Local Topological Constraints Research Articles

3D hand pose and mesh estimation via a generic Topology-aware Transformer model.

In Human-Robot Interaction (HRI), accurate 3D hand pose and mesh estimation hold critical importance. However, inferring reasonable and accurate poses in severe self-occlusion and high self-similarity remains an inherent challenge. In order to alleviate the ambiguity caused by invisible and similar joints during HRI, we propose a new Topology-aware Transformer network named HandGCNFormer with depth image as input, incorporating prior knowledge of hand kinematic topology into the network while modeling long-range contextual information. Specifically, we propose a novel Graphformer decoder with an additional Node-offset Graph Convolutional layer (NoffGConv). The Graphformer decoder optimizes the synergy between the Transformer and GCN, capturing long-range dependencies and local topological connections between joints. On top of that, we replace the standard MLP prediction head with a novel Topology-aware head to better exploit local topological constraints for more reasonable and accurate poses. Our method achieves state-of-the-art 3D hand pose estimation performance on four challenging datasets, including Hands2017, NYU, ICVL, and MSRA. To further demonstrate the effectiveness and scalability of our proposed Graphformer Decoder and Topology aware head, we extend our framework to HandGCNFormer-Mesh for the 3D hand mesh estimation task. The extended framework efficiently integrates a shape regressor with the original Graphformer Decoder and Topology aware head, producing Mano parameters. The results on the HO-3D dataset, which contains various and challenging occlusions, show that our HandGCNFormer-Mesh achieves competitive results compared to previous state-of-the-art 3D hand mesh estimation methods.

Transcription-induced domains form the elementary constraining building blocks of bacterial chromosomes

Transcription generates local topological and mechanical constraints on the DNA fiber, leading to the generation of supercoiled chromosome domains in bacteria. However, the global impact of transcription on chromosome organization remains elusive, as the scale of genes and operons in bacteria remains well below the resolution of chromosomal contact maps generated using Hi-C (~5–10 kb). Here we combined sub-kb Hi-C contact maps and chromosome engineering to visualize individual transcriptional units. We show that transcriptional units form discrete three-dimensional transcription-induced domains that impose mechanical and topological constraints on their neighboring sequences at larger scales, modifying their localization and dynamics. These results show that transcriptional domains constitute primary building blocks of bacterial chromosome folding and locally impose structural and dynamic constraints.

Spherical Hough Transform for Robust Line Detection Toward a 2D–3D Integrated Mobile Mapping System

Line features are of great importance for the registration of the Vehicle-Borne Mobile Mapping System that contains both lidar and multiple-lens panoramic cameras. In this work, a spherical straight- line model is proposed to detect the unified line features in the panoramic imaging surface based on the Spherical Hough Transform. The local topological constraints and gradient image voting are also combined to register the line features between panoramic images and lidar point clouds within the Hough parameter space. Experimental results show that the proposed method can accurately extract the long strip targets on the panoramic images and avoid spurious or broken line-segments. Meanwhile, the line matching precision between point clouds and panoramic images are also improved.

Ollivier–Ricci Curvature Based Spatio-Temporal Graph Neural Networks for Traffic Flow Forecasting

Traffic flow forecasting is a basic function of intelligent transportation systems, and the accuracy of prediction is of great significance for traffic management and urban planning. The main difficulty of traffic flow predictions is that there is complex underlying spatiotemporal dependence in traffic flow; thus, the existing spatiotemporal graph neural network (STGNN) models need to model both temporal dependence and spatial dependence. Graph neural networks (GNNs) are adopted to capture the spatial dependence in traffic flow, which can model the symmetric or asymmetric spatial relations between nodes in the traffic network. The transmission process of traffic features in GNNs is guided by the node-to-node relationship (e.g., adjacency or spatial distance) between nodes, ignoring the spatial dependence caused by local topological constraints in the road network. To further consider the influence of local topology on the spatial dependence of road networks, in this paper, we introduce Ollivier–Ricci curvature information between connected edges in the road network, which is based on optimal transport theory and makes comprehensive use of the neighborhood-to-neighborhood relationship to guide the transmission process of traffic features between nodes in STGNNs. Experiments on real-world traffic datasets show that the models with Ollivier–Ricci curvature information outperforms those based on only node-to-node relationships between nodes by ten percent on average in the RMSE metric. This study indicates that by utilizing complex topological features in road networks, spatial dependence can be captured more sufficiently, further improving the predictive ability of traffic forecasting models.

