This paper completes the classification of discrete conformal structures on surfaces.
problem Classifying discrete conformal structures on surfaces.
method Axiomatic approach and study of existing structures.
result Find new classes of discrete conformal structures, including generalized circle packing metrics.
The paper classifies para-Kähler structures on Lie groups.
problem Classifying para-Kähler structures on Lie groups.
method Classification based on symplectic Lie algebras, finding compatible para-complex structures and pseudo-Riemannian metrics.
result Explicit forms of para-complex structures and pseudo-Riemannian metrics are found.
Improved protein structure classification using weighted graphlets and deep neural networks.
problem Protein structure classification for function prediction.
method Developed a weighted network and graphlet-based measure, combined with a deep neural network.
result Significantly improved performance on 36 real datasets compared to existing methods.
Structured entropy improves classification performance on structured targets.
problem Cross-entropy loss fails to account for target variable structure.
method Proposes structured entropy, a generalization of entropy using random partitions.
result Structured cross-entropy loss yields better results on classification problems with known structure.
Classifies homogeneous Riemannian structures on 3D Lie groups.
problem Classifying homogeneous Riemannian structures on 3D Lie groups.
method Classification based on left invariant metrics and previous classifications.
result Complete classification of homogeneous Riemannian structures on 3D Lie groups.
New method classifies symplectic structures on Lie groups.
problem Classifying left-invariant symplectic structures on Lie groups.
method Using moduli space of left-invariant nondegenerate 2-forms.
result Classified left-invariant symplectic structures on specific Lie groups.
This paper converts NACE classification into embeddings to preserve hierarchical structure.
problem Preserving hierarchical structure in NACE classification while reducing dimensions.
method Custom metrics for hierarchical structure retention; state-of-the-art models and dimensionality reduction.
result The proposed approach effectively preserves hierarchical structures in NACE classification.
Classifies tight contact structures with special symmetries.
problem Classifying tight contact structures with specific symmetries.
method Proves classification results for tight contact structures in 3-space, ball, and sphere with a new integral torsion.
result New integral torsion dictates a splitting between equivalence classes.
Paper uses genome Markov structure for outlier detection and read classification.
problem Identifying outliers and classifying reads in genome databases.
method Applying second-order Markov models to triplet base distributions.
result Improved accuracy in outlier identification and read classification.
Complete classification of para-Kähler structures on Lie groups.
problem Classifying para-Kähler structures on Lie groups.
method Complete classification via automorphism consideration.
result Classification of para-Kähler structures on four-dimensional Lie groups.
This paper completes the classification of certain nilpotent Lie groups with specific geometric structures.
problem Classifying nilpotent Lie groups with purely coclosed G2-structures.
method Analyzing seven-dimensional nilpotent Lie groups of various steps.
result Classification of indecomposable 5- and 6-step nilpotent Lie groups with these structures.
Recently, there have been several breakthroughs in the classification of tight contact structures. We give an outline on how to exploit methods developed by Ko Honda and John Etnyre to obtain classification results for specific examples of small Seifert manifolds.
Electroencephalography (EEG) is a useful way to implicitly monitor the users perceptual state during multimedia consumption. One of the primary challenges for the practical use of EEG-based monitoring is to achieve a satisfactory level of accuracy in EEG classification. Connectivity between different brain regions is a…
This text is about geometric structures imposed by robust dynamical behaviour. We explain recent results towards the classification of partially hyperbolic systems in dimension 3 using the theory of foliations and its interaction with topology. We also present recent examples which introduce a challenge in the classifi…
Classification of G2-structures on Lie groups with Ricci pinched conditions.
problem Classifying G2-structures on Lie groups under specific geometric conditions.
method Complete classification of left-invariant closed G2-structures on Lie groups, extremally Ricci pinched, up to equivalence and scaling.
result Five distinct G2-structures on five different completely solvable Lie groups, with one unimodular case being exact.
