Defines new operations on random sets in Banach spaces.
problem Assessing multivariate risks in mathematical finance.
method Introduces conditional core and convex hull operations for random sets.
result Generalised conditional expectation is sandwiched between conditional core and convex hull.
Classifies stability of flat-core p p p -elasticae pinned at boundaries.
problem Stability of flat-core p p p -elasticae under pinned boundary conditions. method Classification based on previous work for all p ∈ ( 1 , ∞ ) p\in(1,\infty) p ∈ ( 1 , ∞ ) and d ≥ 2 d\geq2 d ≥ 2 . result Completes the classification of stable pinned p p p -elasticae in R d \mathbf{R}^d R d . Probabilistic programming aids in automatically dating ice cores, reducing manual error and uncertainty.
problem Automatically dating ice cores with high accuracy and capturing uncertainty.
method Probabilistic models and probabilistic programming for automatic inference.
result Demonstrated the use of probabilistic programming for ice core dating, showcasing its benefits and limitations.
Study on core consistency preservation in compressed tensors.
problem Ensuring low-rank structure is maintained during tensor compression.
method Theoretical analysis and experimental validation of compression schemes.
result Identified sufficient conditions for preserving core consistency.
Method improves deep learning robustness to domain shifts.
problem Domain shift robustness in deep learning.
method Conditional variance regularization (CoRe) to penalize style feature changes.
result Improves predictive accuracy in domain shifts.
Generalizes surgery theorem for positive Ricci curvature metrics.
problem Preserving positive Ricci curvature under surgery.
method Gluing a sphere bundle with a core metric.
result Constructs new metrics of positive Ricci curvature.
A new framework improves solving mixed-integer convex problems with binary indicators.
problem Optimizing mixed-integer convex problems with binary indicators controlling continuous variables.
method Coordinate Optimality Reformulation (CORe) framework, incorporating coordinate-wise optimality information.
result CORe reformulations improve branch-and-bound performance, especially in sparse and structured settings.
We carry out the first main step towards the construction of new examples of complete embedded self-similar surfaces under mean curvature flow. An approximate solution is obtained by taking two known examples of self-similar surfaces and desingularizing the intersection circle using an appropriately modified singly per…
Density mode clustering is a nonparametric clustering method. The clusters are the basins of attraction of the modes of a density estimator. We study the risk of mode-based clustering. We show that the clustering risk over the cluster cores --- the regions where the density is high --- is very small even in high dimens…
Core-Halo solves large-scale fixed-point problems by decentralizing updates.
problem Large-scale fixed-point equations with block dependencies.
method Core-Halo decomposition separates write ownership from read-only context, aligning with block-dependence structure.
result Core-Halo achieves near-centralized performance while retaining parallelism.
Foundation for learning in changing conditions.
problem Learning under varying conditions and states.
method Admissible transport, protected-core preservation, and evaluator-aware learning evolution.
result Established first theorem-supporting layer for regime-varying learning.
Paper studies embedding conditions for homogeneous quandles.
problem Embedding problem of homogeneous quandles.
method Necessary and sufficient condition for quandle homomorphisms to be embeddings.
result Generalization of embedding theorem for generalized Alexander quandles.
Reduces proper actions to simpler core actions for analysis.
problem Understanding properties of proper actions on manifolds.
method Extending Skjelbred and Straume's construction to non-compact groups, focusing on core of actions.
result Properties of proper actions are determined by simpler core actions.
This paper establishes an equivalence between transitive double Lie algebroids and core diagrams.
problem Understanding and characterizing transitive double Lie algebroids.
method Using core diagrams and equivalence of transitive core diagrams with transitive double Lie groupoids.
result Transitive double Lie algebroids are completely determined by their core diagrams.
Classifies geodesic planes outside convex core of geometrically finite 3-manifolds.
problem Classifying geodesic planes in geometrically finite 3-manifolds.
method Constructive proof involving exotic rays and roofs.
result Existence of exotic roofs depends on the existence of exotic rays and bending lamination properties.
Recovering core nodes in hypergraphs from fringe interactions.
problem Recovering core nodes from fringe interactions in hypergraphs.
method Modeling core recovery as a hitting set problem in hypergraphs, developing a practical algorithm.
result Demonstrated the effectiveness of the algorithm on real-world datasets.
