Quantum genetic algorithm optimizes SVM for efficient human action recognition.
problem Efficiently extracting motion features for human skeleton dynamics.
method Quantum genetic algorithm optimization of SVM with joint angles and variance.
result Proposed approach outperforms conventional SVM by 2.3% accuracy.
Convex optimisation solves inverse kinematics problems more reliably.
problem Finding the best parameters of a kinematic skeleton from observed joint locations.
method Convex optimisation using semidefinite programming.
result The proposed method significantly outperforms local optimisation methods.
mm-Pose detects human skeletons in real-time using mmWave radar and CNNs.
problem Real-time human skeletal posture estimation in various scenarios.
method mmWave radar, radar-to-image representation, forked CNN architecture.
result Accurate predictions for human skeletal joints in 3D space.
SPOT improves differentiable causal discovery by estimating skeleton posterior for latent confounders.
problem Scalable and accurate estimation of causal skeletons in the presence of latent confounders.
method SPOT (Skeleton Posterior-guided OpTimization) framework that estimates skeleton posterior and integrates it with differentiable causal discovery.
result SPOT enhances differentiable causal discovery by reducing the search space and improving accuracy.
The study examines the topology of complements of polytopal skeletons.
problem Characterizing topological properties of polytopal complexes and their skeletons.
method Constructing a long exact sequence relating homologies of skeleton complements and links of faces.
result Characterizations of Cohen-Macaulay and Leray complexes, stacked balls, and neighbourly spheres in terms of skeleton complements.
Criterion for manifold skeletons embeddability in Euclidean space.
problem Embeddability of manifold skeletons in Euclidean space.
method Criterion based on the complement of a submanifold.
result Embeddability of (q−1)-skeleton of a triangulation of an Sp-bundle over Sq into Rp+q. New method for constructing space-filling curves for self-similar sets.
problem Constructing space-filling curves for self-similar sets.
method Skeleton concept and neighbor graph analysis.
result Connected self-similar sets satisfying the finite type condition always possess skeletons.
New triangulations show harder skeletons for hyperbolic orbifolds.
problem Embedding tricky skeletons of hyperbolic orbifolds in Euclidean space.
method Generalized Gromov-Guth inequality for hyperbolic n-orbifolds, finding nearly optimal geodesic triangulations.
result Triangulations of skeletons become increasingly difficult to embed nicely in Euclidean space.
We have completely rewritten the paper, and corrected the proofs. We construct an exponential map at any point in the (n-1)-skeleton minus the (n-2)-skeleton of an n-dimensional Riemannian polyhedron. We have added allover the extra-assumption that the exponential map is totally geodesic at points in the (n-1)-skeleton…
We consider the problem of learning a causal graph over a set of variables with interventions. We study the cost-optimal causal graph learning problem: For a given skeleton (undirected version of the causal graph), design the set of interventions with minimum total cost, that can uniquely identify any causal graph with…
The extension functors between categories of Cartan geometries can be used to define different categories of Cartan geometries with additional morphisms. The Cartan geometries modeled on skeletons can be used for the description of such categories of Cartan geometries and therefore we develop the theory of Cartan geome…
Fixed point sets of certain group actions are contractible.
problem Fixed point sets of group actions on specific types of complexes.
method Analyzing group actions on diagrammatically reducible complexes with fine 1-skeleton.
result Fixed point sets are contractible under certain conditions.
Mapper tool preserves graph structures for better visualization.
problem Graphs can be hard to visualize for large datasets.
method Developed a variation of mapper for weighted, undirected graphs.
result Homology-preserving skeletons enable multi-scale visualization.
Skeleton clustering detects clusters in high-dimensional data without needing prototypes.
problem Detecting clusters in high-dimensional data with irregular shapes.
method Skeleton clustering combines prototype methods, density-based clustering, and hierarchical clustering using surrogate density measures.
result Skeleton clustering reliably detects clusters in multivariate and high-dimensional data.
Tensor-based method simplifies causal skeleton discovery.
problem Discover causal relationships between variables.
method Express associations as tensors to reduce dimensionality.
result Causal skeleton can be determined using pair-wise tensors.
Efficiently learns polytrees with known skeleton in polynomial time and sample complexity.
problem Learning polytrees with known skeleton structure.
method Proposes an efficient algorithm for learning d-polytrees in polynomial time and sample complexity when the skeleton is known. result Establishes finite-sample guarantees for efficient learning of d-polytrees. New theorem shows embedding restrictions for manifold skeletons.
problem Embedding restrictions for triangulated manifolds.
method Proves van Kampen-Flores theorem for manifolds with specific Stiefel-Whitney classes.
result Triangulated manifolds with non-trivial Stiefel-Whitney classes cannot embed into R2d. Our main theorem identifies a class of totally geodesic subgraphs of the 1-skeleton of the pants complex, each isomorphic to the product of two Farey graphs. We deduce the existence of many convex planes in the 1-skeleton of the pants complex.
