Reflection groups and cones of sums of squares

We consider cones of real forms which are sums of squares and invariant under a (finite) reflection group. Using the representation theory of these groups we are able to use the symmetry inherent in these cones to give more efficient descriptions. We focus especially on the An, Bn and Dn case where we use so-called higher Specht polynomials to give a uniform description of these cones. These descriptions allow us, to deduce that the description of the cones of sums of squares of fixed degree 2d stabilizes with. Furthermore, in cases of small degree, we are able to analyze these cones more explicitly and compare them to the cones of non-negative forms

Towards 10 cm/s radial velocity accuracy on the Sun using a Fourier transform spectrometer

The IAG solar observatory is producing high-fidelity, ultra-high-resolution spectra (R>500000) of the spatially resolved surface of the Sun using a Fourier Transform spectrometer (FTS). The radial velocity (RV) calibration of these spectra is currently performed using absorption lines from Earth's atmosphere, limiting the precision and accuracy. To improve the frequency calibration precision and accuracy we plan to use a Fabry-Perot etalon (FP) setup that is an evolution of the CARMENES FP design and an iodine cell in combination. To create an accurate wavelength solution, the iodine cell is measured in parallel with the FP. The FP can then be used to transfer the accurate wavelength solution provided by the iodine via simultaneous calibration of solar observations. To verify the stability and precision of the FTS we perform parallel measurements of the FP and an iodine cell. The measurements show an intrinsic stability of the FTS of a level of 1 m/s over 90 hours. The difference between the FP RVs and the iodine cell RVs show no significant trends during the same time span. The RMS of the RV difference between FP and iodine cell is 10.7 cm/s, which can be largely attributed to the intrinsic RV precisions of the iodine cell and the FP (10.2 cm/s and 1.0 cm/s, respectively). This shows that we can calibrate the FTS to a level of 10 cm/s, competitive with current state-of-the-art precision RV instruments. Based on these results we argue that the spectrum of iodine can be used as an absolute reference to reach an RV accuracy of 10 cm/s.Comment: 13 pages, 9 figures, to be published in Journal of Astronomical Telescopes, Instruments, and Systems (JATIS

The poset of Specht ideals for hyperoctahedral groups

Specht polynomials classically realize the irreducible representations of the symmetric group. The ideals defined by these polynomials provide a strong connection with the combinatorics of Young tableaux and have been intensively studied by several authors. We initiate similar investigations for the ideals defined by the Specht polynomials associated to the hyperoctahedral group Bn. We introduce a bidominance order on bipartitions which describes the poset of inclusions of these ideals and study algebraic consequences on general Bn-invariant ideals and varieties, which can lead to computational simplifications

Prior surgical intervention and tumor size impact clinical outcome after precision radiotherapy for the treatment of optic nerve sheath meningiomas (ONSM)

<p>Abstract</p> <p>Purpose</p> <p>We analyzed our long-term experience with fractionated stereotactic radiotherapy (FSRT) in patients with meningioma of the optic nerve sheath (ONSM).</p> <p>Patients and Methods</p> <p>Between January 1991 and January 2010, 40 patients with ONSM were treated using FSRT. Of these, 19 patients received radiotherapy as primary treatment, and 21 patients were treated after surgical resection. The median target volume was 9.2 ml, median total dose was 54 Gy in median single fractions of 1,8 Gy.</p> <p>Results</p> <p>Local progression-free survival was 100%. Median survival after FSRT was 60 months (range 4-228 months). In all patients overall toleration of FSRT was very good. Acute toxicity was mild. Prior to RT, 29 patients complained about any kind of visual impairment including visual field deficits, diplopia or amaurosis. Prior surgical resection was identified as a negative prognostic factor for visual outcome, whereas patients with larger tumor volumes demonstrated a higher number of patients with improvement of pre-existing visual deficits.</p> <p>Conclusion</p> <p>Long-term outcome after FSRT for ONSM shows improved vision in patients not treated surgically prior to RT; moreover, the best improvement of visual deficits are observed in patients with larger target volumes. The absence of tumor recurrences supports that FSRT is a strong alternative to surgical resection especially in small tumors without extensive compression of normal tissue structures</p

