Unification through extra dimensions at two loops

The presence of an extra dimension of size R\equiv M_c^{-1} introduces corrections of order (\mu/M_c)\alpha to the gauge and Yukawa couplings and accelerates their running at scales \mu larger than M_c. This could result in a grand unification scale M_X\approx 20 M_c. We study the corrections at the two-loop level. We find corrections of order (\mu/M_c)\alpha^2 for the gauge couplings and of order (\mu/M_c)^2\alpha^2 for the Yukawa couplings. Therefore, in the Yukawa sector one and two-loop contributions can be of the same order below M_X. We show that in the usual scenarios the dominant gauge and Yukawa couplings are decreasing functions of the scale, in such a way that (\mu/M_c)\alpha becomes approximately constant and two-loop contributions introduce just a 30% correction which does not increase with the scale.Comment: 14 pages, added references, corrected typo

A Comparison of Solar Cycle Variations in the Equatorial Rotation Rates of the Sun's Subsurface, Surface, Corona, and Sunspot Groups

Using the Solar Optical Observing Network (SOON) sunspot-group data for the period 1985-2010, the variations in the annual mean equatorial-rotation rates of the sunspot groups are determined and compared with the known variations in the solar equatorial-rotation rates determined from the following data: i) the plasma rotation rates at 0.94Rsun, 0.95Rsun,...,1.0Rsun measured by Global Oscillation Network Group (GONG) during the period 1995-2010, ii) the data on the soft X-ray corona determined from Yohkoh/SXT full disk images for the years 1992-2001, iii) the data on small bright coronal structures (SBCS) which were traced in Solar and Heliospheric Observatory (SOHO)/EIT images during the period 1998-2006, and iv) the Mount Wilson Doppler-velocity measurements during the period 1986-2007. A large portion (up to approximate 30 deg latitude) of the mean differential-rotation profile of the sunspot groups lies between those of the internal differential-rotation rates at 0.94Rsun and 0.98Rsun.The variation in the yearly mean equatorial-rotation rate of the sunspot groups seems to be lagging that of the equatorial-rotation rate determined from the GONG measurements by one to two years.The amplitude of the latter is very small.The solar-cycle variation in the equatorial-rotation rate of the solar corona closely matches that determined from the sunspot-group data.The variation in the equatorial-rotation rate determined from the Mount Wilson Doppler-velocity data closely resembles the corresponding variation in the equatorial-rotation rate determined from the sunspot-group data that included the values of the abnormal angular motions (> 3 deg per day) of the sunspot groups. Implications of these results are pointed out.Comment: 22 pages, 10 figures, accepted by Solar Physic

A quantum analogue of the first fundamental theorem of invariant theory

We establish a noncommutative analogue of the first fundamental theorem of classical invariant theory. For each quantum group associated with a classical Lie algebra, we construct a noncommutative associative algebra whose underlying vector space forms a module for the quantum group and whose algebraic structure is preserved by the quantum group action. The subspace of invariants is shown to form a subalgebra, which is finitely generated. We determine generators of this subalgebra of invariants and determine their commutation relations. In each case considered, the noncommutative modules we construct are flat deformations of their classical commutative analogues. Thus by taking the limit as $q\to 1$, our results imply the first fundamental theorem of classical invariant theory, and therefore generalise them to the noncommutative case.Comment: 44 pages, 3 figure

Combination chemotherapy with cyclophosphamide, epirubicin and 5-fluorouracil causes trabecular bone loss, bone marrow cell depletion and marrow adiposity in female rats

The introduction of anthracyclines to adjuvant chemotherapy has increased survival rates among breast cancer patients. Cyclophosphamide, epirubicin and 5-fluorouracil (CEF) combination therapy is now one of the preferred regimens for treating node-positive breast cancer due to better survival with less toxicity involved. Despite the increasing use of CEF, its potential in causing adverse skeletal effects remains unclear. Using a mature female rat model mimicking the clinical setting, this study examined the effects of CEF treatment on bone and bone marrow in long bones. Following six cycles of CEF treatment (weekly intravenous injections of cyclophosphamide at 10 mg/kg, epirubicin at 2.5 mg/kg and 5-flurouracil at 10 mg/kg), a significant reduction in trabecular bone volume was observed at the metaphysis, which was associated with a reduced serum level of bone formation marker alkaline phosphatase (ALP), increased trends of osteoclast density and osteoclast area at the metaphysis, as well as an increased size of osteoclasts being formed from the bone marrow cells ex vivo. Moreover, a severe reduction of bone marrow cellularity was observed following CEF treatment, which was accompanied by an increase in marrow adipose tissue volume. This increase in marrow adiposity was associated with an expansion in adipocyte size but not in marrow adipocyte density. Overall, this study indicates that six cycles of CEF chemotherapy may induce some bone loss and severe bone marrow damage. Mechanisms for CEF-induced bone/bone marrow pathologies and potential preventive strategies warrant further investigation.Chiaming Fan, Kristen R. Georgiou, Ross A. McKinnon, Dorothy M. K. Keefe, Peter R. C. Howe and Cory J. Xia

Model building, mathematics and logo

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An Augmentation System for Fine Manipulation

. Augmented surgical manipulation tasks can be viewed as a sequence of smaller, simpler steps driven primarily by the surgeon's input. These steps can be abstracted as controlled interaction of the tool/end-effector with the environment. The basic research problem here is performing a sequence of control primitives. In computing terms, each of the primitives is a predefined computational routine(e.g. compliant motion or some other "macro") with initiation and termination predicates. The sequencing of these primitives depends upon user control and effects of the environmental interaction. We explore a sensor driven system to perform simple manipulation tasks. The system is composed of a core set of "safe" system states and task specific states and transitions. Using the "steady hand" robot as the experimental platform we investigate using such a system. 1 Introduction Dexterous manipulation is a key element in the speed, safety, and, ultimately, the success of most surgical i..