Binacox detects multiple cut-points in high-dimensional Cox models for genetic cancer data.
problem Detecting multiple cut-points in high-dimensional Cox models with many continuous features.
method Combines one-hot encoding with binarsity penalty for feature selection and regularization.
result Significantly outperforms state-of-the-art survival models in terms of C-index and computational speed.
The paper confirms a conjecture and extends arrow polynomial to twisted links.
problem Extending classical invariants to virtual and twisted links.
method Checkerboard framings, cut points, and normalized arrow polynomial.
result The normalized arrow polynomial is an invariant for twisted links.
We show that twin building lattices have linear divergence, which implies that all asymptotic cones are without cut-points.
A local cut point is by definition a point that disconnectes its sufficiently small neighborhood. We show that there exists an upper bound for the degree of a local cut point in a metric measure space satisfying the generalized Bishop--Gromov inequality. As a corollary, we obtain an upper bound for the number of ends o…
We show how to associate an R-tree to the set of cut points of a continuum. If X is a continuum without cut points we show how to associate an R-tree to the set of cut pairs of X.
The study identifies conjugate and cut points in ideal fluid motion configurations.
problem Understanding stability and re-convergence of fluid configurations.
method Existence and non-existence of conjugate points in specific fluid configurations, using geometric and physical analysis.
result Existence of conjugate points in Kolmogorov flows and non-existence in Arnold steady states.
Study examines how discretization affects anomaly detection in datasets.
problem Detecting six types of anomalies in datasets using different discretization methods.
method Conducted experiments with SECODA, a general-purpose algorithm for unsupervised anomaly detection.
result Different discretization methods favor the discovery of certain anomaly types.
Groups with semistable peripheral subgroups are semistable.
problem Semistability of fundamental groups in relatively hyperbolic groups.
method Generalization of semistability from 1-ended subgroups to finitely generated subgroups with semistable fundamental groups.
result Semistability of fundamental groups in more general relatively hyperbolic groups.
The paper shows how local cut points imply group splittings in relatively hyperbolic groups.
problem Understanding splittings of relatively hyperbolic groups based on boundary properties.
method Analyzing Bowditch boundaries and using new end definitions.
result The existence of non-parabolic local cut points implies group splittings over 2-ended subgroups.
We show that for an arbitrarily given closed Riemannian manifold M admitting a point p∈M with a single cut point, every closed Riemannian manifold N admitting a point q∈N with a single cut point is diffeomorphic to M if the radial curvatures of N at q are sufficiently close in the sense of L1-n…
We define and give explicit construction of the universal tree-graded space with a given collection of pieces. We apply that to proving uniqueness of asymptotic cones of relatively hyperbolic groups whose peripheral subgroups have unique asymptotic cones. Modulo the Continuum Hypothesis, we show that if an asymptotic c…
FILTER model uses fusion penalized logistic threshold regression for high-dimensional data with unknown cut points.
problem Modeling high-dimensional data with unknown cut points and binary responses.
method Fusion penalized logistic threshold regression (FILTER) model with fused lasso penalty for variable selection.
result Established non-asymptotic error bounds for coefficient estimation and model selection consistency.
ABM automates feature engineering and variable selection for loss-based models.
problem Improving model performance through better feature engineering and variable selection.
method ABM uses group and fused lasso regularization to automatically select cutting points and variables.
result ABM integrates feature engineering, variable selection, and model training.
Study of group boundaries and subgroup properties.
problem Characterizing boundaries of relatively hyperbolic group pairs.
method Analyzing Bowditch boundaries and convergence group actions.
result Rigidity of group pairs leads to specific subgroup properties.
Let G be a one-ended group acting discretely and co-compactly on a CAT(0) space X. We show that the boundary of X has no cut points and that one can detect splittings of G over two-ended groups and recover its JSJ decomposition from the boundary. We show that any discrete action of a group G on a CAT(0) space X satis…
Study proves rigidity results for analytic spacetimes without boundary or timelike boundary.
problem Determining compact subsets and spacetimes from scattering data.
method Analytic spacetimes, thin exterior layers, non-trapping lightlike geodesics.
result Time separation and scattering relations uniquely determine spacetimes.
