🍩 Database of Original & NonTheoretical Uses of Topology
(found 12 matches in 0.001981s)


Weighted Persistent Homology for Biomolecular Data Analysis (2020)
Zhenyu Meng, D. Vijay Anand, Yunpeng Lu, Jie Wu, Kelin XiaAbstract
In this paper, we systematically review weighted persistent homology (WPH) models and their applications in biomolecular data analysis. Essentially, the weight value, which reflects physical, chemical and biological properties, can be assigned to vertices (atom centers), edges (bonds), or higher order simplexes (cluster of atoms), depending on the biomolecular structure, function, and dynamics properties. Further, we propose the first localized weighted persistent homology (LWPH). Inspired by the great success of element specific persistent homology (ESPH), we do not treat biomolecules as an inseparable system like all previous weighted models, instead we decompose them into a series of local domains, which may be overlapped with each other. The general persistent homology or weighted persistent homology analysis is then applied on each of these local domains. In this way, functional properties, that are embedded in local structures, can be revealed. Our model has been applied to systematically study DNA structures. It has been found that our LWPH based features can be used to successfully discriminate the A, B, and Ztypes of DNA. More importantly, our LWPH based principal component analysis (PCA) model can identify two configurational states of DNA structures in ion liquid environment, which can be revealed only by the complicated helical coordinate system. The great consistence with the helicalcoordinate model demonstrates that our model captures local structure variations so well that it is comparable with geometric models. Moreover, geometric measurements are usually defined in local regions. For instance, the helicalcoordinate system is limited to one or two basepairs. However, our LWPH can quantitatively characterize structure information in regions or domains with arbitrary sizes and shapes, where traditional geometrical measurements fail. 
Understanding Diffraction Patterns of Glassy, Liquid and Amorphous Materials via Persistent Homology Analyses (2019)
Yohei Onodera, Shinji Kohara, Shuta Tahara, Atsunobu Masuno, Hiroyuki Inoue, Motoki Shiga, Akihiko Hirata, Koichi Tsuchiya, Yasuaki Hiraoka, Ippei Obayashi, Koji Ohara, Akitoshi Mizuno, Osami SakataAbstract
The structure of glassy, liquid, and amorphous materials is still not well understood, due to the insufficient structural information from diffraction data. In this article, attempts are made to understand the origin of diffraction peaks, particularly of the first sharp diffraction peak (FSDP, Q1), the principal peak (PP, Q2), and the third peak (Q3), observed in the measured diffraction patterns of disordered materials whose structure contains tetrahedral motifs. It is confirmed that the FSDP (Q1) is not a signature of the formation of a network, because an FSDP is observed in tetrahedral molecular liquids. It is found that the PP (Q2) reflects orientational correlations of tetrahedra. Q3, that can be observed in all disordered materials, even in common liquid metals, stems from simple pair correlations. Moreover, information on the topology of disordered materials was revealed by utilizing persistent homology analyses. The persistence diagram of silica (SiO2) glass suggests that the shape of rings in the glass is similar not only to those in the crystalline phase with comparable density (αcristobalite), but also to rings present in crystalline phases with higher density (αquartz and coesite); this is thought to be the signature of disorder. Furthermore, we have succeeded in revealing the differences, in terms of persistent homology, between tetrahedral networks and tetrahedral molecular liquids, and the difference/similarity between liquid and amorphous (glassy) states. Our series of analyses demonstrated that a combination of diffraction data and persistent homology analyses is a useful tool for allowing us to uncover structural features hidden in halo pattern of disordered materials. 
