Topological Fingerprints Research Articles

Topological Fingerprints for Audio Identification

Topological Fingerprints for Audio Identification

Time-Aware Knowledge Representations of Dynamic Objects with Multidimensional Persistence

Learning time-evolving objects such as multivariate time series and dynamic networks requires the development of novel knowledge representation mechanisms and neural network architectures, which allow for capturing implicit time-dependent information contained in the data. Such information is typically not directly observed but plays a key role in the learning task performance. In turn, lack of time dimension in knowledge encoding mechanisms for time-dependent data leads to frequent model updates, poor learning performance, and, as a result, subpar decision-making. Here we propose a new approach to a time-aware knowledge representation mechanism that notably focuses on implicit time-dependent topological information along multiple geometric dimensions. In particular, we propose a new approach, named Temporal MultiPersistence (TMP), which produces multidimensional topological fingerprints of the data by using the existing single parameter topological summaries. The main idea behind TMP is to merge the two newest directions in topological representation learning, that is, multi-persistence which simultaneously describes data shape evolution along multiple key parameters, and zigzag persistence to enable us to extract the most salient data shape information over time. We derive theoretical guarantees of TMP vectorizations and show its utility, in application to forecasting on benchmark traffic flow, Ethereum blockchain, and electrocardiogram datasets, demonstrating the competitive performance, especially, in scenarios of limited data records. In addition, our TMP method improves the computational efficiency of the state-of-the-art multipersistence summaries up to 59.5 times.

Two excited-state datasets for quantum chemical UV-vis spectra of organic molecules

We present two open-source datasets that provide time-dependent density-functional tight-binding (TD-DFTB) electronic excitation spectra of organic molecules. These datasets represent predictions of UV-vis absorption spectra performed on optimized geometries of the molecules in their electronic ground state. The GDB-9-Ex dataset contains a subset of 96,766 organic molecules from the original open-source GDB-9 dataset. The ORNL_AISD-Ex dataset consists of 10,502,904 organic molecules that contain between 5 and 71 non-hydrogen atoms. The data reveals the close correlation between the magnitude of the gaps between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), and the excitation energy of the lowest singlet excited state energies quantitatively. The chemical variability of the large number of molecules was examined with a topological fingerprint estimation based on extended-connectivity fingerprints (ECFPs) followed by uniform manifold approximation and projection (UMAP) for dimension reduction. Both datasets were generated using the DFTB+ software on the “Andes” cluster of the Oak Ridge Leadership Computing Facility (OLCF).

Simulation study of shape memory polymer networks formed by free radical polymerization

Chemically crosslinked thermoset shape memory polymers (TSMPs) can combine the strength required for load-carrying structures and devices with stimuli-responsive properties that can allow them to perform crack-closing or other multifunctional properties. In particular, UV-curable shape memory polymers can be used for 3D printing, and to enhance the design process, a molecular dynamics (MD) modeling framework was developed to study them. The MD simulations were used to calculate thermophysical, mechanical, and shape memory properties for glycerolate dimethacrylate after UV-curing to form a polymer network. Semiquantitative agreement between simulation and experiment was achieved for the different properties compared. By examining various conditions for network formation, a range of distinct cross-linking topologies were generated and their effects on properties were evaluated. In particular, it was found that the percentage of monomers with the maximum number of possible links with other monomers had a greater correlation with recovery stress than the number of monomers reacted overall. A new topological fingerprint, the average minimum pathway between monomers, was proposed and found to have the strongest correlation with recovery stress than all properties examined.

Classification analysis of fatty acid synthase inhibitors using multialgorithms on topological descriptors and structural fingerprints.

Fatty acid synthase (FASN) is one of the enzymes required for fatty acid biosynthesis and is expressed as low or absent in most normal cells/tissues. However, this enzyme is upregulated in various cancer cells; hence, it can act as an important target to design and develop novel FASN inhibitors for cancer therapy. In the present investigation, a series of structurally diverse compounds that possessed FASN inhibitory activities were subjected to classification analysis using different algorithms such as support vector machine, decision tree, Naïve Bayes and random forest. The physicochemical descriptors and MACCS fingerprints were calculated using PaDEL software, and the WEKA software was utilized for the classification model building. The statistical parameters/confusion matrix calculated from the analysis revealed that the selected models have significant predictive performances. The results showed that the topological properties of the molecules are the main determinant for the activity classification. The key descriptors comprised of hydrogen bonding groups, especially acceptor (nHBAcc, minHBint9, minHBint5 and nwHBa), charge on the topological surface of the molecules (JGI10 & GGI2), ionization potential (GATS5i and GATS1i) and branching and distance between the groups (ETA_Eta_B_RC) are significantly contributed in the classification models. Further, the presence of heteroatoms (MACCSFP82, MACCSFP93 and MACCSFP131), especially nitrogen atom(s) and hydrogen bond acceptor groups (N-N group, NC(=O)N, N-C(=O)), actively contributed to the inhibitory activities. The results concluded that the topological polar properties concentrated in a specific region have significant FASN inhibitory activity. Hence, these results shall be used to develop novel molecules with increased FASN inhibitory activity.

