Essential embeddings of metric graphs on hyperbolic surfaces are constructed and studied.
problem Embedding metric graphs on hyperbolic surfaces with negative Euler characteristic.
method Construction of essential embeddings and study of minimal embeddings.
result Formula to compute essential genus and method for explicit essential embedding.
The study finds infinite meridional essential surfaces in hyperbolic knot exteriors of various genera.
problem Existence of meridional essential surfaces in hyperbolic knot exteriors.
method Essential tangle decompositions and meridional essential embeddings.
result Infinite collection of hyperbolic knots with meridional essential surfaces of arbitrary genus and boundary components.
The study finds infinite knot exteriors with meridional surfaces of any genus and boundary components.
problem Existence of meridional essential surfaces in knot exteriors.
method Analyzing knot exteriors and their surfaces.
result Existence of infinitely many knot exteriors with meridional essential surfaces of any genus and boundary components.
The study embeds graphs on translation surfaces, proving essential-systolic embeddings and estimating surface genera.
problem Embedding graphs on translation surfaces with specific properties.
method Proving essential-systolic embeddings and estimating surface genera.
result Finite graphs admit essential-systolic embeddings on translation surfaces with estimated genera.
Paper proposes a method to refine embeddings efficiently.
problem Efficiently refining embeddings after their creation.
method Uses a Domain Adversarial Network (DAN) with constraints.
result Significantly outperforms state-of-the-art unsupervised algorithms.
The second author and Hara introduced the notion of an essential tribranched surface that is a generalisation of the notion of an essential embedded surface in a 3-manifold. We show that any 3-manifold for which the fundamental group has at least rank four admits an essential tribranched surface.
3D Schoenflies theorem for simply-connected 2-complexes.
problem Embedding simply-connected 2-complexes in 3-space uniquely.
method Proving a 3-dimensional Schoenflies theorem for 3-connected link graphs.
result Essentially unique locally flat embedding into 3-sphere.
The paper introduces the spirality character of the almost fiber part for a closed essentially immersed subsurface of a closed orientable aspherical 3-manifold, which generalizes an invariant due to Rubinstein and Wang. The subsurface is virtually embedded if and only if the almost fiber part is aspiral, and in this ca…
We provide a classification of the essential surfaces of non-negative Euler characteristic in the exteriors of genus two handlebodies embedded in the 3-sphere.
The concern of this paper is to clarify a relationship between the curvatures at infinity and the spectral structure of the Laplacian. In particular, this paper discusses the question of whether there is an eigenvalue of the Laplacian embedded in the essential spectrum or not. The borderline-behavior of the radial curv…
Characterizes 3-punctured spheres in non-hyperbolic link exteriors.
problem Characterizing 3-punctured spheres in non-hyperbolic link exteriors.
method Analyzes non-hyperbolic 3-component links and multibranched surfaces.
result Existence of embeddings of multibranched surfaces in the 3-sphere.
Unique embeddings found for 3-manifolds in S4 with abelian fundamental groups.
problem Embeddings of 3-manifolds in S4 with specific fundamental group properties. method Analyzing the fundamental groups and using homology handles to determine embeddings.
result Essentially unique embeddings for homology handles with perfect commutator subgroups.
The paper finds infinite knots with surfaces of any positive genus.
problem Finding knots with surfaces of arbitrary positive genus.
method Constructing knot exteriors with longitudinal essential surfaces of any positive genus.
result Existence of infinitely many knots with surfaces of any positive genus.
We study the way a strongly irreducible Heegaard surface Σ intersects a knot exterior X embedded in a 3-manifold, and show that if Σ∩∂X consists of simple closed curves which are essential in both Σ and ∂X, then the intersection X∩Σ consists of meridional annuli only. As an applicat…
If X is a compact set, a {\it topological contraction} is a self-embedding f such that the intersection of the successive images fk(X), k>0, consists of one point. In dimension 3, we prove that there are smooth topological contractions of the handlebodies of genus ≥2 whose image is essential. Our proof i…
Paper defines a partial order on multibranched surfaces in 3-manifolds.
problem Classifying and ordering essential multibranched surfaces in 3-manifolds.
method Introducing a partial order on neighborhood equivalence classes of multibranched surfaces.
result Atoroidal and acylindrical surfaces are minimal in the partial order.
The study provides polynomial bounds for essential surfaces in various 3-manifolds.
problem Bounding the number of isotopy classes of embedded essential surfaces in 3-manifolds.
method Restricting to alternating link complements in 3-sphere, then extending results to other classes of cusped 3-manifolds.
result Explicit polynomial bounds on all embedded essential surfaces in 3-manifolds.
