A family of quantum projective spaces and related q-hypergeometric orthogonal polynomials

We define a one-parameter family of two-sided coideals in U_q(gl(n)) and study the corresponding algebras of infinitesimally right invariant functions on the quantum unitary group U_q(n). The Plancherel decomposition of these algebras with respect to the natural transitive U_q(n)-action is shown to be the same as in the case of a complex projective space. By computing the radial part of a suitable Casimir operator, we identify the zonal spherical functions (i.e. infinitesimally bi-invariant matrix coefficients of finite-dimensional irreducible representations) as Askey-Wilson polynomials containing two continuous and one discrete parameter. In certain limit cases, the zonal spherical functions are expressed as big and little q-Jacobi polynomials depending on one discrete parameter.Comment: 31 pages, AMS-TeX 2.1, no figure

CQG algebras: a direct algebraic approach to compact quantum groups

The purely algebraic notion of CQG algebra (algebra of functions on a compact quantum group) is defined. In a straightforward algebraic manner, the Peter-Weyl theorem for CQG algebras and the existence of a unique positive definite Haar functional on any CQG algebra are established. It is shown that a CQG algebra can be naturally completed to a $C^\ast$-algebra. The relations between our approach and several other approaches to compact quantum groups are discussed.Comment: 14 pp., Plain TeX, accepted by Lett. Math. Phy

A Bacillus megaterium plasmid system for the production, export, and one-step purification of affinity-tagged heterologous levansucrase from growth medium

A multiple vector system for the production and export of recombinant affinity-tagged proteins in Bacillus megaterium was developed. Up to 1 mg/liter of a His(6)-tagged or Strep-tagged Lactobacillus reuteri levansucrase was directed into the growth medium, using the B. megaterium esterase LipA signal peptide, and recovered by one-step affinity chromatography

Quantum planes and quantum cylinders from Poisson homogeneous spaces

Quantum planes and a new quantum cylinder are obtained as quantization of Poisson homogeneous spaces of two different Poisson structures on classical Euclidean group E(2).Comment: 13 pages, plain Tex, no figure

Goat Milk Oligosaccharides:Their Diversity, Quantity, and Functional Properties in Comparison to Human Milk Oligosaccharides

Human milk is considered the golden standard in infant nutrition. Free oligosaccharides in human milk provide important health benefits. These oligosaccharides function as prebiotics, immune modulators, and pathogen inhibitors and were found to improve barrier function in the gut. Infant formulas nowadays often contain prebiotics but lack the specific functions of human milk oligosaccharides (hMOS). Milk from domesticated animals also contains milk oligosaccharides but at much lower levels and with less diversity. Goat milk contains significantly more oligosaccharides (gMOS) than bovine (bMOS) or sheep (sMOS) milk and also has a larger diversity of structures. This review summarizes structural studies, revealing a diversity of up to 77 annotated gMOS structures with almost 40 structures fully characterized. Quantitative studies of goat milk oligosaccharides range from 60 to 350 mg/L in mature milk and from 200 to 650 mg/L in colostrum. These levels are clearly lower than in human milk (5-20 g/L) but higher than in other domesticated dairy animals, e.g., bovine (30-60 mg/L) and sheep (20-40 mg/L). Finally, the review focuses on demonstrated and potential functionalities of gMOS. Some studies have shown anti-inflammatory effects of mixtures enriched in gMOS. Goat MOS also display prebiotic potential, particularly in stimulating growth of bifidobacteria preferentially. Although functional studies of gMOS are still limited, several structures are also found in human milk and have known functions as immune modulators and pathogen inhibitors. In conclusion, goat milk constitutes a promising alternative source for milk oligosaccharides, which can be used in infant formula

Quantum symmetric pairs and representations of double affine Hecke algebras of type C∨CnC^\vee C_n

We build representations of the affine and double affine braid groups and Hecke algebras of type $C^\vee C_n$, based upon the theory of quantum symmetric pairs $(U,B)$. In the case $U=U_q(gl_N)$, our constructions provide a quantization of the representations constructed by Etingof, Freund and Ma in arXiv:0801.1530, and also a type $BC$ generalization of the results in arXiv:0805.2766.Comment: Final version, to appear in Selecta Mathematic

Motor recovery and cortical reorganization after constraint-induced movement therapy in stroke patients: a preliminary study.

