Renormalization : A number theoretical model

We analyse the Dirichlet convolution ring of arithmetic number theoretic functions. It turns out to fail to be a Hopf algebra on the diagonal, due to the lack of complete multiplicativity of the product and coproduct. A related Hopf algebra can be established, which however overcounts the diagonal. We argue that the mechanism of renormalization in quantum field theory is modelled after the same principle. Singularities hence arise as a (now continuously indexed) overcounting on the diagonals. Renormalization is given by the map from the auxiliary Hopf algebra to the weaker multiplicative structure, called Hopf gebra, rescaling the diagonals.Comment: 15 pages, extended version of talks delivered at SLC55 Bertinoro,Sep 2005, and the Bob Delbourgo QFT Fest in Hobart, Dec 200

Idempotents of Clifford Algebras

A classification of idempotents in Clifford algebras C(p,q) is presented. It is shown that using isomorphisms between Clifford algebras C(p,q) and appropriate matrix rings, it is possible to classify idempotents in any Clifford algebra into continuous families. These families include primitive idempotents used to generate minimal one sided ideals in Clifford algebras. Some low dimensional examples are discussed

Products, coproducts and singular value decomposition

Products and coproducts may be recognized as morphisms in a monoidal tensor category of vector spaces. To gain invariant data of these morphisms, we can use singular value decomposition which attaches singular values, ie generalized eigenvalues, to these maps. We show, for the case of Grassmann and Clifford products, that twist maps significantly alter these data reducing degeneracies. Since non group like coproducts give rise to non classical behavior of the algebra of functions, ie make them noncommutative, we hope to be able to learn more about such geometries. Remarkably the coproduct for positive singular values of eigenvectors in $A$ yields directly corresponding eigenvectors in A\otimes A.Comment: 17 pages, three eps-figure

Grobner Bases for Finite-temperature Quantum Computing and their Complexity

Following the recent approach of using order domains to construct Grobner bases from general projective varieties, we examine the parity and time-reversal arguments relating de Witt and Lyman's assertion that all path weights associated with homotopy in dimensions d <= 2 form a faithful representation of the fundamental group of a quantum system. We then show how the most general polynomial ring obtained for a fermionic quantum system does not, in fact, admit a faithful representation, and so give a general prescription for calcluating Grobner bases for finite temperature many-body quantum system and show that their complexity class is BQP

On an easy transition from operator dynamics to generating functionals by Clifford algebras

Clifford geometric algebras of multivectors are treated in detail. These algebras are build over a graded space and exhibit a grading or multivector structure. The careful study of the endomorphisms of this space makes it clear, that opposite Clifford algebras have to be used also. Based on this mathematics, we give a fully Clifford algebraic account on generating functionals, which is thereby geometric. The field operators are shown to be Clifford and opposite Clifford maps. This picture relying on geometry does not need positivity in principle. Furthermore, we propose a transition from operator dynamics to corresponding generating functionals, which is based on the algebraic techniques. As a calculational benefit, this transition is considerable short compared to standard ones. The transition is not injective (unique) and depends additionally on the choice of an ordering. We obtain a direct and constructive connection between orderings and the explicit form of the functional Hamiltonian. These orderings depend on the propagator of the theory and thus on the ground state. This is invisible in path integral formulations. The method is demonstrated within two examples, a non-linear spinor field theory and spinor QED. Antisymmetrized and normal-ordered functional equations are derived in both cases.Comment: 23p., 76kB, plain LaTeX, [email protected]

Data from an Observational Study

Introduction Effective management and development of new treatment strategies for response fluctuations in advanced Parkinson’s disease (PD) largely depends on clinical rating instruments such as the PD home diary. The Parkinson’s kinetigraph (PKG) measures movement accelerations and analyzes the spectral power of the low frequencies of the accelerometer data. New algorithms convert each hour of continuous PKG data into one of the three motor categories used in the PD home diary, namely motor Off state and On state with and without dyskinesia. Objective To compare quantitative motor state assessment in fluctuating PD patients using the PKG with motor state ratings from PD home diaries. Methods Observational cohort study on 24 in-patients with documented motor fluctuations who completed diaries by rating motor Off, On without dyskinesia, On with dyskinesia, and asleep for every hour for 5 consecutive days. Simultaneously collected PKG data (recorded between 6 am and 10 pm) were analyzed and calibrated to the patient’s individual thresholds for Off and dyskinetic state by novel algorithms classifying the continuous accelerometer data into these motor states for every hour between 6 am and 10 pm. Results From a total of 2,040 hours, 1,752 hours (87.4%) were available for analyses from calibrated PKG data (7.5% sleeping time and 5.1% unclassified motor state time were excluded from analyses). Distributions of total motor state hours per day measured by PKG showed moderate-to-strong correlation to those assessed by diaries for the different motor states (Pearson’s correlations coefficients: 0.404–0.658), but inter-rating method agreements on the single- hour-level were only low-to-moderate (Cohen’s κ: 0.215–0.324). Conclusion The PKG has been shown to capture motor fluctuations in patients with advanced PD. The limited correlation of hour-to-hour diary and PKG recordings should be addressed in further studies

The structure of Green functions in quantum field theory with a general state

In quantum field theory, the Green function is usually calculated as the expectation value of the time-ordered product of fields over the vacuum. In some cases, especially in degenerate systems, expectation values over general states are required. The corresponding Green functions are essentially more complex than in the vacuum, because they cannot be written in terms of standard Feynman diagrams. Here, a method is proposed to determine the structure of these Green functions and to derive nonperturbative equations for them. The main idea is to transform the cumulants describing correlations into interaction terms.Comment: 13 pages, 6 figure