New method certifies risks of LLM outputs, improving accuracy and reliability.
problem Uncertain and incorrect outputs from large language models.
method Information-lift certificates using PAC-Bayes bounds and skeleton design.
result Achieves 77.0% coverage at 2% risk, outperforming baselines.
The present paper is devoted to the joint motion of two immiscible incompressible liquids in porous media. The liquids have different densities and initially separated by a surface of strong discontinuity (free boundary). We discuss the results of numerical simulations for exact free boundary problems on the microscopi…
DACNN improves skeleton-based action recognition and segmentation.
problem Lack of spatial relationships and non-uniform temporal scalings in skeleton-based data.
method Introduces deep-aligned convolutional neural network (DACNN) with new filters trained on local subsequences.
result DACNN achieves competitive performance compared to state-of-the-art models.
The paper tackles entity induction and reference in visual storytelling.
problem Coherence in visual storytelling through proper entity introduction and reference.
method Building an entity skeleton, using an encoder-decoder framework, and proposing a glocal hierarchical attention model.
result The proposed models outperform the baseline in automatic evaluation metrics and human preference.
Paper analyzes Bezier simplex fitting risks and optimal sampling.
problem Analyzing risks and optimal sampling for Bezier simplex fitting.
method Two fitting methods: inductive skeleton and all-at-once.
result Optimal subsample ratio for inductive skeleton fitting reduces risk.
Proposes a neural network for recognizing 3D skeleton-based interactions.
problem Recognizing two-person interactions from 3D skeleton sequences.
method Uses Gaussian distributions and Riemannian geometry of SPD matrices and matrix groups.
result Achieves competitive results on three benchmarks for 3D human activity understanding.
The paper finds and visualizes unique geometric polyhedra and tori with few vertices.
problem Finding and visualizing geometric polyhedra and tori with specific vertex configurations.
method Using Schlegel diagrams and geometric realization in 3D and 4D space.
result Identifies and visualizes 12 triangulations of the 2-torus and 12 triangulations of the 2D projective plane.
We create a 3-skeleton for a symmetric group's classifying space.
problem Classifying space construction for symmetric groups.
method Combining rewriting systems and combinatorial methods.
result Correctness of the constructed 3-skeleton.
A new graph-based approach for estimating complex data with manifold structure.
problem Regression of large-scale, complex data with underlying geometric structure and noises.
method Constructing a skeleton graph to capture geometric structure, defining metrics, and applying nonparametric regression.
result Statistical guarantees and effectiveness demonstrated through simulations and real data examples.
A method for learning skeleton of Bayesian networks robust to outliers and corruption.
problem Learning the exact skeleton of discrete Bayesian networks from corrupted data.
method Distributionally robust optimization and regression approach, optimizing worst-case risk over distributions within bounded Wasserstein distance or KL divergence.
result Logarithmic sample complexities for successful structure learning of bounded-degree graphs.
Quantization on even-dimensional compact manifolds using cell decomposition.
problem Quantization of compact even-dimensional manifolds.
method Cell decomposition and embedding in CP^d, inducing local Poisson structure and star product.
result Achieved Berezin-type quantization on compact even-dimensional manifolds.
Every cubic graph is a bridge trisection's 1-skeleton for a knotted surface.
problem Understanding cubic graphs and their relation to bridge trisections.
method Proving every Tait-colored cubic graph is a 1-skeleton of a bridge trisection.
result Every Tait-colored cubic graph corresponds to a bridge trisection of a knotted surface.
Study positive scalar curvature on manifolds with skeleton singularities.
problem Positive scalar curvature on manifolds with skeleton singularities.
method Polyhedral comparison theory and edge metrics.
result Edge singularities do not affect the Yamabe type in all dimensions.
The one-skeleton of a G-manifold M is the set of points p in M where dimGp≥dimG−1; and M is a GKM manifold if the dimension of this one-skeleton is 2. Goresky, Kottwitz and MacPherson show that for such a manifold this one-skeleton has the structure of a ``labeled" graph, (Γ,α), and that the equivariant…
Finite simplicial complexes dominate certain manifolds with a bounded number of simplices.
problem Understanding the finite domination of manifolds by simplicial complexes.
method Proving that a manifold can be dominated by the n-skeleton of a finite simplicial complex with a bounded number of simplices. result The total number of simplices in the n-skeleton is bounded above by a constant depending only on n and the embolic volume of the manifold. Defines a new category structure on Weinstein manifolds using h-principle.
problem Defining a category structure on Weinstein manifolds.
method Defines a co/sheaf of categories on the skeleton of a Weinstein manifold using h-principle.
result Existence and uniqueness of the co/sheaf of categories up to isotopy.