Correlation between cyclic topology and shape memory properties of an amine-based thermoset shape memory polymer: a coarse-grained molecular dynamics study

Defects in crosslinked networks have a negative effect on mechanical and functional properties. In this study, an epoxy resin diglycidyl ether of bisphenol A crosslinked by a hardener 4,4-diaminodiphenyl methane with various cyclic topologies was simulated to find correlations between the mechanical/shape memory properties (i.e. glassy/rubbery elastic modulus, shape recovery ratio, and recovery stress) and cyclic topologies (i.e. number of total loops, number of defective loops (DLs), etc). The effect of cyclic topology on shape memory properties was more significant than its effect on mechanical properties, altering recovery stress by more than 25% on average. After analyzing several topological fingerprints such as total number of loops, number of DLs, and number of higher order loops, we found that the effect of cyclic topology on the mechanical/shape memory properties of the systems can be best understood by the fraction of hardeners reacted with four distinct epoxy molecules (tetra-distinctly-reacted (TDR) hardeners). By increasing the number of TDR hardeners, the network is closer to ideal, resulting in an increase in the number of higher order loops and a reduction in the number of DLs, which in turn leads to an increase in rubbery elastic modulus and shape recovery ratio to a lesser degree, but a substantial increase in recovery stress. These results suggest that utilization of experimental techniques such as semibatch monomer addition, which leads to a more expanded and defect-free network, can result in a simultaneous increase in both shape recovery ratio and recovery stress in thermoset shape memory polymers (TSMPs). Moreover, topology alteration can be used to synthesize TSMPs with improved recovery stress without significantly increasing their stiffness.

Taiwan Controlled Substances Database

New psychoactive substances (NPS) have increasingly been illegally synthesized and used around the world in recent years. Due to the large volume and the variety of NPS, most do not have sufficient information about their addictive potential and harmful effects to human subjects. This makes it difficult to evaluate these potential substances of abuse. This study aims to build a database based on Taiwan's controlled substances, to provide quick structural and pharmacological feedback. Taiwan Controlled Substances Database (TCSD) includes the collection of controlled substances, relevant experimental and structural information, as well as computational features such as molecular fingerprints and descriptors. Two types of structural search were added: substructure search and topological fingerprint similarity search. A web framework was used to enhance accessibility and usability (https://cs2search.cmdm.tw).

Classification models and SAR analysis on HDAC1 inhibitors using machine learning methods.

Histone deacetylase (HDAC) 1, a member of the histone deacetylases family, plays a pivotal role in various tumors. In this study, we collected 7313 human HDAC1 inhibitors with bioactivities to form a dataset. Then, the dataset was divided into a training set and a test set using two splitting methods: (1) Kohonen's self-organizing map and (2) random splitting. The molecular structures were represented by MACCS fingerprints, RDKit fingerprints, topological torsions fingerprints and ECFP4 fingerprints. A total of 80 classification models were built by using five machine learning methods, including decision tree (DT), random forest, support vector machine, eXtreme Gradient Boosting and deep neural network. Model 15A_2 built by the XGBoost algorithm based on ECFP4 fingerprints showed the best performance, with an accuracy of 88.08% and an MCC value of 0.76 on the test set. Finally, we clustered the 7313 HDAC1 inhibitors into 31 subsets, and the substructural features in each subset were investigated. Moreover, using DT algorithm we analyzed the structure-activity relationship of HDAC1 inhibitors. It may conclude that some substructures have a significant effect on high activity, such as N-(2-amino-phenyl)-benzamide, benzimidazole, AR-42 analogues, hydroxamic acid with a middle chain alkyl and 4-aryl imidazole with a midchain of alkyl whose α carbon is chiral.

Efficient Screening of Target-Specific Selected Compounds in Mixtures by 19 F NMR Binding Assay with Predicted 19 F NMR Chemical Shifts.

