A Note on the Caristi Fixed Point Theorem

We generalise the Caristi Fixed Point Theorem to the mappings of the complete semi-metric spaces.Comment: this paper has been withdrawn by the author due to the results on the whole are standar

A note on the primal-dual method for the semi-metric labeling problem

Recently, Komodakis et al. [6] developed the FastPD algorithm for the semi-metric labeling problem, which extends the expansion move algorithm of Boykov et al. [2]. We present a slightly different derivation of the FastPD method

Semi-Metric Topology of the Human Connectome: Sensitivity and Specificity to Autism and Major Depressive Disorder.

INTRODUCTION: The human functional connectome is a graphical representation, consisting of nodes connected by edges, of the inter-relationships of blood oxygenation-level dependent (BOLD) time-series measured by MRI from regions encompassing the cerebral cortices and, often, the cerebellum. Semi-metric analysis of the weighted, undirected connectome distinguishes an edge as either direct (metric), such that there is no alternative path that is accumulatively stronger, or indirect (semi-metric), where one or more alternative paths exist that have greater strength than the direct edge. The sensitivity and specificity of this method of analysis is illustrated by two case-control analyses with independent, matched groups of adolescents with autism spectrum conditions (ASC) and major depressive disorder (MDD). RESULTS: Significance differences in the global percentage of semi-metric edges was observed in both groups, with increases in ASC and decreases in MDD relative to controls. Furthermore, MDD was associated with regional differences in left frontal and temporal lobes, the right limbic system and cerebellum. In contrast, ASC had a broadly increased percentage of semi-metric edges with a more generalised distribution of effects and some areas of reduction. In summary, MDD was characterised by localised, large reductions in the percentage of semi-metric edges, whilst ASC is characterised by more generalised, subtle increases. These differences were corroborated in greater detail by inspection of the semi-metric backbone for each group; that is, the sub-graph of semi-metric edges present in >90% of participants, and by nodal degree differences in the semi-metric connectome. CONCLUSION: These encouraging results, in what we believe is the first application of semi-metric analysis to neuroimaging data, raise confidence in the methodology as potentially capable of detection and characterisation of a range of neurodevelopmental and psychiatric disorders.This study was funded by the UK Medial Research Council (grants: G0802226 and G0701919), the National Institute for Health Research (NIHR) (grant: 06/05/01) and the Behavioural and Clinical Neuroscience Institute (BCNI), University of Cambridge. The BCNI is jointly funded by the Medical Research Council and the Wellcome Trust. Additional support was received from the NIHR Cambridge Biomedical Research Centre. CCH is supported by a Parke Davis Fellowship from the University of Cambridge and resides at Columbia University.This is the final version of the article. It first appeared from PLOS via http://dx.doi.org/10.1371/journal.pone.013638