Topological and Geometric Data Analysis

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We introduce a method for training neural networks to perform image or volume segmentation in which prior knowledge about the topology of the segmented object can be explicitly provided and then incorporated into the training process. By using the differentiable properties of persistent homology, a concept used in top…

• İLKAY ÖKSÜZ

We introduce a method for training neural networks to perform image or volume segmentation in which prior knowledge about the topology of the segmented object can be explicitly provided and then incorporated into the training process. By using the differentiable properties of persistent homology, a concept used in top…

• İLKAY ÖKSÜZ

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• ALİ ÇİVRİL

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• ONUR UĞURLU

We establish a direct map between refined topological vertex and sl(N) homological invariants of the of Hopf link, which include Khovanov-Rozansky homology as a special case. This relation provides an exact answer for homological invariants of the Hopf link, whose components are colored by arbitrary representations of…

• CAN KOZÇAZ

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• MEHMET NİYAZİ ÇANKAYA

In this paper we introduce a method that offers a detailed overview of the entanglement of an open protein chain. Further, we present a purely topological model for classifying open protein chains by also taking into account any bridge involving the backbone. To this end, we implemented the concepts of planar knotoids…

• NESLİHAN GÜGÜMCÜ

modulo 2 analogues of the Betti numbers of Poincaré.

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• ATABEY KAYGUN

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• ATABEY KAYGUN

Numerous dimensionality reduction problems in data analysis involve the recovery of low-dimensional models or the learning of manifolds underlying sets of data. Many manifold learning methods require the estimation of the tangent space of the manifold at a point from locally available data samples. Local sampling cond…

• ELİF VURAL AGHAEI MAZAHERI