arXiv research

The paper constructs Levi flat structures using structure sheaves and differential complexes.

Global invariant for path structures and differential equations defined on torus.

Global graph structure improves GNN performance.

This paper clarifies a global structure of Stokes-Dirac structures used for describing interconnected port-Hamiltonian systems defined on manifolds with non-trivial topology under consistent boundary condition.

Paper proves a quantitative estimate for transforming almost complex structures into standard ones.

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 $\R^4$. Similarly, a smooth 4-manifold homeomorphic to the produc…

Let $S$ be a closed oriented surface of genus at least $2$. Using the parameterisation of the deformation space of globally hyperbolic maximal anti-de Sitter structures on $S \times \mathbb{R}$ by the cotangent bundle over the Teichmüller space of $S$, we study the behaviour of these geometric structures along pinching…

Surveying integrability of Lie algebroids and structures.

New DR algorithm preserves both local and global structure.

Global fixed income returns span across multiple maturities and economies, that is, they naturally reside on multi-dimensional data structures referred to as tensors. In contrast to standard "flat-view" multivariate models that are agnostic to data structure and only describe linear pairwise relationships, we introduce…

DM2L tackles missing labels in multi-label learning by modeling local and global rank structures.

Study causal structure of warped spacetimes using novel pre-length spaces.

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…

Clarifies definitions of global hyperbolicity in various spaces.

Study well-posedness of Faraday tensor problem on specific spacetime manifolds.

ETC improves Transformer models for long and structured inputs.

New approach combines PCA and t-sne for better data analysis.

This work explores gradient flows and Riemannian structure in Gromov-Wasserstein geometry for data with global structure.

The abstract introduces golden Finsler structures and explores their local and global properties.

TADA detects anomalies in time series using topological data analysis.

Smooth actions on manifolds can be globally defined under certain conditions.

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 …

We find formal and holomorphic normal forms for a class of meromorphic connections (the so-called $(TE)$-structures) over the irreducible $2$-dimensional globally nilpotent $F$-manifold germ $\mathcal N_{2}$. We find normal forms for Euler fields on $\mathcal N_{2}$ and we characterize the Euler fields on $\mathcal N_{…

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…

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.

A Poisson structure is represented by a bivector whose Schouten bracket vanishes. We study a global Poisson structure on $S^4$ associated with a holomorphic Poisson structure on $\mathbb{CP}^3$. The space of the Poisson structures on $S^4$ is a real algebraic variety in the space of holomorphic Poisson structures on $\…

Study global geometry of dynamical systems with entire vector fields.

Paper proposes G-CRD to improve GNNs by preserving global graph topology.

Study the boundaries of ε-neighborhoods of planar sets, showing their structure and curvature.

Trade finance history traced from medieval origins to modern markets.

iREPA shows spatial structure, not global semantic, drives generation performance in REPA.

This thesis explores GNNs, categorizing them into local and global approaches.

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…

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 …

This paper generalizes Batchelor's theorem in $C^\infty$-superschemes.

This study analyzes the correlation structure of global agricultural futures markets using RMT.

GAMLA learns manifold structures with auto-encoding for global insights.

We investigate the structure of global inter-firm linkages using a dataset that contains information on business partners for about 400,000 firms worldwide, including all the firms listed on the major stock exchanges. Among the firms, we examine three networks, which are based on customer-supplier, licensee-licensor, a…

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 …

Significant strides have been made toward designing better generative models in recent years. Despite this progress, however, state-of-the-art approaches are still largely unable to capture complex global structure in data. For example, images of buildings typically contain spatial patterns such as windows repeating at…

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…

PerCDL learns personalized dictionaries for physiological signals combining global and local structures.

Paper solves globally optimal k-means for low dimensional data.

In this paper we combine our recent work on regular globally hyperbolic maximal anti-de Sitter structures with the classical theory of globally hyperbolic maximal Cauchy-compact anti-de Sitter manifolds in order to define an augmented moduli space. Moreover, we introduce a coordinate system in this space that resembles…

New discrete conformal structures on surfaces with boundary, proving global rigidity and constructing hyperbolic metrics.

Efficient audio synthesis is an inherently difficult machine learning task, as human perception is sensitive to both global structure and fine-scale waveform coherence. Autoregressive models, such as WaveNet, model local structure at the expense of global latent structure and slow iterative sampling, while Generative A…

Gradient descent finds a global minimum in training deep neural networks despite the objective function being non-convex. The current paper proves gradient descent achieves zero training loss in polynomial time for a deep over-parameterized neural network with residual connections (ResNet). Our analysis relies on the p…