Partial covariance factorizes in path diagrams, simplifying analysis.
problem Understanding partial covariance in complex diagrams.
method Factorization of partial covariance over nodes and edges.
result Simpson's paradox cannot occur in singly-connected diagrams.
Mathematical analysis of Prytz planimeter using sub-Riemannian geometry.
problem Historical use of Prytz planimeter to approximate areas.
method Sub-Riemannian geometry and connections/horizontal lifts.
result Mathematical description and analysis of Prytz planimeter.
This work connects LLE, factor analysis, and probabilistic PCA through a stochastic perspective.
problem Exploring the theoretical connection between LLE, factor analysis, and probabilistic PCA.
method Solving the stochastic linear reconstruction of LLE using expectation maximization.
result LLE, factor analysis, and probabilistic PCA are shown to be connected through a stochastic perspective.
The paper uses deep learning to speed up spatial and visual connectivity analysis.
problem Slow calculation of spatial and visual connectivity metrics.
method Investigates machine learning models and a pipeline for training them on spatial and visual connectivity analysis.
result Deep learning models significantly speed up the analysis process.
Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to connect persistent homology with machine learning techniques. We contribute a kernel…
Consumers with low demand, like households, are generally supplied single-phase power by connecting their service mains to one of the phases of a distribution transformer. The distribution companies face the problem of keeping a record of consumer connectivity to a phase due to uninformed changes that happen. The exact…
The paper reveals surprising star-shaped connectivity in neural networks.
problem Understanding mode connectivity in neural network landscapes.
method Fine-grained analysis of connectivity in overparameterized and finite minima cases.
result Star-shaped connectivity exists in neural network landscapes, suggesting near convexity.
Method estimates network connectivity and dimensionality from multiple networks.
problem Estimating connectivity and dimensionality in samples of networks.
method Convex optimization with alternating direction method of multipliers.
result Method outperforms conventional methods in estimating connectivity and dimensionality.
Proposes QGC to distinguish between lower and upper tail connectivity in financial networks.
problem Identifying systemically important firms using financial data.
method Quantile Granger Causality (QGC) using Lasso penalized quantile regressions.
result QGC networks detect systemic risk more accurately than mean-based networks.
New analysis shows D-SGD can generalize well regardless of graph connectivity.
problem Improving generalization of D-SGD in decentralized settings.
method Algorithmic stability analysis and optimization-dependent generalization bounds.
result D-SGD can achieve generalization bounds similar to classical SGD, independent of graph connectivity.
New heuristics for predicting links in multiplex networks.
problem Link prediction in networks with multiple types of connections.
method Proposed a general framework and three families of heuristics.
result Significantly outperformed baseline heuristics for ordinary networks.
The paper analyzes spectral properties of connection Laplacian on tori, proving convergence to real torus.
problem Spectral analysis of connection Laplacian on tori.
method Employing parallel orthonormal basis in pullback bundle, examining eigenvalues of connection Laplacian on real and discrete tori.
result Eigenvalues of connection Laplacian on discrete tori converge to those on real torus, with unique twist in torsion matrix.
The paper explores SHAP scores and their connection to functional ANOVA, highlighting challenges in approximations.
problem Estimating SHAP scores and understanding their limitations.
method Using the connection to functional ANOVA, the paper outlines the challenges in SHAP approximations and their relation to feature distribution and ANOVA terms.
result Challenges in SHAP approximations are primarily due to feature distribution and the number of ANOVA terms estimated.
New method for constructing gluing parameterizations in geometric analysis.
problem Constructing gluing parameterizations for anti-self-dual connections.
method Using C1 maps of smooth Banach manifolds with corners. result Provides a method applicable to other nonlinear PDE problems.
Detects anomalous behavior in social media users by analyzing content and connections.
problem Identifying disruptive patterns in user behavior on social media platforms.
method Joint representation learning of content and connection to detect anomalous behavior.
result Observed densely connected users engaging in local politics and exhibiting troll-like behavior.
