Positive Ricci curvature achieved by adding edges in a graph.
problem Achieving positive Ricci curvature in graphs.
method Adding edges to a complete graph to increase Ricci curvature.
result Least number of edges needed for positive Ricci curvature.
We study differential geometric properties of cuspidal edges with boundary. There are several differential geometric invariants which are related with the behavior of the boundary in addition to usual differential geometric invariants of cuspidal edges. We study the relation of these invariants with several other invar…
Graph pruning improves neural network performance by addressing squashing and smoothing issues.
problem Over-squashing and over-smoothing in Graph Neural Networks.
method Proposes edge deletions to simultaneously address over-squashing and over-smoothing, optimizing spectral gap.
result Edge deletions improve generalization and distinguishability of nodes of different classes.
A new method for identifying causal directions in complex systems.
problem Identifying causal relationships in nonlinear systems with limited data.
method Sequential edge orientation approach using pairwise additive noise model.
result The method can recover true causal DAGs under nonlinear additive noise models.
Previous work in network analysis has focused on modeling the mixed-memberships of node roles in the graph, but not the roles of edges. We introduce the edge role discovery problem and present a generalizable framework for learning and extracting edge roles from arbitrary graphs automatically. Furthermore, while existi…
We introduce new sufficient conditions for intrinsic knotting and linking. A graph on n vertices with at least 4n-9 edges is intrinsically linked. A graph on n vertices with at least 5n-14 edges is intrinsically knotted. We also classify graphs that are 0, 1, or 2 edges short of being complete partite graphs with respe…
New edge features improve GNN performance in biological datasets.
problem Inefficient use of edge features in GNNs.
method Self-supervised and unsupervised learning for new edge features, incorporating Forman-Ricci curvature.
result Improved node classification performance over baseline GNN models.
Model distinguishes homophily and triadic closure in network analysis.
problem Conflated properties of homophily and transitivity in network analysis.
method Generative model with triadic closure edges and inference procedure.
result Can identify mechanisms responsible for network edges and community structure.
We introduce a new family of graphical models that consists of graphs with possibly directed, undirected and bidirected edges but without directed cycles. We show that these models are suitable for representing causal models with additive error terms. We provide a set of sufficient graphical criteria for the identifica…
Efficient framework for training machine learning models at edge without data movement.
problem Lack of privacy-preserving and computationally efficient methods for deep learning model training.
method Privacy preserving FedCollabNN framework for federated learning.
result Framework is computationally efficient and robust against adversarial attacks.
RECON reconstructs regulatory networks from time-course data, reducing spurious edges and preserving true regulatory edges.
problem Reconstructing regulatory networks from time-course data with minimal spurious edges and preserving true regulatory relationships.
method RECON uses an integral-based additive nonparametric ODE model with five methodological advances to reconstruct regulatory networks.
result RECON consistently outperforms existing methods, reducing spurious edges and preserving true regulatory edges across various scenarios.
Research explores hyperbolic space groups and their fundamental domains.
problem Investigating fundamental domains of space groups in hyperbolic spaces.
method Analyzing symmetries of fundamental polyhedra and considering edge conditions.
result Identifies edge conditions for simplicial fundamental domains of Family F12.
A new framework reduces data upload for image classification while protecting user privacy.
problem Data upload limitations and privacy concerns in cloud-based image classification.
method Unsupervised autoencoder training at edge devices, followed by latent vector transmission to server for classifier training.
result The framework reduces communications overhead and protects user data privacy.
Edge computing addresses AI on IoT devices by processing data locally.
problem Processing AI on resource-constrained IoT devices is challenging.
method Deploying machine learning systems at the edge of the network.
result Edge computing reduces latency and communication costs.
New model for network analysis using functional data.
problem Existing network models treat nodes as functions, but this paper introduces functional edges.
method Transform adjacency matrix into functional adjacency tensor, apply Tucker decomposition, regularize basis matrices, and solve tensor completion problem.
result The model effectively captures community structure and handles irregular functional edge data.
We study rerouting edges on surfaces without crossings.
problem Reconfiguring edge paths on surfaces without crossing.
method Rerouting one edge at a time, maintaining crossing-free intermediate embeddings.
result Reconfiguration is always possible on the torus and any orientable surface of genus at least one.
