Currents on Grassmann algebras

We define currents on a Grassmann algebra $Gr(N)$ with $N$ generators as distributions on its exterior algebra (using the symmetric wedge product). We interpret the currents in terms of ${\Z}_2$-graded Hochschild cohomology and closed currents in terms of cyclic cocycles (they are particular multilinear forms on $Gr(N)$). An explicit construction of the vector space of closed currents of degree $p$ on $Gr(N)$ is given by using Berezin integration.Comment: 20 pages, CPT-93/P.2935 and ENSLAPP-440/9

The Gervais-Neveu-Felder equation for the Jordanian quasi-Hopf U_{h;y}(sl(2)) algebra

Using a contraction procedure, we construct a twist operator that satisfies a shifted cocycle condition, and leads to the Jordanian quasi-Hopf U_{h;y}(sl(2)) algebra. The corresponding universal ${\cal R}_{h}(y)$ matrix obeys a Gervais-Neveu-Felder equation associated with the U_{h;y}(sl(2)) algebra. For a class of representations, the dynamical Yang-Baxter equation may be expressed as a compatibility condition for the algebra of the Lax operators.Comment: Latex, 9 pages, no figure

Impaired receptor-mediated endocytosis by the asialoglycoprotein receptor in ethanol-fed mice: implications for studying the role of this receptor in alcoholic apoptosis

During receptor-mediated endocytosis (RME), extracellular molecules are internalized after being recognized and bound to specific cell surface receptors. In previous studies of the asialoglycoprotein receptor (ASGPR) in rats, we showed that ethanol impairs RME at multiple ASGPR sites. Ethanol administration has been shown to increase apoptosis, and we demonstrated increased sensitization to apoptotic induction in hepatocytes from ethanol-fed rats. Although a physiological role for the ASGPR has not been identified, investigators have shown its involvement in the uptake/clearance of apoptotic cells in vitvo. This suggests a potential role for the ASGPR in the removal of apoptotic cells, and the recent availability of an ASGPR-deficient mouse strain provides an excellent opportunity to examine the role of the ASGPR during ethanol impairment. In this study, we examined ethanol-impaired RME in mice and began the characterization of ASGPR-deficient mice for use in ethanol studies. Similar to our findings with rats, ligand binding, internalization, and degradation were decreased 45-50% in hepatocytes from ethanol-fed wild-type mice. In ASGPR-deficient mice, these parameters did not vary among the chow-fed, pair-fed control, or ethanol groups and were negligible compared with those of wild-type mice. TUNEL analysis of liver sections showed an ethanol-induced increase in apoptotic bodies in all mouse strains with a significant difference in the receptor-deficient mice. Further, the livers of ASGPR-deficient mice had three times more apoptotic bodies, in all feeding groups, compared with wild-type mice. These results support the use of the ASGPR-deficient mouse model for studying ethanol-induced liver injury, specifically ethanol-induced apoptosis

Long Duration Exposure Facility (LDEF) attitude measurements of the Interplanetary Dust Experiment

Analysis of the data from the Long Duration Exposure Facility (LDEF) Interplanetary Dust Experiment (IDE) sun sensors has allowed a confirmation of the attitude of LDEF during its first year in orbit. Eight observations of the yaw angle at specific times were made and are tabulated in this paper. These values range from 4.3 to 12.4 deg with maximum uncertainty of plus or minus 2.0 deg and an average of 7.9 deg. No specific measurements of pitch or roll were made but the data indicates that LDEF had an average pitch down attitude of less than 0.7 deg

Zeta function regularization in Casimir effect calculations and J.S. Dowker's contribution

A summary of relevant contributions, ordered in time, to the subject of operator zeta functions and their application to physical issues is provided. The description ends with the seminal contributions of Stephen Hawking and Stuart Dowker and collaborators, considered by many authors as the actual starting point of the introduction of zeta function regularization methods in theoretical physics, in particular, for quantum vacuum fluctuation and Casimir effect calculations. After recalling a number of the strengths of this powerful and elegant method, some of its limitations are discussed. Finally, recent results of the so called operator regularization procedure are presented.Comment: 16 pages, dedicated to J.S. Dowker, version to appear in International Journal of Modern Physics

N-complexes as functors, amplitude cohomology and fusion rules

We consider N-complexes as functors over an appropriate linear category in order to show first that the Krull-Schmidt Theorem holds, then to prove that amplitude cohomology only vanishes on injective functors providing a well defined functor on the stable category. For left truncated N-complexes, we show that amplitude cohomology discriminates the isomorphism class up to a projective functor summand. Moreover amplitude cohomology of positive N-complexes is proved to be isomorphic to an Ext functor of an indecomposable N-complex inside the abelian functor category. Finally we show that for the monoidal structure of N-complexes a Clebsch-Gordan formula holds, in other words the fusion rules for N-complexes can be determined.Comment: Final versio

Using the Hopf Algebra Structure of QFT in Calculations

We employ the recently discovered Hopf algebra structure underlying perturbative Quantum Field Theory to derive iterated integral representations for Feynman diagrams. We give two applications: to massless Yukawa theory and quantum electrodynamics in four dimensions.Comment: 28 p, Revtex, epsf for figures, minor changes, to appear in Phys.Rev.

A Practical Cryptanalysis of the Algebraic Eraser

Anshel, Anshel, Goldfeld and Lemieaux introduced the Colored Burau Key Agreement Protocol (CBKAP) as the concrete instantiation of their Algebraic Eraser scheme. This scheme, based on techniques from permutation groups, matrix groups and braid groups, is designed for lightweight environments such as RFID tags and other IoT applications. It is proposed as an underlying technology for ISO/IEC 29167-20. SecureRF, the company owning the trademark Algebraic Eraser, has presented the scheme to the IRTF with a view towards standardisation. We present a novel cryptanalysis of this scheme. For parameter sizes corresponding to claimed 128-bit security, our implementation recovers the shared key using less than 8 CPU hours, and less than 64MB of memory.Comment: 15 pages. Updated references, with brief comments added. Minor typos corrected. Final version, accepted for CRYPTO 201

Wodzicki Residue for Operators on Manifolds with Cylindrical Ends

We define the Wodzicki Residue TR(A) for A in a space of operators with double order (m_1,m_2). Such operators are globally defined initially on R^n and then, more generally, on a class of non-compact manifolds, namely, the manifolds with cylindrical ends. The definition is based on the analysis of the associate zeta function. Using this approach, under suitable ellipticity assumptions, we also compute a two terms leading part of the Weyl formula for a positive selfadjoint operator belonging the mentioned class in the case m_1=m_2.Comment: 24 pages, picture changed, added references, corrected typo

On centralizer algebras for spin representations

We give a presentation of the centralizer algebras for tensor products of spinor representations of quantum groups via generators and relations. In the even-dimensional case, this can be described in terms of non-standard q-deformations of orthogonal Lie algebras; in the odd-dimensional case only a certain subalgebra will appear. In the classical case q = 1 the relations boil down to Lie algebra relations