Regular line-symmetric graphs

AbstractWe say that a graph is Point-symmetric if, given any two points of the graph, there is an automorphism of the graph that sends the first point to the second. Similarly, we say that a graph is line-symmetric if, given any two lines of the graph, there is an automorphism that sends the first line to the second.In general a line-symmetric graph need not be point-symmetric. For example, any complete bipartite graph is line-symmetric, but if it is not regular then it is not point-symmetric. In this paper we investigate the extent to which line symmetry and regularity imply point symmetry.We first give some conditions on the number of points and the degree of regularity under which line symmetry and regularity imply point symmetry. We then give some general methods for constructing graphs which are line-symmetric and regular but not point-symmetric. Finally we summarize what is known about the number of points that a regular line-symmetric graph which is not point-symmetric can have. We conclude with a list of unsolved problems in this area

High Interstitial Fluid Pressure Is Associated with Tumor-Line Specific Vascular Abnormalities in Human Melanoma Xenografts

PURPOSE: Interstitial fluid pressure (IFP) is highly elevated in many solid tumors. High IFP has been associated with low radiocurability and high metastatic frequency in human melanoma xenografts and with poor survival after radiation therapy in cervical cancer patients. Abnormalities in tumor vascular networks have been identified as an important cause of elevated tumor IFP. The aim of this study was to investigate the relationship between tumor IFP and the functional and morphological properties of tumor vascular networks. MATERIALS AND METHODS: A-07-GFP and R-18-GFP human melanomas growing in dorsal window chambers in BALB/c nu/nu mice were used as preclinical tumor models. Functional and morphological parameters of the vascular network were assessed from first-pass imaging movies and vascular maps recorded after intravenous bolus injection of 155-kDa tetramethylrhodamine isothiocyanate-labeled dextran. IFP was measured in the center of the tumors using a Millar catheter. Angiogenic profiles of A-07-GFP and R-18-GFP cells were obtained with a quantitative PCR array. RESULTS: High IFP was associated with low growth rate and low vascular density in A-07-GFP tumors, and with high growth rate and high vascular density in R-18-GFP tumors. A-07-GFP tumors showed chaotic and highly disorganized vascular networks, while R-18-GFP tumors showed more organized vascular networks with supplying arterioles in the tumor center and draining venules in the tumor periphery. Furthermore, A-07-GFP and R-18-GFP cells differed substantially in angiogenic profiles. A-07-GFP tumors with high IFP showed high geometric resistance to blood flow due to high vessel tortuosity. R-18-GFP tumors with high IFP showed high geometric resistance to blood flow due to a large number of narrow tumor capillaries. CONCLUSIONS: High IFP in A-07-GFP and R-18-GFP human melanoma xenografts was primarily a consequence of high blood flow resistance caused by tumor-line specific vascular abnormalities

Multi-plate interceptive electron beam energy diagnostic—Implementation and validation

A previous publication [P. D. McChesney, “Multi-plate interceptive electron beam energy diagnostic—Theoretical design,” AIP Adv. (submitted)] reported a new interceptive electron beam kinetic energy measurement technique based on the beam penetration depth within a stack of conductive plates and gave results on the theoretical design of such a device. This paper expands on this and gives further results on the actual implementation of the diagnostic. The device geometry and measurement electronics system are described in detail. A prototype version of the multi-plate diagnostic was fabricated and tested using an electron linear accelerator at the Idaho Accelerator Center (IAC). A high-precision magnetic spectrometer system was designed and built for the purpose of validating the multi-plate diagnostic’s energy measurement capabilities. It was found that the diagnostic provides electron beam energy estimates that are accurate to better than the 10% level