Efficient Generation of Different Topological Representations of Graphs Beyond-Planarity

Beyond-planarity focuses on combinatorial properties of classes of non-planar graphs that allow for representations satisfying certain local geometric or topological constraints on their edge crossings. Beside the study of a specific graph class for its maximum edge density, another parameter that is often considered in the literature is the size of the largest complete or complete bipartite graph belonging to it. Overcoming the limitations of standard combinatorial arguments, we present a technique to systematically generate all non-isomorphic topological representations of complete and complete bipartite graphs, taking into account the constraints of the specific class. As a proof of concept, we apply our technique to various beyond-planarity classes and achieve new tight bounds for the aforementioned parameter.

Deformable Registration of Coronary Arteries with Topological Constraints for Image-Guided Vascular Interventions.

2D/3D registration of preoperative computed tomography angiography with intra-operative X-ray angiography improves image guidance in percutaneous coronary intervention. However, previous registration methods are inaccurate and time-consuming due to simple deformation and iterative optimization, respectively. In this paper, we propose a novel method for non-rigid registration of coronary arteries based on a point set registration network, which predicts the complex deformation field directly without iterative optimization. In order to maintain the structure of coronary arteries, we advance the classical point set registration network with a loss function containing global and local topological constraints. The method was evaluated on ten clinical data, and it achieved a median chamfer distance of 73.60 pixels with a run time of less than 1s on CPU. Experimental results demonstrate that the proposed method is highly accurate and efficient.

Do housing bubbles generate fiscal bubbles?

This paper examines the effects of the most recent U.S. housing bubble on the fiscal policy of California cities. We use an instrumental variables approach that helps isolate the fiscal consequences of house price appreciation by taking advantage of the influence of local topological constraints on the elasticity of house prices with respect to interest rates. Our analysis generates three main findings. First, despite Prop 13 fiscal constraints, rapid house price appreciation has a strong effect on property tax revenue. Second, the resulting increase in property tax revenue was largely offset by a reduction in other local tax revenue. This offsetting response leaves total city expenditure unrelated to local house prices. In that sense the housing bubble did not produce local fiscal bubbles. Third, we find that fiscal adjustments to house price appreciation depend on local political institutions.

Do Housing Bubbles Generate Fiscal Bubbles? Evidence from California Cities

This paper examines the effects of the most recent U.S. housing bubble on the fiscal policy of California cities. We use an instrumental variables approach that helps isolate fiscal consequences of house price appreciation by taking advantage of the influence of local topological constraints on the elasticity of house prices with respect to interest rates. Our analysis generates three main findings. First, despite Prop 13 fiscal constraints, rapid house price appreciation has a strong effect on property tax revenue. Second, the resulting increase in property tax revenue was largely offset by a reduction in other local tax revenue. This offsetting response leaves total city expenditure unrelated to local house prices. In that sense the housing bubble did not produce local fiscal bubbles. Third, we find that fiscal adjustments to house price appreciation depend on local political institutions.

Multiple routes lead to the native state in the energy landscape of the β-trefoil family

In general, the energy landscapes of real proteins are sufficiently well designed that the depths of local energetic minima are small compared with the global bias of the native state. Because of the funneled nature of energy landscapes, models that lack energetic frustration have been able to capture the main structural features of the transition states and intermediates found in experimental studies of both small and large proteins. In this study we ask: Are the experimental differences in folding mechanisms among members of a particular structural family due to local topological constraints that deviate from the tertiary fold common to the family? The beta-trefoil structural family members IL-1beta, hisactophilin, and acidic/basic FGFs were chosen to address this question. It has been observed that the topological landscape of the beta-trefoils allows for the population of diverse, geometrically disconnected routes that provide energetically similar but structurally distinct ways for this family to fold. Small changes in topology or energetics can alter the preferred route. Taken together, these results indicate that the global fold of the beta-trefoil family determines the energy landscape but that the routes accessed on that landscape might differ as a result of functional requirements of the individual family members.