Study reveals multiple core-periphery structures in interbank markets, transforming during financial crises.
problem Understanding the complex structure and transformation of interbank markets during financial crises.
method Novel core-periphery detection method on eMID interbank market data.
result Interbank markets exhibit multiple core-periphery pairs and transition to bipartite structures over short time scales.
New peripheral structure for core groups detects noninvertible knots.
problem Detecting noninvertible knots and links.
method Introduced a new peripheral structure for core groups.
result The new structure detects noninvertibility of some knots and links.
AL ℓ 0 \ell_0 ℓ 0 CORE tensor decomposition reduces computational cost for sparse count data.
problem Efficiently decompose sparse count data matrices.
method Probabilistic Tucker decomposition with ℓ 0 \ell_0 ℓ 0 -norm constraint. result AL ℓ 0 \ell_0 ℓ 0 CORE achieves similar results to full Tucker decomposition at a fraction of the cost. 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.
problem Representing subgroups of surface groups in a combinatorial way.
method Introducing core surfaces as 2-dimensional complexes made up of vertices, labeled edges, and 4g-gons.
result Core surfaces are compact when corresponding subgroups are finitely generated.
Study examines financial market structure changes during the COVID-19 crash using a novel MI approach.
problem Analyzing nonlinear dependencies among major stocks during market crashes.
method Conditional p-threshold mutual information (MI) and Minimum Spanning Tree (MST) framework.
result Financial networks become more integrated during crashes, with increased periphery vulnerability.
For a connected, locally path connected space X X X , let H H H be a subgroup of the fundamental group of X X X , π 1 ( X , x ) π_1(X,x) π 1 ( X , x ) . We show that there exists an open cover U \cal U U of X X X such that H H H contains the Spanier group $π({\U},x)$ if and only if the core of H H H in π 1 ( X , x ) π_1(X,x) π 1 ( X , x ) is open in the quasitopological fundamental grou…
The paper studies graph products of groups and recovers graph and vertex groups under certain conditions.
problem Recovering graph and vertex groups from graph products of groups.
method Using non-generic almost positive sentences, the authors show that under specific conditions, the underlying graph and vertex groups can be recovered.
result The core of the defining graph determines an invariant of the elementary theory of a right-angled Artin group.
Paper introduces a core-periphery model for identifying informative network structures.
problem Noise and bias in non-informative periphery structures obscure the informative core in complex networks.
method Spectral algorithms for core identification as a preprocessing step for network analysis.
result The proposed method outperforms traditional core-periphery methods in various downstream tasks.
Publish a core-set of data to protect against adversarial use.
problem Protecting datasets from adversarial use.
method Construct a fair core-set for linear and neural models.
result Core-sets improve primary task performance while hindering unwanted tasks.
Estimates covariance matrices for matrix-variate data via core covariance geometry.
problem Estimating covariance matrices for matrix-variate data with partial isotropy.
method Fixed-rank core covariance geometry, partial-isotropy rank-r core shrinkage estimator.
result The geometry of the space of rank-r cores is a smooth manifold.
Paper studies nonnegative Tucker decomposition identifiability with sparsity conditions.
problem Identify nonnegative Tucker decomposition factors uniquely.
method Adapting NMF identifiability results, derive procedures using tensor unfoldings or slices.
result Nonnegative Tucker decomposition factors are identifiable under certain sparsity conditions.
Study shows the volume of convex core for once-punctured torus groups is close to a fixed value.
problem Understanding the volume of convex cores in once-punctured torus groups.
method Analyzing a sequence of quasi-Fuchsian manifolds associated with a pseudo-Anosov mapping class.
result The volume of the convex core differs from a fixed value by at most a uniformly bounded constant.
Generative models create H&E-stained and destained prostate biopsy images.
problem Lack of H&E-stained prostate biopsy images.
method Conditional GAN for H&E staining, destaining model learning from stained to non-stained images.
result Generated images maintain structural similarity to non-stained biopsy.
