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We describe a prototype of a new experimental GeoGebra command and tool, Discover, that analyzes geometric figures for salient patterns, properties, and theorems. This tool is a basic implementation of automated discovery in elementary planar geometry. The paper focuses on the mathematical background of the implementation, as well as methods to avoid combinatorial explosion when storing the interesting properties of a geometric figure., Comment: In Proceedings ThEdu'21, arXiv:2202.02144. arXiv admin note: substantial text overlap with arXiv:2007.12447

Cholangiocarcinoma, a tumor of biliary epithelium, is increasing in incidence. The imaging appearance, behavior, and treatment of cholangiocarcinoma differ according to its location and morphology. Cholangiocarcinoma is usually classified as intrahepatic, perihilar, or distal. The three morphologies are mass-forming, periductal sclerosing, and intraductal growing. As surgical resection is the only cure, prompt diagnosis and accurate staging is crucial. In staging, vascular involvement, longitudinal spread, and lymphadenopathy are important to assess. The role of liver transplantation for unresectable peripheral cholangiocarcinoma will be discussed. Locoregional therapy can extend survival for those with unresectable intrahepatic tumors. The main risk factors predisposing to cholangiocarcinoma are parasitic infections, primary sclerosing cholangitis, choledochal cysts, and viral hepatitis. Several inflammatory conditions can mimic cholangiocarcinoma, including IgG4 disease, sclerosing cholangitis, Mirizzi's syndrome, and recurrent pyogenic cholangitis. The role of PET in diagnosis and staging will also be discussed. Radiologists play a crucial role in diagnosis, staging, and treatment of this disease.

OBJECTIVE. Rosai-Dorfman disease (RDD) is an uncommon benign histiocytic disorder. Extranodal involvement occurs in 43% and most commonly involves the head and neck, skin, and bones. We review less common imaging findings outside the head and neck. CONCLUSION. The imaging manifestations of RDD overlap with a variety of neoplastic and nonneoplastic conditions. Confirmation of an RDD diagnosis is based on specific histologic features. Radiologic assessment is used to rule out multifocality on initial workup and to evaluate treatment response.

Freiberg's infraction is an ostechondrosis of a lesser metatarsal head resulting in degeneration of the metatarsophalangeal joint. Several mechanisms have been suggested in its pathenogenesis. Freiberg first described the entity and believed single impact trauma was the underlying cause. Repetitive biomechanical microtrauma is the most widely accepted etiologic theory. Other factors contributing to its development include aseptic necrosis, ischemia, and a congenital predisposition. We present a case report of Freiberg's infraction occurring in identical twins involving multiple metatarsals in various stages of degeneration. One of the twins was affected unilaterally whereas the other twin was affected bilaterally. Both twins had involvement of the second metatarsal on the same side extremity. The occurrence of Freiberg's infraction in identical twins suggests that an underlying congenital predisposition to the condition may play more of a role than previously considered.

Novel trapped particle asymmetry modes propagate on cylindrical electron columns when axial variations in the wall voltage cause particle trapping. These modes consist of E×B drifts of edge-trapped particles, partially shielded by axial flows of interior untrapped particles. A simple theory model agrees well with the observed frequencies and eigenfunctions; but the strong mode damping is as yet unexplained. These modes may be important in coupling trap asymmetries to particle motions and low frequency E×B drift modes.

Experimental observation of a nonlinear fluid echo is presented which demonstrates the reversible nature of spatial Landau damping, and that non-neutral plasmas behave as nearly ideal 2D fluids. These experiments are performed on UCSD’s CamV Penning-Malmberg trap with magnetized electron plasmas. An initial mi=2 diocotron wave is excited, and the received wall signal damps away in about 5 wave periods. The density perturbation filaments are observed to wrap up as the wave is spatially Landau damped. An mt=4 “tickler” wave is then excited, and this wave also Landau damps. The echo consists of a spontaneous appearance of a third me=2 wave after the responses to the first two waves have inviscidly damped away. The appearance time of the echo agrees with theory, and data suggests the echo is destroyed at least partly due to saturation.