Classification of Protein-Binding Sites Using a Spherical Convolutional Neural Network

The analysis and comparison of protein-binding sites aid various applications in the drug discovery process, e.g., hit finding, drug repurposing, and polypharmacology. Classification of binding sites has been a hot topic for the past 30 years, and many different methods have been published. The rapid development of machine learning computational algorithms, coupled with the large volume of publicly available protein–ligand 3D structures, makes it possible to apply deep learning techniques in binding site comparison. Our method uses a cutting-edge spherical convolutional neural network based on the DeepSphere architecture to learn global representations of protein-binding sites. The model was trained on TOUGH-C1 and TOUGH-M1 data and validated with the ProSPECCTs datasets. Our results show that our model can (1) perform well in protein-binding site similarity and classification tasks and (2) learn and separate the physicochemical properties of binding sites. Lastly, we tested the model on a set of kinases, where the results show that it is able to cluster the different kinase subfamilies effectively. This example demonstrates the method’s promise for lead hopping within or outside a protein target, directly based on binding site information

Learning Equivariant Representations

State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of this principle, their defining characteristic being the shift-equivariance. By sliding a filter over the input, when the input shifts, the response shifts by the same amount, exploiting the structure of natural images where semantic content is independent of absolute pixel positions. This property is essential to the success of CNNs in audio, image and video recognition tasks. In this thesis, we extend equivariance to other kinds of transformations, such as rotation and scaling. We propose equivariant models for different transformations defined by groups of symmetries. The main contributions are (i) polar transformer networks, achieving equivariance to the group of similarities on the plane, (ii) equivariant multi-view networks, achieving equivariance to the group of symmetries of the icosahedron, (iii) spherical CNNs, achieving equivariance to the continuous 3D rotation group, (iv) cross-domain image embeddings, achieving equivariance to 3D rotations for 2D inputs, and (v) spin-weighted spherical CNNs, generalizing the spherical CNNs and achieving equivariance to 3D rotations for spherical vector fields. Applications include image classification, 3D shape classification and retrieval, panoramic image classification and segmentation, shape alignment and pose estimation. What these models have in common is that they leverage symmetries in the data to reduce sample and model complexity and improve generalization performance. The advantages are more significant on (but not limited to) challenging tasks where data is limited or input perturbations such as arbitrary rotations are present

Eigenspectra: A Framework for Identifying Spectra from 3D Eclipse Mapping

Planetary atmospheres are inherently 3D objects that can have strong gradients in latitude, longitude, and altitude. Secondary eclipse mapping is a powerful way to map the 3D distribution of the atmosphere, but the data can have large correlations and errors in the presence of photon and instrument noise. We develop a technique to mitigate the large uncertainties of eclipse maps by identifying a small number of dominant spectra to make them more tractable for individual analysis via atmospheric retrieval. We use the eigencurves method to infer a multi-wavelength map of a planet from spectroscopic secondary eclipse light curves. We then apply a clustering algorithm to the planet map to identify several regions with similar emergent spectra. We combine the similar spectra together to construct an "eigenspectrum" for each distinct region on the planetary map. We demonstrate how this approach could be used to isolate hot from cold regions and/or regions with different chemical compositions in observations of hot Jupiters with the James Webb Space Telescope (JWST). We find that our method struggles to identify sharp edges in maps with sudden discontinuities, but generally can be used as a first step before a more physically motivated modeling approach to determine the primary features observed on the planet.Comment: 13 pages, 17 figures, accepted to MNRA

Robust Object Classification Approach using Spherical Harmonics

Point clouds produced by either 3D scanners or multi-view images are often imperfect and contain noise or outliers. This paper presents an end-to-end robust spherical harmonics approach to classifying 3D objects. The proposed framework first uses the voxel grid of concentric spheres to learn features over the unit ball. We then limit the spherical harmonics order level to suppress the effect of noise and outliers. In addition, the entire classification operation is performed in the Fourier domain. As a result, our proposed model learned features that are less sensitive to data perturbations and corruptions. We tested our proposed model against several types of data perturbations and corruptions, such as noise and outliers. Our results show that the proposed model has fewer parameters, competes with state-of-art networks in terms of robustness to data inaccuracies, and is faster than other robust methods. Our implementation code is also publicly available1

Efficient Generalized Spherical CNNs

Many problems across computer vision and the natural sciences require the analysis of spherical data, for which representations may be learned efficiently by encoding equivariance to rotational symmetries. We present a generalized spherical CNN framework that encompasses various existing approaches and allows them to be leveraged alongside each other. The only existing non-linear spherical CNN layer that is strictly equivariant has complexity OpC2L5q, where C is a measure of representational capacity and L the spherical harmonic bandlimit. Such a high computational cost often prohibits the use of strictly equivariant spherical CNNs. We develop two new strictly equivariant layers with reduced complexity OpCL4q and OpCL3 log Lq, making larger, more expressive models computationally feasible. Moreover, we adopt efficient sampling theory to achieve further computational savings. We show that these developments allow the construction of more expressive hybrid models that achieve state-of-the-art accuracy and parameter efficiency on spherical benchmark problems

