The study examines extensions of Lie algebras with specific geometric structures.
problem Conditions for preserving geometric structures in Lie algebra extensions.
method Analyzes extensions of Sasakian and Frobenius-Kähler Lie algebras.
result Conditions for maintaining Sasakian or Frobenius-Kähler structures after extensions.
We construct a Kruskal-Szekeres-type analytic extension of the Emparan-Reall black ring, and investigate its geometry. We prove that the extension is maximal, globally hyperbolic, and unique within a natural class of extensions. The key to those results is the proof that causal geodesics are either complete, or approac…
Employing Morse theory for the global control of monodromy and the method of analytic discs for local extension, we establish a version of the global Hartogs extension theorem in a singular setting: for every domain D of an (n-1)-complete normal complex space X of pure dimension n >= 2 and for every compact set K in D …
The paper characterizes positivity of holomorphic vector bundles via Lp-estimates and extensions.
problem Characterizing positivity of holomorphic vector bundles using Lp-estimates and extensions. method Introducing four conditions for Hermitian (or Finsler) vector bundles and characterizing Nakano and Griffiths positivity.
result Characterization of Nakano and Griffiths positivity via specific Lp-conditions. In this note, we prove that a random extension of either the free group FN of rank N≥3 or of the fundamental group of a closed, orientable surface Sg of genus g≥2 is a hyperbolic group. Here, a random extension is one corresponding to a subgroup of either Out(FN) or Mod(Sg) generated by k independ…
Classifies solvable symplectic Lie algebras via extensions and proves structural theorems.
problem Characterizing solvable symplectic Lie algebras.
method Symplectic double extension process.
result Classifies Lie algebras of dimensions up to 6 and proves structural theorems.
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast…
Extends extension formulas for Hodge numbers on complex manifolds.
problem Deformation invariance of Hodge numbers on complex manifolds.
method Introduces a canonical isomorphism between complex differential forms on a manifold and its infinitesimal deformations, generalizing an extension formula.
result Proves several deformation invariance theorems for Hodge numbers.
New model explains how concepts grow based on experience.
problem Existing models assume fixed representation; new model allows for growth.
method Geometric framework with MDL criterion for basis extension.
result Conceptual growth is selective and conservative, exposing or amplifying residual error.
We prove the strong Atiyah conjecture for right-angled Artin groups and right-angled Coxeter groups. More generally, we prove it for groups which are certain finite extensions or elementary amenable extensions of such groups.
Study shows Kahler extensions of abelian groups are products or related to mapping class groups.
problem Characterizing Kahler extensions of abelian groups.
method Surface topology and restrictions on Kahler groups.
result Kahler extensions are virtually products or related to mapping class groups.
In this paper we deal with symplectic Lie algebras. All symplectic structures are determined for dimension four and the corresponding Lie algebras are classified up to equivalence. Symplectic four dimensional Lie algebras are described either as solutions of the cotangent extension problem or as symplectic double exten…
Criterion for lifting smooth contact maps between Carnot groups to central extensions.
problem Existence of smooth contact map lifts between Carnot groups and their central extensions.
method Criterion using pullbacks and Lie algebra cohomology classes.
result Necessary and sufficient conditions for lifting are formulated.
The abstract reviews graph clustering models and their extensions.
problem Graph clustering and model-based approaches.
method Different clustering, inference, and topic models for various graph types.
result Comparison of different approaches to graph clustering.
The motivation of this work is to improve the performance of standard stacking approaches or ensembles, which are composed of simple, heterogeneous base models, through the integration of the generation and selection stages for regression problems. We propose two extensions to the standard stacking approach. In the fir…
Compute central extension of mapping class group from stated skein algebra
problem Compute central extension of mapping class group from stated skein algebra
method Compute central extension of mapping class group from stated skein algebra
result Compute central extension of mapping class group from stated skein algebra
The paper explores new structures on cotangent bundles induced by natural Riemann extensions.
problem Investigating new geometric structures on cotangent bundles.
method Constructing and analyzing almost para-Hermitian and paracontact metric structures.
result Conditions for paracontact metric, K-paracontact metric, and para-Sasakian structures.
