Gehring-Hayman theorem for conformal deformations

We study conformal deformations of a uniform space that satisfies the Ahlfors Q-regularity condition on balls of Whitney type. We verify the Gehring–Hayman Theorem by using a Whitney Covering of the space.

Helical tomotherapy (HT) for the treatment of anal canal cancer: preliminary clinical results, and dosimetric comparison between HT and intensity-modulated or 3D conformal radiotherapy

Background: To report a single-center experience in 19 patients (pts) with anal canal cancer treated with helical tomotherapy (HT) and concurrent chemotherapy, and compare the dosimetric results with fixed-field intensitymodulated radiotherapy (IMRT) and 3D conformal radiotherapy (3D RT). Materials and Methods: Between 2007 and 2008, 19 consecutive pts were treated with HT and concurrent CT for anal canal cancer. Median age was 59 years (range, 38−83), and female/male ratio was 14/5. The majority of the pts had T2 or T3 tumours (68.4%), and 52.6% had positive lymph nodes. In all 19 pts, pelvic and inguinal nodes, and tumour irradiation was given using HT upto a median dose of 36 Gy (1.8 Gy/fr) followed by a 1-week gap. A boost dose of 23.4 Gy (1.8 Gy/fr) was delivered to the tumour and involved nodes using 3DRT (n = 12), HT (n = 6), or IMRT (n = 1). Simultaneous integrated boost was used in none of the pts. All but one patient with a T1N0 tumour received concomitant mitomycin/5- fluorouracil (n = 12) or mitomycin/capecitabin (n = 7) CT. Toxicity was scored according to the Common Terminology Criteria for Adverse Events (NCICTCAE v3.0). HT plans and treatments were generated using Tomotherapy, Inc., software and hardware; and 3D or IMRT boost plans with the CMS treatment planning system (TPS), using 6−18 MV photons from a Siemens Primus accelerator. For dosimetric comparison, computed tomography data sets of 10 pts were imported into the TPS, and 3D and 5-field step-andshoot IMRT plans were generated for each case. Plans were optimized with the aim of assessing organs at risk (OAR) and healthy-tissue sparing while enforcing highly conformal target coverage, and evaluated by dose-volume histograms (DVH) of planning target volumes (PTV) and OAR. Results: With a median follow-up of 13 months (range, 3−18), all pts are alive and well; except one patient developing local recurrence at 12 months. No patient developed grade 3 or more acute toxicity. No unplanned treatment interruption was necessary because of toxicity. With 360-degree-of-freedom beam projection, HT showed an advantage over 3D or IMRT plans in terms of dose conformity around the PTV, and dose gradients were steeper outside the PTV, resulting in reduced doses to OARs. Using HT, acute toxicity was acceptable, and seemed to be better than historical standards. Conclusion: We conclude that HT combined with concurrent chemotherapy for anal canal cancer is effective and tolerable. Compared to 3DRT or 5-field IMRT, there is better conformity around the PTV, and OAR sparing.

Invariance and randomness in the Nash program for coalitional games

By introducing physical outcomes in coalitional games we note that coalitional games and social choice problems are equivalent (implying that so are the theory of implementation and the Nash program). This facilitates the understanding of the role of invariance and randomness in the Nash program. Also, the extent to which mechanisms in the Nash program perform ``real implementation'' is examined.

D-String on near horizon geometries and infinite conformal symmetry

We show that the symmetries of effective D-string actions in constant dilaton backgrounds are directly related to homothetic motions of the background metric. In the presence of such motions, there are infinitely many nonlinearly realized rigid symmetries forming a loop (or looplike) algebra. Near horizon (antideSitter) D3 and D1+D5 backgrounds are discussed in detail and shown to provide 2D interacting field theories with infinite conformal symmetry.

Generalized adiabatic invariance

In this paper we find the quantities that are adiabatic invariants of any desired order for a general slowly time-dependent Hamiltonian. In a preceding paper, we chose a quantity that was initially an adiabatic invariant to first order, and sought the conditions to be imposed upon the Hamiltonian so that the quantum mechanical adiabatic theorem would be valid to mth order. [We found that this occurs when the first (m - 1) time derivatives of the Hamiltonian at the initial and final time instants are equal to zero.] Here we look for a quantity that is an adiabatic invariant to mth order for any Hamiltonian that changes slowly in time, and that does not fulfill any special condition (its first time derivatives are not zero initially and finally).

A critical evaluation of secondary cancer risk models applied to Monte Carlo dose distributions of 2-dimensional, 3-dimensional conformal and hybrid intensity-modulated radiation therapy for breast cancer.

