3DPointCaps++: Learning 3D Representations with Capsule Networks.

We present 3DPointCaps++ for learning robust, flexible and generalizable 3D object representations without requiring heavy annotation efforts or supervision. Unlike conventional 3D generative models, our algorithm aims for building a structured latent space where certain factors of shape variations, such as object parts, can be disentangled into independent sub-spaces. Our novel decoder then acts on these individual latent sub-spaces (i.e. capsules) using deconvolution operators to reconstruct 3D points in a self-supervised manner. We further introduce a cluster loss ensuring that the points reconstructed by a single capsule remain local and do not spread across the object uncontrollably. These contributions allow our network to tackle the challenging tasks of part segmentation, part interpolation/replacement as well as correspondence estimation across rigid / non-rigid shape, and across / within category. Our extensive evaluations on ShapeNet objects and human scans demonstrate that our network can learn generic representations that are robust and useful in many applications.

Framework for shape analysis of white matter fiber bundles.

Diffusion imaging coupled with tractography algorithms allows researchers to image human white matter fiber bundles in-vivo. These bundles are three-dimensional structures with shapes that change over time during the course of development as well as in pathologic states. While most studies on white matter variability focus on analysis of tissue properties estimated from the diffusion data, e.g. fractional anisotropy, the shape variability of white matter fiber bundle is much less explored. In this paper, we present a set of tools for shape analysis of white matter fiber bundles, namely: (1) a concise geometric model of bundle shapes; (2) a method for bundle registration between subjects; (3) a method for deformation estimation. Our framework is useful for analysis of shape variability in white matter fiber bundles. We demonstrate our framework by applying our methods on two datasets: one consisting of data for 6 normal adults and another consisting of data for 38 normal children of age 11 days to 8.5 years. We suggest a robust and reproducible method to measure changes in the shape of white matter fiber bundles. We demonstrate how this method can be used to create a model to assess age-dependent changes in the shape of specific fiber bundles. We derive such models for an ensemble of white matter fiber bundles on our pediatric dataset and show that our results agree with normative human head and brain growth data. Creating these models for a large pediatric longitudinal dataset may improve understanding of both normal development and pathologic states and propose novel parameters for the examination of the pediatric brain.

Compressive Network Analysis.

Modern data acquisition routinely produces massive amounts of network data. Though many methods and models have been proposed to analyze such data, the research of network data is largely disconnected with the classical theory of statistical learning and signal processing. In this paper, we present a new framework for modeling network data, which connects two seemingly different areas: network data analysis and compressed sensing. From a nonparametric perspective, we model an observed network using a large dictionary. In particular, we consider the network clique detection problem and show connections between our formulation with a new algebraic tool, namely Randon basis pursuit in homogeneous spaces. Such a connection allows us to identify rigorous recovery conditions for clique detection problems. Though this paper is mainly conceptual, we also develop practical approximation algorithms for solving empirical problems and demonstrate their usefulness on real-world datasets.

Building Markov state models with solvent dynamics.

BACKGROUND: Markov state models have been widely used to study conformational changes of biological macromolecules. These models are built from short timescale simulations and then propagated to extract long timescale dynamics. However, the solvent information in molecular simulations are often ignored in current methods, because of the large number of solvent molecules in a system and the indistinguishability of solvent molecules upon their exchange. METHODS: We present a solvent signature that compactly summarizes the solvent distribution in the high-dimensional data, and then define a distance metric between different configurations using this signature. We next incorporate the solvent information into the construction of Markov state models and present a fast geometric clustering algorithm which combines both the solute-based and solvent-based distances. RESULTS: We have tested our method on several different molecular dynamical systems, including alanine dipeptide, carbon nanotube, and benzene rings. With the new solvent-based signatures, we are able to identify different solvent distributions near the solute. Furthermore, when the solute has a concave shape, we can also capture the water number inside the solute structure. Finally we have compared the performances of different Markov state models. The experiment results show that our approach improves the existing methods both in the computational running time and the metastability. CONCLUSIONS: In this paper we have initiated an study to build Markov state models for molecular dynamical systems with solvent degrees of freedom. The methods we described should also be broadly applicable to a wide range of biomolecular simulation analyses.