Landmark Diffusion Maps reduce manifold learning complexity for high-volume data streams.
problem Complexity of out-of-sample extensions in manifold learning techniques.
method Landmark Diffusion Maps (L-dMaps) using pruned spanning trees or k-medoids to select landmark points.
result Up to 50-fold speedups in out-of-sample extension with less than 4% errors in manifold reconstruction.
Jensen simplifies machine learning and optimization with an extensible toolkit.
problem Complex machine learning and optimization tasks in production environments.
method Develops a framework for convex functions and optimization algorithms, enabling easy deployment and extension.
result Jensen allows for quick model deployment and extension with minimal code, making machine learning accessible.
Extensive rewrite. Tables and proofs have been reformatted and/or rewritten for clarity.
Quandle 2-cocycles yield invariant values for knots under certain algebraic conditions.
problem Defining and understanding invariants of knots using quandle 2-cocycles.
method Analyzing algebraic properties of quandle extensions and their impact on knot invariants.
result The invariant values are constant or follow a restricted form for classical knots under specific conditions.
We address the question of when a covering of the boundary of a surface can be extended to a covering of the surface (equivalently: when is there a branched cover with a prescribed monodromy). If such an extension is possible, when can the total space be taken to be connected? When can the extension be taken to be regu…
We use Klyachko's methods to prove that the natural map G to G-hat, where G is a torsion-free group and G-hat is obtained by adding a new generator t and a new relator w, is surjective only if w is conjugate to gt or gt^{-1} for some g in G. This solves a special case of the surjectivity problem for group extensions, r…
Study of new link types and their invariants, extending previous results.
problem Properties of polynomial invariants and signatures of weakly successively almost positive links.
method Analysis of minimal genus and fibering properties, extending known theorems.
result Extension of Scharlemann-Thompson's theorem to weakly successively almost positive links.
Global invertibility proven for orientation-preserving maps without homeomorphic extension.
problem Global invertibility of orientation-preserving Sobolev maps.
method Avoiding homeomorphic extension, study of strictly orientation-preserving maps.
result Global invertibility can be achieved without homeomorphic extension.
Models predict soccer match outcomes with similar accuracy.
problem Predicting soccer match outcomes (win, draw, loss).
method Compared Bradley-Terry extensions and hierarchical Poisson log-linear model. Parameters estimated using log-likelihood or integrated nested Laplace approximations. Predictive performance assessed using temporal validation.
result Bradley-Terry extensions and hierarchical Poisson log-linear model perform similarly in predicting match outcomes.
In a regression setup with deterministic design, we study the pure aggregation problem and introduce a natural extension from the Gaussian distribution to distributions in the exponential family. While this extension bears strong connections with generalized linear models, it does not require identifiability of the par…
Extends growth properties of hyperbolic groups to their extensions.
problem Quantifying subgroup alternatives in group laws.
method Develops a framework for preserving exponential growth in extensions of hyperbolic groups.
result Automorphism groups of certain hyperbolic and Artin groups have locally uniform exponential growth.
We give necessary and sufficient conditions of the existence of a left-invariant metric of strictly negative Ricci curvature on a solvable Lie group the nilradical of whose Lie algebra g is a filiform Lie algebra n. It turns out that such a metric always exists, except for in the two cases, wh…
In this note we generalize an extension theorem in [5] and [9] of the mean curvature flow to the H^{k} mean curvature flow under some extra conditions. The main difficult problem in proving the extension theorem is to find a suitable version of Michael-Simon inequality for the H^{k} mean curvature flow, and to do a sui…
The most commonly encountered types of complex analytic G-structures and Cartan geometries cannot have singularities of complex codimension 2 or more.
Constructs extensions for Bartnik data to approach mass limits.
problem Finding mass limits for Bartnik data.
method Shi-Tam type metric construction and refined monotonicity.
result Mass of constructed extensions can be made arbitrarily close to half area radius.
The paper proves extension theorems for various geometric properties of groups.
problem Various geometric properties of groups and their extensions.
method Proving extension theorems for asymptotic property C, finite decomposition complexity, and strict finite decomposition complexity.
result Groups with certain properties inherit weaker geometric properties.
Extends Whitney's theorem for functions on rough boundaries.
problem Global extension of manifold-valued functions on domains with rough boundaries.
method Using locally convex spaces of compactly-supported sections of vector bundles, proving the existence of an extension operator.
result The restriction map from everywhere-defined functions is a submersion, allowing local linear splittings.
