Probabilistic estimates for tensor products of random vectors

We prove some probabilistic estimates for tensor products of random vectors. As an application we obtain embeddings of certain matrix spaces into $L_1$.Comment: 15 page

An evaluation of the stability of image quality parameters of Elekta X-ray volume imager and iViewGT imaging systems

INTRODUCTION: A robust image quality assurance and analysis methodology for image-guided localization systems is crucial to ensure the accurate localization and visualization of target tumors. In this study, the long-term stability of selected image parameters was assessed and evaluated for the cone-beam computed tomography (CBCT) mode, planar radiographic kV mode, and the radiographic MV mode of an Elekta VersaHD. MATERIALS AND METHODS: The CATPHAN, QckV-1, and QC-3 phantoms were used to evaluate the image quality parameters. The planar radiographic images were analyzed in PIPSpro™ with spatial resolution (f30, f40, f50), contrast to noise ratio (CNR) and noise being recorded. For XVI CBCT, Head and Neck Small20 (S20) and Pelvis Medium20 (M20) standard acquisition modes were evaluated for uniformity, noise, spatial resolution, and HU constancy. Dose and kVp for the XVI were recorded using the Unfors RaySafe Xi system with the R/F low detector for the kV planar radiographic mode. For each metric, values were normalized to the mean and the standard deviations were recorded. RESULTS: A total of 30 measurements were performed on a single Elekta VersaHD linear accelerator over an 18-month period without significant adjustment or recalibration to the XVI or iViewGT systems during the evaluated time frame. For the planar radiographic spatial resolution, the normalized standard deviation values of the f30, f40, and f50 were 0.004, 0.003, and 0.003 and 0.015, 0.009, and 0.017 for kV and MV, respectively. The average recorded dose for kV was 67.96 μGy. The standard deviations of the evaluated metrics for the S20 acquisition were 0.083(f30), 0.058(f40), 0.056(f50), 0.021(Water/poly-HU constancy), 0.029(uniformity) and 0.028(noise). The standard deviations for the M20 acquisition were 0.093(f30), 0.043(f40), 0.037(f50), 0.016(Water/poly-HU constancy), 0.010(uniformity) and 0.011(Noise). CONCLUSION: A study was performed to assess the stability of the basic image quality parameters recommended by TG-142 for the Elekta XVI and iViewGT imaging systems. The two systems show consistent imaging and dosimetric properties over the evaluated time frame

Variability of Breast Surface Positioning Using an Active Breathing Coordinator for a Deep Inspiration Breath Hold Technique

Purpose The Elekta Active Breathing CoordinatorTM (ABC) is used to control breathing and guide deep inspiration breath hold (DIBH). It has been shown to be accurate in lung cancers, but limited analysis has been performed on the spatial accuracy and reproducibility of the breast surface. The use of optical surface-image guidance for patient positioning has grown in popularity and is an alternative solution for breast DIBH. This study aims to evaluate the breast surface variability of an ABC-guided DIBH by using a three-dimensional (3D) surface imaging system to record surface position. Methods Ten participants were placed in the treatment position, and breathing baselines and inhalation volume threshold baselines were monitored and recorded using the ABC. Over 60 minutes, the breathing patterns were recorded by the ABC and CatalystHD TM (C-RAD, Uppsala, Sweden). For each breath hold, the valve of the ABC closed at the baseline inhalation threshold and a 3D surface image was acquired. For each point on the baseline breast surface, a 3D vector was calculated to the subsequent breath hold surface as well as a root mean square (RMS) vector magnitude for the entire surface. Results The average and standard deviation for the RMS difference between the baseline and subsequent evaluated images were 7.12 ± 2.70 mm. Conclusion This study shows that while the ABC-guided inhalation volume is kept constant, a non-negligible variability of the breast surface position exists. Special considerations should be used in clinical situations, where the positioning of the surface is considered more important than inhalation volume

Comparison of initial patient setup accuracy between surface imaging and three point localization: A retrospective analysis

PURPOSE: Historically, the process of positioning a patient prior to imaging verification used a set of permanent patient marks, or tattoos, placed subcutaneously. After aligning to these tattoos, plan specific shifts are applied and the position is verified with imaging, such as cone-beam computed tomography (CBCT). Due to a variety of factors, these marks may deviate from the desired position or it may be hard to align the patient to these marks. Surface-based imaging systems are an alternative method of verifying initial positioning with the entire skin surface instead of tattoos. The aim of this study was to retrospectively compare the CBCT-based 3D corrections of patients initially positioned with tattoos against those positioned with the C-RAD CatalystHD surface imager system. METHODS: A total of 6000 individual fractions (600-900 per site per method) were randomly selected and the post-CBCT 3D corrections were calculated and recorded. For both positioning methods, four common treatment site combinations were evaluated: pelvis/lower extremities, abdomen, chest/upper extremities, and breast. Statistical differences were evaluated using a paired sample Wilcoxon signed-rank test with significance level of \u3c0.01. RESULTS: The average magnitudes of the 3D shift vectors for tattoos were 0.9 ± 0.4 cm, 1.0 ± 0.5 cm, 0.9 ± 0.6 cm and 1.4 ± 0.7 cm for the pelvis/lower extremities, abdomen, chest/upper extremities and breast, respectively. For the CatalystHD, the average magnitude of the 3D shifts for the pelvis/lower extremities, abdomen, chest/upper extremities and breast were 0.6 ± 0.3 cm, 0.5 ± 0.3 cm, 0.5 ± 0.3 cm and 0.6 ± 0.2 cm, respectively. Statistically significant differences (P \u3c 0.01) in the 3D shift vectors were found for all four sites. CONCLUSION: This study shows that the overall 3D shift corrections for patients initially aligned with the C-RAD CatalystHD were significantly smaller than those aligned with subcutaneous tattoos. Surface imaging systems can be considered a viable option for initial patient setup and may be preferable to permanent marks for specific clinics and patients

On the Distribution of Random variables corresponding to Musielak-Orlicz norms

Given a normalized Orlicz function $M$ we provide an easy formula for a distribution such that, if $X$ is a random variable distributed accordingly and $X_1,...,X_n$ are independent copies of $X$, then the expected value of the p-norm of the vector $(x_iX_i)_{i=1}^n$ is of the order $\| x \|_M$ (up to constants dependent on p only). In case $p=2$ we need the function $t\mapsto tM'(t) - M(t)$ to be 2-concave and as an application immediately obtain an embedding of the corresponding Orlicz spaces into $L_1[0,1]$. We also provide a general result replacing the $\ell_p$-norm by an arbitrary $N$-norm. This complements some deep results obtained by Gordon, Litvak, Sch\"utt, and Werner. We also prove a result in the spirit of their work which is of a simpler form and easier to apply. All results are true in the more general setting of Musielak-Orlicz spaces

Movilidad urbana no motorizada como medio de acceso a unidades económicas urbanas

Se plantea el desarrollo de una metodología en cuestión de movilidad urbana no motorizada para ciudades menores a 50,000 habitantes en la que se analizan factores poblacionales , transporte pública, acceso a unidades económicas y morfología vial. El reto es fomentar el desarrollo de estrategias que permitan la implemenntación de este modo de movilidad.El objetivo de proponer un método de análisis que defina los factores a investigar en la implementación de la movilidad urbana no motorizada en ciudades pequeñas, los factores prioritarios a considerar son: patrón de viaje, lozalización poblacional, transporte público y morfología vial.Friedrich-Ebert-Stiftung (FES-ILDIS) Ecuado