Constraint-induced movement therapy (CIMT) is a physical rehabilitation regime that has been previously shown to improve motor function in chronic hemiparetic stroke patients. However, the neural mechanisms supporting rehabilitation-induced motor recovery are poorly understood. The goal of this study was to assess motor cortical reorganization after CIMT using functional magnetic resonance imaging (fMRI). In a repeated-measures design, 4 incompletely recovered chronic stroke patients treated with CIMT underwent motor function testing and fMRI. Five age-matched normal subjects were also imaged. A laterality index (LI) was determined from the fMRI data, reflecting the distribution of activation in motor cortices contralateral compared with ipsilateral to the moving hand. Pre-intervention fMRI showed a lower LI during affected hand movement of stroke patients (LI = 0.23+/-0.07) compared to controls (LI unaffected patient hand = 0.65+/-0.10; LI dominant normal hand = 0.65+/-0.11; LI nondominant normal hand = 0.69+/-0.11; P < 0.05) due to trends toward increased ipsilateral motor cortical activation. Motor function testing showed that patients made significant gains in functional use of the stroke-affected upper extremity (detected by the Motor Activity Log) and significant reductions in motor impairment (detected by the Fugl-Meyer Stroke Scale and the Wolf Motor Function Test) immediately after CIMT, and these effects persisted at 6-month follow-up. The behavioral effects of CIMT were associated with a trend toward a reduced LI from pre-intervention to immediately post-intervention (LI = -0.01+/-0.06, P = 0.077) and 6 months post-intervention (LI = -0.03+/-0.15). Stroke-affected hand movement was not accompanied by mirror movements during fMRI, and electromyographic measures of mirror recruitment under simulated fMRI conditions were not correlated with LI values. These data provide preliminary evidence that gains in motor function produced by CIMT in chronic stroke patients may be associated with a shift in laterality of motor cortical activation toward the undamaged hemisphere

Laparoscopic subtotal hysterectomy versus laparoscopic total hysterectomy: a decade of experience

At present, there are only few data on the surgical outcomes of laparoscopic hysterectomy (LH). Up till now, it has been unclear whether there is a difference in number of complications among the subcategories of laparoscopic total hysterectomy and laparoscopic subtotal hysterectomy (LSH). Therefore, we have performed a retrospective analysis to evaluate the peri- and postoperative outcomes in women undergoing LSH versus LH. This multi-centre retrospective cohort study (Canadian Task Force classification II-2) was conducted in multi-centres (two teaching hospitals and one university medical centre) in the Netherlands, all experienced in minimally invasive gynaecology. In a multi-centre retrospective cohort study we compared the long-term outcomes of laparoscopic subtotal hysterectomy and laparoscopic total hysterectomy (including laparoscopic assisted vaginal hysterectomy, laparoscopic hysterectomy and total laparoscopic hysterectomy). All laparoscopic hysterectomies from the last 10 years (January 1998 till December 2007) were included. Patient characteristics, intra- and postoperative complications, operating time and duration of hospital stay were recorded. The minimum follow-up was 6 months. A total of 390 cases of laparoscopic hysterectomies were included in the analysis: 192 laparoscopic subtotal hysterectomies and 198 laparoscopic total hysterectomies. Patient characteristics such as age and parity were equal in the groups. The overall number of short-term and long-term complications was comparable in both groups: 17% and 15%. Short-term complications (bleeding, fever) were 3% in the LSH group and 12% in the LH group. Long-term complications were (tubal prolapse and cervical stump reoperations) 15% in the LSH group and 3% in the LH group. Laparoscopic subtotal hysterectomy as compared with the different types of laparoscopic total hysterectomy is associated with more long-term postoperative complications, whereas laparoscopic total hysterectomy is associated with more short-term complications

Free q-Schrodinger Equation from Homogeneous Spaces of the 2-dim Euclidean Quantum Group

After a preliminary review of the definition and the general properties of the homogeneous spaces of quantum groups, the quantum hyperboloid qH and the quantum plane qP are determined as homogeneous spaces of Fq(E(2)). The canonical action of Eq(2) is used to define a natural q-analog of the free Schro"dinger equation, that is studied in the momentum and angular momentum bases. In the first case the eigenfunctions are factorized in terms of products of two q-exponentials. In the second case we determine the eigenstates of the unitary representation, which, in the qP case, are given in terms of Hahn-Exton functions. Introducing the universal T-matrix for Eq(2) we prove that the Hahn-Exton as well as Jackson q-Bessel functions are also obtained as matrix elements of T, thus giving the correct extension to quantum groups of well known methods in harmonic analysis.Comment: 19 pages, plain tex, revised version with added materia