arXiv research

This paper establishes an equivalence between transitive double Lie algebroids and core diagrams.

New peripheral structure for core groups detects noninvertible knots.

In various application areas, networked data is collected by measuring interactions involving some specific set of core nodes. This results in a network dataset containing the core nodes along with a potentially much larger set of fringe nodes that all have at least one interaction with a core node. In many settings, t…

AL$\ell_0$CORE tensor decomposition reduces computational cost for sparse count data.

Interbank markets are often characterised in terms of a core-periphery network structure, with a highly interconnected core of banks holding the market together, and a periphery of banks connected mostly to the core but not internally. This paradigm has recently been challenged for short time scales, where interbank ma…

We introduce the notion of the visual core of a hyperbolic 3-manifold N and explore its basic properties. The visual core can be thought of as a harmonic analysis analogue of the convex core. We investigate circumstances in which the visual core of a cover N' of N embeds under the covering map from N' to N. We apply th…

New combinatorial structures represent subgroups of surface groups, analogous to Stallings core graphs.

Paper introduces a core-periphery model for identifying informative network structures.

Estimates covariance matrices for matrix-variate data via core covariance geometry.

Probabilistic programming aids in automatically dating ice cores, reducing manual error and uncertainty.

Classifies stability of flat-core $p$-elasticae pinned at boundaries.

The term "CoRE kernel" stands for correlation-resemblance kernel. In many applications (e.g., vision), the data are often high-dimensional, sparse, and non-binary. We propose two types of (nonlinear) CoRE kernels for non-binary sparse data and demonstrate the effectiveness of the new kernels through a classification ex…

We obtain upper and lower bounds on the difference between the renormalized volume and the volume of the convex core of a convex cocompact hyperbolic 3-manifold which depend on the injectivity radius of the boundary of the universal cover of the convex core and the Euler characteristic of the boundary of the convex cor…

New algorithm detects cores in graphs with community structure, improving vertex selection for better clustering.

Deep learning predicts nuclear equation of state from rotating core collapse GW signals.

This study examines cores within superclusters, highlighting their transitional nature and dynamical state.

The study allows for connected sums in manifolds with positive intermediate Ricci curvature.

Study signatures of torus links and their cores using Neumann's equivariant signatures and Hirzebruch's formula.

Proves NP and co-NP status for knot core recognition in solid torus.

Core groups are link invariants defined by arc or region presentations.

Empty core found in max-loss non-centroid clustering.

We show that in any triangulation of a solid torus, there is a pre-core curve that lies in the 2-skeleton and that intersects the interior of each face in at most 10 straight arcs. By definition, a pre-core curve is a simple closed curve that becomes a core curve when a collar is attached to the boundary of the solid t…

CORe uses randomization to explore bandit problems without external noise.

Convex cores found for group actions on median spaces.

Introduces Levi core for CR manifolds, linking it to global invariants.

The study shows portfolios based on core-periphery stock structure outperform traditional strategies.

The main result is that an s-cobordism (topological or smooth) of 4-manifolds has a product structure outside a ``core'' sub s-cobordism. These cores are arranged to have quite a bit of structure, for example they are smooth and abstractly (forgetting boundary structure) diffeomorphic to a standard neighborhood of a 1-…

Totally geodesic submanifolds in convex cores are properly immersed and have finite volume.

Word2vec is a widely used algorithm for extracting low-dimensional vector representations of words. State-of-the-art algorithms including those by Mikolov et al. have been parallelized for multi-core CPU architectures, but are based on vector-vector operations with "Hogwild" updates that are memory-bandwidth intensive …

A typical way in which network data is recorded is to measure all the interactions among a specified set of core nodes; this produces a graph containing this core together with a potentially larger set of fringe nodes that have links to the core. Interactions between pairs of nodes in the fringe, however, are not recor…

We propose improving the privacy properties of a dataset by publishing only a strategically chosen "core-set" of the data containing a subset of the instances. The core-set allows strong performance on primary tasks, but forces poor performance on unwanted tasks. We give methods for both linear models and neural networ…

In 3-dimensional hyperbolic geometry, the classical Schlafli formula expresses the variation of the volume of a hyperbolic polyhedron in terms of the length of its edges and of the variation of its dihedral angles. We prove a similar formula for the variation of the volume of the convex core of a geometrically finite h…

The study identifies core and satellite segments in the cryptocurrency market.

New GPU algorithm boosts machine learning with larger datasets.

Study shows infimum of dual volume equals convex core volume for hyperbolic 3-manifolds.

KCoreMotif clusters large networks efficiently by exploiting k-core decomposition and motifs.

A new algorithm reduces graph complexity for better dense subgraph analysis.

The study preserves positive Ricci curvature on connected sums of fibre bundles.

This paper investigates the relationship between the topology of hyperbolizable 3-manifolds M with incompressible boundary and the volume of hyperbolic convex cores homotopy equivalent to M. Specifically, it proves a conjecture of Bonahon stating that the volume of a convex core is at least half the simplicial volume o…

Core-Halo solves large-scale fixed-point problems by decentralizing updates.

New core inflation measure predicts future headline inflation.

Paper constructs geometric transitions between hyperbolic and Anti-de Sitter geometries.

Paper simulates LR fuzzy intervals with interval-valued cores.

Generalizes surgery theorem for positive Ricci curvature metrics.

Using PL-methods, we prove the Marden's conjecture that a hyperbolic 3-manifold $M$ with finitely generated fundamental group and with no parabolics are topologically tame. Our approach is to form an exhaustion $M_i$ of $M$ and modify the boundary to make them 2-convex. We use the induced path-metric, which makes the s…

This paper proposes the use of wavelet methods to estimate U.S. core inflation. It explains wavelet methods and suggests they are ideally suited to this task. Comparisons are made with traditional CPI-based and regression-based measures for their performance in following trend inflation and predicting future inflation.…

Gradient flow converges to a minimal convex structure.

Plastikstufes and overtwistedness for higher-dimensional contact manifolds are studied in this paper. It is proved that a contact structure is overtwisted if and only if there exists a small plastikstufe with toric core that has trivial rotation.