Large deviations for heavy-tailed random elements in convex cones

We prove large deviation results for sums of heavy-tailed random elements in rather general convex cones being semigroups equipped with a rescaling operation by positive real numbers. In difference to previous results for the cone of convex sets, our technique does not use the embedding of cones in linear spaces. Examples include the cone of convex sets with the Minkowski addition, positive half-line with maximum operation and the family of square integrable functions with arithmetic addition and argument rescaling.

Simple beam models for Monte Carlo photon beam dose calculations in radiotherapy

Monte Carlo (code GEANT) produced 6 and 15 MV phase space (PS) data were used to define several simple photon beam models. For creating the PS data the energy of starting electrons hitting the target was tuned to get correct depth dose data compared to measurements. The modeling process used the full PS information within the geometrical boundaries of the beam including all scattered radiation of the accelerator head. Scattered radiation outside the boundaries was neglected. Photons and electrons were assumed to be radiated from point sources. Four different models were investigated which involved different ways to determine the energies and locations of beam particles in the output plane. Depth dose curves, profiles, and relative output factors were calculated with these models for six field sizes from 5x5 to 40x40cm2 and compared to measurements. Model 1 uses a photon energy spectrum independent of location in the PS plane and a constant photon fluence in this plane. Model 2 takes into account the spatial particle fluence distribution in the PS plane. A constant fluence is used again in model 3, but the photon energy spectrum depends upon the off axis position. Model 4, finally uses the spatial particle fluence distribution and off axis dependent photon energy spectra in the PS plane. Depth dose curves and profiles for field sizes up to 10x10cm2 were not model sensitive. Good agreement between measured and calculated depth dose curves and profiles for all field sizes was reached for model 4. However, increasing deviations were found for increasing field sizes for models 1-3. Large deviations resulted for the profiles of models 2 and 3. This is due to the fact that these models overestimate and underestimate the energy fluence at large off axis distances. Relative output factors consistent with measurements resulted only for model 4.

Does hyoid bone resection according to Sistrunk influence normal craniofacial growth? A cephalometric study

PURPOSE: To retrospectively evaluate the influence of hyoid bone resection according to Sistrunk in early age due to a thyroglossal duct cyst on craniofacial growth. MATERIALS AND METHODS: We retrospectively examined 10 patients (2 females and 8 males) having had hyoid bone resection according to Sistrunk due to thyroglossal duct cysts by lateral cephalograms taken before orthodontic treatment (mean, 17.1 years; range, 8.6-31.9 years). Surgery was carried out at a mean age of 4.4 years (range, 0.37-9.8 years). All lateral cephalograms were evaluated and traced by hand. Descriptive statistics were calculated, and data from each patient were compared individually with corresponding standard values (age and gender) from Bathia and Leighton. RESULTS: With regard to sagittal parameters, the SNB angles were by trend too small and the ANB angles were too large. However, the ratio of mandibular to maxillary length showed that the patients had a mandible that was too large or maxilla that was too small. With regard to vertical parameters, large deviations from normal values in both directions (hyperdivergent to hypodivergent pattern) could be detected when we analyzed NSL/ML', NL/ML', and NSL/NL. With regard to dental parameters, the majority of the patients had retroclined upper (IsL/NL, IsL/N-A) and lower (IiL/ML, IiL/N-B) incisors. CONCLUSIONS: Several vertical and horizontal skeletal and dental cephalometric parameters were shown to be different by trend when compared with control values. A possible negative impact on craniofacial growth potential and direction as a result of hyoid resection in early age according to Sistrunk cannot be excluded.

Saddlepoint Approximations to the Probability of Ruin in Finite Time for the Compound Poisson Risk Process Perturbed by Diffusion

A large deviations type approximation to the probability of ruin within a finite time for the compound Poisson risk process perturbed by diffusion is derived. This approximation is based on the saddlepoint method and generalizes the approximation for the non-perturbed risk process by Barndorff-Nielsen and Schmidli (Scand Actuar J 1995(2):169–186, 1995). An importance sampling approximation to this probability of ruin is also provided. Numerical illustrations assess the accuracy of the saddlepoint approximation using importance sampling as a benchmark. The relative deviations between saddlepoint approximation and importance sampling are very small, even for extremely small probabilities of ruin. The saddlepoint approximation is however substantially faster to compute.

Saddlepoint approximations

The saddlepoint method provides accurate approximations for the distributions of many test statistics, estimators and for important probabilities arising in various stochastic models. The saddlepoint approximation is a large deviations technique which is substantially more accurate than limiting normal or Edgeworth approximations, especially in presence of very small sample sizes or very small probabilities. The outstanding accuracy of the saddlepoint approximation can be explained by the fact that it has bounded relative error.

Search for contact interactions and large extra dimensions in dilepton events from pp collisions at sqrts=7 TeV with the ATLAS detector

A search for nonresonant new phenomena, originating from either contact interactions or large extra spatial dimensions, has been carried out using events with two isolated electrons or muons. These events, produced at the LHC in proton-proton collisions at root s = 7 TeV, were recorded by the ATLAS detector. The data sample, collected throughout 2011, corresponds to an integrated luminosity of 4.9 and 5.0 fb(-1) in the e(+)e(-) and mu(+)mu(-) channels, respectively. No significant deviations from the Standard Model expectation are observed. Using a Bayesian approach, 95% confidence level lower limits ranging from 9.0 to 13.9 TeV are placed on the energy scale of llqq contact interactions in the left-left isoscalar model. Lower limits ranging from 2.4 to 3.9 TeV are also set on the string scale in large extra dimension models. After combining these limits with results from a similar search in the diphoton channel, slightly more stringent limits are obtained.

Search for contact interactions and large extra dimensions in the dilepton channel using proton-proton collisions at s√ = 8 TeV with the ATLAS detector

A search is conducted for non-resonant new phenomena in dielectron and dimuon final states, originating from either contact interactions or large extra spatial dimensions. The LHC 2012 proton–proton collision dataset recorded by the ATLAS detector is used, corresponding to 20 fb−1 at √ s = 8 TeV. The dilepton invariant mass spectrum is a discriminating variable in both searches, with the contact interaction search additionally utilizing the dilepton forward-backward asymmetry. No significant deviations from the Standard Model expectation are observed. Lower limits are set on the ℓℓqq contact interaction scale ʌ between 15.4 TeVand 26.3 TeV, at the 95%credibility level. For large extra spatial dimensions, lower limits are set on the string scale MS between 3.2 TeV to 5.0 TeV.