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.
Generalizes global hyperbolicity to higher signatures and proves compactness.
problem Global hyperbolicity in higher pseudo-Riemannian signatures.
method Generalization and proof of compactness of causal diamonds.
result Existence of solutions to a Plateau problem and characterization of holonomies.
Global methods outperform local in forecasting groups of time series, even in heterogeneous datasets.
problem Forecasting groups of time series, especially in heterogeneous datasets.
method Local methods consider each series separately, global methods fit a single model to all series.
result Global methods can outperform local methods in forecasting groups of time series, even in heterogeneous datasets.
In this note a proof is given for global existence and uniqueness of minimal surfaces of Lorentzian type from a cylinder into globally hyperbolic Lorentzian manifolds for given initial values up to the first derivatives.
New spacetimes found that are refocusing but not strongly refocusing.
problem Characterizing spacetimes that are refocusing but not strongly refocusing.
method Analyzing globally hyperbolic spacetimes and introducing new refocusing concepts.
result Existence of spacetimes that are refocusing but not strongly refocusing.
Global and local blowups of manifolds are proven equivalent.
problem Equivalence of global and local blowups in differential topology.
method Proof of equivalence between global and local constructions of blowups.
result Global and local constructions of blowups are shown to be equivalent.
Global calculus for manifolds with boundary, solving evolution problems.
problem Global solvability of evolution problems on manifolds with boundary.
method Established global functional calculus and Gårding inequality for pseudo-differential operators without local coordinates.
result Global solvability for a class of evolution problems.
Study calculates global sections on complex curves.
problem Global sections of chiral de Rham complexes on complex curves.
method Calculation on closed complex curves with genus g ≥ 2.
result Space of global sections determined.
Smooth convergence shown for curve diffusion flows.
problem Embeddedness and global existence of curves.
method Exponentially fast convergence established.
result Smooth convergence for curve diffusion flows.
We prove the global existence of Dirac-wave maps with curvature term with small initial data on globally hyperbolic manifolds of arbitrary dimension which satisfy a suitable growth condition. In addition, we also prove a global existence result for wave maps under similar assumptions.
Global optimization in Bayesian inference yields little additional benefit.
problem Improving psychometric parameter estimation using global optimization strategies.
method Experimental simulations comparing myopic and global strategies in multiple models.
result Global optimization strategies provide negligible additional utility improvement beyond the immediate next steps.
Combines global and local search for efficient global optimization with Gaussian processes.
problem Difficulties in building accurate GP models and getting stuck in suboptimal regions.
method Adopting AGLGP model combining global and local GP models, dividing space into regions, and switching between global and local searches.
result Efficiently locates the global optimum with benefits of both global and local search.
Global implicit function theorem for Fréchet spaces, solving derivative loss problems.
problem Solving initial value problems with derivative loss in Fréchet spaces.
method Global implicit function theorems for Keller's Cc1-mappings in Fréchet spaces, applied through submersions and transversality. result Global existence and uniqueness of solutions to initial value problems with derivative loss.
New global section found for geodesic flows on convex hypersurfaces.
problem Finding global sections for geodesic flows on convex hypersurfaces.
method Constructing a global hypersurface of section with an isometric involution.
result Generalized Birkhoff annulus to higher dimensions.
Improves global counterfactual explanations for model recourse.
problem Inability to provide explanations beyond local instances.
method Investigates and improves Actionable Recourse Summaries (AReS) for global counterfactual explanations.
result Develops more efficient and interactive explainability tools.
We show global existence and convergence results for the pluriclosed flow on manifolds for which certain naturally associated tensor bundles are globally generated.
Graph products inherit Morse local-to-global property from their components.
problem Generalizing local-to-global property to graph products of infinite groups.
method Generalizing maximization procedure for relatively hierarchically hyperbolic groups and showing stable embeddings.
result Graph products of infinite Morse local-to-global groups have the Morse local-to-global property.
Develops methods to calculate global index of real polynomials.
problem Calculating the global index of real polynomials.
method Two methods: via atypical fibres and Milnor arcs clusters.
result Derives upper bounds for the global index, refining Durfee's degree-based bound.
Study curve flows with global forcing terms using a distance comparison principle.
problem Analyse the behavior of curves under curve flows with global forcing terms.
method Prove a distance comparison principle for curve shortening flow with arbitrary global forcing terms.
result Established a distance comparison principle for curve flows with global forcing terms.
A new deep generative model captures global dependencies without supervision.
problem Global modeling in deep generative models.
method Non-i.i.d. variational autoencoders with mixture model and global Gaussian latent variable.
result Captures interpretable disentangled representations and domain alignment.
We show that the definition of global hyperbolicity in terms of the compactness of the causal diamonds and non-total imprisonment can be extended to spacetimes with continuous metrics, while retaining all of the equivalences to other notions of global hyperbolicity. In fact, global hyperbolicity is equivalent to the co…
We study global aspects of complete, non-singular asymptotically locally AdS spacetimes solving the vacuum Einstein equations whose conformal infinity is an arbitrary globally stationary spacetime. It is proved that any such solution which is asymptotically stationary to the past and future is itself globally stationar…
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.