Automorphisms of a genus-2 surface extend over 3-sphere.
problem Extending automorphisms of a genus-2 surface over the 3-sphere.
method Classification of essential annuli in genus-2 handlebodies embedded in 3-sphere.
result An automorphism of a genus-2 surface extends to an automorphism of the pair (S^3, Σ) over the 3-sphere.
New Polish word embeddings improve temporal expression recognition.
problem Recognizing temporal expressions in Polish text.
method Created KGR10 corpus, used BiLSTM-CRF model with custom embeddings.
result Custom embeddings enhance BiLSTM-CRF model's performance.
Constructs manifolds with specific spectral properties.
problem Spectral properties of Riemannian manifolds.
method Asymptotically hyperbolic manifolds with sharp curvature bounds.
result Embeds singular continuous spectrum into the essential spectrum of the Laplacian.
Sharp criteria found for dense eigenvalues in Riemannian manifolds.
problem Finding conditions for dense eigenvalues in Riemannian manifolds.
method Sharp criteria on radial curvature for existence of asymptotically flat or hyperbolic manifolds.
result Construction of manifolds with dense embedded point spectrum and sharp curvature bounds.
Polynomial bound on surfaces in hyperbolic 3-manifolds.
problem Bounding the number of surfaces in hyperbolic 3-manifolds.
method Using polynomial functions of the volume of the manifold and the Euler characteristic.
result An upper bound for the number of compact essential surfaces is a polynomial function of the volume of the manifold.
Explicit high-order feature interactions efficiently capture essential structural knowledge about the data of interest and have been used for constructing generative models. We present a supervised discriminative High-Order Parametric Embedding (HOPE) approach to data visualization and compression. Compared to deep emb…
This paper provides a dictionary of closed-form kernel mean embeddings.
problem Challenges in deriving closed-form kernel mean embeddings.
method Comprehensive dictionary and practical tools for deriving new embeddings.
result Provides a Python library with minimal implementations of embeddings.
Counted essential surfaces in a knot's exterior, finding a unique pattern.
problem Counting essential surfaces in a knot's exterior.
method Counted essential surfaces by genus, using Euler totient function. Showed normal surfaces are connected by counting their components. Used Agol, Hass, and Thurston's tools to convert component counting into orbit counting.
result Found a unique pattern in the number of essential surfaces by genus.
Study essential diagrams of knots in SgimesS1 and their relation to virtual knots.
problem Understanding essential diagrams and their relation to virtual knots in SgimesS1. method Analyzing knots with minimal double lines and embedding virtual knot theory.
result Virtual knot theory is embedded in the theory of knots in SgimesS1. Algorithm morphs graphs on hyperbolic surfaces.
problem Morphing graphs on hyperbolic surfaces.
method Generalization of Tutte's spring embedding theorem.
result First algorithm for morphing graphs on hyperbolic surfaces.
This paper classifies Lie groups embeddable into 4D space.
problem Determining the minimum dimensional Euclidean space for Lie group embeddings.
method Used algebraic equations (Gauss and derived Gauss) to classify Lie groups.
result Classified Lie groups embeddable into 4D space.
We give a solution to the equivalence and the embedding problems for smooth CR-submanifolds of complex spaces (and, more generally, for abstract CR-manifolds) in terms of complete differential systems in jet bundles satisfied by all CR-equivalences or CR-embeddings respectively (local and global). For the equivalence p…
GMVAE improves clustering in molecular simulations data.
problem Clustering metastable states in multi-basin free-energy landscapes.
method Gaussian mixture variational autoencoder (GMVAE) for dimensionality reduction and clustering.
result Enhanced clustering of metastable states compared to standard VAEs.
This work proposes an FFT-based DNN model for embedded systems.
problem Large DNN models burden embedded platforms with intensive computation and storage.
method Develops FFT-based training and inference algorithms for DNNs.
result Achieves extraordinary processing speed on embedded platforms.
A new method simplifies HLLE for better robustness.
problem Improving robustness of Hessian locally linear embedding.
method Replacing Hessian with arbitrary weights and modifying manifold dimension.
result Achieved a new LLE-type method called tangential LLE.
