Integrals Over Polytopes, Multiple Zeta Values and Polylogarithms, and Euler's Constant

Let $T$ be the triangle with vertices (1,0), (0,1), (1,1). We study certain integrals over $T$, one of which was computed by Euler. We give expressions for them both as a linear combination of multiple zeta values, and as a polynomial in single zeta values. We obtain asymptotic expansions of the integrals, and of sums of certain multiple zeta values with constant weight. We also give related expressions for Euler's constant. In the final section, we evaluate more general integrals -- one is a Chen (Drinfeld-Kontsevich) iterated integral -- over some polytopes that are higher-dimensional analogs of $T$. This leads to a relation between certain multiple polylogarithm values and multiple zeta values.Comment: 19 pages, to appear in Mat Zametki. Ver 2.: Added Remark 3 on a Chen (Drinfeld-Kontsevich) iterated integral; simplified Proposition 2; gave reference for (19); corrected [16]; fixed typ

Retinoic Acid Signaling in B Cells Is Required for the Generation of an Effective T-Independent Immune Response

Retinoic acid (RA) plays an important role in the balance of inflammation and tolerance in T cells. Furthermore, it has been demonstrated that RA facilitates IgA isotype switching in B cells in vivo. However, it is unclear whether RA has a direct effect on T-independent B cell responses in vivo. To address this question, we generated a mouse model where RA signaling is specifically silenced in the B cell lineage. This was achieved through the overexpression of a dominant negative receptor a for RA (dnRARα) in the B cell lineage. In this model, we found a dramatic reduction in marginal zone (MZ) B cells and accumulation of transitional 2 B cells in the spleen. We also observed a reduction in B1 B cells in the peritoneum with a defect in the T-independent B cell response against 2,4,6-trinitrophenyl. This was not a result of inhibited development of B cells in the bone marrow, but likely the result of both defective expression of S1P1 in MZ B cells and a defect in the development of MZ and B1 B cells. This suggests that RARα expression in B cells is important for B cell frequency in the MZ and peritoneum, which is crucial for the generation of T-independent humoral responses.</p

Elliptic Thermal Correlation Functions and Modular Forms in a Globally Conformal Invariant QFT

Global conformal invariance (GCI) of quantum field theory (QFT) in two and higher space-time dimensions implies the Huygens' principle, and hence, rationality of correlation functions of observable fields (see Commun. Math. Phys. 218 (2001) 417-436; hep-th/0009004). The conformal Hamiltonian $H$ has discrete spectrum assumed here to be finitely degenerate. We then prove that thermal expectation values of field products on compactified Minkowski space can be represented as finite linear combinations of basic (doubly periodic) elliptic functions in the conformal time variables (of periods 1 and $\tau$) whose coefficients are, in general, formal power series in $q^{1/2}=e^{i\pi\tau}$ involving spherical functions of the "space-like" fields' arguments. As a corollary, if the resulting expansions converge to meromorphic functions, then the finite temperature correlation functions are elliptic. Thermal 2-point functions of free fields are computed and shown to display these features. We also study modular transformation properties of Gibbs energy mean values with respect to the (complex) inverse temperature $\tau$ ($Im(\tau)=\beta/(2\pi)>0$). The results are used to obtain the thermodynamic limit of thermal energy densities and correlation functions.Comment: LaTex. 56 pages. The concept of global conformal invariance set in a historical perspective (new Sect. 1.1 in the Introduction), references added; minor corrections in the rest of the pape

Holomorphic Quantization on the Torus and Finite Quantum Mechanics

We construct explicitly the quantization of classical linear maps of $SL(2, R)$ on toroidal phase space, of arbitrary modulus, using the holomorphic (chiral) version of the metaplectic representation. We show that Finite Quantum Mechanics (FQM) on tori of arbitrary integer discretization, is a consistent restriction of the holomorphic quantization of $SL(2, Z)$ to the subgroup $SL(2, Z)/\Gamma_l$, $\Gamma_l$ being the principal congruent subgroup mod l, on a finite dimensional Hilbert space. The generators of the ``rotation group'' mod l, $O_{l}(2)\subset SL(2,l)$, for arbitrary values of l are determined as well as their quantum mechanical eigenvalues and eigenstates.Comment: 12 pages LaTeX (needs amssymb.sty). Version as will appear in J. Phys.

Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order epsilon-expansion of generalized hypergeometric functions with one half-integer value of parameter

We continue the study of the construction of analytical coefficients of the epsilon-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we show the following results: Theorem A: The multiple (inverse) binomial sums of arbitrary weight and depth (see Eq. (1.1)) are expressible in terms of Remiddi-Vermaseren functions. Theorem B: The epsilon expansion of a hypergeometric function with one half-integer value of parameter (see Eq. (1.2)) is expressible in terms of the harmonic polylogarithms of Remiddi and Vermaseren with coefficients that are ratios of polynomials. Some extra materials are available via the www at this http://theor.jinr.ru/~kalmykov/hypergeom/hyper.htmlComment: 24 pages, latex with amsmath and JHEP3.cls; v2: some typos corrected and a few references added; v3: few references added

Population structure and genetic diversity in Gynaikothrips uzeli (Thysanoptera: Phlaeothripidae): Is there a correlation between genetic and geographic proximity?

Gynaikothrips uzeli (Thysanoptera: Phlaeothripidae) is a minuscule insect species, which forms galls, is subsocial, and parthenogenetic. It is associated with Ficus benjamina L. (Moraceae) and has a pantropical occurrence. The paucity of genetic studies on the order Thysanoptera led us to use inter-simple sequence repeat molecular marker to assess intra- and inter-gall, as well as intra- and inter-site, genetic variability and population structure of G. uzeli. Analyses indicated low genetic variability, probably related to haplodiploidy, genetic drift, the galling habit, and the low dispersal ability of G. uzeli. Populations were highly structured, with higher variation within populations than among them. Geographic distance does not appear to affect structure and genetic diversity, the latter being influenced by G. uzeli’s bioecological traits, by numerous introductions during a short period, and by a possible recent, common ancestry. © FUNPEC-RP

Linac Coherent Light Source Undulator RF BPM System

The Linac Coherent Light Source (LCLS) will be the world's first x-ray free-electron laser (FEL) when it becomes operational in 2009. The LCLS is currently in the construction phase. The beam position monitor (BPM) system planned for the LCLS undulator will incorporate a high-resolution X-band cavity BPM system described in this paper. The BPM system will provide high-resolution measurements of the electron beam trajectory on a pulse-to-pulse basis and over many shots. The X-band cavity BPM size, simple fabrication, and high resolution make it an ideal choice for LCLS beam position detection. We will discuss the system specifications, design, and prototype test results

Design and Performance of the LCLS Cavity BPM System

In this paper we present the design of the beam position monitor (BPM) system for the LCLS undulator, which features a high-resolution X-band cavity BPM. Each BPM has a TM{sub 010} monopole reference cavity and a TM{sub 110} dipole cavity designed to operate at a center frequency of 11.384 GHz. The signal processing electronics features a low noise single-stage three-channel heterodyne receiver that has selectable gain and a phase locking local oscillator. We will discuss the system specifications, design, and prototype test results