We present a constructive proof that there exists a decomposition of the 2-skeleton of the k-dimensional cross polytope βk into closed surfaces of genus g≤1, each with a transitive automorphism group given by the vertex transitive Z2k-action on βk. Furthermore we show that for each $k \equiv …
The paper introduces negative controls to evaluate causal discovery algorithms, improving their reliability.
problem Lack of a general guideline for evaluating causal discovery algorithms.
method Derive exact distributional results under random guessing for evaluation metrics and propose a pipeline for using negative controls.
result Evaluation metrics can achieve very favorable values under random guessing, highlighting the need for negative control results.
Study Monge-Ampère equations on Calabi-Yau hypersurfaces, proving unique solutions and implications for special Lagrangian fibrations.
problem Existence of special Lagrangian fibrations in Calabi-Yau hypersurfaces.
method Non-Archimedean and tropical Monge-Ampère equations on Berkovich and skeleton spaces, proving uniqueness and deriving solutions.
result Unique solutions to tropical and non-Archimedean Monge-Ampère equations, leading to existence of special Lagrangian fibrations.
Study the limit of Calabi-Yau metrics with degenerate skeletons.
problem Understanding the behavior of Calabi-Yau metrics with degenerate skeletons.
method Using polarised degenerations and optimal transport problems.
result Describe the limiting behaviour of the Calabi-Yau potential.
We present a constructive proof, that there exists a decomposition of the 2-skeleton of the k-dimensional cross polytope β^k into closed surfaces of genus \leq 1, each with a transitive automorphism group given by the vertex transitive Z_{2k}-action on β^k. Furthermore we show, that for each k \equiv 1,5(6) the 2-skele…
The paper extends local h-principles to complex structures on Stein manifolds.
problem Existence of local h-principles for complex structures on Stein manifolds.
method Introducing realifications of partial holomorphic relations and proving h-principles for them.
result Local h-principles can be extended to complex structures on Stein manifolds.
Topological methods improve neuron analysis and tracer injection summary.
problem Traditional methods fail to capture the tree-like structure of neurons.
method Discrete Morse (DM) Theory for neuron skeletonization and consensus tree summarization.
result Significant performance improvements over non-topological methods.
S3Attention improves long sequence attention with smoothed skeleton sketching.
problem Quadratic complexity of vanilla Attention makes it unsuitable for long sequence tasks.
method S3Attention uses smoothing and matrix sketching to balance information preservation and computation. result S3Attention significantly outperforms vanilla Attention and other Attention variants. Tensor neural network improves human pose classification from 3D skeleton data.
problem Efficiently processing spatiotemporal data for human pose classification.
method Proposes a tensor-based neural network with three components: spatiotemporal feature construction, tensor fusion, and tensor-based neural network processing.
result Achieves state-of-the-art performance in human pose classification.
We study the singularities of the isotropic skeleton of a Weinstein manifold in relation to Nadler's program of arboreal singularities. By deforming the skeleton via homotopies of the Weinstein structure, we produce a Morse-Bott* representative of the Weinstein homotopy class whose stratified skeleton determines its sy…
We describe a generalization of GKM theory for actions of arbitrary compact connected Lie groups. To an action satisfying the non-abelian GKM conditions we attach a graph encoding the structure of the non-abelian 1-skeleton, i.e., the subspace of points with isotopy rank at most one less than the rank of the acting gro…
We study Weinstein 4-manifolds which admit Lagrangian skeleta given by attaching disks to a surface along a collection of simple closed curves. In terms of the curves describing one such skeleton, we describe surgeries that preserve the ambient Weinstein manifold, but change the skeleton. The surgeries can be iterated …
Constructs unique bases for CY varieties over valued fields.
problem Finding unique bases for CY varieties over valued fields.
method Uses techniques from higher rank degenerations in K-stability.
result Induces canonical functions on skeletons and agrees with tropicalizations of theta functions.
3D pseudomanifolds have minimal g2 when their skeletons match star of a vertex.
problem Finding 3D pseudomanifolds with minimal g2.
method Analyzing the structure of the one-skeleton and link of vertices.
result In 3D, only structures matching the star of a vertex have minimal g2.