Digitalizing the backbone torsional dynamics of a folding protein

This work deals with the elucidation of the dominant modes that entrain or subordinate the torsional dynamics of a peptide chain in the long-time limit relevant to the folding process. A timescale separation enables us to view local potential energy contributions as determining coarse constraints to which soft modes are subject, while long-range contributions are responsible for the deviations from the locally-optimized geometries within such constraints. These local steric constraints to backbone torsions are side-chain-dependent and incorporated by taking into account that torsional dynamics are enslaved by a discretized version in which local torsional states are viewed modulo basins of attraction in the Ramachandran (R-) maps. Thus, torsional dynamics are subordinated by the evolution of the so-called LTM (local topological constraints matrix). This basic assumption begets a ‘‘gears caricature’’ of each residue, with as many ‘‘arrested positions ’’ as there are basins in its Ramachandran map. This picture is consistent with the fact that equilibration within R-basins is incommensurably faster than the occurrence of folding events requiring interbasin transitions. Long-range interactions, encoded as a contact matrix (CM), may be determined by factorizing the LTM→CM map through the possible 3-D realizations of each LTM. Each such realization takes into account the dominant detailed torsional isomers within each R-basin. The CM time evolution eventually entrains the LTM dynamics through a feedback mechanism whereby R-basin hopping is slowed down according to the structural hierarchy to which the particular residue belongs, as inferred from the CM. This model incorporates the side-chain dependence of the local torsional entropy of the backbone, shows how the fine (geometric) structure of each R-basin is delineated by the long-range potential contributions, and ultimately reveals how the local steric constraints bias the 3-D organization. In order to test the predictive power of our treatment, the feedback LTM evolution is computed for a relatively large protein endowed with conformational plasticity, the β-lactoglobulin (N=162). The computations reveal distortions of locally-optimized geometries for α-helix patterns as long-range energetic interactions entrain the LTM dynamics in the long-time limit, eventually leading to a predominantly β-sheet motif. In accord with experimental evidence, no molten globule intermediate or hierarchical folding scenario is observed. Instead, as the CM dynamics subordinates the evolution of the LTM, locally-optimized torsional states of the predominantly α-helical intermediates are shown to be distorted while belonging to the same topological class. The dominant structural features of the native folding pattern are identifiable in the destination CM obtained in our simulations.

Discretized torsional dynamics and the folding of an RNA chain.

The aim of this work is to implement a discrete coarse codification of local torsional states of the RNA chain backbone in order to explore the long-time limit dynamics and ultimately obtain a coarse solution to the RNA folding problem. A discrete representation of the soft-mode dynamics is turned into an algorithm for a rough structure prediction. The algorithm itself is inherently parallel, as it evaluates concurrent folding possibilities by pattern recognition, but it may be implemented in a personal computer as a chain of perturbation-translation-renormalization cycles performed on a binary matrix of local topological constraints. This requires suitable representational tools and a periodic quenching of the dynamics for system renormalization. A binary coding of local topological constraints associated with each structural motif is introduced, with each local topological constraint corresponding to a local torsional state. This treatment enables us to adopt a computation time step far larger than hydrodynamic drag time scales. Accordingly, the solvent is no longer treated as a hydrodynamic drag medium. Instead we incorporate its capacity for forming local conformation-dependent dielectric domains. Each translation of the matrix of local topological constraints (LTM's) depends on the conformation-dependent local dielectric created by a confined solvent. Folding pathways are resolved as transitions between patterns of locally encoded structural signals which change within the 1 ns-100 ms time scale range. These coarse folding pathways are generated by a search at regular intervals for structural patterns in the LTM. Each pattern is recorded as a base-pairing pattern (BPP) matrix, a consensus-evaluation operation subject to a renormalization feedback loop. Since several mutually conflicting consensus evaluations might occur at a given time, the need arises for a probabilistic approach appropriate for an ensemble of RNA molecules. Thus, a statistical dynamics of consensus formation is determined by the time evolution of the base pairing probability matrix. These dynamics are generated for a functional RNA molecule, a representative of the so-called group I ribozymes, in order to test the model. The resulting ensemble of conformations is sharply peaked and the most probable structure features the predominance of all phylogenetically conserved intrachain helices tantamount to ribozyme function. Furthermore, the magnesium-aided cooperativity that leads to the shaping of the catalytic core is elucidated. Once the predictive folding algorithm has been implemented, the validity of the so-called "adiabatic approximation" is tested. This approximation requires that conformational microstates be lumped up into BPP's which are treated as quasiequilibrium states, while folding pathways are coarsely represented as sequences of BPP transitions. To test the validity of this adiabatic ansatz, a computation of the coarse Shannon information entropy sigma associated to the specific partition of conformation space into BPP's is performed taking into account the LTM evolution and contrasted with the adiabatic computation. The results reveal a subordination of torsional microstate dynamics to BPP transitions within time scales relevant to folding. This adiabatic entrainment in the long-time limit is thus identified as responsible for the expediency of the folding process.

Folding a protein by discretizing its backbone torsional dynamics.