Ligand-based 19 F NMR screening is a highly effective and well-established hit-finding approach. The high sensitivity to protein binding makes it particularly suitable for fragment screening. Different criteria can be considered for generating fluorinated fragment libraries. One common strategy is to assemble a large, diverse, well-designed and characterized fragment library which is screened in mixtures, generated based on experimental 19 F NMR chemical shifts. Here, we introduce a complementary knowledge-based 19 F NMR screening approach, named 19 Focused screening, enabling the efficient screening of putative active molecules selected by computational hit finding methodologies, in mixtures assembled and on-the-fly deconvoluted based on predicted 19 F NMR chemical shifts. In this study, we developed a novel approach, named LEFshift, for 19 F NMR chemical shift prediction using rooted topological fluorine torsion fingerprints in combination with a random forest machine learning method. A demonstration of this approach to a real test case is reported.

Origin independent current density vector fields induced by time-dependent magnetic field. I. The LiH molecule.

The electronic current density, induced in a molecule by the optical magnetic field associated with a frequency-dependent monochromatic plane wave, assumed to be spatially uniform within the electric quadrupole approximation, has been studied by using a theoretical method based on a continuous translation of its origin. The induced electronic current density vector field designated by this procedure, invariant of the origin for any point of the molecular domain, is obtained via a computational scheme, formally annihilating the diamagnetic contribution of the conventional common-origin approach based on perturbation theory. In a preliminary application of the theoretical methods outlined in the present work, the simple molecule of lithium hydride has been investigated. Particular attention has been paid to the structure of induced electronic current density for several values of the magnetic field frequency by investigating equilibrium points of four different types, organized in stagnation lines, which constitute its stagnation graph, i.e., a topological fingerprint of the vector field conveying complete information in the condensed form, to verify the fulfillment of fundamental requirements, e.g., the continuity equation and the Poincaré-Hopf theorem on spherical and toroidal surfaces.

Comparison of Combinatorial Fragment Spaces and Its Application to Ultralarge Make-on-Demand Compound Catalogs.

The set of chemical compounds shared by two or more chemical libraries is assessed routinely as means of comparing these libraries for various applications. Traditionally this is achieved by comparing the members of the chemical libraries individually for identity. This approach becomes impractical when operating on chemical libraries exceeding billions or even trillions of compounds in size. As a result, no such analysis exists for ultralarge chemical spaces like the Enamine REAL Space containing over 20 billion compounds. In this work, we present a novel tool called SpaceCompare for the overlap calculation of large, nonenumerable combinatorial fragment spaces. In contrast to existing methods, SpaceCompare utilizes topological fingerprints and the combinatorial character of these chemical spaces. The tool is able to determine the exact overlap of prominent spaces like Enamine's REAL Space, WuXi's GalaXi Space, and Otava's CHEMriya for the first time.

Fracton physics of spatially extended excitations. II. Polynomial ground state degeneracy of exactly solvable models

Generally, ``fracton'' topological orders are referred to as gapped phases that support \textit{point-like topological excitations} whose mobility is, to some extent, restricted. In our previous work [Phys. Rev. B 101, 245134 (2020)], a large class of exactly solvable models on hypercubic lattices are constructed. In these models, \textit{spatially extended excitations} possess generalized fracton-like properties: not only mobility but also deformability is restricted. As a series work, in this paper, we proceed further to compute ground state degeneracy (GSD) in both isotropic and anisotropic lattices. We decompose and reconstruct ground states through a consistent collection of subsystem ground state sectors, in which mathematical game ``coloring method'' is applied. Finally, we are able to systematically obtain GSD formulas (expressed as $\log_2 GSD$) which exhibit diverse kinds of polynomial dependence on system sizes. For example, the GSD of the model labeled as $[0,1,2,4]$ in four dimensional isotropic hypercubic lattice shows $ 12L^2-12L+4$ dependence on the linear size $L$ of the lattice. Inspired by existing results [Phys. Rev. X 8, 031051 (2018)], we expect that the polynomial formulas encode geometrical and topological fingerprints of higher-dimensional manifolds beyond toric manifolds used in this work. This is left to future investigation.

