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

Quantum field theory and Hopf algebra cohomology

We exhibit a Hopf superalgebra structure of the algebra of field operators of quantum field theory (QFT) with the normal product. Based on this we construct the operator product and the time-ordered product as a twist deformation in the sense of Drinfeld. Our approach yields formulas for (perturbative) products and expectation values that allow for a significant enhancement in computational efficiency as compared to traditional methods. Employing Hopf algebra cohomology sheds new light on the structure of QFT and allows the extension to interacting (not necessarily perturbative) QFT. We give a reconstruction theorem for time-ordered products in the spirit of Streater and Wightman and recover the distinction between free and interacting theory from a property of the underlying cocycle. We also demonstrate how non-trivial vacua are described in our approach solving a problem in quantum chemistry.Comment: 39 pages, no figures, LaTeX + AMS macros; title changed, minor corrections, references update

Congenital adrenal hyperplasia

Congenital adrenal hyperplasia consists of a heterogenous group of inherited disorders due to enzymatic defects in the biosynthetic pathway of cortisol and/or aldosterone. This results in glucocorticoid deficiency, mineralocorticoid deficiency, and androgen excess. 95% of CAH cases are due to 21-hydroxylase deficiency. Clinical forms range from the severe, classical CAH associated with complete loss of enzyme function, to milder, non-classical forms (NCAH). Androgen excess affects the pilosebaceous unit, causing cutaneous manifestations such as acne, androgenetic alopecia and hirsutism. Clinical differential diagnosis between NCAH and polycystic ovary syndrome may be difficult. In this review, the evaluation of patients with suspected CAH, the clinical presentation of CAH forms, with emphasis on the cutaneous manifestations of the disease, and available treatment options, will be discussed

Evaluation of serum sphingolipids and the influence of genetic risk factors in age-related macular degeneration

Peer reviewedPublisher PD