A hybrid framework reduces ML complexity on edge devices.
problem Limited memory and energy on edge devices.
method Compressed data collection and tailored deep learning network.
result Significant reduction in computational complexity and memory.
SWRLDA improves LDA for multi-class classification with edge classes.
problem LDA's vulnerability to edge classes causing biased mean and large distances.
method Self-weighted robust LDA with l21-norm distance criterion.
result SWRLDA outperforms other methods on synthetic and real-world datasets.
An efficient method to compute a single linkage dendrogram.
problem Computing a single linkage dendrogram efficiently.
method Form an edge-weighted graph, calculate MST, recursively split longest edge.
result Efficiently determine vertices of subtrees without additional cost.
We study the minimal crossing number c(K1#K2) of composite knots K1#K2, where K1 and K2 are prime, by relating it to the minimal crossing number of spatial graphs, in particular the 2n-theta curve θK1,K2n that results from tying n of the edges of the planar embedding of the $2n…
NEAR improves graph classification by aggregating edge information.
problem Loss of local structure and relationships in 1-hop neighborhood GNNs.
method Proposes NEAR, a framework that aggregates edge information between nodes in the neighborhood.
result NEAR improves graph classification tasks over existing 1-hop based GNN algorithms.
The paper proves ML estimators are strongly consistent for identifying edge weights in BAR models.
problem Identifying edge weights in Bernoulli Autoregressive (BAR) models.
method Maximum Likelihood (ML) estimation for two variants of BAR models.
result ML estimators are strongly consistent for edge weight identification.
Paper learns Erdős-Rényi graphs with few queries.
problem Learning Erdős-Rényi random graphs efficiently.
method Edge detecting queries on groups of nodes.
result Asymptotically vanishing error probability with O(kˉlogn) tests. New pruning method for sparse additive models speeds up causal structure learning.
problem Efficiently prune spurious edges from fully-connected DAG induced by estimated topological order.
method Sparse additive models combined with randomized tree embedding and group-wise sparse regression.
result Significantly faster than existing pruning methods while maintaining comparable accuracy.
Polyhedra's structure is uniquely defined by edge lengths and dihedral angles, even nonconvex.
problem Determining the structure of polyhedra based on edge lengths and dihedral angles.
method Proved rigidity under specific conditions in Euclidean, hyperbolic, and spherical geometries.
result Polyhedra's structure is uniquely defined by edge lengths and dihedral angles, even nonconvex.
ONLAD Core detects anomalies in edge devices with fast learning and low power.
problem Anomaly detection in edge devices with concept drift and data transfers.
method Highly optimized neural network-based anomaly detection on edge devices.
result ONLAD Core achieves fast anomaly detection and low power consumption.
Networks are a useful representation for data on connections between units of interests, but the observed connections are often noisy and/or include missing values. One common approach to network analysis is to treat the network as a realization from a random graph model, and estimate the underlying edge probability ma…
Federated learning on edge devices achieves high accuracy with minimal data exchange.
problem Training deep neural networks on edge devices while maintaining user privacy.
method Training CNN, LSTM, and MLP on MNIST data using federated learning on edge devices (Raspberry Pi4s). Experimentally tested on IID and non-IID samples.
result Up to 85% test accuracy achieved with 2 minutes of training time and <10 MB data exchange per device.
Study Ricci flow on spaces with conical singularities, proving existence and curvature estimates.
problem Analyzing Ricci flow on spaces with conical singularities.
method Existence proof for Ricci flow, curvature estimates, and tangent flow analysis.
result Existence of a solution to Ricci flow for a specific class of spaces.
GTEA learns node representations in temporal interaction graphs.
problem Inductive representation learning on temporal interaction graphs.
method Integrates sequence model with time encoder and self-attention scheme for edge and node embeddings.
result GTEA learns comprehensive node representations capturing temporal and structural characteristics.
Improved KAN model explains brain dynamics through edge learning and synaptic strength.
problem Explaining brain dynamics and frequencies in different brain regions.
method ELKAN (Edge Learning KNN) model with edge learning and trimming, inspired by brain science.
result ELKAN model outperforms KAN in explaining brain frequencies and dynamics.