Predicting gas–particle partitioning coefficients of atmospheric molecules with machine learning

Abstract. The formation, properties, and lifetime of secondary organic aerosols in the atmosphere are largely determined by gas–particle partitioning coefficients of the participating organic vapours. Since these coefficients are often difficult to measure and to compute, we developed a machine learning model to predict them given molecular structure as input. Our data-driven approach is based on the dataset by Wang et al. (2017), who computed the partitioning coefficients and saturation vapour pressures of 3414 atmospheric oxidation products from the Master Chemical Mechanism using the COSMOtherm programme. We trained a kernel ridge regression (KRR) machine learning model on the saturation vapour pressure (Psat) and on two equilibrium partitioning coefficients: between a water-insoluble organic matter phase and the gas phase (KWIOM/G) and between an infinitely dilute solution with pure water and the gas phase (KW/G). For the input representation of the atomic structure of each organic molecule to the machine, we tested different descriptors. We find that the many-body tensor representation (MBTR) works best for our application, but the topological fingerprint (TopFP) approach is almost as good and computationally cheaper to evaluate. Our best machine learning model (KRR with a Gaussian kernel + MBTR) predicts Psat and KWIOM/G to within 0.3 logarithmic units and KW/G to within 0.4 logarithmic units of the original COSMOtherm calculations. This is equal to or better than the typical accuracy of COSMOtherm predictions compared to experimental data (where available). We then applied our machine learning model to a dataset of 35 383 molecules that we generated based on a carbon-10 backbone functionalized with zero to six carboxyl, carbonyl, or hydroxyl groups to evaluate its performance for polyfunctional compounds with potentially low Psat. The resulting saturation vapour pressure and partitioning coefficient distributions were physico-chemically reasonable, for example, in terms of the average effects of the addition of single functional groups. The volatility predictions for the most highly oxidized compounds were in qualitative agreement with experimentally inferred volatilities of, for example, α-pinene oxidation products with as yet unknown structures but similar elemental compositions.

Deep learning to design nuclear-targeting abiotic miniproteins.

There are more amino acid permutations within a 40-residue sequence than atoms on Earth. This vast chemical search space hinders the use of human learning to design functional polymers. Here we show how machine learning enables the de novo design of abiotic nuclear-targeting miniproteins to traffic antisense oligomers to the nucleus of cells. We combined high-throughput experimentation with a directed evolution-inspired deep-learning approach in which the molecular structures of natural and unnatural residues are represented as topological fingerprints. The model is able to predict activities beyond the training dataset, and simultaneously deciphers and visualizes sequence-activity predictions. The predicted miniproteins, termed 'Mach', reach an average mass of 10 kDa, are more effective than any previously known variant in cells and can also deliver proteins into the cytosol. The Mach miniproteins are non-toxic and efficiently deliver antisense cargo in mice. These results demonstrate that deep learning can decipher design principles to generate highly active biomolecules that are unlikely to be discovered by empirical approaches.

Nonlinear dynamics of topological Dirac fermions in 2D spin-orbit coupled materials

The graphene family materials are two-dimensional staggered monolayers with a gapped energy band structure due to intrinsic spin-orbit coupling. The mass gaps in these materials can be manipulated on-demand via biasing with a static electric field, an off-resonance circularly polarized laser, or an exchange interaction field, allowing the monolayer to be driven through a multitude of topological phase transitions. We investigate the dynamics of spin-orbit coupled graphene family materials to unveil topological phase transition fingerprints embedded in the nonlinear regime and show how these signatures manifest in the nonlinear Kerr effect and in third-harmonic generation processes. We show that the resonant nonlinear spectral response of topological fermions can be traced to specific Dirac cones in these materials, enabling characterization of topological invariants in any phase by detecting the cross-polarized component of the electromagnetic field. By shedding light on the unique processes involved in harmonic generation via topological phenomena our findings open an encouraging path towards the development of novel nonlinear systems based on two-dimensional semiconductors of the graphene family.

Topological Similarity Search in Large Combinatorial Fragment Spaces.

In similarity-driven virtual screening, molecular fingerprints are widely used to assess the similarity of all compounds contained in a chemical library to a query compound of interest. This similarity analysis is traditionally done for each member of the library individually. When encoding chemical spaces that surpass billions of compounds in size, it becomes impractical to enumerate all their products, let alone assess their similarity, deeming this approach impossible without investing a substantial amount of resources. In this work, we present a novel search algorithm named SpaceLight for topological fingerprint similarity searching in large, practically non-enumerable combinatorial fragment spaces. In contrast to existing methods, SpaceLight is able to utilize the combinatorial character of these chemical spaces for efficiency while maintaining a high correlation of the description of molecular similarity to well-known molecular fingerprints like ECFP. The resulting software is able to search prominent spaces like EnamineREAL with more than 10 billion compounds in seconds on a standard desktop computer.

