We discuss zeta functions of finite irregular undirected connected graphs (which may be weighted) and apply them to obtain, for example an analog of the prime number theorem for cycles in graphs. We consider 3 types of zeta functions of graphs: vertex, edge, and path. Analogs of the Riemann hypothesis are also introduced.

While acknowledging the limitations of heterogeneous surgical techniques, results from the present meta-analysis suggest potential superiority of the RA compared with the SV at midterm angiographic follow-up. However, the increased incidence of string sign associated with the RA is of potential clinical concern. Further research should be directed at correlating angiographic findings of string sign and graft failure to clinical symptoms and major adverse cardiac and cerebrovascular events at long-term follow-up.

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The use of cryotherapy for the treatment of some unresectable liver tumours has been clearly established as a therapeutic option. Intra-operative ultrasound has enhanced the process by enabling the surgeon to identify hepatic lesions and to allow visualisation of the freezing process to ensure that the cryolesion will include the tumour mass. The purpose of this paper is to provide a practical guide to surgeons who wish to perform cryotherapy of liver tumours. Patient selection and anaesthetic considerations are important. The surgeon should be able to deal with the complications of cryotherapy, particularly the intra-operative haemorrhage which may arise from cracking of the hepatic parenchyma as the iceball thaws. Follow-up is based on tumour marker assay and imaging of the liver and repeat cryotherapy can be considered for selected cases.