In a paper of Menasco and Reid, it is conjectured that there exist no hyperbolic knots in S^3 for which the complement contains a closed embedded totally geodesic surface. In this note, we show that one can get "as close as possible" to a counter-example. Specifically, we construct a sequence of hyperbolic knots {K_n} …
Improves visualization of high-dimensional data by correcting misleading artifacts in neighbor embedding methods.
problem Misleading visual artifacts in t-SNE and UMAP due to lack of data-independent manifold learning interpretations.
method LOO-map framework that extends embedding maps to the entire input space, identifying and correcting map discontinuities.
result Developed point-wise diagnostic scores to detect unreliable embedding points and improve hyperparameter selection.
We show that the following algorithmic problem is decidable: given a 2-dimensional simplicial complex, can it be embedded (topologically, or equivalently, piecewise linearly) in R3? By a known reduction, it suffices to decide the embeddability of a given triangulated 3-manifold X into the 3-sphere S3…
A knot k in a closed orientable 3-manifold is called nonsimple if the exterior of k possesses a properly embedded essential surface of nonnegative Euler characteristic. We show that if k is a nonsimple prime tunnel number one knot in a lens space M (where M does not contain any embedded Klein bottles), then k is a (1,1…
Motivated by the quaternionic geometry corresponding to the homogeneous complex manifolds endowed with (holomorphically) embedded spheres, we introduce and initiate the study of the `quaternionic-like manifolds'. These contain, as particular subclasses, the CR quaternionic and the ρ-quaternionic manifolds. Moreover, …
Embedding right-angled Artin groups in mapping class groups of nonorientable surfaces.
problem Embedding right-angled Artin groups in mapping class groups for nonorientable surfaces.
method Proving embedding for finite full subgraphs and some non-full subgraphs of curve graphs.
result Existence of non-full subgraphs that can be embedded in mapping class groups.
It is shown that given any link-manifold, there is an algorithm to decide if the manifold contains an embedded, essential planar surface; if it does, the algorithm will construct one. If a slope on the boundary of the link-manifold is given, there is an algorithm to determine if the slope bounds an embedded punctured-d…
Researchers mapped clinical jargon to consumer language using embeddings alignment.
problem Mapping and translating clinical jargon to consumer language for better communication.
method Trained embeddings on clinical and consumer language corpora, aligned them using Procrustes algorithm, and refined with adversarial training.
result Procrustes algorithm effectively aligned clinical and consumer language embeddings.
Unified product embeddings improve cross-task performance in e-commerce.
problem Training product embeddings in isolation limits cross-task performance.
method Combining text, clickstream, and image data using denoising auto-encoders, BPR, and Siamese neural networks.
result Unified product embeddings uniformly outperform isolated embeddings across three e-commerce tasks.
Study theta-curves on torus in 3-sphere, classifying them.
problem Classify theta-curves on torus in 3-sphere.
method Analyze nontrivial knots and essential arcs, compute constituent knots, identify structure.
result Complete classification of torus theta-curves up to isotopy and homeomorphism.
Many open problems and important theorems in low-dimensional topology have been formulated as statements about certain 2--complexes called gropes. This paper describes a precise correspondence between embedded gropes in 4--manifolds and the failure of the Whitney move in terms of iterated `towers' of Whitney disks. The…
The paper develops obstructions for embedding 2D complexes into 4D space.
problem Embedding 2D complexes into 4D space and understanding obstructions.
method Uses Goodwillie-Weiss calculus and intersections of Whitney disks.
result Two approaches to obstructions lead to the same result.
A new method for embedding temporal relationships in graphs.
problem Limited performance of existing time-aware graph embedding methods.
method Integrates temporal smoothness and task-oriented negative sampling.
result Improves performance in various tasks, especially entity/relationship/temporal scoping prediction.
A surface F in a 3-manifold M is called cylindrical if M cut open along F admits an essential annulus A. If, in addition, (A,∂A) is embedded in (M,F), then we say that F is strongly cylindrical. Let M be a connected 3-manifold that admits a triangulation using t tetrahedra and F a two-si…
We classify the 3-dimensional hyperbolic polyhedral orbifolds that contain no embedded essential 2-suborbifolds, up to decomposition along embedded hyperbolic triangle orbifolds (turnovers). We give a necessary condition for a 3-dimensional hyperbolic polyhedral orbifold to contain an immersed (singular) hyperbolic tur…
Improved IDS using LSTM and embedding for network traffic data.
problem Network security threats and need for IDS to detect attacks.
method Proposes IDS models using LSTM for time-series and embedding for categorical network traffic data.
result Improves binary classification accuracy to 99.72%.