🍩 Database of Original & Non-Theoretical Uses of Topology

(found 4 matches in 0.001033s)

  1. Text Classification via Network Topology: A Case Study on the Holy Quran (2019)

    Mehmet Emin Aktas, Esra Akbas
    Abstract Due to the growth in the number of texts and documents available online, machine learning based text classification systems are getting more popular recently. Feature extraction, converting unstructured text into a structured feature space, is one of the essential tasks for text classification. In this paper, we propose a novel feature extraction approach for text classification using the network representation of text, network topology, and machine learning techniques. We present experimental results on classifying the Holy Quran chapters based on the place each chapter was revealed to illustrate the effectiveness of the approach.

  2. Topology Highlights Mesoscopic Functional Equivalence Between Imagery and Perception: The Case of Hypnotizability (2019)

    Esther Ibáñez-Marcelo, Lisa Campioni, Angkoon Phinyomark, Giovanni Petri, Enrica L. Santarcangelo
    Abstract The functional equivalence (FE) between imagery and perception or motion has been proposed on the basis of neuroimaging evidence of large spatially overlapping activations between real and imagined sensori-motor conditions. However, similar local activation patterns do not imply the same mesoscopic integration of brain regions, which can be described by tools from Topological Data Analysis (TDA). On the basis of behavioral findings, stronger FE has been hypothesized in the individuals with high scores of hypnotizability scores (highs) with respect to low hypnotizable participants (lows) who differ between each other in the proneness to modify memory, perception and behavior according to specific imaginative suggestions. Here we present the first EEG evidence of stronger FE in highs. In fact, persistent homology shows that the highs EEG topological asset during real and imagined sensory conditions is significantly more similar than the lows. As a corollary finding, persistent homology shows lower restructuring of the EEG asset in highs than in lows during both sensory and imagery tasks with respect to basal conditions. Present findings support the view that greater embodiment of mental images may be responsible for the highs greater proneness to respond to sensori-motor suggestions and to report involuntariness in action. In addition, findings indicate hypnotizability-related sensory and cognitive information processing and suggest that the psycho-physiological trait of hypnotizability may modulate more than one aspect of the everyday life.

  3. Statistical Topology of Bond Networks With Applications to Silica (2020)

    B. Schweinhart, D. Rodney, J. K. Mason
    Abstract Whereas knowledge of a crystalline material's unit cell is fundamental to understanding the material's properties and behavior, there are no obvious analogs to unit cells for disordered materials despite the frequent existence of considerable medium-range order. This article views a material's structure as a collection of local atomic environments that are sampled from some underlying probability distribution of such environments, with the advantage of offering a unified description of both ordered and disordered materials. Crystalline materials can then be regarded as special cases where the underlying probability distribution is highly concentrated around the traditional unit cell. The 𝐻1 barcode is proposed as a descriptor of local atomic environments suitable for disordered bond networks and is applied with three other descriptors to molecular dynamics simulations of silica glasses. Each descriptor reliably distinguishes the structure of glasses produced at different cooling rates, with the 𝐻1 barcode and coordination profile providing the best separation. The approach is generally applicable to any system that can be represented as a sparse graph.

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  4. Multivariate Data Analysis Using Persistence-Based Filtering and Topological Signatures (2012)

    B. Rieck, H. Mara, H. Leitte
    Abstract The extraction of significant structures in arbitrary high-dimensional data sets is a challenging task. Moreover, classifying data points as noise in order to reduce a data set bears special relevance for many application domains. Standard methods such as clustering serve to reduce problem complexity by providing the user with classes of similar entities. However, they usually do not highlight relations between different entities and require a stopping criterion, e.g. the number of clusters to be detected. In this paper, we present a visualization pipeline based on recent advancements in algebraic topology. More precisely, we employ methods from persistent homology that enable topological data analysis on high-dimensional data sets. Our pipeline inherently copes with noisy data and data sets of arbitrary dimensions. It extracts central structures of a data set in a hierarchical manner by using a persistence-based filtering algorithm that is theoretically well-founded. We furthermore introduce persistence rings, a novel visualization technique for a class of topological features-the persistence intervals-of large data sets. Persistence rings provide a unique topological signature of a data set, which helps in recognizing similarities. In addition, we provide interactive visualization techniques that assist the user in evaluating the parameter space of our method in order to extract relevant structures. We describe and evaluate our analysis pipeline by means of two very distinct classes of data sets: First, a class of synthetic data sets containing topological objects is employed to highlight the interaction capabilities of our method. Second, in order to affirm the utility of our technique, we analyse a class of high-dimensional real-world data sets arising from current research in cultural heritage.