Topological data analysis for revealing structural origin of density anomalies in silica glass

Topological data analysis (TDA) is a new emerging and powerful tool to understand the medium range structure ordering of multi-scale data. This study investigates the density anomalies observed during cooling of liquid silica from topological point of view using TDA. The density of liquid silica does not monotonically increase during cooling; it instead shows a maximum and minimum. Despite tremendous efforts, the structural origin of these density anomalies is not clearly understood. Our approach reveals that the one-dimensional topology of the -Si-Si- network changes at the temperatures at which the maximum and minimum densities are observed in our MD simulations, while those of the -O-O- and -Si-O- networks change at lower temperatures. These results are also supported by conventional ring analysis. Our work demonstrates the value of new topological techniques in understanding the transitions in glassy materials and sheds light on the characterization of glass-liquid transitions.Comment: 25 pages, 5 figures, in the main tex

Stability and statistical inferences in the space of topological spatial relationships

Modelling topological properties of the spatial relationship between objects, known as the extit{topological relationship}, represents a fundamental research problem in many domains including Artificial Intelligence (AI) and Geographical Information Science (GIS). Real world data is generally finite and exhibits uncertainty. Therefore, when attempting to model topological relationships from such data it is useful to do so in a manner which is both extit{stable} and facilitates extit{statistical inferences}. Current models of the topological relationships do not exhibit either of these properties. We propose a novel model of topological relationships between objects in the Euclidean plane which encodes topological information regarding connected components and holes. Specifically, a representation of the persistent homology, known as a persistence scale space, is used. This representation forms a Banach space that is stable and, as a consequence of the fact that it obeys the strong law of large numbers and the central limit theorem, facilitates statistical inferences. The utility of this model is demonstrated through a number of experiments

Unsupervised machine learning approaches to the qq-state Potts model

In this paper with study phase transitions of the $q$-state Potts model, through a number of unsupervised machine learning techniques, namely Principal Component Analysis (PCA), $k$-means clustering, Uniform Manifold Approximation and Projection (UMAP), and Topological Data Analysis (TDA). Even though in all cases we are able to retrieve the correct critical temperatures $T_c(q)$, for $q = 3, 4$ and $5$, results show that non-linear methods as UMAP and TDA are less dependent on finite size effects, while still being able to distinguish between first and second order phase transitions. This study may be considered as a benchmark for the use of different unsupervised machine learning algorithms in the investigation of phase transitions.Comment: Added computation of critical exponents; exposition improve

A new class of neural architectures to model episodic memory : computational studies of distal reward learning

A computational cognitive neuroscience model is proposed, which models episodic memory based on the mammalian brain. A computational neural architecture instantiates the proposed model and is tested on a particular task of distal reward learning. Categorical Neural Semantic Theory informs the architecture design. To experiment upon the computational brain model, embodiment and an environment in which the embodiment exists are simulated. This simulated environment realizes the Morris Water Maze task, a well established biological experimental test of distal reward learning. The embodied neural architecture is treated as a virtual rat and the environment it acts in as a virtual water tank. Performance levels of the neural architectures are evaluated through analysis of embodied behavior in the distal reward learning task. Comparison is made to biological rat experimental data, as well as comparison to other published models. In addition, differences in performance are compared between the normal and categorically informed versions of the architecture

Clustering and Topological Data Analysis: Comparison and Application

Clustering is common technique used to demonstrate relationships between data and information. Of recent interest is topological data analysis (TDA), which can represent and cluster data through persistent homology. The TDA algorithms used include the Topological Mode Analysis Tool (ToMATo) algorithm, Garin and Tauzin’s TDA Pipeline, and the Mapper algorithm. First, TDA is compared to ten other clustering algorithms on artificial 2D data where it ranked third overall. TDA had the second-highest performance in terms of average accuracy (97.9%); however, its computation-time performance ranked in the middle of the algorithms. TDA ranked fourth on the qualitative “visual trustworthiness” metric. On real-world data, TDA showed promising classification results (accuracy between 80-95%). Overall, this paper shows TDA is a competitive algorithm performance-wise, though computationally expensive. When TDA is used for visualization, the Mapper algorithm allows for unique alternative views especially effective for visualizing highly dimensional data

Resistance of tick gut microbiome to anti-tick vaccines, pathogen infection and antimicrobial peptides

Ixodes scapularis ticks harbor microbial communities including pathogenic and non-pathogenic microbes. Pathogen infection increases the expression of several tick gut proteins, which disturb the tick gut microbiota and impact bacterial biofilm formation. Anaplasma phagocytophilum induces ticks to express I. scapularis antifreeze glycoprotein (IAFGP), a protein with antimicrobial activity, while Borrelia burgdorferi induces the expression of PIXR. Here, we tested the resistance of I. scapularis microbiome to A. phagocytophilum infection, antimicrobial peptide IAFGP, and anti-tick immunity specific to PIXR. We demonstrate that A. phagocytophilum infection and IAFGP affect the taxonomic composition and taxa co-occurrence networks, but had limited impact on the functional traits of tick microbiome. In contrast, anti-tick immunity disturbed the taxonomic composition and the functional profile of tick microbiome, by increasing both the taxonomic and pathways diversity. Mechanistically, we show that anti-tick immunity increases the representation and importance of the polysaccharide biosynthesis pathways involved in biofilm formation, while these pathways are under-represented in the microbiome of ticks infected by A. phagocytophilum or exposed to IAFGP. These analyses revealed that tick microbiota is highly sensitive to anti-tick immunity, while it is less sensitive to pathogen infection and antimicrobial peptides. Results suggest that biofilm formation may be a defensive response of tick microbiome to anti-tick immunity