Twisted Dirac Operators over Quantum Spheres

We construct new families of spectral triples over quantum spheres, with a particular attention focused on the standard Podles quantum sphere and twisted Dirac operators.Comment: 17 page

Non-standard Quantum Group in Toda and WZNW Theories

The basic Poisson brackets in the chira.l sectors of the WZNW theory and its Toda reduction are described in terms of a monodromy dependent r-matrix. In the case of the sl(n) Lie algebras, and only then, this monodromy dependence can be ‘gauged away’. The resulting non-trivial solution of the classical Yang-Baxter equation is the classical limit of the quantum R-matrix of the SL(n) Toda theory found recently by Creminer and Gervais. The deformations of SL(n) and U(sl(n)) defined by this R-matrix are studied in the simplest non-trivial case of n = 3. The multiplicative structure of this deformation of U(sl(3)) can be transformed into that of the standard U_q(sl(3)), but the coproduct is different. Possible generalizations for arbitrary n and applications in conformal field theory and in non-commutative differential geometry are briefly indicated. The Cremmer-Gervais R-matrix is ‘Yang-Baxterized’. The resulting spectral parameter dependent R-matrix may give rise to a new series of integrable models

Reconstruction of universal Drinfeld twists from representations

Universal Drinfeld twists are inner automorphisms which relate the coproduct of a quantum enveloping algebra to the coproduct of the undeformed enveloping algebra. Even though they govern the deformation theory of classical symmetries and have appeared in numerous applications, no twist for a semi-simple quantum enveloping algebra has ever been computed. It is argued that universal twists can be reconstructed from their well known representations. A method to reconstruct an arbitrary element of the enveloping algebra from its irreducible representations is developed. For the twist this yields an algebra valued generating function to all orders in the deformation parameter, expressed by a combination of basic and ordinary hypergeometric functions. An explicit expression for the universal twist of su(2) is given up to third order.Comment: 24 page

On the formfactor of the imaginary part and its coupling to the real optical potential for the α\alpha-nucleus scattering

The model-independent formfactor of the absorptive cc-nucleus potential was calculated and compared with model dependent ones. The coupling between the shapes of the real and imaginary potential is discussed

303. Image registration – precise quality assessment of radiotherapy without necessity of showing corresponding points in simulation and portal images

PurposeEnabling the quality assessment of radiotherapy to be made in daily practice, using the new software tool to analyze the simulation and portal images.MethodIn the registration of the anatomical structures as well as the irradiation fields, the features used as landmarks are the edges. The significant edge fragments must be chosen manually, but without showing any specific corresponding points. Field edges marked with wires in the simulation image are found fully automatically with the original combination of a dedicated line edge detector and a version of hierarchical, combined Hough transform. The registration is guided by the robust accuracy criterion using the modified Hausdorff distance measure. The only parameter of the measure – quantile rank, or share of data used in comparison – is not fixed, but evolves from 1 to 0 during the optimization of the accuracy. This has two advantages. 1: The user can choose the result found for the share corresponding to the actual share of erroneous data in the images, which can be seen only after the results for all the possible ranks are known. 2: The algorithm can avoid the local minima. The registration takes few seconds on a typical PC. The method has been implemented in a software tool which supports the complete process of measurement, and has been tested in clinical triais with positive result.ConclusionsThe modified Hausdorff distance measure with evolving rank is a good and efficient registration accuracy measure for quality assessment of radiotherapy based on the comparison of portal and simulation images

Static response of Fermi liquids with tensor interactions

We use Landau's theory of a normal Fermi liquid to derive expressions for the static response of a system with a general tensor interaction that conserves the total spin and the total angular momentum of the quasiparticle-quasihole pair. The magnetic susceptibility is calculated in detail, with the inclusion of the center of mass tensor and cross vector terms in addition to the exchange tensor one. We also introduce a new parametrization of the tensor Landau parameters which significantly reduces the importance of high angular harmonic contributions. For nuclear matter and neutron matter we find that the two most important effects of the tensor interaction are to give a contribution from multipair states and to renormalize the magnetic moments. Response to a weak probe may be calculated using similar methods, replacing the magnetic moments with the matrix elements of the weak charges

3/Evaluation of set-up deviations during the irradiation of patients suffering from breast cancer treated with two different techniques

