The paper constructs Levi flat structures using structure sheaves and differential complexes.
problem Global solvability and regularity of Levi flat structures.
method Employing formal integrability and differential complexes, the paper constructs a resolution for the structure sheaf.
result Global exactness and Sobolev regularity of the differential complex for Levi flat structures.
Global invariant for path structures and differential equations defined on torus.
problem Global invariant for path structures and differential equations.
method Computed as a secondary invariant from a Cartan connection on a canonical bundle.
result Formula for global invariant of second order differential equations on torus.
Clarifies global structure of Stokes-Dirac structures on manifolds.
problem Global structure of Stokes-Dirac structures on manifolds with non-trivial topology.
method Clarification through consistent boundary conditions.
result Clearer understanding of Stokes-Dirac structures on manifolds.
Global Poisson structures on S4 studied using twistor methods.
problem Global Poisson structures on S4. method Holomorphic Poisson structures on CP3, twistor method. result Examples of Poisson structures on S4 associated with codimension one holomorphic foliations of degree 2 on CP3. Global graph structure improves GNN performance.
problem Limited graph structure in GNNs leads to indistinguishable node embeddings.
method Empirically tested the impact of global graph information on GNN performance.
result Global information can significantly improve GNN performance by more than 5%.
Paper proves a quantitative estimate for transforming almost complex structures into standard ones.
problem Transforming almost complex structures into standard ones on bounded domains.
method Proves existence of global diffeomorphisms under Hölder-Zygmund conditions.
result Existence of a global diffeomorphism in a specified Hölder-Zygmund class.
It is observed that on many 4-manifolds there is a unique smooth structure underlying a globally hyperbolic Lorentz metric. For instance, every contractible smooth 4-manifold admitting a globally hyperbolic Lorentz metric is diffeomorphic to the standard R4. Similarly, a smooth 4-manifold homeomorphic to the produc…
Study pinching sequences to understand degeneration of anti-de Sitter structures.
problem Understanding the degeneration of anti-de Sitter structures along pinching sequences.
method Parameterization of deformation space and analysis of pinching sequences.
result Regular anti-de Sitter structures appear as limiting points.
New DR algorithm preserves both local and global structure.
problem Trade-off between preserving local and global structure in DR methods.
method Analysis of existing DR methods and design principles for loss functions.
result Design of PaCMAP algorithm that preserves both local and global structure.
Surveying integrability of Lie algebroids and structures.
problem Integrability of Lie algebroids and structures.
method Survey and recent results on integrability.
result Recent findings on local and global integrability.
New tensor approach models global fixed income risks across maturities and economies.
problem Lack of models capturing multi-dimensional data in global fixed income markets.
method Introduces tensor-valued approach to model shared risks among multiple interest rate curves.
result Estimates risk factors decomposable into maturity and country domains, enabling tailored portfolio management.
DM2L tackles missing labels in multi-label learning by modeling local and global rank structures.
problem Missing labels in multi-label learning.
method DM2L imposes local low-rank structures and global high-rank structures on predictions of instances from the same and different labels, respectively.
result DM2L outperforms state-of-the-art methods in multi-label learning with missing labels.
Study causal structure of warped spacetimes using novel pre-length spaces.
problem Understanding the causal structure of warped spacetimes.
method Novel notion of Lorentzian pre-length spaces and proof of causal completion as globally hyperbolic pre-length space.
result Causal completion of GRW spacetime is a globally hyperbolic pre-length space under Hausdorff chronological topology.
Study reveals scale-free global buyer-supplier networks and their implications for conflict minerals.
problem Global proliferation of conflict minerals through buyer-supplier linkages.
method Investigated scale-free topology and community structure of global inter-firm networks.
result A limited number of firms play a crucial role in conflict minerals proliferation.
We examine how the structure of the world trade network has been shaped by globalization and recessions over the last 40 years. We show that by treating the world trade network as an evolving system, theory predicts the trade network is more sensitive to evolutionary shocks and recovers more slowly from them now than i…
SDSPCAAN combines supervised and local data structures for better dimensionality reduction.
problem Preserving both global and local data structures for noisy high-dimensional data.
method Supervised discriminative sparse PCA with adaptive neighbors (SDSPCAAN).
result SDSPCAAN improves classification accuracy on high-dimensional datasets.