The ropelength problem asks for the minimum-length configuration of a knotted diameter-one tube embedded in Euclidean three-space. The core curve of such a tube is called a tight knot, and its length is a knot invariant measuring complexity. In terms of the core curve, the thickness constraint has two parts: an upper b…
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…
New algorithm detects cores in graphs with community structure, improving vertex selection for better clustering.
problem Understanding and detecting core-periphery structures in graphs with community structure.
method Introduces relative centrality to detect cores in graphs with community and core-periphery structures.
result Relative centrality solves bias issues in core detection, leading to better vertex selection and improved clustering performance.
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…
Deep learning predicts nuclear equation of state from rotating core collapse GW signals.
problem Classifying the nuclear equation of state from rotating core collapse gravitational wave signals.
method Employed deep convolutional neural networks to classify visual and temporal patterns in GW signals.
result Up to 97% correct classifications of nuclear equation of state in the test set.
This paper uses CNNs to automatically segment ischaemic stroke lesions from MRI sequences.
problem Automatically segmenting ischaemic stroke lesions from MRI sequences is challenging.
method Adversarial training of CNNs on multi-sequence MRI data.
result The method achieves high Dice scores for core and penumbra segmentation.
This study examines cores within superclusters, highlighting their transitional nature and dynamical state.
problem Understanding the morphology and dynamical properties of cores within superclusters.
method Projected and radial velocity distributions of galaxies, morphological analysis, entropy and mass estimates.
result Cores are transitional structures that evolve towards virialisation but remain gravitationally bound.
The study allows for connected sums in manifolds with positive intermediate Ricci curvature.
problem Performing connected sums in manifolds with positive intermediate Ricci curvature.
method Introducing and utilizing k k k -core metrics to show the possibility of connected sums. result Connected sums are possible under certain conditions involving k k k -core metrics. Study signatures of torus links and their cores using Neumann's equivariant signatures and Hirzebruch's formula.
problem Computing signatures of torus links and their cores.
method Use Neumann's equivariant signatures and rewrite Hirzebruch's formula for torus links (without cores) in terms of integral points in a parallelogram.
result Rewritten Hirzebruch's formula for torus links with cores using integral points in a parallelogram.
Proves NP and co-NP status for knot core recognition in solid torus.
problem Determining if a knot is the core of a solid torus.
method Alternate proof and corollary of Hopf link recognition problem.
result Proves NP and co-NP status for solid torus core recognition problem.
Recovering core nodes from graph data with missing fringe interactions.
problem Recovering the core set from graph data with missing fringe interactions.
method Developed a theoretical framework and algorithms based on fixed-parameter tractability.
result Our algorithms outperform existing methods on various real-world datasets.
New method estimates extreme outcomes in heavy-tailed data, breaking circular dependence.
problem Estimating outcomes for extreme events in heavy-tailed data.
method Proposes an ADRF estimator that includes a structured tail-shape output and a diagnostic to evaluate tail shape.
result Successfully reduces MAE in deep-tail and conditional-shortfall predictions.
Core groups are link invariants defined by arc or region presentations.
problem Defining link invariants using different presentations of arcs and regions.
method Introducing core groups as link invariants defined by presentations involving arcs or regions, and extending these to virtual link diagrams.
result Properties of core groups and their extensions to virtual link diagrams are discussed.
Meta-learning approach for adaptive TTS with few data.
problem Adapting TTS systems to new speakers with minimal data.
method Meta-learning with shared WaveNet core and independent speaker embeddings, using three training strategies.
result Successful adaptation of multi-speaker neural network to new speakers with minimal data.
Empty core found in max-loss non-centroid clustering.
problem Core stability in non-centroid clustering under max-loss objective.
method Proof for all k≥3 and n≥9 agents, computer-aided proof for 2D Euclidean points.
result Core can be empty in non-centroid clustering under max-loss objective.
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.
problem Exploration in stochastic bandit problems.
method Randomizes past observations to exploit variance in rewards.
result Achieves i l d e O ( d n log K ) ilde O(d\sqrt{n\log K}) i l d e O ( d n log K ) regret bound in stochastic linear bandits. Introduces Levi core for CR manifolds, linking it to global invariants.
problem Understanding global invariants of CR manifolds.
method Introduces Levi core, relates to Diederich-Fornæss index and D'Angelo class.
result Levi core is trivial under certain conditions, nontrivial otherwise.