In this paper we consider three deeply connected classificational problems on four-dimensional manifolds. First we consider and describe locally regular distributions. Second we give a classification of almost complex structures of general position in terms of distributions. Finally we classify nondegenerate Monge-Ampe…
Several real problems ranging from text classification to computational biology are characterized by hierarchical multi-label classification tasks. Most of the methods presented in literature focused on tree-structured taxonomies, but only few on taxonomies structured according to a Directed Acyclic Graph (DAG). In thi…
We propose a method to visualize class similarity in large-scale classifiers.
problem Analyzing hierarchical structures and relationships in large-scale classification.
method Compute class similarity based on prediction scores and visualize the class similarity matrix.
result Visualizing class similarity matrices reveals hierarchical structures and relationships.
This work refines Cover's theory for binary classification on low-dimensional data.
problem The challenge of analyzing how low-dimensional data structures affect classification models.
method Refines Cover's function-counting theory to account for low-dimensional data structure.
result Derives dichotomy counts and analyzes the impact of data structure on classification models.
New framework tackles geometric structure existence and classification.
problem Existence and classification of geometric structures.
method Developed a new framework of relative algebroids.
result New framework addresses geometric structure problems.
Ray-based framework classifies high-dimensional structures with reduced data.
problem Classifying complex geometrical structures in high dimensions.
method Uses minimal one-dimensional rays to construct structure fingerprints.
result Performance of ray-based classifier matches traditional methods for low-dimensional systems.
Paper investigates methods to improve classification by inducing a hierarchy from flat labels.
problem Improving classification performance on datasets lacking a natural hierarchy.
method The approach involves clustering conditional distributions and using a hierarchical classifier with the induced hierarchy.
result The methods can discover latent hierarchies and improve accuracy in various applications.
The study classifies b-contact structures on b-manifolds, especially on S3.
problem Existence and classification of b-contact structures on b-manifolds. method Existence h-principle and classification method. result Classification of b-contact structures on S3. Suffering from the multi-view data diversity and complexity for semi-supervised classification, most of existing graph convolutional networks focus on the networks architecture construction or the salient graph structure preservation, and ignore the the complete graph structure for semi-supervised classification contri…
This research classifies invariant complex structures and Kähler metrics on principal bundles.
problem Classifying invariant complex structures and Kähler metrics on principal bundles.
method Using Wang's theory of invariant connections and the Levi-Civita connection, the study provides direct geometric proofs and extends the classification from Hermitian to general symmetric spaces.
result The invariant integrable complex structures are unique in the reduced frame bundles of the upper half-plane and complex projective spaces.
The Ozsvath-Szabo contact invariant is a complete classification invariant for tight contact structures on small Seifert fibered 3-manifolds which are L-spaces.
Classifies and computes cohomologies of complex structures on Lie groups.
problem Classifying and computing cohomologies of complex structures on Lie groups.
method Complete classification and computation of invariant cohomologies for left invariant structures.
result Computed invariant cohomologies for various generalized complex and Kähler structures.
The existence of some complex geometrical structures on a compact manifold such as complex structures, Kaehler (pseudo-Kaehler) structures often impose certain restrictions on its underling topological or differentiable manifold. In this article we survey recent developments in the study of the existence, classificatio…
We give a local classification of generalized complex structures. About a point, a generalized complex structure is equivalent to a product of a symplectic manifold with a holomorphic Poisson manifold. We use a Nash-Moser type argument in the style of Conn's linearization theorem.
Hierarchical text classification has many real-world applications. However, labeling a large number of documents is costly. In practice, we can use semi-supervised learning or weakly supervised learning (e.g., dataless classification) to reduce the labeling cost. In this paper, we propose a path cost-sensitive learning…
This paper discovers classification models from sequential data without prior knowledge.
problem Lack of prior knowledge in defining kernels for online classification.
method Adapts GP-based time-series structure discovery with SMC to learn new features from sequential data.
result Improves classification accuracy by 10% on real-world data.
Completes classification of G2-structures on specific nilpotent Lie groups.
problem Classifying seven-dimensional nilpotent Lie groups with purely coclosed G2-structures.
method Analyzing nilpotent Lie groups of various steps and dimensions.
result Classification of indecomposable 5- and 6-step nilpotent Lie groups.