The aim of this work is to provide a coarse codification of local conformational constraints associated with each folding motif of a peptide chain in order to obtain a rough solution to the protein folding problem. This is accomplished by implementing a discretized version of the soft-mode dynamics on a personal computer (PC). Our algorithm mimics a parallel process as it evaluates concurrent folding possibilities by pattern recognition. It may be implemented in a PC as a sequence of perturbation-translation-renormalization (p-t-r) cycles performed on a matrix of local topological constraints (LTM). This requires suitable representational tools and a periodic quenching of the dynamics required for renormalization. We introduce a description of the peptide chain based on a local discrete variable the values of which label the basins of attraction of the Ramachandran map for each residue. Thus, the local variable indicates the basin in which the torsional coordinates of each residue lie at a given time. In addition, a coding of local topological constraints associated with each secondary and tertiary structural motif is introduced. Our treatment enables us to adopt a computation time step of 81 ps, a value far larger than hydrodynamic drag time scales. Folding pathways are resolved as transitions between patterns of locally encoded structural signals that change within the 10 micros-100 ms time scale range. These coarse folding pathways are generated by the periodic search for structural patterns in the time-evolving LTM. Each pattern is recorded as a contact matrix, an operation subject to a renormalization feedback loop. The validity of our approach is tested vis-a-vis experimentally-probed folding pathways eventually generating tertiary interactions in proteins which recover their active structure under in vitro renaturation conditions. As an illustration, we focus on determining significant folding intermediates and late kinetic bottlenecks that occur within the first 10 ms of the bovine pancreatic trypsin inhibitor renaturation process. The probed cooperativity and nucleation effects, as well as diffusion-collision stabilization of secondary structure are shown to result from the persistence of relatively stable patterns through successive (p-t-r) cycles, thus acting as seeding patterns for further growth or hierarchical development.

Coarsely defined solution to the protein folding problem

In this work we introduce a least-action formulation of the protein folding problem casted within a coarse description of the peptide chain dynamics. Thus, a binary coding of local topological costraints associated to each structural motif is introduced to computationally mimick the long-time dynamics. Folding pathways are resolved as transitions between patterns of locally encoded structural signals. Our variational approach is aimed at identifying the most economic pathway with respect to the stepwise cost in conformational freedom. Our treatment allows us to account for the expediency of the process in proteins effectively capable of in vitro renaturation. We identify the dominant pathway by introducing a coarse version of Lagrangian microscopic dynamics. The coarse folding pathways are generated by a parallel search for structural patterns in a matrix of local topological constraints (LTM) of the chain. Each local topological constraint represents a coarse description of a local torsional state and each pattern is evaluated, translated and finally recorded as a contact matrix (CM), an operation which is subject to a renormalization feedback loop. The renormalization operation periodically introduces long-range correlations on the LTM according to the latest CM generated by translation. Local topological constraints may form consensus regions in portions of the chain which translate as secondary structure motifs or tertiary interactions. Nucleation steps and cooperative effects are accounted for by means of the renormalization operation which warrants the persistence of seeding patterns upon successive LTM evaluations. Relevant folding timescales beyond the realm of molecular-dynamics simulations become accessible through the coarsely codified representation of local torsional constraints. The validity of our approach is tested vis-a-vis experimentally probed folding pathways generating tertiary interactions in proteins which may recover their active structure under in vitro renaturation conditions. We focus on determining significant folding intermediates and the late kinetic bottlenecks which occur within the first 1/100 s of the renaturation process.

Microscopic dynamics from a coarsely defined solution to the protein folding problem

In this work we introduce a least-action formulation of the protein folding problem casted within a coarse description of the soft mode dynamics of the peptide chain. Ultimately, we show that this coarse variational approach can be lifted to yield the microscopic long-time torsional dynamics responsible for the actual folding process. As a first step, a binary coding of local topological constraints associated to each structural motif is introduced to coarsely mimic the long-time dynamics. Folding pathways are initially resolved as transitions between patterns of locally encoded structural signals. Our variational approach is aimed at identifying the most economic pathway with respect to the stepwise cost in conformational freedom. Our treatment allows us to account for the expediency of the process in proteins effectively capable of in vitro renaturation. We identify the dominant pathway by introducing a coarse version of Lagrangian microscopic dynamics. The coarse folding pathways are generated by a parallel search for structural patterns in a matrix of local topological constraints (LTM) of the chain. Each local topological constraint represents a coarse description of a local torsional state and each pattern is evaluated, translated, and finally recorded as a contact matrix (CM), an operation that is subject to a renormalization feedback loop. The renormalization operation periodically introduces long-range correlations on the LTM according to the latest CM generated by translation. Local topological constraints may form consensus regions in portions of the chain that translate as secondary structure motifs or tertiary interactions. Nucleation steps and cooperative effects are accounted for by means of the renormalization operation, which warrants the persistence of seeding patterns upon successive LTM evaluations. Relevant folding time scales beyond the realm of molecular dynamics simulations become accessible through the coarsely codified representation of local torsional constraints. The validity of our approach is tested vis à vis experimentally probed folding pathways generating tertiary interactions in proteins that may recover their active structure under in vitro renaturation conditions. We focus on determining significant folding intermediates and the late kinetic bottlenecks that occur within the first 1100 s of the renaturation process. After the computational accessibility of this coarse solution of the folding problem becomes apparent, we show how to lift our variational problem to microscopic dynamics of the peptide chain. The consistency of our approach is revealed by an actual generation of Newton’s laws at the microscopic level through an inverse projection of the coarse dynamics originally generated through the pattern recognition computation.