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

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

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.

Laparoscopic Sacropexy: A Retrospective Analysis of the Subjective Outcome in 310 Cases

Background and Objective. The aim of this study was to assess the subjective outcome following laparoscopic sacropexy. Methods. We performed a retrospective cohort study among women treated for descensus with laparoscopic sacropexy between January 2000 and December 2007. 310 patients received questionnaires during followup assessing major pre- and postoperative symptoms and overall satisfaction. Results. 214 (69%) patients responded to the questionnaire. Mean followup was 24.5 months. The number of patients with back or lower abdominal pain, foreign body sensation in the vagina and prolapse-related symptoms, urinary symptoms, vaginal and bladder infections, and the need for pessary usage decreased significantly postsurgically. Bowel symptoms increased slightly but not significantly. Two years after surgery, nearly 2 thirds of the women were satisfied or very satisfied with the outcome. Conclusion. Laparoscopic sacropexy is an effective treatment of descensus, with favorable or satisfactory subjective outcomes

H\"older-continuous rough paths by Fourier normal ordering

We construct in this article an explicit geometric rough path over arbitrary $d$-dimensional paths with finite $1/\alpha$-variation for any $\alpha\in(0,1)$. The method may be coined as 'Fourier normal ordering', since it consists in a regularization obtained after permuting the order of integration in iterated integrals so that innermost integrals have highest Fourier frequencies. In doing so, there appear non-trivial tree combinatorics, which are best understood by using the structure of the Hopf algebra of decorated rooted trees (in connection with the Chen or multiplicative property) and of the Hopf shuffle algebra (in connection with the shuffle or geometric property). H\"older continuity is proved by using Besov norms. The method is well-suited in particular in view of applications to probability theory (see the companion article \cite{Unt09} for the construction of a rough path over multidimensional fractional Brownian motion with Hurst index $\alpha<1/4$, or \cite{Unt09ter} for a short survey in that case).Comment: 50 pages, 6 figure

Does thermoregulatory behavior maximize reproductive fitness of natural isolates of Caenorhabditis elegans?

BACKGROUND: A central premise of physiological ecology is that an animal's preferred body temperature should correspond closely with the temperature maximizing performance and Darwinian fitness. Testing this co-adaptational hypothesis has been problematic for several reasons. First, reproductive fitness is the appropriate measure, but is difficult to measure in most animals. Second, no single fitness measure applies to all demographic situations, complicating interpretations. Here we test the co-adaptation hypothesis by studying an organism (Caenorhabditis elegans) in which both fitness and thermal preference can be reliably measured.RESULTS: We find that natural isolates of C. elegans display a range of mean thermal preferences and also vary in their thermal sensitivities for fitness. Hot-seeking isolates CB4854 and CB4857 prefer temperatures that favor population growth rate (r), whereas the cold-seeking isolate CB4856 prefers temperatures that favor Lifetime Reproductive Success (LRS).CONCLUSIONS: Correlations between fitness and thermal preference in natural isolates of C. elegans are driven primarily by isolate-specific differences in thermal preference. If these differences are the result of natural selection, then this suggests that the appropriate measure of fitness for use in evolutionary ecology studies might differ even within species, depending on the unique ecological and evolutionary history of each population.</p

The Justy mutation identifies Gon4-like as a gene that is essential for B lymphopoiesis

A recessive mutation named Justy was found that abolishes B lymphopoiesis but does not impair other major aspects of hematopoiesis. Transplantation experiments showed that homozygosity for Justy prevented hematopoietic progenitors from generating B cells but did not affect the ability of bone marrow stroma to support B lymphopoiesis. In bone marrow from mutant mice, common lymphoid progenitors and pre-pro–B cells appeared normal, but cells at subsequent stages of B lymphopoiesis were dramatically reduced in number. Under culture conditions that promoted B lymphopoiesis, mutant pre-pro–B cells remained alive and began expressing the B cell marker CD19 but failed to proliferate. In contrast, these cells were able to generate myeloid or T/NK precursors. Genetic and molecular analysis demonstrated that Justy is a point mutation within the Gon4-like (Gon4l) gene, which encodes a protein with homology to transcriptional regulators. This mutation was found to disrupt Gon4l pre-mRNA splicing and dramatically reduce expression of wild-type Gon4l RNA and protein. Consistent with a role for Gon4l in transcriptional regulation, the levels of RNA encoding C/EBPα and PU.1 were abnormally high in mutant B cell progenitors. Our findings indicate that the Gon4l protein is required for B lymphopoiesis and may function to regulate gene expression during this process

NASH limits anti-tumour surveillance in immunotherapy-treated HCC

Hepatocellular carcinoma (HCC) can have viral or non-viral causes(1-5). Non-alcoholic steatohepatitis (NASH) is an important driver of HCC. Immunotherapy has been approved for treating HCC, but biomarker-based stratification of patients for optimal response to therapy is an unmet need(6,7). Here we report the progressive accumulation of exhausted, unconventionally activated CD8(+)PD1(+) T cells in NASH-affected livers. In preclinical models of NASH-induced HCC, therapeutic immunotherapy targeted at programmed death-1 (PD1) expanded activated CD8(+)PD1(+) T cells within tumours but did not lead to tumour regression, which indicates that tumour immune surveillance was impaired. When given prophylactically, anti-PD1 treatment led to an increase in the incidence of NASH-HCC and in the number and size of tumour nodules, which correlated with increased hepatic CD8(+)PD1(+)CXCR6(+), TOX+, and TNF+ T cells. The increase in HCC triggered by anti-PD1 treatment was prevented by depletion of CD8(+) T cells or TNF neutralization, suggesting that CD8(+) T cells help to induce NASH-HCC, rather than invigorating or executing immune surveillance. We found similar phenotypic and functional profiles in hepatic CD8(+)PD1(+) T cells from humans with NAFLD or NASH. A meta-analysis of three randomized phase III clinical trials that tested inhibitors of PDL1 (programmed death-ligand 1) or PD1 in more than 1,600 patients with advanced HCC revealed that immune therapy did not improve survival in patients with non-viral HCC. In two additional cohorts, patients with NASH-driven HCC who received anti-PD1 or anti-PDL1 treatment showed reduced overall survival compared to patients with other aetiologies. Collectively, these data show that non-viral HCC, and particularly NASH-HCC, might be less responsive to immunotherapy, probably owing to NASH-related aberrant T cell activation causing tissue damage that leads to impaired immune surveillance. Our data provide a rationale for stratification of patients with HCC according to underlying aetiology in studies of immunotherapy as a primary or adjuvant treatment