Tigran Ishkhanov

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The availability of the assembled mouse genome makes possible, for the first time, an alignment and comparison of two large vertebrate genomes. We investigated different strategies of alignment for the subsequent analysis of conservation of genomes that are effective for assemblies of different quality. These strategies were applied to the comparison of the(More)
In this study we concentrate on qualitative topological analysis of the local behavior of the space of natural images. To this end, we use a space of 3 by 3 high-contrast patches ℳ. We develop a theoretical model for the high-density 2-dimensional submanifold of ℳ showing that it has the topology of the Klein bottle. Using our topological software package(More)
The authors prove that the sufficient condition for the existence of an augmentation of the Chekanov–Eliashberg differential algebra of a Legendrian knot, which is contained in a recent work of the first author, is also necessary. As a by-product, the authors describe an algorithm for calculating Chekanov–Eliashberg invariants in terms of the front diagram(More)
Information in the cortex is thought to be represented by the joint activity of neurons. Here we describe how fundamental questions about neural representation can be cast in terms of the topological structure of population activity. A new method, based on the concept of persistent homology, is introduced and applied to the study of population activity in(More)
We develop a topology-based method which can be used as a measure of the dissimilarity between shapes. For us, a shape is a point cloud dataset in Euclidean space. In the experiments described in this paper a shape comes with a particular choice of triangulation (mesh). However, the method can be applied to a more general situation when no particular(More)
Time-varying topological simplifications of the space of votes in the US House of Representatives (US HoR) display several interesting features unavailable with classical methods of machine learning. In this paper we demonstrate how a recently developed topological simplification method, MAPPER, can detect changes in collaboration structures within the US(More)
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