The convergence rate and final performance of common deep learning models have significantly benefited from heuristics such as learning rate schedules, knowledge distillation, skip connections, and normalization layers. In the absence of theoretical underpinnings, controlled experiments aimed at explaining these strate…
Simplified construction of contact triad connection for analysis.
problem Analyzing contact instanton equation on contact triads.
method Characterization via almost contact structure and construction using almost contact moving frame.
result Simpler and more canonical construction of contact triad connection.
Research covers geometry, analysis, and integration on infinite-dimensional spaces.
problem Exploring geometric and analytical structures in infinite-dimensional settings.
method Analyzes numerical schemes, Lie groups, connections, and integration theory.
result Developed new methods for integration and analysis on infinite-dimensional manifolds.
Resurgent analysis reveals full partition function for 3-manifold invariants.
problem Analyzing resurgence in 3-manifold invariants for SL(2,C). method Resurgent analysis applied to infinite families of Seifert manifolds and torus knot complements.
result The contribution from abelian flat connections contains information of all non-abelian flat connections, indicating a full partition function.
Algorithm finds connected components on Lie groups for multi-orientation image analysis.
problem Finding connected components in complex, multi-orientation images.
method Iterative algorithm using morphological dilations and Hamilton-Jacobi-Bellman kernels on Lie groups.
result Algorithm converges in finitely many steps and can differentiate between crossing and aligned structures.
The paper connects harmonic mappings to Ricci flow using geometric analysis.
problem Global geometry of harmonic mappings and Ricci solutions.
method Geometric analysis, focusing on subharmonic functions.
result Results on connections between manifold geometry and subharmonic functions.
Separation of the sources and analysis of their connectivity have been an important topic in EEG/MEG analysis. To solve this problem in an automatic manner, we propose a two-layer model, in which the sources are conditionally uncorrelated from each other, but not independent; the dependence is caused by the causality i…
Paper proves stability for recovering connections from holonomy traces.
problem Recovering a connection from holonomy traces on Riemannian manifolds.
method Combination of microlocal analysis and non-Abelian approximate Livsic Theorem.
result Hölder type stability estimates for holonomy inverse problem.
NTFA models participant and stimulus variations in fMRI data.
problem Lack of statistical tools to examine participant differences in neuroimaging studies.
method NTFA, a probabilistic factor analysis model inferring embeddings for participants and stimuli.
result NTFA improves predictive generalization and downstream tasks.
Transfer entropy shows abnormal brain connectivity in depression.
problem Abnormal brain connectivity in depression.
method Transfer entropy analysis on EEG recordings.
result Aberrated dynamics and direction of information between brain centers in depression.
We present a unifying framework which reduces the construction of probabilistic component analysis techniques to a mere selection of the latent neighbourhood, thus providing an elegant and principled framework for creating novel component analysis models as well as constructing probabilistic equivalents of deterministi…
The information-theoretic analysis by Russo and Van Roy (2014) in combination with minimax duality has proved a powerful tool for the analysis of online learning algorithms in full and partial information settings. In most applications there is a tantalising similarity to the classical analysis based on mirror descent.…
We propose a novel denoising framework for task functional Magnetic Resonance Imaging (tfMRI) data to delineate the high-resolution spatial pattern of the brain functional connectivity via dictionary learning and sparse coding (DLSC). In order to address the limitations of the unsupervised DLSC-based fMRI studies, we u…
Natural disasters can have catastrophic impacts on the functionality of infrastructure systems and cause severe physical and socio-economic losses. Given budget constraints, it is crucial to optimize decisions regarding mitigation, preparedness, response, and recovery practices for these systems. This requires accurate…
Generalized diffusion type equations are considered and point symmetry analysis is applied to them. The equations with extremal order point symmetry algebras are described. Some old geometrical results are rederived in connection with theory of these equation.
GNNs improve brain activity forecasting in fMRI studies.
problem Understanding neural dynamics in the brain.
method Comparison of GNN architectures for modeling fMRI data.
result GNNs outperform VAR models in robustly scaling to large network studies.
Attention learns PCA on Gaussian data, proving its connection to principal component analysis.
problem Principal component analysis on Gaussian data.
method Analysis of attention mechanisms through PCA, covering finite and infinite prompt regimes.
result Attention aligns with principal eigenvectors of covariance matrices, converging to optimal solutions in the infinite-prompt limit.