The comparison of radiotherapy techniques regarding secondary cancer risk has yielded contradictory results possibly stemming from the many different approaches used to estimate risk. The purpose of this study was to make a comprehensive evaluation of different available risk models applied to detailed whole-body dose distributions computed by Monte Carlo for various breast radiotherapy techniques including conventional open tangents, 3D conformal wedged tangents and hybrid intensity modulated radiation therapy (IMRT). First, organ-specific linear risk models developed by the International Commission on Radiological Protection (ICRP) and the Biological Effects of Ionizing Radiation (BEIR) VII committee were applied to mean doses for remote organs only and all solid organs. Then, different general non-linear risk models were applied to the whole body dose distribution. Finally, organ-specific non-linear risk models for the lung and breast were used to assess the secondary cancer risk for these two specific organs. A total of 32 different calculated absolute risks resulted in a broad range of values (between 0.1% and 48.5%) underlying the large uncertainties in absolute risk calculation. The ratio of risk between two techniques has often been proposed as a more robust assessment of risk than the absolute risk. We found that the ratio of risk between two techniques could also vary substantially considering the different approaches to risk estimation. Sometimes the ratio of risk between two techniques would range between values smaller and larger than one, which then translates into inconsistent results on the potential higher risk of one technique compared to another. We found however that the hybrid IMRT technique resulted in a systematic reduction of risk compared to the other techniques investigated even though the magnitude of this reduction varied substantially with the different approaches investigated. Based on the epidemiological data available, a reasonable approach to risk estimation would be to use organ-specific non-linear risk models applied to the dose distributions of organs within or near the treatment fields (lungs and contralateral breast in the case of breast radiotherapy) as the majority of radiation-induced secondary cancers are found in the beam-bordering regions.

Aggregation invariance in general clustering approaches

General clustering deals with weighted objects and fuzzy memberships. We investigate the group- or object-aggregation-invariance properties possessed by the relevant functionals (effective number of groups or objects, centroids, dispersion, mutual object-group information, etc.). The classical squared Euclidean case can be generalized to non-Euclidean distances, as well as to non-linear transformations of the memberships, yielding the c-means clustering algorithm as well as two presumably new procedures, the convex and pairwise convex clustering. Cluster stability and aggregation-invariance of the optimal memberships associated to the various clustering schemes are examined as well.

Helical tomotherapy for the treatment of anal canal cancer: a dosimetric comparison with 3D conformal radiotherapy.

AIMS AND BACKGROUND: The standard treatment of anal canal cancer (ACC) is combined chemotherapy and radiation therapy (RT), which is complex because of the shape of the target volumes and the need to minimize the irradiation of normal pelvic structures. In this study we compared the dosimetric results of helical tomotherapy (HT) plans with traditional 3D conformal RT (3DRT) plans for the treatment of ACC. METHODS AND STUDY DESIGN: Twelve patients (median age 57 years, range 38-83; F/M 8/4) treated with HT and concurrent chemotherapy for locally advanced ACC were selected. All had histologically confirmed squamous-cell carcinoma. A clinical target volume including the tumor and pelvic and inguinal lymph nodes was treated with HT to a total dose of 36 Gy in 1.8-Gy daily fractions. Then a sequential boost of 23.4 Gy in 1.8-Gy daily fractions (total dose 59.4 Gy) was delivered to the tumor and involved nodes. For all 12 patients, 3DRT plans were generated for comparison. Treatment plans were evaluated by means of standard dose-volume histograms. Dose coverage of the planning target volumes (PTVs), homogeneity index (HI), and mean doses to organs at risk (OARs) were compared. RESULTS: The coverage of PTV was comparable between the two treatment plans. HI was better in the HT vs. 3DRT plans (1.25 and 3.57, respectively; p<0.0001). HT plans resulted in better sparing of OARs (p<0.0001). CONCLUSIONS: HT showed superior target dose conformality and significant sparing of pelvic structures compared with 3DRT. Further investigation should determine if these dosimetric improvements will improve clinical outcomes regarding locoregional control, survival, and treatment-related acute and late morbidity.

The univalent Bloch-Landau constant, harmonic symmetry and conformal glueing

By modifying a domain first suggested by Ruth Goodman in 1935 and by exploiting the explicit solution by Fedorov of the Polyá-Chebotarev problem in the case of four symmetrically placed points, an improved upper bound for the univalent Bloch-Landau constant is obtained. The domain that leads to this improved bound takes the form of a disk from which some arcs are removed in such a way that the resulting simply connected domain is harmonically symmetric in each arc with respect to the origin. The existence of domains of this type is established, using techniques from conformal welding, and some general properties of harmonically symmetric arcs in this setting are established.

The Measurement Invariance of Schizotypy in Europe

The short version of the Oxford-Liverpool Inventory of Feelings and Experiences (sO-LIFE) is a widely used measure assessing schizotypy. There is limited information, however, on how sO-LIFE scores compare across different countries. The main goal of the present study is to test the measurement invariance of the sO-LIFE scores in a large sample of non-clinical adolescents and young adults from four European countries (UK, Switzerland, Italy, and Spain). The scores were obtained from validated versions of the sO-LIFE in their respective languages. The sample comprised 4190 participants (M = 20.87 years; SD = 3.71 years). The study of the internal structure, using confirmatory factor analysis, revealed that both three (i.e., positive schizotypy, cognitive disorganisation, and introvertive anhedonia) and four-factor (i.e., positive schizotypy, cognitive disorganisation, introvertive anhedonia, and impulsive nonconformity) models fitted the data moderately well. Multi-group confirmatory factor analysis showed that the three-factor model had partial strong measurement invariance across countries. Eight items were non-invariant across samples. Significant statistical differences in the mean scores of the s-OLIFE were found by country. Reliability scores, estimated with Ordinal alpha ranged from 0.75 to 0.87. Using the Item Response Theory framework, the sO-LIFE provides more accuracy information at the medium and high end of the latent trait. The current results show further evidence in support of the psychometric proprieties of the sO-LIFE, provide new information about the cross-cultural equivalence of schizotypy and support the use of this measure to screen for psychotic-like features and liability to psychosis in general population samples from different European countries.