An Extension of the Character Ring of sl(3) and Its Quantisation

We construct a commutative ring with identity which extends the ring of characters of finite dimensional representations of sl(3). It is generated by characters with values in the group ring $Z[\tilde{W}]$ of the extended affine Weyl group of $\hat{sl}(3)_k$ at $k\not \in Q$. The `quantised' version at rational level $k+3=3/p$ realises the fusion rules of a WZW conformal field theory based on admissible representations of $\hat{sl}(3)_k$.Comment: contains two TeX files: main file using harvmac.tex, amssym.def, amssym.tex, 35p.; file with figures using XY-pic package, 4p; v2: minor corrections, Note adde

Non-critical string pentagon equations and their solutions

We derive pentagon type relations for the 3-point boundary tachyon correlation functions in the non-critical open string theory with generic c_{matter} < 1 and study their solutions in the case of FZZ branes. A new general formula for the Liouville 3-point factor is derived.Comment: 18 pages, harvmac; misprints corrected, section 3.2 extended, a new general formula for the Liouville 3-point factor adde

On the crossing relation in the presence of defects

The OPE of local operators in the presence of defect lines is considered both in the rational CFT and the $c>25$ Virasoro (Liouville) theory. The duality transformation of the 4-point function with inserted defect operators is explicitly computed. The two channels of the correlator reproduce the expectation values of the Wilson and 't Hooft operators, recently discussed in Liouville theory in relation to the AGT conjecture.Comment: TEX file with harvmac; v3: JHEP versio

Conformal Field Theories, Graphs and Quantum Algebras

This article reviews some recent progress in our understanding of the structure of Rational Conformal Field Theories, based on ideas that originate for a large part in the work of A. Ocneanu. The consistency conditions that generalize modular invariance for a given RCFT in the presence of various types of boundary conditions --open, twisted-- are encoded in a system of integer multiplicities that form matrix representations of fusion-like algebras. These multiplicities are also the combinatorial data that enable one to construct an abstract ``quantum'' algebra, whose $6j$- and $3j$-symbols contain essential information on the Operator Product Algebra of the RCFT and are part of a cell system, subject to pentagonal identities. It looks quite plausible that the classification of a wide class of RCFT amounts to a classification of ``Weak $C^*$- Hopf algebras''.Comment: 23 pages, 12 figures, LateX. To appear in MATHPHYS ODYSSEY 2001 --Integrable Models and Beyond, ed. M. Kashiwara and T. Miwa, Progress in Math., Birkhauser. References and comments adde

Anomalous thickness dependence of the Hall effect in ultrathin Pb layers on Si(111)

The magnetoconductive properties of ultrathin Pb films deposited on Si(111) are measured and compared with density-functional electronic band-structure calculations on two-dimensional, free-standing, 1 to 8 monolayers thick Pb(111) slabs. A description with free-standing slabs is possible because it turned out that the Hall coefficient is independent of the substrate and of the crystalline order in the film. We show that the oscillations in sign of the Hall coefficient observed as a function of film thickness can be explained directly from the thickness dependent variations of the electronic bandstructure at the Fermi energy.Comment: 4 pages incl. 3 figures, RevTeX, to appear in Phys. Rev.

On the Classification of Bulk and Boundary Conformal Field Theories

The classification of rational conformal field theories is reconsidered from the standpoint of boundary conditions. Solving Cardy's equation expressing the consistency condition on a cylinder is equivalent to finding integer valued representations of the fusion algebra. A complete solution not only yields the admissible boundary conditions but also gives valuable information on the bulk properties.Comment: 7 pages, LaTeX; minor correction

Runx1 and Runx3 Are Involved in the Generation and Function of Highly Suppressive IL-17-Producing T Regulatory Cells

CD4+Foxp3+ T regulatory cells (Tregs) display phenotypic and functional plasticity that is regulated by cytokines and other immune cells. Previously, we determined that during co-culture with CD4+CD25− T cells and antigen presenting cells, Tregs produced IL-17. Here, we investigated the mechanisms underlying the differentiation of IL-17-producing Treg (Tr17) cells and their molecular and functional properties. We determined that during stimulation via TCR/CD3 and CD28, the combination of IL-1β and IL-2 was necessary and sufficient for the generation of Tr17 cells. Tr17 cells expressed Runx1 transcription factor, which was required for sustained expression of Foxp3 and RORγt and for production of IL-17. Surprisingly, Tr17 cells also expressed Runx3, which regulated transcription of perforin and granzyme B thereby mediating cytotoxic activity. Our studies indicate that Tr17 cells concomitantly express Foxp3, RORγt, Runx1 and Runx3 and are capable of producing IL-17 while mediating potent suppressive and cytotoxic function

Bilateral Simultaneous Retrobulbar Neuritis After Swine Flu: A Clinical Case Report

Retrobulbar neuritis is most commonly demyelinating and associated with multiple sclerosis. Rarely, it has been associated with viral and bacterial infections, systemic autoimmune diseases, vaccinations, and certain medications. We present a case of bilateral simultaneous optic neuritis following swine flu. We did a case report on a 56-year-old male patient with retrobulbar neuritis after swine flu, who had been treated in Alexandrovska Hospital, Sofia, Bulgaria. The diagnosis was based on the clinical exam, clinical course and on specialized investigations. The follow-up period was from February 2015 until April 2021. On admission in the hospital the best-corrected visual acuity of both eyes was decreased – VOD=0.6, VOS=PPLC. 30-2 visual field testing demonstrated no light sensitivity in the left eye, and decreased – in the right. Therapy was begun with methylprednisolone, pentoxiphylline, vinpocetine, piracetam, and clopidogrel. On day 19 the visual fields were significantly improved. On discharge, BCVA was 0.6-0.7 of the right eye and 0.7-0.8 – of the left, and improved to 1.0 during the follow-up period. Bilateral simultaneous retrobulbar neuritis is an infrequent immune complication after swine flu. In our case, we achieved recovery of normal visual acuity and a significant improvement in the visual fieds of both eyes. Therapy included systemic corticosteroids, pentoxiphylline, vinpocetine, piracetam, and clopidogrel

Use of Peptide Libraries for Identification and Optimization of Novel Antimicrobial Peptides.

The increasing rates of resistance among bacteria and to a lesser extent fungi have resulted in an urgent need to find new molecules that hold therapeutic promise against multidrug-resistant strains. Antimicrobial peptides have proven very effective against a variety of multidrug-resistant bacteria. Additionally, the low levels of resistance reported towards these molecules are an attractive feature for antimicrobial drug development. Here we summarise information on diverse peptide libraries used to discover or to optimize antimicrobial peptides. Chemical synthesized peptide libraries, for example split and mix method, tea bag method, multi-pin method and cellulose spot method are discussed. In addition biological peptide library screening methods are summarized, like phage display, bacterial display, mRNA-display and ribosomal display. A few examples are given for small peptide libraries, which almost exclusively follow a rational design of peptides of interest rather than a combinatorial approach