Multiway Non-Rigid Point Cloud Registration via Learned Functional Map Synchronization.

We present SyNoRiM, a novel way to jointly register multiple non-rigid shapes by synchronizing the maps that relate learned functions defined on the point clouds. Even though the ability to process non-rigid shapes is critical in various applications ranging from computer animation to 3D digitization, the literature still lacks a robust and flexible framework to match and align a collection of real, noisy scans observed under occlusions. Given a set of such point clouds, our method first computes the pairwise correspondences parameterized via functional maps. We simultaneously learn potentially non-orthogonal basis functions to effectively regularize the deformations, while handling the occlusions in an elegant way. To maximally benefit from the multi-way information provided by the inferred pairwise deformation fields, we synchronize the pairwise functional maps into a cycle-consistent whole thanks to our novel and principled optimization formulation. We demonstrate via extensive experiments that our method achieves a state-of-the-art performance in registration accuracy, while being flexible and efficient as we handle both non-rigid and multi-body cases in a unified framework and avoid the costly optimization over point-wise permutations by the use of basis function maps.

SceneHGN: Hierarchical Graph Networks for 3D Indoor Scene Generation With Fine-Grained Geometry.

3D indoor scenes are widely used in computer graphics, with applications ranging from interior design to gaming to virtual and augmented reality. They also contain rich information, including room layout, as well as furniture type, geometry, and placement. High-quality 3D indoor scenes are highly demanded while it requires expertise and is time-consuming to design high-quality 3D indoor scenes manually. Existing research only addresses partial problems: some works learn to generate room layout, and other works focus on generating detailed structure and geometry of individual furniture objects. However, these partial steps are related and should be addressed together for optimal synthesis. We propose SceneHGN, a hierarchical graph network for 3D indoor scenes that takes into account the full hierarchy from the room level to the object level, then finally to the object part level. Therefore for the first time, our method is able to directly generate plausible 3D room content, including furniture objects with fine-grained geometry, and their layout. To address the challenge, we introduce functional regions as intermediate proxies between the room and object levels to make learning more manageable. To ensure plausibility, our graph-based representation incorporates both vertical edges connecting child nodes with parent nodes from different levels, and horizontal edges encoding relationships between nodes at the same level. Our generation network is a conditional recursive neural network (RvNN) based variational autoencoder (VAE) that learns to generate detailed content with fine-grained geometry for a room, given the room boundary as the condition. Extensive experiments demonstrate that our method produces superior generation results, even when comparing results of partial steps with alternative methods that can only achieve these. We also demonstrate that our method is effective for various applications such as part-level room editing, room interpolation, and room generation by arbitrary room boundaries.

Next-generation deep learning based on simulators and synthetic data.

Deep learning (DL) is being successfully applied across multiple domains, yet these models learn in a most artificial way: they require large quantities of labeled data to grasp even simple concepts. Thus, the main bottleneck is often access to supervised data. Here, we highlight a trend in a potential solution to this challenge: synthetic data. Synthetic data are becoming accessible due to progress in rendering pipelines, generative adversarial models, and fusion models. Moreover, advancements in domain adaptation techniques help close the statistical gap between synthetic and real data. Paradoxically, this artificial solution is also likely to enable more natural learning, as seen in biological systems, including continual, multimodal, and embodied learning. Complementary to this, simulators and deep neural networks (DNNs) will also have a critical role in providing insight into the cognitive and neural functioning of biological systems. We also review the strengths of, and opportunities and novel challenges associated with, synthetic data.

Topological methods for exploring low-density states in biomolecular folding pathways.