Generative models learn complex spatial patterns using program synthesis.
problem Capturing complex global structure in data, especially in images.
method Incorporates programs representing global structure into generative models and learns these models through program synthesis.
result Significantly better at generating and completing images with global structure compared to state-of-the-art methods.
Clarifies definitions of global hyperbolicity in various spaces.
problem Clarifying terminology in recent literature on global hyperbolicity.
method Comparing definitions in Lorentzian length spaces, optimal transport, and topological preordered spaces.
result The causal relation is a closed order and preserves compactness in all cases.
This work explores gradient flows and Riemannian structure in Gromov-Wasserstein geometry for data with global structure.
problem Suitable geometry for tasks requiring preservation of global data structure.
method Study of gradient flows and Riemannian structure in Gromov-Wasserstein geometry for distributions on \(\mathbb{R}^d\).
result Established a Benamou-Brenier-like formula for IGW and derived the IGW gradient.
New approach combines PCA and t-sne for better data analysis.
problem Multiscale complexity in high-dimensional data.
method Multiscale joint characterization using PCA and t-sne.
result Joint characterization detects signals not seen by PCA or t-sne alone.
ETC improves Transformer models for long and structured inputs.
problem Scaling input length and encoding structured inputs in Transformers.
method Introduces global-local attention, relative position encodings, and CPC pre-training.
result Achieves state-of-the-art results on four natural language datasets.
Study well-posedness of Faraday tensor problem on specific spacetime manifolds.
problem Well-posedness of the Cauchy problem for the Faraday tensor on globally hyperbolic manifolds with timelike boundary.
method Existence of Green operators for the operator d+δ and a suitable pre-symplectic structure on the space of solutions. result Existence of Green operators and pre-symplectic structure for the operator d+δ. The abstract introduces golden Finsler structures and explores their local and global properties.
problem Investigating geometric properties of golden Finsler structures.
method Local and global analysis of golden Finsler structures, including explicit computations and transformations.
result Proved that golden Finsler structures cannot be projectively related.
New method detects global structures in sparse or noisy data.
problem Localization of eigenvectors in sparse or noisy data.
method Learn a regularization matrix from localized eigenvectors.
result Suppresses eigenvalues associated with localized eigenvectors.
Gradient descent efficiently finds global minima in deep neural networks.
problem Training deep neural networks efficiently and reliably.
method Gradient descent, leveraging the stability of the Gram matrix induced by the network architecture.
result Gradient descent achieves zero training loss in polynomial time for deep over-parameterized neural networks with residual connections.
Smooth actions on manifolds can be globally defined under certain conditions.
problem Globalizing partial smooth actions of Lie groupoids on smooth manifolds.
method Providing necessary and sufficient conditions for globalizability and analyzing orbit and stabilizer spaces.
result There exists a unique differentiable structure on the quotient space for free and proper actions.
TADA detects anomalies in time series using topological data analysis.
problem Detecting global changes in dependency structure between channels in multivariate time series.
method Topological Data Analysis for detecting anomalies in multivariate time series.
result The approach is more suitable for detecting global changes of correlation structures than existing methods.
The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international …
New proof shows minimal surfaces globally exist for compact data.
problem Global existence of minimal surfaces on R1,1. method Geometric proof using null structure, fewer derivatives, and mild decay assumptions.
result Global existence for minimal surfaces on R1,1 for compact data. We investigate the community structure of the global ownership network of transnational corporations. We find a pronounced organization in communities that cannot be explained by randomness. Despite the global character of this network, communities reflect first of all the geographical location of firms, while the indu…
Combines multi-layer graphs to infer global network structure.
problem Leveraging domain knowledge in structure inference for multi-layer graphs.
method Mask combination of multi-layer graphs using optimization.
result Enhanced structure inference through multi-layer graph integration.
Paper proposes G-CRD to improve GNNs by preserving global graph topology.
problem Improving lightweight GNNs for robust performance on large-scale real-world graphs.
method Introduces Graph Contrastive Representation Distillation (G-CRD) using contrastive learning.
result G-CRD consistently boosts GNN performance and robustness, outperforming existing methods.
