For a right-angled Artin group A Γ , the untwisted outer automorphism group U(A Γ ) is the subgroup of Out(A Γ ) generated by all of the Laurence-Servatius generators except twists (where a twist is an automorphisms of the form v → vw with vw = wv). We define a space Σ Γ on which U(A Γ ) acts properly and prove that Σ Γ is contractible, providing a geometric model for U(A Γ ) and its subgroups. We also propose a geometric model for all of Out(A Γ ) defined by allowing more general markings and metrics on points of Σ Γ .

We study the automorphisms of graph products of cyclic groups, a class of groups that includes all right-angled Coxeter and right-angled Artin groups. We show that the group of automorphism generated by partial conjugations is itself a graph product of cyclic groups providing its defining graph does not contain any separating intersection of links (SIL). In the case that all the cyclic groups are finite, this implies that the automorphism group is virtually CAT(0); it has a finite index subgroup which acts geometrically on a right-angled building.R.

To investigate time efficiency, applicability, and accuracy of using a web-based, independent quality assurance (QA) platform and vendor-dependent based system check for daily linear accelerator (LINAC) QA. MethodsTime needed to perform daily QA on a single (n=1) LINAC was collected for three months. Task Group report 142 (TG-142) compliant daily QA included dosimetry checks (four photon, four electron beams); imaging checks (planar kilovolt (kV) & megavolt (MV), kV cone-beam computed tomography (CBCT)); and mechanical and safety checks using SunCHECK Machine (SCM) (Sun Nuclear Inc., Melbourne, FL, USA). Additionally, Machine Performance Check (MPC) (Varian Medical Systems, Inc., Palo Alto, CA, USA) was performed for all energies. Four trained radiation therapists performed daily QA on both platforms. Data were collected to identify the time required to complete both SCM and MPC. Additionally, the two platforms were evaluated on usability and features. Output results were compared to our monthly standard to assess accuracy. ResultsOn average, SCM took 22 minutes with a standard deviation of six minutes and MPC took 15 minutes with a standard deviation of three minutes. MPC output results were impacted due to the beam output being coupled to the beam profile changes. As a result, the two systems on average disagreed by -1.41% after three months despite being baselined at the same time point and output agreeing well initially (average difference of -0.1% across all energies). While there was overlap in the tests performed, SCM tests were more relevant to TG-142 while MPC tests were beneficial to machine service and, with a clear understanding of the limitations of the system, found suitable as a secondary backup to SCM for daily output verification. ConclusionsThis work demonstrates that a comprehensive TG-142 daily QA can be designed using SCM and MPC can be added as a beneficial tool and backup for output verification while still maintaining an efficient daily QA process.

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