Diffusion in a continuum model of self-propelled particles with alignment interaction

In this paper, we provide the $O(\epsilon)$ corrections to the hydrodynamic model derived by Degond and Motsch from a kinetic version of the model by Vicsek & coauthors describing flocking biological agents. The parameter $\epsilon$ stands for the ratio of the microscopic to the macroscopic scales. The $O(\epsilon)$ corrected model involves diffusion terms in both the mass and velocity equations as well as terms which are quadratic functions of the first order derivatives of the density and velocity. The derivation method is based on the standard Chapman-Enskog theory, but is significantly more complex than usual due to both the non-isotropy of the fluid and the lack of momentum conservation

Geometric Permutations of Non-Overlapping Unit Balls Revisited

Given four congruent balls $A, B, C, D$ in $R^{d}$ that have disjoint interior and admit a line that intersects them in the order $ABCD$, we show that the distance between the centers of consecutive balls is smaller than the distance between the centers of $A$ and $D$. This allows us to give a new short proof that $n$ interior-disjoint congruent balls admit at most three geometric permutations, two if $n\ge 7$. We also make a conjecture that would imply that $n\geq 4$ such balls admit at most two geometric permutations, and show that if the conjecture is false, then there is a counter-example of a highly degenerate nature

The Yangian symmetry of the Hubbard Model

We discovered new hidden symmetry of the one-dimensional Hubbard model. We showthat the one-dimensional Hubbard model on the infinite chain has the infinite-dimensional algebra of symmetries. This algebra is a direct sum of two $sl(2)$-Yangians. This $Y(sl(2)) \oplus Y(sl(2))$ symmetry is an extension of the well-known $sl(2) \oplus sl(2)$ . The deformation parameters of the Yangians are equal up to the signs to the coupling constant of the Hubbard model hamiltonian.Comment: 7 pages, ITP-SB-93-6

Symmetries and exact solutions of some integrable Haldane-Shastry like spin chains

By using a class of `anyon like' representations of permutation algebra, which pick up nontrivial phase factors while interchanging the spins of two lattice sites, we construct some integrable variants of $SU(M)$ Haldane-Shastry (HS) spin chain. Lax pairs and conserved quantities for these spin chains are also found and it is established that these models exhibit multi-parameter deformed or nonstandard variants of $Y(gl_M)$ Yangian symmetry. Moreover, by projecting the eigenstates of Dunkl operators in a suitable way, we derive a class of exact eigenfunctions for such HS like spin chain and subsequently conjecture that these exact eigenfunctions would lead to the highest weight states associated with a multi-parameter deformed or nonstandard variant of $Y(gl_M)$ Yangian algebra. By using this conjecture, and acting descendent operator on the highest weight states associated with a nonstandard $Y(gl_2)$ Yangian algebra, we are able to find out the complete set of eigenvalues and eigenfunctions for the related HS like spin-${1\over 2}$ chain. It turns out that some additional energy levels, which are forbidden due to a selection rule in the case of SU(2) HS model, interestingly appear in the spectrum of above mentioned HS like spin chain having nonstandard $Y(gl_2)$ Yangian symmetry.Comment: 35 pages, latex, no figures, minor type errors are corrected, version to appear in Nucl. Phys.

Anveshak - A Groundtruth Generation Tool for Foreground Regions of Document Images

We propose a graphical user interface based groundtruth generation tool in this paper. Here, annotation of an input document image is done based on the foreground pixels. Foreground pixels are grouped together with user interaction to form labeling units. These units are then labeled by the user with the user defined labels. The output produced by the tool is an image with an XML file containing its metadata information. This annotated data can be further used in different applications of document image analysis.Comment: Accepted in DAR 201

Cell-type specific potent Wnt signaling blockade by bispecific antibody.

Cell signaling pathways are often shared between normal and diseased cells. How to achieve cell type-specific, potent inhibition of signaling pathways is a major challenge with implications for therapeutic development. Using the Wnt/β-catenin signaling pathway as a model system, we report here a novel and generally applicable method to achieve cell type-selective signaling blockade. We constructed a bispecific antibody targeting the Wnt co-receptor LRP6 (the effector antigen) and a cell type-associated antigen (the guide antigen) that provides the targeting specificity. We found that the bispecific antibody inhibits Wnt-induced reporter activities with over one hundred-fold enhancement in potency, and in a cell type-selective manner. Potency enhancement is dependent on the expression level of the guide antigen on the target cell surface and the apparent affinity of the anti-guide antibody. Both internalizing and non-internalizing guide antigens can be used, with internalizing bispecific antibody being able to block signaling by all ligands binding to the target receptor due to its removal from the cell surface. It is thus feasible to develop bispecific-based therapeutic strategies that potently and selectively inhibit signaling pathways in a cell type-selective manner, creating opportunity for therapeutic targeting