The Peculiar Phase Structure of Random Graph Bisection

The mincut graph bisection problem involves partitioning the n vertices of a graph into disjoint subsets, each containing exactly n/2 vertices, while minimizing the number of "cut" edges with an endpoint in each subset. When considered over sparse random graphs, the phase structure of the graph bisection problem displays certain familiar properties, but also some surprises. It is known that when the mean degree is below the critical value of 2 log 2, the cutsize is zero with high probability. We study how the minimum cutsize increases with mean degree above this critical threshold, finding a new analytical upper bound that improves considerably upon previous bounds. Combined with recent results on expander graphs, our bound suggests the unusual scenario that random graph bisection is replica symmetric up to and beyond the critical threshold, with a replica symmetry breaking transition possibly taking place above the threshold. An intriguing algorithmic consequence is that although the problem is NP-hard, we can find near-optimal cutsizes (whose ratio to the optimal value approaches 1 asymptotically) in polynomial time for typical instances near the phase transition.Comment: substantially revised section 2, changed figures 3, 4 and 6, made minor stylistic changes and added reference

Transforming gendered lives and livelihoods in post-disaster settings in the Bangladesh Sundarbans forest

This chapter surveys literature on gendered livelihoods, disasters and community resilience, and contributes to the application of intersectionality in research on the post-cyclone influences of Cyclone Aila on gendered livelihoods in the Sundarbans forest communities of south-west Bangladesh and Aila’s intersectional impacts on the forest communities’ resilience. Overall, the literature has established Aila’s severe impacts on the gendered livelihood-seeking behaviours of the forest-dependents in the Sundarbans. This review chapter examines the resilience-building of the rural poor communities of the Sundarbans forest areas, and patterns of livelihood support services given to the Aila survivors by the four national NGOs (Shushilan, BRAC, SAMS and LEADRS). Thereafter, the paper investigates the intersectional dimensions of gender, religion and marital status influencing the gendered relations of the Aila survivors. Finally, the study demonstrates the utility of intersectionality as a theoretical tool for delving into livelihood transformation and gendered relations of two contrasting Sundarbans forest communities

FUS immunogold labelling TEM analysis of the neuronal cytoplasmic inclusions of neuronal intermediate filament inclusion disease: a frontotemporal lobar degeneration with FUS proteinopathy.

Fused in sarcoma (FUS)-immunoreactive neuronal and glial inclusions define a novel molecular pathology called FUS proteinopathy. FUS has been shown to be a component of inclusions of familial amyotrophic lateral sclerosis with FUS mutation and three frontotemporal lobar degeneration entities, including neuronal intermediate filament inclusion disease (NIFID). The pathogenic role of FUS is unknown. In addition to FUS, many neuronal cytoplasmic inclusions (NCI) of NIFID contain aggregates of -internexin and neurofilament proteins. Herein, we have shown that: (1) FUS becomes relatively insoluble in NIFID and there are no apparent posttranslational modifications, (2) there are no pathogenic abnormalities in the FUS gene in NIFID, and (3) immunoelectron microscopy demonstrates the fine structural localization of FUS in NIFID which has not previously been described. FUS localized to euchromatin, and strongly with paraspeckles, in nuclei, consistent with its RNA/DNA-binding functions. NCI of varying morphologies were observed. Most frequent were the "loosely aggregated cytoplasmic inclusions," 81% of which had moderate or high levels of FUS immunoreactivity. Much rarer "compact cytoplasmic inclusions" and "tangled twine ball inclusions" were FUS-immunoreactive at their granular peripheries, or heavily FUS-positive throughout, respectively. Thus, FUS may aggregate in the cytoplasm and then admix with neuronal intermediate filament accumulations