Indoor Localization System Based on Hybrid Wi-Fi/BLE and Hierarchical Topological Fingerprinting Approach

Wi-Fi-based localization using received signal strength (RSS) with pedestrian dead reckoning (PDR) algorithm is widely used to track pedestrians in indoor environments. However, the unsatisfactory deployment of Wi-Fi access points (APs) in buildings and the unstable performance of PDR are still key problems that lead to low localization accuracy. In this paper, we make contributions on proposing a hybrid Wi-Fi and Bluetooth Low Energy (BLE) indoor localization system (ILS) based on an efficient BLE deployment strategy and hierarchical topological fingerprinting (HTF). For the BLE deployment strategy, we deploy BLE beacons in places that do not have clear Wi-Fi signals for localization. This efficiently increases the localization accuracy. For HTF, we hierarchically localize targets based on a topological fingerprint (TF) map. First of all, we quickly localize the room in which the target is located by Dendogram-based support vector machine (DSVM). Then, the specific position of the target is estimated by fusing Wi-Fi and BLE signals with the TF map. The new BLE-based fingerprinting algorithm is used to localize targets in environments sparsely populated by BLE beacons. We conduct physical experiments in a real building. The experimental results demonstrate that the beacons deployed based on our proposed deployment strategy results in greater localization accuracy. Furthermore, the HTF approach performs better than the other commonly used localization methods.

Prediction of pKa Using Machine Learning Methods with Rooted Topological Torsion Fingerprints: Application to Aliphatic Amines.

The acid-base dissociation constant, pKa, is a key parameter to define the ionization state of a compound and directly affects its biopharmaceutical profile. In this study, we developed a novel approach for pKa prediction using rooted topological torsion fingerprints in combination with five machine learning (ML) methods: random forest, partial least squares, extreme gradient boosting, lasso regression, and support vector regression. With a large and diverse set of 14 499 experimental pKa values, pKa models were developed for aliphatic amines. The models demonstrated consistently good prediction statistics and were able to generate accurate prospective predictions as validated with an external test set of 726 pKa values (RMSE 0.45, MAE 0.33, and R2 0.84 by the top model). The factors that may affect prediction accuracy and model applicability were carefully assessed. The results demonstrated that rooted topological torsion fingerprints coupled with ML methods provide a promising approach for developing accurate pKa prediction models.

Evaluation of different virtual screening strategies on the basis of compound sets with characteristic core distributions and dissimilarity relationships.

In this work, computational compound screening strategies on the basis of two- and three-dimensional (2D and 3D) molecular representations were investigated including similarity searching and support vector machine (SVM) ranking. Calculations based on topological fingerprints and molecular shape queries and features were compared. A unique aspect of the analysis setting apart from previous comparisons of 2D and 3D virtual screening approaches has been the design of compound reference, training, and test data sets with controlled incremental increases in intra-set structural diversity and different categories of structural relationships between reference/training and test sets. The use of these data sets made it possible to assess the relative performance of 2D and 3D screening strategies under increasingly challenging conditions ultimately leading to the use of training and test sets with essentially unrelated structures. The results showed that 3D similarity searching had little advantage over 2D searching in identifying active compounds with remote structural relationships. However, 3D SVM models trained on the basis of shape features were superior to other approaches (including 2D SVM) when the detection of structure-activity relationships became increasingly challenging. Such 3D SVM methods has thus far only been little investigated in virtual screening, proving a wealth of opportunities for further analyses.

Simulating the NaK Eutectic Alloy with Monte Carlo and Machine Learning

Combining atomistic simulations and machine learning techniques can expedite significantly the materials discovery process. We present an application of such methodological combination for the prediction of the melting transition and amorphous-solid behavior of the NaK alloy at the eutectic concentration. We show that efficient prediction of these properties is possible via machine learning methods trained on the topological local structural properties. The configurations resulting from Monte Carlo annealing of the NaK eutectic alloy are analyzed with topological attributes based on the Voronoi tessellation and using expectation-maximization clustering and Random Forest classification. We show that the Voronoi topological fingerprints make an accurate and fast prediction of the alloy thermal behavior by cataloguing the atomic configurations into three distinct phases: liquid, amorphous solid, and crystalline solid. Melting is found at 230 K by the sharp split of configurations classified as crystalline solid and as liquid. With the proposed metrics, an arrest-motion temperature is identified at 130–140 K through a top down clustering of the atomic configurations catalogued as amorphous solid. This statistical learning paradigm is not restricted to eutectic alloys or thermodynamics, extends the utility of topological attributes in a significant way, and harnesses the discovery of new material properties.