Characterization of transient intermediate or transition states is crucial for the description of biomolecular folding pathways, which is, however, difficult in both experiments and computer simulations. Such transient states are typically of low population in simulation samples. Even for simple systems such as RNA hairpins, recently there are mounting debates over the existence of multiple intermediate states. In this paper, we develop a computational approach to explore the relatively low populated transition or intermediate states in biomolecular folding pathways, based on a topological data analysis tool, MAPPER, with simulation data from large-scale distributed computing. The method is inspired by the classical Morse theory in mathematics which characterizes the topology of high-dimensional shapes via some functional level sets. In this paper we exploit a conditional density filter which enables us to focus on the structures on pathways, followed by clustering analysis on its level sets, which helps separate low populated intermediates from high populated folded/unfolded structures. A successful application of this method is given on a motivating example, a RNA hairpin with GCAA tetraloop, where we are able to provide structural evidence from computer simulations on the multiple intermediate states and exhibit different pictures about unfolding and refolding pathways. The method is effective in dealing with high degree of heterogeneity in distribution, capturing structural features in multiple pathways, and being less sensitive to the distance metric than nonlinear dimensionality reduction or geometric embedding methods. The methodology described in this paper admits various implementations or extensions to incorporate more information and adapt to different settings, which thus provides a systematic tool to explore the low-density intermediate states in complex biomolecular folding systems.

Structural insight into RNA hairpin folding intermediates.

Hairpins are a ubiquitous secondary structure motif in RNA molecules. Despite their simple structure, there is some debate over whether they fold in a two-state or multi-state manner. We have studied the folding of a small tetraloop hairpin using a serial version of replica exchange molecular dynamics on a distributed computing environment. On the basis of these simulations, we have identified a number of intermediates that are consistent with experimental results. We also find that folding is not simply the reverse of high-temperature unfolding and suggest that this may be a general feature of biomolecular folding.

Persistent voids: a new structural metric for membrane fusion.

MOTIVATION: Membrane fusion constitutes a key stage in cellular processes such as synaptic neurotransmission and infection by enveloped viruses. Current experimental assays for fusion have thus far been unable to resolve early fusion events in fine structural detail. We have previously used molecular dynamics simulations to develop mechanistic models of fusion by small lipid vesicles. Here, we introduce a novel structural measurement of vesicle topology and fusion geometry: persistent voids. RESULTS: Persistent voids calculations enable systematic measurement of structural changes in vesicle fusion by assessing fusion stalk widths. They also constitute a generally applicable technique for assessing lipid topological change. We use persistent voids to compute dynamic relationships between hemifusion neck widening and formation of a full fusion pore in our simulation data. We predict that a tightly coordinated process of hemifusion neck expansion and pore formation is responsible for the rapid vesicle fusion mechanism, while isolated enlargement of the hemifusion diaphragm leads to the formation of a metastable hemifused intermediate. These findings suggest that rapid fusion between small vesicles proceeds via a small hemifusion diaphragm rather than a fully expanded one. AVAILABILITY: Software available upon request pending public release. SUPPLEMENTARY INFORMATION: Supplementary data are available on Bioinformatics online.

A package for exact kinetic data structures and sweepline algorithms.

In this paper we present a package for implementing exact kinetic data structures built on objects which move along polynomial trajectories. We discuss how the package design was influenced by various considerations, including extensibility, support for multiple kinetic data structures, access to existing data structures and algorithms in CGAL, as well as debugging. Due to the similarity between the operations involved, the software can also be used to compute arrangements of polynomial objects using a sweepline approach. The package consists of three main parts, the kinetic data structure framework support code, an algebraic kernel which implements the set of algebraic operations required for kinetic data structure processing, and kinetic data structures for Delaunay triangulations in one and two dimensions, and Delaunay and regular triangulations in three dimensions. The models provided for the algebraic kernel support both exact operations and inexact approximations with heuristics to improve numerical stability.