The paper studies metric connections with torsion on cotangent bundles with modified Riemannian extensions.
problem Characterizing and studying properties of metric connections with torsion on cotangent bundles.
method Characterization of fibre-preserving projective vector fields, semi-symmetry conditions, and Schouten-Van Kampen connection.
result Conditions for semi-symmetry, Ricci semi-symmetry, and local conharmonically flatness with respect to the metric connection.
The abstract presents a new theorem using Ross-Witt Nyström correspondence and Berndtsson's theorem.
problem The abstract tackles the Ohsawa-Takegoshi extension theorem and its applications.
method The approach uses Ross-Witt Nyström correspondence and Berndtsson's theorem in \(\mathbb{C}^*\)-degeneration.
result The approach provides a quick proof of the Ohsawa-Takegoshi extension theorem without limits or singular weights.
The paper proves extension theorems for complex manifolds with Levi q-concave domains.
problem Holomorphic extension theorems for complex manifolds with Levi q-concave domains. method The proof relies on holomorphic Morse inequalities, the Kohn-Rossi extension theorem, and a general Nakano-Griffiths inequality.
result Holomorphic extension theorems for (0,ℓ)-forms on Levi q-concave domains. The paper studies Poisson structures on Bott-Samelson varieties and their applications.
problem Understanding Poisson structures on Bott-Samelson varieties.
method Explicitly express Poisson structure πn on each affine coordinate chart of $Z_{f u}$ and show it is an iterated Poisson Ore extension. result Explicit formulas for Poisson structures on generalized Bruhat cells.
The Gumbel-max trick and its extensions simplify sampling from categorical distributions in machine learning.
problem Sampling from categorical distributions with unnormalized probabilities.
method Extensions of the Gumbel-max trick for various applications.
result Simplified and efficient methods for sampling and gradient estimation.
In this paper, we present the optimization formulation of the Kalman filtering and smoothing problems, and use this perspective to develop a variety of extensions and applications. We first formulate classic Kalman smoothing as a least squares problem, highlight special structure, and show that the classic filtering an…
Analytic completeness criterion applied to constant mean curvature surfaces.
problem Determining the analytic completeness of constant mean curvature surfaces.
method Defining arc-properness and applying it to surfaces in de Sitter 3-space.
result A criterion for the analytic completeness of G-catenoids and their extensions.
This paper presents a new method for dimensionality reduction and out-of-sample extension.
problem Dimensionality reduction and out-of-sample extension in high-dimensional data.
method Adaptive non-linear embedding using positive semi-definite kernel eigenvectors.
result The embedding method is more robust to outliers compared to spectral embedding.
We present an approach to cohomological dimension theory based on infinite symmetric products and on the general theory of dimension called the extension dimension. The notion of the extension dimension $\ExD(X)$ was introduced by A.N.Dranishnikov \cite {D5} in the context of compact spaces and CW complexes. This pa…
Study connects weighted isoperimetric problems to nonlocal elliptic operator extensions.
problem Sharp inequalities for weighted Poisson integrals and their extremizers.
method Formulates variational problem on conformal metric measure space.
result Sharp inequalities are linked to variational problem on CCE manifolds.
Non-negative matrix factorization (NMF) approximates a non-negative matrix X by a product of two non-negative low-rank factor matrices W and H. NMF and its extensions minimize either the Kullback-Leibler divergence or the Euclidean distance between X and WTH to model the Poisson noise or the Gaussian noise.…
The paper extends Bonnet-Myers theorem for manifolds with nonnegative Ricci curvature.
problem Compactness and diameter estimation for manifolds with nonnegative Ricci curvature.
method General curvature conditions for estimating diameter and compactness criteria.
result Established compactness theorems for manifolds with polynomial or exponential Ricci curvature decay.
Study group extensions and bundles on manifolds.
problem Understanding group extensions and their relation to bundles on manifolds.
method Establish and study a correspondence between extensions and equivariant bundles using non-abelian cohomology.
result A correspondence between G^-bundles and twisted Γ-equivariant bundles on Galois Γ-coverings. New method uses DNNs to efficiently extend graph embeddings.
problem Efficiently extending embeddings for novel data samples.
method Deep neural networks for out-of-sample extension.
result DNNs can generalize with equal or better fidelity and require less computation.