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 highdensity 2-dimensional submanifold of M showing that it has the topology of the Klein bottle. Using our topological software package PLEX we experimentally verify our theoretical conclusions. We use polynomial representation to give coordinatization to various subspaces of M. We find the best-fitting embedding of the Klein bottle into the ambient space of M. Our results are currently being used in developing a compression algorithm based on a Klein bottle dictionary.

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 primary visual cortex (V1). We found that the topological structure of activity patterns when the cortex is spontaneously active is similar to those evoked by natural image stimulation and consistent with the topology of a two sphere. We discuss how this structure could emerge from the functional organization of orientation and spatial frequency maps and their mutual relationship. Our findings extend prior results on the relationship between spontaneous and evoked activity in V1 and illustrates how computational topology can help tackle elementary questions about the representation of information in the nervous system.

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In the regular course of business, companies spend a lot of effort reading and interpreting documents, a highly manual process that involves tedious tasks, such as identifying dates and names or locating the presence or absence of certain clauses in a contract. Dealing with natural language is complex and further complicated by the fact that these documents come in various formats (scanned image, digital formats) and have different degrees of internal structure (spreadsheets, invoices, text documents). We present DICR, an end-to-end, modular, and trainable system that automates the mundane aspects of document review and allows humans to perform the validation. The system is able to speed up this work while increasing quality of information extracted, consistency, throughput, and decreasing time to decision. Extracted data can be fed into other downstream applications (from dashboards to Q&A and to report generation).