Nonsupplemented luteal phase characteristics after the administration of recombinant human chorionic gonadotropin, recombinant luteinizing hormone, or gonadotropin-releasing hormone (GnRH) agonist to induce final oocyte maturation in in vitro fertilization patients after ovarian stimulation with recombinant follicle-stimulating hormone and GnRH antagonist cotreatment

Replacing GnRH agonist cotreatment for the prevention of a premature rise in LH during ovarian stimulation for in vitro fertilization (IVF) by the late follicular phase administration of GnRH antagonist may render supplementation of the luteal phase redundant, because of the known rapid recovery of pituitary function after antagonist cessation. This randomized two-center study was performed to compare nonsupplemented luteal phase characteristics after three different strategies for inducing final oocyte maturation. Forty patients underwent ovarian stimulation using recombinant (r-)FSH (150 IU/d, fixed) combined with a GnRH antagonist (antide; 1 mg/d) during the late follicular phase. When at least one follicle above 18 mm was observed, patients were randomized to induce oocyte maturation by a single injection of either r-human (h)CG (250 microg) (n = 11), r-LH (1 mg) (n = 13), or GnRH agonist (triptorelin; 0.2 mg) (n = 15). Retrieved oocytes were fertilized by either IVF or intracytoplasmatic sperm injection, depending on sperm quality. Embryo transfer was performed 3-4 d after oocyte retrieval. No luteal support was provided. Serum concentrations of FSH, LH, estradiol (E(2)), progesterone (P), and hCG were assessed at fixed intervals during the follicular and luteal phase. The median duration of the luteal phase was 13, 10, and 9 d for the r-hCG, the r-LH, and the GnRH agonist group, respectively (P = 0.005). The median area under the curve per day (from 4 d post randomization until the onset of menses) for LH was 0.50, 2.34, and 1.07 for the r-hCG, the r-LH, and the GnRH agonist group, respectively (P = 0.001). The median area under the curve per day for P was 269 vs. 41 and 16 for the r-hCG, the r-LH, and the GnRH agonist group, respectively (P < 0.001). Low pregnancy rates (overall, 7.5%; range, 0-18% per started cycle) were observed in all groups. In conclusion, the nonsupplemented luteal phase was insufficient in all three groups. In the patients receiving r-hCG, the luteal phase was less disturbed, compared with both other groups, presumably because of prolonged clearance of hCG from the circulation and the resulting extended support of the corpus luteum. Despite high P and E(2) concentrations during the early luteal phase in all three groups, luteolysis started prematurely, presumably because of excessive negative steroid feedback resulting in suppressed pituitary LH release. Hence, support of corpus luteum function remains mandatory after ovarian stimulation for IVF with GnRH antagonist cotreatment

Off shell behaviour of the in medium nucleon-nucleon cross section

The properties of nucleon-nucleon scattering inside dense nuclear matter are investigated. We use the relativistic Brueckner-Hartree-Fock model to determine on-shell and half off-shell in-medium transition amplitudes and cross sections. At finite densities the on-shell cross sections are generally suppressed. This reduction is, however, less pronounced than found in previous works. In the case that the outgoing momenta are allowed to be off energy shell the amplitudes show a strong variation with momentum. This description allows to determine in-medium cross sections beyond the quasi-particle approximation accounting thereby for the finite width which nucleons acquire in the dense nuclear medium. For reasonable choices of the in-medium nuclear spectral width, i.e. $\Gamma\leq 40$ MeV, the resulting total cross sections are, however, reduced by not more than about 25% compared to the on-shell values. Off-shell effect are generally more pronounced at large nuclear matter densities.Comment: 31 pages Revtex, 12 figures, typos corrected, to appear in Phys. Rev.

GWAS study using DNA pooling strategy identifies association of variant rs4910623 in OR52B4 gene with anti-VEGF treatment response in age-related macular degeneration

This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/Pooled DNA based GWAS to determine genetic association of SNPs with visual acuity (VA) outcome in anti-vascular endothelial growth factor (anti-VEGF) treated neovascular age-related macular degeneration (nAMD) patients. We performed pooled DNA based GWAS on 285 anti-VEGF treated nAMD patients using high density Illumina 4.3 M array. Primary outcome was change in VA in Early Treatment Diabetic Retinopathy Study (ETDRS) letters after 6 months of anti-VEGF treatment (patients who lost ≥5 ETDRS letters classified as non-responders and all remaining classified as responders). GWAS analysis identified 44 SNPs of interest: 37 with strong evidence of association (p < 9 × 10−8), 2 in drug resistance genes (p < 5 × 10−6) and 5 nonsynonymous changes (p < 1 × 10−4). In the validation phase, individual genotyping of 44 variants showed three SNPs (rs4910623 p = 5.6 × 10−5, rs323085 p = 6.5 × 10−4 and rs10198937 p = 1.30 × 10−3) remained associated with VA response at 6 months. SNP rs4910623 also associated with treatment response at 3 months (p = 1.5 × 10−3). Replication of these three SNPs in 376 patients revealed association of rs4910623 with poor VA response after 3 and 6 months of treatment (p = 2.4 × 10−3 and p = 3.5 × 10−2, respectively). Meta-analysis of both cohorts (673 samples) confirmed association of rs4910623 with poor VA response after 3 months (p = 1.2 × 10−5) and 6 months (p = 9.3 × 10−6) of treatment in nAMD patients