Recent fMRI research shows that perceptual and cognitive representations are instantiated in high-dimensional multivoxel patterns in the brain. However, the methods for detecting these representations are limited. Topological data analysis (TDA) is a new approach, based on the mathematical field of topology, that can detect unique types of geometric features in patterns of data. Several recent studies have successfully applied TDA to study various forms of neural data; however, to our knowledge, TDA has not been successfully applied to data from event-related fMRI designs. Event-related fMRI is very common but limited in terms of the number of events that can be run within a practical time frame and the effect size that can be expected. Here, we investigate whether persistent homology—a popular TDA tool that identifies topological features in data and quantifies their robustness—can identify known signals given these constraints. We use fmrisim, a Python-based simulator of realistic fMRI data, to assess the plausibility of recovering a simple topological representation under a variety of conditions. Our results suggest that persistent homology can be used under certain circumstances to recover topological structure embedded in realistic fMRI data simulations.
<div> <div> <div> <p>Finding new medicines is one of the most important tasks of pharmaceutical companies. One of the best approaches to finding a new drug starts with answering this simple question: Given a known effective drug X, what are the top 100 molecules in our database most similar to X? Thus the essence of the problem is a nearest-neighbors search, and the key question is how to define the distance between two molecules in the database. In this paper, we investigate the use of topological, rather than geometric, or chemical, signatures for molecules, and two notions of distance that come from comparing these topological signatures. We introduce PH_VS (Persistent Homology for Virtual Screening), a new system for ligand-based screening using a topological technique known as multi-parameter persistent homology. We show that our approach can match or exceed a reasonable estimate of current state of the art (including well-funded commercial tools), even with relatively little domain-specific tuning. Indeed, most of the components we have built for this system are general-purpose tools for data science and will be released soon as open source software. </p> </div> </div> </div>
No abstract
Recent fMRI research shows that perceptual and cognitive representations are instantiated in high-dimensional multi-voxel patterns in the brain. However, the methods for detecting these representations are limited. Topological Data Analysis (TDA) is a new approach, based on the mathematical field of topology, that can detect unique types of geometric features in patterns of data. Several recent studies have successfully applied TDA to study various forms of neural data; however, to our knowledge, TDA has not been successfully applied to data from event-related fMRI designs. Event-related fMRI is very common but limited in terms of the number of events that can be run within a practical time frame and the effect size that can be expected. Here, we investigate whether persistent homology -a popular TDA tool that identifies topological features in data and quantifies their robustness -can identify known signals given these constraints. We use fmrisim, a Python-based simulator of realistic fMRI data, to assess the plausibility of recovering a simple topological representation under a variety of conditions. Our results suggest that persistent homology can be used under certain circumstances to recover topological structure embedded in realistic fMRI data simulations.
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