Subscript>4</Subscript>-Sparse Graphs

A b-coloring of a graph is a coloring such that every color class admits a vertex adjacent to at least one vertex receiving each of the colors not assigned to it. The b-chromatic number of a graph G, denoted by χ _b (G), is the maximum number t such that G admits a b-coloring with t colors. A graph G is b-continuous if it admits a b-coloring with t colors, for every . We define a graph G to be b-monotonic if χ _b (H ₁) ≥ χ _b (H ₂) for every induced subgraph H ₁ of G, and every induced subgraph H ₂ of H ₁. In this work, we prove that P ₄-sparse graphs (and, in particular, cographs) are b-continuous and b-monotonic. Besides, we describe a dynamic programming algorithm to compute the b-chromatic number in polynomial time within these graph classes. Flavia Bonomo: Partially supported by ANPCyT PICT-2007-00533 and PICT-2007-00518, and UBACyT Grants X069 and X606 (Argentina). Guillermo Durán: Partially supported by FONDECyT Grant 1080286 and Millennium Science Institute “Complex Engineering Systems” (Chile), and ANPCyT PICT-2007-00518 and UBACyT Grant X069 (Argentina). Javier Marenco: Partially supported by ANPCyT PICT-2007-00518 and UBACyT Grant X069 (Argentina).     

Inhibition of HLA-DQ2-mediated antigen presentation by analogues of a high affinity 33-residue peptide from alpha2-gliadin

Human leukocyte antigen DQ2 is a class II major histocompatibility complex protein that plays a critical role in the pathogenesis of Celiac Sprue by binding to epitopes derived from dietary gluten and triggering the inflammatory response of disease-specific T cells. Inhibition of DQ2-mediated antigen presentation in the small intestinal mucosa of Celiac Sprue patients therefore represents a potentially attractive mode of therapy for this widespread but unmet medical need. Starting from a pro-inflammatory, proteolytically resistant, 33-residue peptide, LQLQPFPQPELPYPQPELPYPQPELPYPQPQPF, we embarked upon a systematic effort to dissect the relationships between peptide structure and DQ2 affinity and to translate these insights into prototypical DQ2 blocking agents. Three structural determinants within the first 20 residues of this 33-mer peptide, including a PQPELPYPQ epitope, its N-terminal flanking sequence, and a downstream Glu residue, were found to be important for DQ2 binding. Guided by the X-ray crystal structure of DQ2, the L11 and L18 residues in the truncated 20-mer analogue were replaced with sterically bulky groups so as to retain high DQ2 affinity but abrogate T cell recognition. A dimeric ligand, synthesized by regiospecific coupling of the 20-mer peptide with a bifunctional linker, was identified as an especially potent DQ2 binding agent. Two such ligands were able to attenuate the proliferation of disease-specific T cell lines in response to gluten antigens and, therefore, represent prototypical examples of pharmacologically suitable DQ2 blocking agents for the potential treatment of Celiac Sprue.