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

Z_2-gradings of Clifford algebras and multivector structures

Let Cl(V,g) be the real Clifford algebra associated to the real vector space V, endowed with a nondegenerate metric g. In this paper, we study the class of Z_2-gradings of Cl(V,g) which are somehow compatible with the multivector structure of the Grassmann algebra over V. A complete characterization for such Z_2-gradings is obtained by classifying all the even subalgebras coming from them. An expression relating such subalgebras to the usual even part of Cl(V,g) is also obtained. Finally, we employ this framework to define spinor spaces, and to parametrize all the possible signature changes on Cl(V,g) by Z_2-gradings of this algebra.Comment: 10 pages, LaTeX; v2 accepted for publication in J. Phys.

A Hopf laboratory for symmetric functions

An analysis of symmetric function theory is given from the perspective of the underlying Hopf and bi-algebraic structures. These are presented explicitly in terms of standard symmetric function operations. Particular attention is focussed on Laplace pairing, Sweedler cohomology for 1- and 2-cochains, and twisted products (Rota cliffordizations) induced by branching operators in the symmetric function context. The latter are shown to include the algebras of symmetric functions of orthogonal and symplectic type. A commentary on related issues in the combinatorial approach to quantum field theory is given.Comment: 29 pages, LaTeX, uses amsmat

Early transitions and tertiary enrolment: The cumulative impact of primary and secondary effects on entering university in Germany

Our aim is to assess how the number of working class students entering German universities can effectively be increased. Therefore, we estimate the proportion of students from the working class that would successfully enter university if certain policy interventions were in place to eliminate primary effects (performance differentials between social classes) and/or secondary effects (choice differentials net of performance) at different transition points. We extend previous research by analysing the sequence of transitions between elementary school enrolment and university enrolment and by accounting for the impact that manipulations at earlier transitions have on the performance distribution and size of the student ‘risk-set’ at subsequent transitions. To this end, we develop a novel simulation procedure which also seeks to find viable solutions to the shortcomings in the German data landscape. Our findings show that interventions are most effective if they take place early in the educational career. Neutralizing secondary effects at the transition to upper secondary school proves to be the single most effective means to increase participation rates in tertiary education among working class students. However, this comes at the expense of lower average performance levels. (DIPF/author

Endocrine profiles after triggering of final oocyte maturation with GnRH agonist after cotreatment with the GnRH antagonist ganirelix during ovarian hyperstimulation for in vitro fertilization

In a randomized multicenter study, the efficacies of two different GnRH agonists were compared with that of hCG for triggering final stages of oocyte maturation after ovarian hyperstimulation for in vitro fertilization. Ovarian stimulation was conducted by recombinant FSH (Puregon), and the GnRH antagonist ganirelix (Orgalutran) was coadministered for the prevention of a premature LH rise. Luteal support was provided by daily progestin administration. Frequent blood sampling was performed at midcycle in the first 47 eligible subjects included in the current study, who were randomized for a single dose of 0.2 mg triptorelin (n = 17), 0.5 mg leuprorelin (n = 15), or 10,000 IU hCG (n = 15). Serum concentrations of LH, FSH, E2, and progesterone (P) were assessed at variable intervals. LH peaked at 4 h after both triptorelin and leuprorelin administration, with median LH levels of 130 and 107 IU/liter (P < 0.001), respectively. LH levels returned to baseline after 24 h. Subjects receiving hCG showed peak levels of 240 IU/liter hCG 24 h after administration. A rise in FSH to 19 IU/liter (P < 0.001) was noted in both GnRH agonist groups 8 h after injection. Within 24 h the areas under the curve for LH and FSH were significantly higher (P < 0.001) in both GnRH agonist groups compared with that for hCG. E2 and P levels were similar for all groups up to the day of oocyte retrieval. Luteal phase areas under the curve for P and E2 were significantly elevated (P < 0.001) in the hCG group. The mean (+/-SD) numbers of oocytes retrieved were 9.8 +/- 5.4, 8.7 +/- 4.5, and 8.3 +/- 3.3; the percentages of metaphase II oocytes were 72%, 85%, and 86%; and fertilization rates were 61%, 62%, and 56% in the triptorelin, leuprorelin, and hCG group, respectively (P = NS for all three comparisons). These findings support the effective induction of final oocyte maturation in both GnRH agonist groups. In summary, after treatment with the GnRH antagonist ganirelix for the prevention of premature LH surges, triggering of final stages of oocyte maturation can be induced effectively by a single bolus injection of GnRH agonist, as demonstrated by the induced endogenous LH and FSH surge and the quality and fertilization rate of recovered oocytes. Moreover, corpus luteum formation is induced by GnRH agonists with luteal phase steroid levels closer to the physiological range compared with hCG. This more physiological approach for inducing oocyte maturation may represent a successful and safer alternative for in vitro fertilization patients undergoing ovarian hyperstimulation

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

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.

BRE modulates granulosa cell death to affect ovarian follicle development and atresia in the mouse

The BRE (brain and reproductive expression) gene, highly expressed in nervous and reproductive system organs, plays an important role in modulating DNA damage repair under stress response and pathological conditions. Folliculogenesis, a process that ovarian follicle develops into maturation, is closely associated with the interaction between somatic granulosa cell and oocyte. However, the regulatory role of BRE in follicular development remains undetermined. In this context, we found that BRE is normally expressed in the oocytes and granulosa cells from the primordial follicle stage. There was a reduction in follicles number of BRE mutant (BRE(−/−)) mice. It was attributed to increase the follicular atresia in ovaries, as a result of retarded follicular development. We established that cell proliferation was inhibited, while apoptosis was markedly increased in the granulosa cells in the absence of BRE. In addition, expressions of γ-H2AX (marker for showing DNA double-strand breaks) and DNA damage-relevant genes are both upregulated in BRE(−/−) mice. In sum, these results suggest that the absence of BRE, deficiency in DNA damage repair, causes increased apoptosis in granulosa cells, which in turn induces follicular atresia in BRE(−/−) mice

HtrA1 Mediated Intracellular Effects on Tubulin Using a Polarized RPE Disease Model

Age-related macular degeneration (AMD) is the leading cause of irreversible vision loss. The protein HtrA1 is enriched in retinal pigment epithelial (RPE) cells isolated from AMD patients and in drusen deposits. However, it is poorly understood how increased levels of HtrA1 affect the physiological function of the RPE at the intracellular level. Here, we developed hfRPE (human fetal retinal pigment epithelial) cell culture model where cells fully differentiated into a polarized functional monolayer. In this model, we fine-tuned the cellular levels of HtrA1 by targeted overexpression. Our data show that HtrA1 enzymatic activity leads to intracellular degradation of tubulin with a corresponding reduction in the number of microtubules, and consequently to an altered mechanical cell phenotype. HtrA1 overexpression further leads to impaired apical processes and decreased phagocytosis, an essential function for photoreceptor survival. These cellular alterations correlate with the AMD phenotype and thus highlight HtrA1 as an intracellular target for therapeutic interventions towards AMD treatment