Problem of global integration of geometric structures arising in the theory of dynamical systems admitting the normal shift is considered. In the case when such integration is possible the problem of globalization for shift maps is studied.
Study global geometry of dynamical systems with entire vector fields.
problem Understanding the global structure of equilibria and their basins.
method Step-by-step analysis of basins of centers, nodes, and foci; introduction of global elliptic sectors.
result Characterization of heteroclinic regions connecting equilibria.
iREPA shows spatial structure, not global semantic, drives generation performance in REPA.
problem Understanding what aspect of the target representation matters for generation.
method Empirical analysis of 27 vision encoders, two modifications to REPA.
result Spatial structure, not global semantic, drives generation performance.
Trade finance history traced from medieval origins to modern markets.
problem Evolution and standardization of trade finance products.
method Historical analysis of market structures and regulatory changes.
result Global trade finance market evolved from local to centralized, then decentralized.
Study the boundaries of ε-neighborhoods of planar sets, showing their structure and curvature.
problem Understanding the structure and smoothness of boundaries of ε-neighborhoods of planar sets.
method Analyzing the global topological structure and smoothness of boundaries of ε-neighborhoods of compact planar sets.
result The boundary of ε-neighborhoods can be expressed as a disjoint union of Jordan curves and singularities.
Trade is a fundamental pillar of economy and a form of social organization. Its empirical characterization at the worldwide scale is represented by the World Trade Web (WTW), the network built upon the trade relationships between the different countries. Several scientific studies have focused on the structural charact…
This thesis explores GNNs, categorizing them into local and global approaches.
problem Understanding the convergence of global GNNs and connecting local and global approaches.
method Categorization of GNNs into local and global, study of Invariant Graph Networks, connecting local and global approaches, and using local MPNN for graph coarsening.
result Established a connection between local and global GNN approaches.
Combines local and global smoothing for multivariate density estimation.
problem Non-parametric multivariate density estimation.
method Combines local and global smoothing techniques.
result Simulation shows effectiveness of the method.
It is common for CCTV operators to overlook inter- esting events taking place within the crowd due to large number of people in the crowded scene (i.e. marathon, rally). Thus, there is a dire need to automate the detection of salient crowd regions acquiring immediate attention for a more effective and proactive surveil…
We describe the flat surfaces with flat normal bundle and regular Gauss map immersed in R^4 using spinors and Lorentz numbers. We obtain a new proof of the local structure of these surfaces. We also study the flat tori in the sphere S^3 and obtain a new representation formula. We then deduce new proofs of their global …
GAMLA learns manifold structures with auto-encoding for global insights.
problem Limited global insight and lack of interpretable analytical descriptions in manifold learning.
method Two-round auto-encoding process to derive character and complementary representations.
result GAMLA provides global and analytical descriptions of smooth manifolds.
This paper generalizes Batchelor's theorem in C∞-superschemes.
problem Establishing global splittings in C∞-superschemes. method Structural generalization of Batchelor's theorem.
result Global splittings of C∞-superspaces can be characterized by Euler vector fields. This study analyzes the correlation structure of global agricultural futures markets using RMT.
problem Understanding the complex correlation structure of global agricultural futures markets.
method Random Matrix Theory (RMT) applied to analyze correlation coefficients and eigenvalues.
result The correlation structure is asymmetric and right skewed, with significant eigenvalues indicating market effects and commodity groups.
With the random matrix theory, we study the spatial structure of the Chinese stock market, American stock market and global market indices. After taking into account the signs of the components in the eigenvectors of the cross-correlation matrix, we detect the subsector structure of the financial systems. The positive …
Recently ({\em Class. Quant. Grav.} {\bf 20} 625-664) the concept of {\em causal mapping} between spacetimes --essentially equivalent in this context to the {\em chronological map} one in abstract chronological spaces--, and the related notion of {\em causal structure}, have been introduced as new tools to study causal…
SEARNN improves RNN training by incorporating global-local losses.
problem RNNs trained with MLE fail to exploit structured losses and suffer from exposure bias.
method SEARNN introduces global-local losses through test-alike search space exploration.
result SEARNN outperforms MLE on OCR, spelling correction, and machine translation tasks.