Study connects boundary geometry to symbol of Dirichlet-to-Neumann operator.
problem Determining geometric data from boundary symbol of connection Laplacian.
method Analyze symbol of Dirichlet-to-Neumann operator associated with connection Laplacian.
result Geometric data on boundary and normal derivatives are determined by symbol.
Unified model learns joint and individual features from brain imaging data.
problem Integrating structural and functional connectivity data for behavioral phenotypes.
method Cross-Modal Joint-Individual Variational Network (CM-JIVNet) with multi-head attention fusion.
result CM-JIVNet outperforms in cross-modal reconstruction and behavioral trait prediction.
Study on autoencoder denoising in high dimensions.
problem Denoising data from Gaussian mixtures.
method Two-layer non-linear autoencoder with skip connection in high-dimensional limit.
result Closed-form expressions for denoising mean-squared test error.
Paper connects surface shape analysis and unbalanced optimal transport.
problem Computing the SRNF shape distance on piecewise linear surfaces.
method Characterizes SRNF shape distance as WFR distance pullback, proposes new algorithm for WFR distance computation.
result Direct computation of SRNF shape distance on piecewise linear surfaces.
New connection between complex analysis and PDE for spherical conical metrics.
problem Understanding spectral properties of spherical conical metrics.
method Analyzing monodromy, eigenfunctions, and developing maps.
result Monodromy reducibility implies real-valued eigenfunction with eigenvalue 2.
Study reveals how dengue spread patterns vary across different years in Recife, Brazil.
problem Understanding spatial organization of dengue transmission in urban areas.
method Spatial analysis of dengue cases using topological data analysis and Vietoris-Rips filtrations.
result Critical percolation thresholds define distinct geometric regimes of dengue spread.
Combines topological and geometric approaches to data analysis.
problem Understanding when and how geometric objects intersect.
method Connects topological and geometric concepts of curvature.
result Reconceptualizes curvature and links it to hyperconvexity.
The chapter explores globally hyperbolic spacetimes using topology and functional analysis.
problem Understanding global hyperbolicity in spacetimes.
method Foundational tools from order theory and topology, geometric analysis, and connections to physics.
result A connection between global hyperbolicity and geodesic completeness of space-like surfaces.
We consider the problem of accelerating distributed optimization in multi-agent networks by sequentially adding edges. Specifically, we extend the distributed dual averaging (DDA) subgradient algorithm to evolving networks of growing connectivity and analyze the corresponding improvement in convergence rate. It is know…
Investigates connections in Lie group bundles, focusing on geometric reduction.
problem Geometric reduction of gauge field theories.
method Definition and analysis of equivariant connections in Lie group bundles.
result Provides conditions for the existence and properties of equivariant connections.
GJMS operators connect geometry, analysis, and physics.
problem None explicitly stated; focus on operators and their impact.
method Construction of conformally invariant differential operators.
result GJMS operators have significant impact in geometry, analysis, and physics.
LA-VDM accelerates VDM using landmarks to improve data analysis.
problem Efficiently analyzing complex datasets with nonuniform sampling densities.
method Landmark-constrained two-stage normalization to accelerate VDM.
result LA-VDM accurately recovers parallel transport and converges to the connection Laplacian.
The paper examines Matsumoto change and its Cartan connection equivalence.
problem Analyzing the Matsumoto change and its geometric implications.
method Derived fundamental tensors and conditions for Cartan connection equivalence.
result Conditions for Cartan connection coefficients to be the same for both spaces.
Proposes MVGPR for spatiotemporal data modal analysis.
problem Sparse and irregularly sampled data in complex flows.
method Multivariate Gaussian process regression (MVGPR) with kernel design.
result MVGPR outperforms DMD and SPOD in modal analysis of sparse and irregular data.
Modern data acquisition routinely produces massive amounts of network data. Though many methods and models have been proposed to analyze such data, the research of network data is largely disconnected with the classical theory of statistical learning and signal processing. In this paper, we present a new framework for …
Visualizes board connections for socially responsible investing insights.
problem Understanding corporate governance and sustainability through board connections.
method Data Visualization tool to reveal connections between Directors and Executives.
result Strength of tool in investigating corporate governance and sustainability.