We prove that ideal boundary of a 7-systolic group is strongly hereditarily aspherical. For some class of 7-systolic groups we show their boundaries are connected and without local cut points, thus getting some results concerning splittings of those groups.
We construct a finitely presented group with infinitely many non-homeomorphic asymptotic cones. We also show that the existence of cut points in asymptotic cones of finitely presented groups does, in general, depend on the choice of scaling constants and ultrafilters.
Study on metric spaces with Möbius self-homeomorphisms and their properties.
problem Characterizing metric spaces with specific homogeneity properties.
method Investigation of homogeneity with Möbius and quasi-Möbius self-homeomorphisms.
result New characterization of snowflakes of boundaries of rank-one symmetric spaces.
BoostForest combines multiple BoostTree models for improved accuracy.
problem Improving ensemble learning performance.
method BoostTree uses gradient boosting and random cut-points. BoostForest bootstraps training data and randomly samples parameters.
result BoostForest outperforms classical ensemble methods on 35 datasets.
In this paper we prove that if a point p in a complete Riemannian manifold is not a cut point of any point whose distance to p is r, then the injectivity radius of p is strictly large than r. As a corollary we give a positive answer to a problem raised by Z. Sun and J. Wan.
We study the bilipschitz equivalence type of tree-graded spaces, showing that asymptotic cones of relatively hyperbolic groups (resp. asymptotic cones of groups containing a cut-point) only depend on the bilipschitz equivalence types of the pieces in the standard (resp. minimal) tree-graded structure. In particular, th…
We give a group theoretic characterization of geodesics with superlinear divergence in the Cayley graph of a right-angled Artin group A(G) with connected defining graph G. We use this to determine when two points in an asymptotic cone of A(G) are separated by a cut-point. As an application, we show that if G does not d…
A method is given for calculating the strict minimum message length (SMML) estimator for 1-dimensional exponential families with continuous sufficient statistics. A set of n equations are found that the n cut-points of the SMML estimator must satisfy. These equations can be solved using Newton's method and this app…
Proves convergence groups on a 2-sphere are Kleinian groups.
problem Proving convergence groups on a 2-sphere are Kleinian groups.
method Analyzing relatively hyperbolic groups with planar boundaries and applying to various versions of the Cannon conjecture.
result Proves relatively hyperbolic groups with planar boundaries are virtually Kleinian.
These notes on Riemannian geometry use the bases bundle and frame bundle, as in Geometry of Manifolds, to express the geometric structures. It has more problems and omits the background material. It starts with the definition of Riemannian and semi-Riemannian structures on manifolds. Affine connections, geodesics, tors…
We show that the co-rays to a ray in a complete non-compact Finsler manifold contain geodesic segments to upper level sets of Busemann functions. Moreover, we characterise the co-point set to a ray as the cut locus of such level sets. The structure theorem of the co-point set on a surface, namely that is a local tree, …
Under the definition of Ricci curvature bounded below for Alexandrov spaces introduced by Zhang-Zhu, we generalize a result by Colding that an n dimentional manifold with Ricci curvature greater or equal to n minus 1 and volume close to that of the unit n sphere is close (in the Gromov-Hausdorff distance) to the sphere…
Tree-graded spaces are generalizations of R-trees. They appear as asymptotic cones of groups (when the cones have cut points). Since many questions about endomorphisms and automorphisms of groups, solving equations over groups, studying embeddings of a group into another group, etc. lead to actions of groups on the asy…
Develops piecewise visual, linearly connected metrics on group boundaries.
problem Creating metrics on group boundaries with cut points.
method Graph of groups decompositions and piecewise visual metrics.
result Linearly connected metrics on boundaries with cut points.
In this paper we provide a classification theorem for 1-dimensional boundaries of groups with isolated flats. Given a group Γ acting geometrically on a CAT(0) space X with isolated flats and 1-dimensional boundary, we show that if Γ does not split over a virtually cyclic subgroup, then ∂X is homeomorp…
By adapting a technique of Molchanov, we obtain the heat kernel asymptotics at the sub-Riemannian cut locus, when the cut points are reached by an r-dimensional parametric family of optimal geodesics. We apply these results to the bi-Heisenberg group, that is, a nilpotent left-invariant sub-Rieman\-nian structure on …
This paper introduces a new method to create mod m almost classical links from virtual knots.
problem Creating mod m almost classical links from virtual knots.
method Using knots in S_g × S^1 to construct m-fold coverings.
result A new family of m-fold coverings over virtual knots are mod m almost classical.
