Perturbations of planar algebras

We analyze the effect of pivotal structures (on a 2-category) on the planar algebra associated to a 1-cell as in \cite{Gho08} and come up with the notion of {\em perturbations of planar algebras by weights} (a concept that appeared earlier in Michael Burns' thesis \cite{Bur03}); we establish a one-to-one correspondence between weights and pivotal structures. Using the construction of \cite{Gho08}, to each bifinite bimodule over $II_1$-factors, we associate a {\em bimodule planar algebra} in such a way that extremality of the bimodule corresponds to sphericality of the planar algebra. As a consequence of this, we reproduce an extension of Jones' theorem (\cite{Jon}) (of associating `subfactor planar algebras' to extremal subfactors). Conversely, given a bimodule planar algebra, we construct a bifinite bimodule whose associated bimodule planar algebra is the one which we start with, using perturbations and Jones-Walker-Shlyakhtenko-Kodiyalam-Sunder method of reconstructing an extremal subfactor from a subfactor planar algebra. The perturbation technique helps us to construct an example of a family of non-spherical planar algebras starting from a particular spherical one; we also show that this family is associated to a known family of subfactors constructed by Jones.Comment: 28 page

Self-regulation of rat liver GAP junction by phosphorylation

AbstractWe have studied the functioning of rat liver Connexin 32 (Cx32) at the single channel level in presence of ATP. It was observed that ATP regulates the functioning of the channel by running down the junctional conductance. A non-specific exogenous protein phosphatase (alkaline phosphatase) reversed the rundown of junctional activity to its normal functioning state. Autoradiograhic studies demonstrate autophosphorylation of rat liver Cx32. These findings indicate a self-regulatory mechanism of the channel

Improvement of nutritive value of sesame oil cake in formulated diets for rohu, Labeo rohita (Hamilton) after bio-processing through solid state fermentation by a phytase-producing fish gut bacterium

Sesame oil cake (SSC) was bio-processed through solid state fermentation (SSF) under optimized conditions by a phytase-producing fish gut bacterium, Bacillus subtilis subsp. subtilis (JX292128). SSF significantly reduced anti-nutritional factors (e.g., phytic acid, tannins and trypsin inhibitor) and crude fibre, while enhanced free amino acids, fatty acids and different minerals. Phytase production (39.72 ± 1.06 U/g) during SSF was also recorded. Along with a fish meal based reference diet (RD), 8 isonitrogenous (36% crude protein) and isocaloric (4.60 kcal g-1) experimental diets incorporating raw (R1-R4) and SSF processed (F1-F4) SSC(20%, 30%, 40% and 50%, w/w) were fed to rohu, Labeo rohita fingerlings (mean weight 3.28 ± 0.15 g) in triplicate treatments for 70 days. In general, growth and feed utilization efficiencies in fish fed diets containing SSF-processed SSC were superior to the groups fed diets containing raw SSC. The diet F3 (40% fermented SSC) showed significantly (P<0.05) better result in terms of weight gain, feed conversion ratio, protein efficiency ratio, apparent net protein utilization, activities of digestive enzymes, carcass composition and apparent digestibility of protein, lipid and phosphorus. Faecal phosphorus discharge reduced significantly (P<0.05) in fish fed fermented diets. The results indicated that incorporation of SSF-processed SSC might be practiced as a function to replace fish meal in the diets of L. rohita fingerlings

WAFERS: AN INNOVATIVE ADVANCEMENT OF ORO-DISPERSIBLE FILMS

The formulation of oral disintegrating films has led to the development of wafers which has modified itself in the recent past years. Wafers are more advantageous over other conventional dosage forms as well as from other oral disintegrating solid dosage forms. The major difficulty in formulating wafers is the choice of drugs to be incorporated. Wafers with low dose of active pharmaceutical ingredient (API) and with a good mouth feel are prepared for making it more patients compliant. The manufacturing procedures are quite similar to oral disintegrating film but the composition of polymers may vary. The wafers requires expensive packaging and care should be taken while handling, storage &amp; transport. In spite of these hardships, wafers have become popular between geriatric and paediatric population because of its ease of administration and bioavailability. Keywords: Transmucosal route, Oral films, Wafers, Fast dissolving dosage forms, Oral administratio

Unitary connections on Bratteli diagrams

In this paper, we extend Ocneanu's theory of connections on graphs to define a 2-category whose 0-cells are tracial Bratteli diagrams, and whose 1-cells are generalizations of unitary connections. We show that this 2-category admits an embedding into the 2-category of hyperfinite von Neumann algebras, generalizing fundamental results from subfactor theory to a 2-categorical setting.Comment: 35 page