Proposes a graph learning framework for clustering and semi-supervised classification.
problem Graph-based clustering and semi-supervised classification techniques have shown impressive performance but lack explicit cluster structure.
method Uses self-expressiveness of samples for global structure and adaptive neighbor approach for local structure. Incorporates rank constraint to ensure optimal performance.
result The proposed method achieves better performance than state-of-the-art methods in clustering and semi-supervised classification.
HyperBERT enhances BERT for node classification on text-attributed hypergraphs.
problem Challenges in capturing hypergraph structure and text attributes in node classification.
method Mixing hypergraph-aware layers with BERT for improved node classification.
result HyperBERT achieves state-of-the-art results on text-attributed hypergraph benchmarks.
We call two Engel structures isotopic if they are homotopic through Engel structures by a homotopy that fixes the characteristic line field. In the present paper we define an isotopy invariant of Engel structures on oriented circle bundles over closed oriented three-manifolds and apply it to give an isotopy classificat…
Improves GNN prediction sets with conformal prediction for node classification.
problem Lack of predictive uncertainty for GNN models.
method Adapted conformal prediction for graph data, weighting scores based on graph structure.
result Better calibrated and tighter prediction sets than naive conformal prediction.
We study a number of local and global classification problems in generalized complex geometry. In the first topic, we characterize the local structure of generalized complex manifolds by proving that a generalized complex structure near a complex point arises from a holomorphic Poisson structure. In the proof we use a …
The article classifies G2-structures with conformally flat metrics.
problem Identifying G2-structures with specific geometric properties.
method Classifying closed G2-structures with conformally flat metrics.
result Any closed G2-structure with conformally flat metric is locally equivalent to one of three explicit examples.
Researchers found all homogeneous structure tensors on two specific 3D manifolds.
problem Classifying homogeneous structure tensors on specific 3D manifolds.
method Determined all homogeneous structure tensors on S2imesR and H2imesR. result Complete classification of homogeneous structure tensors on three-dimensional homogeneous Riemannian manifolds.
The study classifies flat solvmanifolds and finds G2-structures on them.
problem Classifying and finding G2-structures on flat solvmanifolds. method Classification of flat splittable solvmanifolds and search for compatible G2-structures. result Examples of compact flat manifolds with specific G2-structures. Paper classifies structures on 5D manifolds with specific rank and conditions.
problem Classifying tangent distributions on 5D manifolds.
method Established necessary and sufficient topological condition for existence.
result Classification of structures up to homotopy as formal Cartan distributions.
Pixel-wise classification, where each pixel is assigned to a predefined class, is one of the most important procedures in hyperspectral image (HSI) analysis. By representing a test pixel as a linear combination of a small subset of labeled pixels, a sparse representation classifier (SRC) gives rather plausible results …
Cellular Electron Cryo-Tomography (CECT) is a powerful 3D imaging tool for studying the native structure and organization of macromolecules inside single cells. For systematic recognition and recovery of macromolecular structures captured by CECT, methods for several important tasks such as subtomogram classification a…
We use Bott-Chern cohomology to measure the non-Kählerianity of 6-dimensional nilmanifolds endowed with the invariant complex structures in M. Ceballos, A. Otal, L. Ugarte, and R. Villacampa's classification, [Invariant Complex Structures on 6-Nilmanifolds: Classification, Frölicher Spectral Sequence and Special Hermit…
We study the classification performance of Kronecker-structured models in two asymptotic regimes and developed an algorithm for separable, fast and compact K-S dictionary learning for better classification and representation of multidimensional signals by exploiting the structure in the signal. First, we study the clas…
Text classification on drug SMILES strings yields competitive drug type classification results.
problem Classifying drug types using conventional text classification methods.
method Treated drug SMILES as sentences and applied basic NLP methods for classification.
result Competitive drug type classification results achieved.
Proposes GIL for semi-supervised graph classification.
problem Semi-supervised classification of graph data with limited labeled nodes.
method Graph Inference Learning framework that learns node label inference from graph topology.
result Significantly improves semi-supervised node classification performance.
We extend the characterization of the integrability of an almost complex structure J on differentiable manifolds via the vanishing of the Frölicher-Nijenhuis bracket [J,J]FN to an analogous characterization of torsion-free G2-structures and torsion-free Spin(7)-structures. We also explain the Fernández-Gray…