A pp-adic RanSaC algorithm for stereo vision using Hensel lifting

A $p$-adic variation of the Ran(dom) Sa(mple) C(onsensus) method for solving the relative pose problem in stereo vision is developped. From two 2-adically encoded images a random sample of five pairs of corresponding points is taken, and the equations for the essential matrix are solved by lifting solutions modulo 2 to the 2-adic integers. A recently devised $p$-adic hierarchical classification algorithm imitating the known LBG quantisation method classifies the solutions for all the samples after having determined the number of clusters using the known intra-inter validity of clusterings. In the successful case, a cluster ranking will determine the cluster containing a 2-adic approximation to the "true" solution of the problem.Comment: 15 pages; typos removed, abstract changed, computation error remove

Binomial Mitotic Segregation of MYCN-Carrying Double Minutes in Neuroblastoma Illustrates the Role of Randomness in Oncogene Amplification

BACKGROUND: Amplification of the oncogene MYCN in double minutes (DMs) is a common finding in neuroblastoma (NB). Because DMs lack centromeric sequences it has been unclear how NB cells retain and amplify extrachromosomal MYCN copies during tumour development. PRINCIPAL FINDINGS: We show that MYCN-carrying DMs in NB cells translocate from the nuclear interior to the periphery of the condensing chromatin at transition from interphase to prophase and are preferentially located adjacent to the telomere repeat sequences of the chromosomes throughout cell division. However, DM segregation was not affected by disruption of the telosome nucleoprotein complex and DMs readily migrated from human to murine chromatin in human/mouse cell hybrids, indicating that they do not bind to specific positional elements in human chromosomes. Scoring DM copy-numbers in ana/telophase cells revealed that DM segregation could be closely approximated by a binomial random distribution. Colony-forming assay demonstrated a strong growth-advantage for NB cells with high DM (MYCN) copy-numbers, compared to NB cells with lower copy-numbers. In fact, the overall distribution of DMs in growing NB cell populations could be readily reproduced by a mathematical model assuming binomial segregation at cell division combined with a proliferative advantage for cells with high DM copy-numbers. CONCLUSION: Binomial segregation at cell division explains the high degree of MYCN copy-number variability in NB. Our findings also provide a proof-of-principle for oncogene amplification through creation of genetic diversity by random events followed by Darwinian selection

Genetic intratumour heterogeneity in high-grade brain tumours is associated with telomere-dependent mitotic instability.

Glioblastoma multiforme (GBM) and other high-grade brain tumours are typically characterized by complex chromosome abnormalities and extensive intratumour cytogenetic heterogeneity. The mechanisms behind this diversity have been little explored. In this study, we analysed the pattern of chromosome segregation at mitosis in 20 brain tumours. We found an abnormal segregation of chromatids at mitosis through anaphase bridging (10-25% of anaphase cells) in all 10 GBMs. Anaphase bridging was also found in two medulloblastomas (7-15%), one anaplastic astrocytoma (17%) and one oligodendroglioma (6%). These tumours showed a relatively high degree of cytogenetic complexity and heterogeneity. In contrast, cell division abnormalities were not found in low-grade brain tumours with less complex karyotypes, including two pilocytic astrocytomas and two ependymomas. Further analysis of two GBMs by fluorescence in situ hybridization with telomeric repeat probes revealed excessive shortening of TTAGGG repeats, indicating dysfunctional protection of chromosome ends. In xenografts established from these GBMs, there was a gradual reduction in cytogenetic heterogeneity through successive passages as the proportion of abnormally short telomeres was reduced and the frequency of anaphase bridges decreased from >25% to 0. However, bridging could be reintroduced in late-passage xenograft cells by pharmacological induction of telomere shortening, using a small-molecule telomerase inhibitor. Telomere-dependent abnormal segregation of chromosomes at mitosis is thus a common phenomenon in high-grade brain tumours and may be one important factor behind cytogenetic intratumour diversity in GBM