HighThroughput Screening Approach for Nanoporous Materials Genome Using Topological Data Analysis: Application to Zeolites (2018)
Yongjin Lee, Senja D. Barthel, Pawe\\textbackslash\l D\\textbackslash\lotko, Seyed Mohamad Moosavi, Kathryn Hess, Berend Smit 
Improved Understanding of Aqueous Solubility Modeling Through Topological Data Analysis (2018)
Mariam Pirashvili, Lee Steinberg, Francisco Belchi Guillamon, Mahesan Niranjan, Jeremy G. Frey, Jacek BrodzkiAbstract
Topological data analysis is a family of recent mathematical techniques seeking to understand the ‘shape’ of data, and has been used to understand the structure of the descriptor space produced from a standard chemical informatics software from the point of view of solubility. We have used the mapper algorithm, a TDA method that creates lowdimensional representations of data, to create a network visualization of the solubility space. While descriptors with clear chemical implications are prominent features in this space, reflecting their importance to the chemical properties, an unexpected and interesting correlation between chlorine content and rings and their implication for solubility prediction is revealed. A parallel representation of the chemical space was generated using persistent homology applied to molecular graphs. Links between this chemical space and the descriptor space were shown to be in agreement with chemical heuristics. The use of persistent homology on molecular graphs, extended by the use of norms on the associated persistence landscapes allow the conversion of discrete shape descriptors to continuous ones, and a perspective of the application of these descriptors to quantitative structure property relations is presented. 
Representability of Algebraic Topology for Biomolecules in Machine Learning Based Scoring and Virtual Screening (2018)
Zixuan Cang, Lin Mu, GuoWei WeiAbstract
This work introduces a number of algebraic topology approaches, including multicomponent persistent homology, multilevel persistent homology, and electrostatic persistence for the representation, characterization, and description of small molecules and biomolecular complexes. In contrast to the conventional persistent homology, multicomponent persistent homology retains critical chemical and biological information during the topological simplification of biomolecular geometric complexity. Multilevel persistent homology enables a tailored topological description of inter and/or intramolecular interactions of interest. Electrostatic persistence incorporates partial charge information into topological invariants. These topological methods are paired with Wasserstein distance to characterize similarities between molecules and are further integrated with a variety of machine learning algorithms, including knearest neighbors, ensemble of trees, and deep convolutional neural networks, to manifest their descriptive and predictive powers for proteinligand binding analysis and virtual screening of small molecules. Extensive numerical experiments involving 4,414 proteinligand complexes from the PDBBind database and 128,374 ligandtarget and decoytarget pairs in the DUD database are performed to test respectively the scoring power and the discriminatory power of the proposed topological learning strategies. It is demonstrated that the present topological learning outperforms other existing methods in proteinligand binding affinity prediction and liganddecoy discrimination. 
Topological Data Analysis for the Characterization of Atomic Scale Morphology From Atom Probe Tomography Images (2018)
Tianmu Zhang, Scott R. Broderick, Krishna RajanAbstract
Atom probe tomography (APT) represents a revolutionary characterization tool for materials that combine atomic imaging with a timeofflight (TOF) mass spectrometer to provide direct space threedimensional, atomic scale resolution images of materials with the chemical identities of hundreds of millions of atoms. It involves the controlled removal of atoms from a specimen’s surface by field evaporation and then sequentially analyzing them with a position sensitive detector and TOF mass spectrometer. A paradox in APT is that while on the one hand, it provides an unprecedented level of imaging resolution in three dimensions, it is very difficult to obtain an accurate perspective of morphology or shape outlined by atoms of similar chemistry and microstructure. The origins of this problem are numerous, including incomplete detection of atoms and the complexity of the evaporation fields of atoms at or near interfaces. Hence, unlike scattering techniques such as electron microscopy, interfaces appear diffused, not sharp. This, in turn, makes it challenging to visualize and quantitatively interpret the microstructure at the “meso” scale, where one is interested in the shape and form of the interfaces and their associated chemical gradients. It is here that the application of informatics at the nanoscale and statistical learning methods plays a critical role in both defining the level of uncertainty and helping to make quantitative, statistically objective interpretations where heuristics often dominate. In this chapter, we show how the tools of Topological Data Analysis provide a new and powerful tool in the field of nanoinformatics for materials characterization. 