Study describes global sections of chiral de Rham complex on compact Ricci-flat Kähler manifolds.
problem None explicitly stated; focuses on description of global sections.
method Complete description of vertex algebra of global sections.
result Complete description of vertex algebra of global sections of chiral de Rham complex.
Smooth distributions on subcartesian spaces can be globally finitely generated.
problem Understanding smooth distributions on subcartesian spaces.
method Embedding in Euclidean space, Whitney Embedding Theorem, and distribution theory.
result Smooth generalized distributions and subbundles on connected subcartesian spaces are globally finitely generated.
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…
It has been shown that deep neural networks (DNNs) may be vulnerable to adversarial attacks, raising the concern on their robustness particularly for safety-critical applications. Recognizing the local nature and limitations of existing adversarial attacks, we present a new type of global adversarial attacks for assess…
Throughout economic history, the global economy has experienced recurring crises. The persistent recurrence of such economic crises calls for an understanding of their generic features rather than treating them as singular events. The global economic system is a highly complex system and can best be viewed in terms of …
Global models outperform local models in forecasting intermittent time series.
problem Forecasting intermittent time series with zeros in supply chains.
method Comparison of state-of-the-art probabilistic local and global models on five datasets.
result TiDE, a simple neural network architecture, achieves the best accuracy among global models.
Global EQG sums boundary states over manifold diffeomorphism classes.
problem Summing boundary states over manifold diffeomorphism classes.
method Formulated as classical statistical physics, weights determined by general principles.
result Hartle-Hawking state as a probability measure.
We introduce a special class of knots, called global knots, in F^2 x R and we construct new isotopy invariants, called T-invariants, for global knots. Some T-invariants are of finite type but they cannot be extracted from the generalized Kontsevitch integral (which is consequently not the universal invariant of finite …
Proves globally hyperbolic spacetimes via null distance completeness.
problem No Hopf-Rinow Theorem in Lorentzian Geometry.
method Observation of null distances and their behavior with time functions.
result Proves globally hyperbolic spacetimes via null distance completeness.
Global obstructions found for conformally Einstein metrics in 6D.
problem Obstructing the existence of conformally Einstein metrics in six dimensions.
method Presentation of global conformal invariants.
result Nontrivial global conformal invariant obstructing conformally Einstein metrics.
We develop the global moduli theory of symplectic varieties in the sense of Beauville. We prove a number of analogs of classical results from the smooth case, including a global Torelli theorem. In particular, this yields a new proof of Verbitsky's global Torelli theorem in the smooth case (assuming b2≥5) which …
The fragmentation of production across countries has become an important feature of the globalization in recent decades and is often conceptualized by the term, global value chains (GVCs). When empirically investigating the GVCs, previous studies are mainly interested in knowing how global the GVCs are rather than how …
Global regularity proved for 4D Ricci flow with scalar curvature integral bound.
problem Global regularity of 4D Ricci flow with integral scalar curvature bound.
method Extended Ge-Jiang's result to include integral bound on scalar curvature.
result Global ε-regularity for 4D Ricci flow with integral scalar curvature bound. Paper proves global optimality of a simple optimization scheme for learning DAG models.
problem Learning acyclic directed graphical models from data.
method Path-following optimization scheme for bivariate setting.
result Simple optimization scheme globally converges to global minimum.
Study local and global aspects of complex plane curve embeddings.
problem Local and global problems of complex plane curve embeddings.
method Braid monodromy, local and global analysis.
result Historical progress in understanding complex plane curve embeddings.
In this paper, a new sequential surrogate-based optimization (SSBO) algorithm is developed, which aims to improve the global search ability and local search efficiency for the global optimization of expensive black-box models. The proposed method involves three basic sub-criteria to infill new samples asynchronously to…
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.
GAIL with neural networks converges to global optima and has a known rate.
problem Uncertainty about GAIL with neural networks achieving global optimality.
method Gradient-based alternating updates algorithm.
result Established sublinear convergence to globally optimal solution.
A new TwinGP framework for efficient large-scale GP modeling.
problem Efficiently modeling large-scale Gaussian processes with computational constraints.
method Combines global and local approximations using a subset-of-data approach.
result TwinGP framework performs on par or better than state-of-the-art methods at a fraction of the computational cost.
Language is dynamic, constantly evolving and adapting with respect to time, domain or topic. The adaptability of language is an active research area, where researchers discover social, cultural and domain-specific changes in language using distributional tools such as word embeddings. In this paper, we introduce the gl…
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 minima found for multidimensional scaling with penalties.
problem Finding global minima in multidimensional scaling.
method Combining stress loss function with a quadratic penalty term to find minimizers.
result Trajectory of minimizers leads to global minima.
Proposes a tool to contrast global vs personalized models in clinical prediction.
problem Balancing global vs personalized models in clinical prediction.
method Localized regression approach using autoencoder for dimension reduction.
result Identification of patient subgroups where global models fall short.
Global balance index measures systemic risk in financial networks.
problem Measuring systemic risk in financial networks.
method Defined global balance index based on a diffusive process and linear system.
result Global balance index correlates with systemic risk measures.
Global inverse function theorem proved easily using Riemannian geometry.
problem Global inverse function theorem in Riemannian geometry.
method Hopf--Rinow theorem in Riemannian geometry.
result Hadamard's global inverse function theorem is proven easily.