We prove, as our main theorem, the finiteness of topological type of a complete open Riemannian manifold M with a base point p∈M whose radial curvature at p is bounded from below by that of a non-compact model surface of revolution M~ which admits a finite total curvature and has no pair of cut point…
We call a finitely generated group lacunary hyperbolic if one of its asymptotic cones is an R-tree. We characterize lacunary hyperbolic groups as direct limits of Gromov hyperbolic groups satisfying certain restrictions on the hyperbolicity constants and injectivity radii. Using central extensions of lacunary hyperboli…
Study on focal locus of submanifolds in Finsler manifolds, showing regularity and smoothness.
problem Investigating the focal locus of submanifolds in Finsler manifolds.
method Using the normal exponential map and extending Warner's ideas, studying connected components and smoothness of focal time maps.
result Identified an open and dense subset where focal time maps are smooth, provided they are finite.
The method learns to partition event time space for better prediction.
problem Improving event time prediction in clinical settings with limited data.
method Develops a method to learn cut points for partitioning event time space.
result Improved prediction performance on real-world datasets.
Enhances random forests by smoothing predictions for better performance.
problem Suboptimal performance due to piecewise constant predictions in random forests.
method Kernel-based smoothing mechanism to introduce local regularity.
result Smoothed random forest model consistently improves predictive performance.
Let G be a group acting geometrically on a CAT(0) cube complex X. We prove first that G is hyperbolic relative to the collection P of subgroups if and only if the simplicial boundary of X is the disjoint union of a nonempty discrete set, together with a pairwise-disjoint collection of subcomplexes corresponding, in the…
The paper explores the injectivity of the light ray transform on Lorentzian manifolds.
problem Injectivity of the light ray transform on functions and tensors.
method Analyzes injectivity conditions for scalar and tensor fields on stationary and static Lorentzian manifolds.
result Injectivity of the light ray transform on functions and tensors is proven under specific conditions.
Recent results on the maximization of the charged-particle action I in a globally hyperbolic spacetime are discussed and generalized. We focus on the maximization of I over a given causal homotopy class C of curves connecting two causally related events x_0 <= x_1. Action I is proved to admit a maximum on C, and also o…
We study the geometry of nonrelatively hyperbolic groups. Generalizing a result of Schwartz, any quasi-isometric image of a non-relatively hyperbolic space in a relatively hyperbolic space is contained in a bounded neighborhood of a single peripheral subgroup. This implies that a group being relatively hyperbolic with …
In this note, we study the cut locus of the free, step two Carnot groups Gk with k generators, equipped with their left-invariant Carnot-Carathéodory metric. In particular, we disprove the conjectures on the shape of the cut loci proposed in [Myasnichenko - 2002] and [Montanari, Morbidelli - 2016], by exh…
Divergence functions of a metric space estimate the length of a path connecting two points A, B at distance ≤n avoiding a large enough ball around a third point C. We characterize groups with non-linear divergence functions as groups having cut-points in their asymptotic cones. By Olshanskii-Osin-Sapir, that…
New link detection results using closures of 3-braids.
problem Link detection using homology theories.
method Closure operations on 3-braids and homology theories.
result Detection of specific links using link Floer homology, Khovanov homology, and annular Khovanov homology.
Deep learning improves anomaly detection across various fields.
problem Detecting anomalies in data with advanced approaches.
method Survey of deep learning methods for anomaly detection.
result Advancements in deep anomaly detection address unique challenges.
Flexible pipeline for 3D vehicle detection from 2D images.
problem Current methods lack 3D perception of vehicles and other objects.
method Adopt any 2D detection network, fuse with 3D point cloud, develop model fitting algorithm, refine with CNN.
result 3D detection results rank second among algorithms, demonstrating competencies.
Deep learning improves combustor anomaly detection in gas turbines.
problem Improving anomaly detection performance in gas turbine combustors.
method Hierarchically learned features from exhaust gas temperature sensor measurements using deep learning.
result Deep learning-based anomaly detection significantly improved combustor anomaly detection performance.