Shape-Attributes of Brain Structures as Biomarkers for Alzheimer's Disease.

We describe a fully automatic framework for classification of two types of dementia based on the differences in the shape of brain structures. We consider Alzheimer's disease (AD), mild cognitive impairment of individuals who converted to AD within 18 months (MCIc), and normal controls (NC). Our approach uses statistical learning and a feature space consisting of projection-based shape descriptors, allowing for canonical representation of brain regions. Our framework automatically identifies the structures most affected by the disease. We evaluate our results by comparing to other methods using a standardized data set of 375 adults available from the Alzheimer's Disease Neuroimaging Initiative (ADNI). Our framework is sensitive to identifying the onset of Alzheimer's disease, achieving up to 88.13% accuracy in classifying MCIc versus NC, outperforming previous methods.

Deformable spanners and applications.

For a set S of points in ℝ(d), an s-spanner is a subgraph of the complete graph with node set S such that any pair of points is connected via some path in the spanner whose total length is at most s times the Euclidean distance between the points. In this paper we propose a new sparse (1 + ε)-spanner with O(n/ε(d)) edges, where ε is a specified parameter. The key property of this spanner is that it can be efficiently maintained under dynamic insertion or deletion of points, as well as under continuous motion of the points in both the kinetic data structures setting and in the more realistic blackbox displacement model we introduce. Our deformable spanner succinctly encodes all proximity information in a deforming point cloud, giving us efficient kinetic algorithms for problems such as the closest pair, the near neighbors of all points, approximate nearest neighbor search (aka approximate Voronoi diagram), well-separated pair decompositions, and approximate k-centers.

Small libraries of protein fragments model native protein structures accurately.

Prediction of protein structure depends on the accuracy and complexity of the models used. Here, we represent the polypeptide chain by a sequence of rigid fragments that are concatenated without any degrees of freedom. Fragments chosen from a library of representative fragments are fit to the native structure using a greedy build-up method. This gives a one-dimensional representation of native protein three-dimensional structure whose quality depends on the nature of the library. We use a novel clustering method to construct libraries that differ in the fragment length (four to seven residues) and number of representative fragments they contain (25-300). Each library is characterized by the quality of fit (accuracy) and the number of allowed states per residue (complexity). We find that the accuracy depends on the complexity and varies from 2.9A for a 2.7-state model on the basis of fragments of length 7-0.76A for a 15-state model on the basis of fragments of length 5. Our goal is to find representations that are both accurate and economical (low complexity). The models defined here are substantially better in this regard: with ten states per residue we approximate native protein structure to 1A compared to over 20 states per residue needed previously. For the same complexity, we find that longer fragments provide better fits. Unfortunately, libraries of longer fragments must be much larger (for ten states per residue, a seven-residue library is 100 times larger than a five-residue library). As the number of known protein native structures increases, it will be possible to construct larger libraries to better exploit this correlation between neighboring residues. Our fragment libraries, which offer a wide range of optimal fragments suited to different accuracies of fit, may prove to be useful for generating better decoy sets for ab initio protein folding and for generating accurate loop conformations in homology modeling.

Compact and informative representation of functional connectivity for predictive modeling.

Resting state functional connectivity holds great potential for diagnostic prediction of neurological and psychiatric illness. This paper introduces a compact and information-rich representation of connectivity that is geared directly towards predictive modeling. Our representation does not require a priori identification of localized regions of interest, yet provides a mechanism for interpretation of classifier weights. Experiments confirm increased accuracy associated with our representation and yield interpretations consistent with known physiology.

Geometric algorithms for sensor networks.

This paper surveys the use of geometric methods for wireless sensor networks. The close relationship of sensor nodes with their embedded physical space imposes a unique geometric character on such systems. The physical locations of the sensor nodes greatly impact on system design in all aspects, from low-level networking and organization to high-level information processing and applications. This paper reviews work in the past 10 years on topics such as network localization, geometric routing, information discovery, data-centric routing and topology discovery.