Nonlinear data analysis of the CMB

Das kosmologische Prinzip der Homogenität und statistischen Isotropie des Raumes ist eine fundamentale Annahme der modernen Kosmologie. Auf dieser Basis wird die Existenz einer inflationären Phase im jungen Universum postuliert, welche wiederum primordiale Gaußverteilte Fluktuationen vorhersagt, welche sich im kosmischen Mikrowellenhintergrund als Temperatur- und Polarisationsanisotropien manifestieren. Die Grundidee meiner Arbeit war die Weiterentwicklung einer modellunabhängigen Untersuchungsmethode, welche die Gauß’sche Hypothese für die Dichtefluktuationen testet, wobei die Gaußianität eines Ensembles mit der Zufallsverteilung der Fourier Phasen im Phasenraum definiert wird. Die Methode basiert auf einer nichtlinearen Datenanalyse mit Hilfe von Surrogatkarten, welche die linearen Eigenschaften eines Datensatzes imitieren. Im Rahmen der Surrogatmethode habe ich unter Verwendung zweier verschiedener Bildanalyseverfahren, nämlich den Minkowski Funktionalen und den Skalierungsindizes, beide sensitiv auf Korrelationen höherer Ordnung, Karten der kosmischen Mikrowellenhintergrundstrahlung des WMAP und des Planck Experimentes auf skalenabhängige Phasenkorrelationen untersucht. Ein Schwerpunkt lag hierbei auf Studien zu hemisphärischen Asymmetrien und zum Einfluss der galaktischen Ebene auf die Resultate. Aus der Analyse der Phasenkorrelationen im Phasenraum entwickelte ich neue Methoden zur Untersuchung von Korrelationen zwischen Statistiken höherer Ordnung im Ortsraum und den Informationen des Phasenraumes. Beide Bildanalyseverfahren detektierten Phasenkorrelationen auf den größten Skalen des kosmischen Mikrowellenhintergrundes in vergleichbarer Ausprägung. Der Einfluss der galaktischen Ebene auf diese Resultate zeigte sich in Cutsky Analysen und beim Vergleichen verschiedener Vordergrundsubtraktionsverfahren innerhalb der zwei Experimente als vernachlässigbar gering. Hemisphärische Anomalien auf den größten Skalen der Hintergrundstrahlung wurden wiederholt bestätigt. Die Parametrisierung von Nicht-Gaußianität durch den fNL-Parameter zeigte sich beim Vergleich von fNL-Simulationen mit experimentellen Daten als unzureichend. In Analysen der Daten mit Hilfe von Bianchi-Modellen zeigten sich Hinweise auf eine nicht-triviale Topologie des Universums. Die Resultate meiner Arbeit deuten auf eine Verletzung des standardmäßigen Single Field Slow-Roll Modells für Inflation hin, und widersprechen den Vorhersagen von isotropen Kosmologien. Meine Studien eröffnen im Allgemeinen neue Wege zu einem besseren Verständnis von Nicht-Gauß'schen Signaturen in komplexen räumlichen Strukturen, insbesondere durch die Analyse von Korrelationen der Fourier-Phasen und deren Einfluss auf Statistiken höherer Ordnung im Ortsraum. In naher Zukunft können die Polarisationsdaten des Planck Experimentes weiteren Aufschluss über die Anomalien der kosmischen Mikrowellenhintergrundstrahlung bringen. Die Beschreibung des polarisierten Mikrowellenhintergrundes innerhalb einer Phasenanalyse wäre eine wichtige Ergänzung zu klassischen Studien

Improving the census of open clusters in the Milky Way with data from Gaia

For over a century, open clusters have been a key tool for understanding stellar and galactic evolution. Now, thanks to groundbreaking new astrometric and photometric data from the European Space Agency's Gaia satellite, it is possible to study open clusters to never before seen levels of accuracy and precision. In this thesis, I develop and apply new methodologies to improve the census of open clusters with data from Gaia. I focus on using modern, efficient, and statistically rigorous techniques, aiming to maximise the reliability and usefulness of the open cluster census despite the many challenges of working with the billion-star dataset of Gaia. Firstly, I conducted a comparative study of clustering algorithms for retrieving open clusters blindly from Gaia data. I found that a previously untrialed algorithm, HDBSCAN, is the most sensitive algorithm for open cluster recovery. Next, using this methodology, I used Gaia DR3 data to create the largest homogeneous catalogue of open clusters to date, recovering a total of 7167 clusters -- 2387 of which are candidate new objects. I developed an approximate Bayesian neural network for classifying the reliability of the colour-magnitude diagrams of the clusters in the census. Additionally, I used a modification of this network to infer parameters such as the age and extinction of these clusters. Finally, since many of the objects in my catalogue appeared more compatible with moving groups, I measured accurate masses, Jacobi radii, and velocity dispersions for these clusters, thus creating the largest catalogue of these parameters for open clusters to date. Using said parameters, I showed that no more than 5619 of the clusters in my catalogue are compatible with bound open clusters. I used my mass estimates to derive an approximate completeness estimate for the Gaia DR3 open cluster census, finding that the approximate 100% completeness limit depends strongly on cluster mass. The results of this thesis show that it is possible to reliably create a catalogue of open clusters with a single blind search, in addition to measuring parameters for these objects. The methods developed in this thesis will be applicable to future data releases from Gaia and other sources