PurposeTo present results of patient positioning during routine radiotherapy for patients treated after mastectomy and to compare the inaccuracies in patient set-up for this group of patients and for the patients treated after breast conserving therapy with tangential fields.Methods and materialsIn total, the analysis comprised 56 pairs of portal and simulator films for 14 consecutive patients treated following breast conserving therapy and 98 pairs of portal and simulator films for 20 consecutive patients treated after mastectomy. For the first group the tangential field technique (TF technique) was used, for the second the inverse hockey stick technique (IHS technique). The comparison of the treatment reproducibility obtained for both groups of patients was performed in terms of systematic and random error calculated for the whole groups and by the comparison of cumulative distribution of the length of the displacement vector.ResultsIn the IHS and TF techniques for medial and lateral fields, displacement larger than 5 mm occurred in 28.3%, 15.8% and 25.4% respectively. For the IHS technique, the systematic errors for lateral and cranial-caudal direction were 1.9 and 1.7 mm respectively (1 standard deviation – SD), the random errors for lateral and cranial-caudal direction were 2.0 and 2.5 mm. For the TF technique, the systematic errors for lateral and cranial-caudal direction were 2.6 and 1.3 mm for medial field and 3.7 and 0.7 mm for lateral fields respectively, the random errors for lateral and cranial-caudal direction were 2.2 and 1.0 mm for medial field and 2.9 and 1.1 for lateral field respectively. Rotations were negligible in the HIS technique. For the TF technique the systematic component and random component amounted to about 2.0 degrees (1 SD).ConclusionsBoth the inverse hockey stick and standard tangential techniques showed good reproducibility of patients set-up with respect to cranial-caudal direction. For the TF technique, the accuracy should be improved for the medial field with respect to the ventral-dorsal direction

Curved Noncommutative Tori as Leibniz Quantum Compact Metric Spaces

We prove that curved noncommutative tori, introduced by Dabrowski and Sitarz, are Leibniz quantum compact metric spaces and that they form a continuous family over the group of invertible matrices with entries in the commutant of the quantum tori in the regular representation, when this group is endowed with a natural length function.Comment: 16 Pages, v3: accepted in Journal of Math. Physic

25. Assessment of the accuracy of radiotherapy by digital superposition of portal and rference images

Teleradiotherapy imposes the requirement of high accuracy in reference to its medical as well as technical aspects. Close adherence to the geometrical parameters set up in therapy planning is vital. The current location of the irradiation field and anatomical structures can be recorded in the portal image acquired during the therapy course. Assessment of the treatment accuracy consists in registration (overlaying) of the reference and the portal image to compare the layout of anatomical structures and the irradiation field. Edges of the compared features are difficult to find in the portal image, which is inherently of low contrast. Hence, not all the edges present in the reference image can be found in the portal one, and the comparison of geometries in these images is difficult and time-consuming. There exists a need for a tool that could support and objectify this process.At present the accuracy assessment is done manually by an experienced observer. As a rule, this tedious procedure is not performed routinely. The wide literature on image registration refers to portal images made with beams generated in accelerators rather than with the cobalt apparata. In Poland more than a half of patients are treated with cobalt. There are numerous references to image registration methods tailored for finding the fitting and non-fitting fragments of the compared edges. The majority of these methods lack generality.The methodology to be presented is general and requires little user intervention.•Features to be matched: edges of selected anatomical structures, irradiation field and shields, as seen in scanned images.•Edge detector: zero-second-derivative with scale fitted to noise and scale of edges, separately in portal and reference images.•Geometrical transformation: affine (2 translations, rotation, 2 scalings – along two coordinate axes).•Measure of fitting accuracy: modified Hausdorff distance measure – robust method based on voting. Parts of the contours that do not fit the general tendency are rejected. This is vital if portal images made with cobalt apparata are analysed.•Optimisation method for finding the best transformation: maximum gradient (chamfer matching).•Final fit can be calculated with le least squares method for only those pixels which were classified as fitting.•Speed-ups: hierarchical method (pyramid of resolutions); in some cases: pre-calculated virtual transformations.•Automatic classification of edges as belonging to anatomic structures, irradiation field or shields is possible.•Experiments with enhancing the contrast of portal images using the optical system transfer function concept.The software tool will be presented which makes it possible to correct the therapeutic system geometry or the location of the patient. Full control of the physician over the measurement process will be maintained, according to the requirement of human decision-making in the therapeutical process. The registration (overlaying) of a portal and a reference image is visualised for verification. Manual corrections of the result will be possible in the final version of the program.Acknowledgement The work is supported by the Committee for Scientific Research within the grant no. KBN 4 P05B 064 18

Dirac Operators on Quantum Projective Spaces

We construct a family of self-adjoint operators D_N which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space CP_q(l), for any l>1 and 0<q<1. They provide 0^+ dimensional equivariant even spectral triples. If l is odd and N=(l+1)/2, the spectral triple is real with KO-dimension 2l mod 8.Comment: 54 pages, no figures, dcpic, pdflate