An n-string tangle is a three dimensional ball with n strings which are properly embedded in it. Topological tangle analysis of DNA-protein complexes based on difference topology experiments are studied for last 30 years. In this paper, A 2-string tangle analysis of DNA-Tn3 complex [5, 6] and a 3-string tangle analysis of DNA-Mu complex [3, 13] and a biologically relevant 4-string tangle analys...

Accessibility typically has been applied to urban or transportation problems two dimensionally. However, in large complex buildings as shopping centers or hospitals, inter-spatial accessibility among compartments has to be taken into account such as in building layouts or evacuation planning. This study expands space syntax theory, one of accessibility-related methodologies used for computing c...

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We investigate the topology of the completed 2dF Galaxy Redshift Survey, drawing two flux-limited samples of the local Universe from the 2dFGRS catalogue, which contains over 220,000 galaxies at a median redshift of z = 0.11. The samples are cut at z = 0.2 and corrected for selection effects. We then use the three-dimensional genus statistic to probe the connectedness of the galaxy distribution...

Groups of genes assigned to a pathway, also called a module, have similar functions. Finding such modules, and the topology of the changes of the modules over time, is a fundamental problem in understanding the mechanisms of complex diseases. Here we investigated an approach that categorized variants into rare or common and used a hierarchical model to jointly estimate the group effects of the ...

Current phylogenetic tree reconstruction methods assume that there is a single underlying tree topology for all sites along the sequence. The presence of mosaic sequences due to recombination violates this assumption and will cause phylogenetic methods to give misleading results due to the imposition of a single tree topology on all sites. The detection of mosaic sequences caused by recombinati...

My most significant recent work is in the field of applied topology. While the early development of topology was firmly rooted in applications, many of its later advances have been driven by purely mathematical motivations. More recently there is a growing awareness that some of its powerful tools may be just what is needed to help address outstanding problems in diverse modern applications. I ...

Questions surrounding regional economic convergence have commanded a great deal of recent attention in economics literature. As in other recent cases in the social sciences, the application of spatially explicit methods of data analysis to the convergence question has yielded important insights on regional economic growth. By contrast, the literature on regional income inequality, although some...

Kendall's coefficient concordance (KCC) can measure the similarity of a number of time series. It has been used for purifying a given cluster in functional MRI (fMRI). In the present study, a new method was developed based on the regional homogeneity (ReHo), in which KCC was used to measure the similarity of the time series of a given voxel to those of its nearest neighbors in a voxel-wise way....

This paper commences from a new indirect utility function and derives the corresponding system of equations, relating commodity demands to prices and income, that satisfies the constraints imposed by utility maximisation (aggregation, homogeneity, Slutsky symmetry and negativity). As the famous linear expenditure system (LES) is a special case of this new system, it is named the generalised Sto...