Graph attention improves node classification by distinguishing important edges.
problem Node classification in graph-based learning models.
method Theoretical analysis of graph attention networks for node classification.
result Graph attention can perfectly classify nodes in an 'easy' regime but fails in a 'hard' regime.
Lipid-bilayers are the fundamental constituents of the walls of most living cells and lipid vesicles, giving them shape and compartment. The formation and growing of pores in a lipid bilayer have attracted considerable attention from an energetic point of view in recent years. Such pores permit targeted delivery of dru…
Previously in 2014, we proposed the Nearest Descent (ND) method, capable of generating an efficient Graph, called the in-tree (IT). Due to some beautiful and effective features, this IT structure proves well suited for data clustering. Although there exist some redundant edges in IT, they usually have salient features …
We propose a dynamic edge exchangeable network model that can capture sparse connections observed in real temporal networks, in contrast to existing models which are dense. The model achieved superior link prediction accuracy on multiple data sets when compared to a dynamic variant of the blockmodel, and is able to ext…
A new method finds DAG models without ground truth.
problem Finding DAG models without ground truth.
method Markov Checker test and Cross-Algorithm Frugality Search (CAFS).
result Models can be chosen without ground truth.
While statistical analysis of a single network has received a lot of attention in recent years, with a focus on social networks, analysis of a sample of networks presents its own challenges which require a different set of analytic tools. Here we study the problem of classification of networks with labeled nodes, motiv…
We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information (from social networks, user-item graphs, knowledge bases, etc.) in many machine lear…
New algorithm estimates edge density of random graphs robustly, achieving optimal breakdown point.
problem Estimating edge density of Erdős-Rényi graphs under adversarial edge manipulation.
method Sum-of-Squares (SoS) hierarchy, constructing constant-degree certificates for concentration.
result First polynomial-time algorithm with optimal breakdown point and matching error guarantees.
GCNs adapted for road networks improve performance on edge prediction tasks.
problem Improving machine learning on road networks for edge prediction tasks.
method Introducing Relational Fusion Network (RFN) for road networks.
result RFN outperforms state-of-the-art GCNs on road segment regression and classification tasks.
RILOD enables edge devices to learn new object classes efficiently.
problem Edge devices need to learn new object classes without losing old class detection.
method RILOD uses a novel incremental learning algorithm that trains end-to-end for one-stage deep object detection models.
result RILOD can learn to detect a new object class in just a few minutes.
A branched covering surface-knot over an oriented surface-knot F is a surface-knot in the form of a branched covering over F. A branched covering surface-knot over F is presented by a graph called a chart on a surface diagram of F. For a branched covering surface-knot, an addition of 1-handles equipped with cha…
Differentially private graph learning via bounded sensitivity PPR.
problem Protecting user data in graph learning algorithms.
method Proposes a sensitivity-bounded personalized PageRank (PPR) algorithm.
result Achieves similar accuracy to non-private algorithms with large degrees.
Recent advances in Quantum Topology assign q-series to knots in at least three different ways. The q-series are given by generalized Nahm sums (i.e., special q-hypergeometric sums) and have unknown modular and asymptotic properties. We give an efficient method to compute those q-series that come from planar gra…
A piecewise constant curvature manifold is a triangulated manifold that is assigned a geometry by specifying lengths of edges and stipulating that for a chosen background geometry (Euclidean, hyperbolic, or spherical), each simplex has an isometric embedding into the background geometry with the chosen edge lengths. Ad…
This master thesis focuses on practical application of Convolutional Neural Network models on the task of road labeling with bike attractivity score. We start with an abstraction of real world locations into nodes and scored edges in partially annotated dataset. We enhance information available about each edge with pho…
Edge devices learn a global model collaboratively over wireless channels.
problem Learning a global model from edge devices with imperfect channel state information.
method Proposed analog aggregation scheme, receive beamforming at PS, and convergence analysis.
result Performance improvement with more PS antennas, even with imperfect CSI.
New method reveals true causal functions in nonlinear time series, not just scores.
problem Causal discovery in nonlinear time series often uses scalar edge scores, which hide true function-valued causal influence.
method Formalized function-valued causal influence for additive, contribution-decomposable architectures. Introduced a practical framework based on ICE for estimating causal response functions directly from trained models.
result Edges with indistinguishable scalar scores can exhibit qualitatively different functional behaviors.