Persistent Homology Analysis of Ion Aggregations and HydrogenBonding Networks (2018)
Kelin XiaAbstract
Despite the great advancement of experimental tools and theoretical models, a quantitative characterization of the microscopic structures of ion aggregates and their associated water hydrogenbonding networks still remains a challenging problem. In this paper, a newlyinvented mathematical method called persistent homology is introduced, for the first time, to quantitatively analyze the intrinsic topological properties of ion aggregation systems and hydrogenbonding networks. The two most distinguishable properties of persistent homology analysis of assembly systems are as follows. First, it does not require a predefined bond length to construct the ion or hydrogenbonding network. Persistent homology results are determined by the morphological structure of the data only. Second, it can directly measure the size of circles or holes in ion aggregates and hydrogenbonding networks. To validate our model, we consider two wellstudied systems, i.e., NaCl and KSCN solutions, generated from molecular dynamics simulations. They are believed to represent two morphological types of aggregation, i.e., local clusters and extended ion networks. It has been found that the two aggregation types have distinguishable topological features and can be characterized by our topological model very well. Further, we construct two types of networks, i.e., Onetworks and H2Onetworks, for analyzing the topological properties of hydrogenbonding networks. It is found that for both models, KSCN systems demonstrate much more dramatic variations in their local circle structures with a concentration increase. A consistent increase of largesized local circle structures is observed and the sizes of these circles become more and more diverse. In contrast, NaCl systems show no obvious increase of largesized circles. Instead a consistent decline of the average size of the circle structures is observed and the sizes of these circles become more and more uniform with a concentration increase. As far as we know, these unique intrinsic topological features in ion aggregation systems have never been pointed out before. More importantly, our models can be directly used to quantitatively analyze the intrinsic topological invariants, including circles, loops, holes, and cavities, of any networklike structures, such as nanomaterials, colloidal systems, biomolecular assemblies, among others. These topological invariants cannot be described by traditional graph and network models. 
Exploring Hyperspectral Imaging Data Sets With Topological Data Analysis (2017)
Ludovic Duponchel 
Quantifying Similarity of PoreGeometry in Nanoporous Materials (2017)
Yongjin Lee, Senja D. Barthel, Pawe\\textbackslash\l D\\textbackslash\lotko, S. Mohamad Moosavi, Kathryn Hess, Berend Smit 
Identification of Key Features Using Topological Data Analysis for Accurate Prediction of Manufacturing System Outputs (2017)
Wei Guo, Ashis G. BanerjeeAbstract
Topological data analysis (TDA) has emerged as one of the most promising approaches to extract insights from highdimensional data of varying types such as images, point clouds, and meshes, in an unsupervised manner. To the best of our knowledge, here, we provide the first successful application of TDA in the manufacturing systems domain. We apply a widely used TDA method, known as the Mapper algorithm, on two benchmark data sets for chemical process yield prediction and semiconductor wafer fault detection, respectively. The algorithm yields topological networks that capture the intrinsic clusters and connections among the clusters present in the data sets, which are difficult to detect using traditional methods. We select key process variables or features that impact the system outcomes by analyzing the network shapes. We then use predictive models to evaluate the impact of the selected features. Results show that the models achieve at least the same level of high prediction accuracy as with all the process variables, thereby, providing a way to carry out process monitoring and control in a more costeffective manner. 
Topological Data Analysis: A Promising Big Data Exploration Tool in Biology, Analytical Chemistry and Physical Chemistry (2016)
Marc Offroy, Ludovic DuponchelAbstract
An important feature of experimental science is that data of various kinds is being produced at an unprecedented rate. This is mainly due to the development of new instrumental concepts and experimental methodologies. It is also clear that the nature of acquired data is significantly different. Indeed in every areas of science, data take the form of always bigger tables, where all but a few of the columns (i.e. variables) turn out to be irrelevant to the questions of interest, and further that we do not necessary know which coordinates are the interesting ones. Big data in our lab of biology, analytical chemistry or physical chemistry is a future that might be closer than any of us suppose. It is in this sense that new tools have to be developed in order to explore and valorize such data sets. Topological data analysis (TDA) is one of these. It was developed recently by topologists who discovered that topological concept could be useful for data analysis. The main objective of this paper is to answer the question why topology is well suited for the analysis of big data set in many areas and even more efficient than conventional data analysis methods. Raman analysis of single bacteria should be providing a good opportunity to demonstrate the potential of TDA for the exploration of various spectroscopic data sets considering different experimental conditions (with high noise level, with/without spectral preprocessing, with wavelength shift, with different spectral resolution, with missing data).