Voronoi-Based Curvature and Feature Estimation from Point Clouds.

We present an efficient and robust method for extracting curvature information, sharp features, and normal directions of a piecewise smooth surface from its point cloud sampling in a unified framework. Our method is integral in nature and uses convolved covariance matrices of Voronoi cells of the point cloud which makes it provably robust in the presence of noise. We show that these matrices contain information related to curvature in the smooth parts of the surface, and information about the directions and angles of sharp edges around the features of a piecewise-smooth surface. Our method is applicable in both two and three dimensions, and can be easily parallelized, making it possible to process arbitrarily large point clouds, which was a challenge for Voronoi-based methods. In addition, we describe a Monte-Carlo version of our method, which is applicable in any dimension. We illustrate the correctness of both principal curvature information and feature extraction in the presence of varying levels of noise and sampling density on a variety of models. As a sample application, we use our feature detection method to segment point cloud samplings of piecewise-smooth surfaces.

Constructing multi-resolution Markov State Models (MSMs) to elucidate RNA hairpin folding mechanisms.

Simulating biologically relevant timescales at atomic resolution is a challenging task since typical atomistic simulations are at least two orders of magnitude shorter. Markov State Models (MSMs) provide one means of overcoming this gap without sacrificing atomic resolution by extracting long time dynamics from short simulations. MSMs coarse grain space by dividing conformational space into long-lived, or metastable, states. This is equivalent to coarse graining time by integrating out fast motions within metastable states. By varying the degree of coarse graining one can vary the resolution of an MSM; therefore, MSMs are inherently multi-resolution. Here we introduce a new algorithm Super-level-set Hierarchical Clustering (SHC), to our knowledge, the first algorithm focused on constructing MSMs at multiple resolutions. The key insight of this algorithm is to generate a set of super levels covering different density regions of phase space, then cluster each super level separately, and finally recombine this information into a single MSM. SHC is able to produce MSMs at different resolutions using different super density level sets. To demonstrate the power of this algorithm we apply it to a small RNA hairpin, generating MSMs at four different resolutions. We validate these MSMs by showing that they are able to reproduce the original simulation data. Furthermore, long time folding dynamics are extracted from these models. The results show that there are no metastable on-pathway intermediate states. Instead, the folded state serves as a hub directly connected to multiple unfolded/misfolded states which are separated from each other by large free energy barriers.

Reconstruction Using Witness Complexes.

We present a novel reconstruction algorithm that, given an input point set sampled from an object S, builds a one-parameter family of complexes that approximate S at different scales. At a high level, our method is very similar in spirit to Chew's surface meshing algorithm, with one notable difference though: the restricted Delaunay triangulation is replaced by the witness complex, which makes our algorithm applicable in any metric space. To prove its correctness on curves and surfaces, we highlight the relationship between the witness complex and the restricted Delaunay triangulation in 2d and in 3d. Specifically, we prove that both complexes are equal in 2d and closely related in 3d, under some mild sampling assumptions.

Discovering Structural Regularity in 3D Geometry.

We introduce a computational framework for discovering regular or repeated geometric structures in 3D shapes. We describe and classify possible regular structures and present an effective algorithm for detecting such repeated geometric patterns in point- or mesh-based models. Our method assumes no prior knowledge of the geometry or spatial location of the individual elements that define the pattern. Structure discovery is made possible by a careful analysis of pairwise similarity transformations that reveals prominent lattice structures in a suitable model of transformation space. We introduce an optimization method for detecting such uniform grids specifically designed to deal with outliers and missing elements. This yields a robust algorithm that successfully discovers complex regular structures amidst clutter, noise, and missing geometry. The accuracy of the extracted generating transformations is further improved using a novel simultaneous registration method in the spatial domain. We demonstrate the effectiveness of our algorithm on a variety of examples and show applications to compression, model repair, and geometry synthesis.