Treatment of meningioma and glioma with protons and carbon ions

The rapid rise of particle therapy across the world necessitates evidence to justify its ever-increasing utilization. This narrative review summarizes the current status of these technologies on treatment of both meningiomas and gliomas, the most common benign and malignant primary brain tumors, respectively. Proton beam therapy (PBT) for meningiomas displays high rates of long-term local control, low rates of symptomatic deterioration, along with the potential for safe dose-escalation in select (but not necessarily routine) cases. PBT is also associated with low adverse events and maintenance of functional outcomes, which have implications for quality of life and cost-effectiveness measures going forward. Data on carbon ion radiation therapy (CIRT) are limited; existing series describe virtually no high-grade toxicities and high local control. Regarding the few available data on low-grade gliomas, PBT provides opportunities to dose-escalate while affording no increase of severe toxicities, along with maintaining appropriate quality of life. Although dose-escalation for low-grade disease has been less frequently performed than for glioblastoma, PBT and CIRT continue to be utilized for the latter, and also have potential for safer re-irradiation of high-grade gliomas. For both neoplasms, the impact of superior dosimetric profiles with endpoints such as neurocognitive decline and neurologic funcionality, are also discussed to the extent of requiring more data to support the utility of particle therapy. Caveats to these data are also described, such as the largely retrospective nature of the available studies, patient selection, and heterogeneity in patient population as well as treatment (including mixed photon/particle treatment). Nevertheless, multiple prospective trials (which may partially attenuate those concerns) are also discussed. In light of the low quantity and quality of available data, major questions remain regarding economic concerns as well

Long term results after fractionated stereotactic radiotherapy (FSRT) in patients with craniopharyngioma: maximal tumor control with minimal side effects

Purpose: There are already numerous reports about high local control rates in patients with craniopharyngioma but there are only few studies with follow up times of more than 10 years. This study is an analysis of long term control, tumor response and side effects after fractionated stereotactic radiotherapy (FSRT) for patients with craniopharyngioma. Patients and methods: 55 patients who were treated with FSRT for craniopharyngioma were analyzed. Median age was 37 years (range 6–70 years), among them eight children < 18 years. Radiotherapy (RT) was indicated for progressive disease after neurosurgical resection or postoperatively after repeated resection or partial resection. A median dose of 52.2 Gy (50 – 57.6 Gy) was applied with typical dose per fraction of 1.8 Gy five times per week. The regular follow up examinations comprised in addition to contrast enhanced MRI scans thorough physical examinations and clinical evaluation. Results: During median follow up of 128 months (2 – 276 months) local control rate was 95.3% after 5 years, 92.1% after 10 years and 88.1% after 20 years. Overall survival after 10 years was 83.3% and after 20 years 67.8% whereby none of the deaths were directly attributed to craniopharyngioma. Overall treatment was tolerated well with almost no severe acute or chronic side effects. One patient developed complete anosmia, another one’s initially impaired vision deteriorated further. In 83.6% of the cases with radiological follow up a regression of irradiated tumor residues was monitored, in 7 cases complete response was achieved. 44 patients presented themselves initially with endocrinologic dysfunction none of them showed signs of further deterioration during follow up. No secondary malignancies were observed. Conclusion: Long term results for patients with craniopharyngioma after stereotactic radiotherapy are with respect to low treatment related side effects as well as to local control and overall survival excellent

System Dynamics and Intervention Design

In this article, we transform thoughts from classical strategy and insights from modern complexity science into a novel concept of intervention. In doing so, we pursue two goals: First, to improve the prediction of outcomes, and second, to refine the design of interventions. For the first purpose, we outline approaches to modeling the natural behavior of systems and the effect of interventions. For the second purpose, we propose an idea for the design of interventions. We call the concepts that relate to modeling system behaviors system dynamics, and those that relate to predicting outcomes of interventions intervention dynamics, and we call the concepts that relate to the design of interventions intervention design

Accelerated large volume irradiation with dynamic Jaw/Dynamic Couch Helical Tomotherapy

BACKGROUND: Helical Tomotherapy (HT) has unique capacities for the radiotherapy of large and complicated target volumes. Next generation Dynamic Jaw/Dynamic Couch HT delivery promises faster treatments and reduced exposure of organs at risk due to a reduced dose penumbra. METHODS: Three challenging clinical situations were chosen for comparison between Regular HT delivery with a field width of 2.5 cm (Reg 2.5) and 5.0 cm (Reg 5.0) and DJDC delivery with a maximum field width of 5.0 cm (DJDC 5.0): Hemithoracic Irradiation, Whole Abdominal Irradiation (WAI) and Total Marrow Irradiation (TMI). For each setting, five CT data sets were chosen, and target coverage, conformity, integral dose, dose exposure of organs at risk (OAR) and treatment time were calculated. RESULTS: Both Reg 5.0 and DJDC 5.0 achieved a substantial reduction in treatment time while maintaining similar dose coverage. Treatment time could be reduced from 10:57 min to 3:42 min / 5:10 min (Reg 5.0 / DJDC 5.0) for Hemithoracic Irradiation, from 18:03 min to 8:02 min / 8:03 min for WAI and to 18:25 min / 18:03 min for TMI. In Hemithoracic Irradiation, OAR exposure was identical in all modalities. For WAI, Reg 2.5 resulted in lower exposure of liver and bone. DJDC plans showed a small but significant increase of ∼ 1 Gy to the kidneys, the parotid glans and the thyroid gland. While Reg 5.0 and DJDC were identical in terms of OAR exposure, integral dose was substantially lower with DJDC, caused by a smaller dose penumbra. CONCLUSIONS: Although not clinically available yet, next generation DJDC HT technique is efficient in improving the treatment time while maintaining comparable plan quality