Extends duality preserving singular set images and first fundamental forms to generalized cuspidal edges.
problem Preserving singular set images and first fundamental forms on generalized cuspidal edges.
method Extends previous isometric duality to generalized cuspidal edges including cuspidal cross caps and 5/2-cuspidal edges.
result New geometric insights on the duality.
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.
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.
Let R be a compact, connected, orientable surface of genus g with n boundary components with g≥2, n≥0. Let N(R) be the nonseparating curve graph, C(R) be the curve graph and HT(R) be the Hatcher-Thurston graph of R. We prove that if $λ: \mathcal{N}(R) \rightarro…
Study on matching nodes between graphs to preserve edges, focusing on limits and algorithms.
problem Matching nodes between graphs to preserve most edges, especially in random graphs.
method Investigates fundamental limits and designs algorithms to recover alignments in planted graphs.
result High probability guarantees on the success or failure of graph alignment algorithms.
Proposes a new loss function for better super-resolution images.
problem Improving the quality of super-resolution images.
method Introduces a robust loss function based on edge preservation using the Canny operator.
result Enhanced performance in PSNR and SSIM metrics compared to MSE loss function.
This paper presents a method to summarize directed graphs while preserving edge information.
problem Summarizing directed graphs while maintaining edge directionality.
method A model based on minimizing reconstruction error with non-negative constraints, related to Max-Cut criterion, using multiplicative update algorithms.
result The proposed method identifies compressed nodes and directed compressed relations, providing a more accurate representation of directed graphs.
Let R be a compact, connected, orientable surface of genus g with n boundary components. Let C(R) be the curve graph of R. We prove that if g=0,n≥5 or g=1,n≥3, and λ:C(R)→C(R) is an edge preserving map, then λ is induced by a homeomorphism of R, …
We show that the edges of every 3-connected planar graph except K4 can be colored with two colors in such a way that the graph has no color preserving automorphisms. Also, we characterize all graphs which have the property that their edges can be 2-colored so that no matter how the graph is embedded in any orienta…
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.
Proposes a novel approach using vector cross product to preserve directional edges in directed graphs.
problem Preserving directional edges in directed graphs for tasks like link prediction and node recommendation.
method Integrates the non-commutative property of vector cross product into a Siamese neural network to learn N-dimensional embeddings.
result Low-dimensional embeddings effectively preserve directional properties and outperform state-of-the-art methods.
Paper presents privacy-preserving techniques for HD computing.
problem Privacy loss in HD computing due to reversible computation.
method Quantization and pruning of hypervectors for differential privacy.
result Differentially private HD model for cloud inference.
Suppose S1 and S2 are orientable surfaces of finite topological type such that S1 has genus at least 3 and the complexity of S1 is an upper bound of the complexity of S2. Let φ:C(S1)→C(S2) be an edge-preserving map; then S1 is homeomorphic …
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…
Along cuspidal edge singularities on a given surface in Euclidean 3-space, which can be parametrized by a regular space curve, a unit normal vector field ν is well-defined as a smooth vector field of the surface. A cuspidal edge singular point is called generic if the osculating plane of the cuspidal edge (as a regul…
ACERL embeds networks into a low-dimensional space preserving structural and semantic properties.
problem Challenges in brain connectivity data analysis with subject-specific, high-dimensional, and sparse networks.
method Contrastive learning of augmented network pairs with adaptive random masking.
result Achieves minimax optimal convergence rate for edge representation learning.
Study proposes BFEL framework for privacy-preserving FL in personalized healthcare.
problem Privacy and security concerns in traditional cloud-centric ML, especially in wearable devices.
method Develops a blockchain-enhanced federated edge learning (BFEL) framework based on FedCurv, incorporating fisher information matrix and public key encryption.
result Significant reduction in communication cost and high efficiency for federated training on non-iid and heterogeneous data.
The eigendeomposition of nearest-neighbor (NN) graph Laplacian matrices is the main computational bottleneck in spectral clustering. In this work, we introduce a highly-scalable, spectrum-preserving graph sparsification algorithm that enables to build ultra-sparse NN (u-NN) graphs with guaranteed preservation of the or…
A linkage is a finite graph with lengths assigned to each edge. A planar realization is a map to the plane which preserves edge lengths. It can be thought of as a mechanical device formed from stiff rods and rotating joints. We look at the configuration space of all planar realizations of a linkage (following work of K…
Characterizes metrics on triangulated surfaces using glued Euclidean triangles.
problem Describing metrics on triangulated surfaces constructed from glued Euclidean triangles.
method Carefully constructing polyhedral metrics and proving their uniqueness.
result Polyhedral metrics are the only intrinsic metrics preserving Euclidean triangle lengths.
A dessin is a 2-cell embedding of a connected bipartite graph into an orientable closed surface. An automorphism of a dessin is a permutation of the edges of the underlying graph which preserves the colouring of the vertices and extends to an orientation-preserving self-homeomorphism of the supporting surface. A dessin…
The study explores convex unions and completions in simplicial pseudomanifolds, revealing unexpected behavior.
problem Understanding the behavior of convex unions in simplicial pseudomanifolds.
method Generalization to simplicial pseudomanifolds, considering PL homeomorphisms and edge subdivisions.
result Unexpected behavior in convex unions and completions, including empty contraction spaces and large/small contraction spaces.
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.
Paper presents a lightweight, unobtrusive method to protect edge device data privacy.
problem Protecting inference data privacy in IoT edge devices with limited compute power.
method A lightweight neural network at edge devices to obfuscate inference data without indicating obfuscation.
result Effectively protects inference data confidentiality while preserving backend accuracy.
This article presents an analysis of the normalized Yamabe flow starting at and preserving a class of compact Riemannian manifolds with incomplete edge singularities and negative Yamabe invariant. Our main results include uniqueness, long-time existence and convergence of the edge Yamabe flow starting at a metric with …
VFGNN tackles privacy-preserving node classification with federated GNN.
problem Data isolation problem in graph data.
method Vertically partitioned federated GNN, differential privacy.
result Demonstrates effectiveness of VFGNN on three benchmarks.
Method certifies edge predictions with cloud-level reliability.
problem Ensuring reliability of edge intelligence models.
method Conformal alignment-based cascading mechanism.
result Certifies conditional coverage with user control over risk level.
OL4EL optimizes edge learning on resource-constrained servers.
problem Resource constraints on edge servers hinder effective distributed machine learning.
method Online Learning for EL (OL4EL) framework using budget-limited multi-armed bandit model.
result OL4EL significantly improves learning performance while conserving resources.
New method preserves privacy while detecting communities in distributed networks.
problem Privacy-preserving community detection in locally distributed multi-layer networks.
method Privacy-preserving Distributed Spectral Clustering (ppDSC) using randomized response mechanism.
result Developed a novel algorithm that maintains community structure while protecting privacy.
Edge subdivision affects the Perron eigenvalue of tree Ricci matrices.
problem Understanding how edge subdivision impacts the Perron eigenvalue of tree Ricci matrices.
method Compressing branches into scalar feedback functions via Schur complement, reducing the spectral problem to a one-dimensional Chebyshev equation.
result Edge subdivision can decrease, preserve, or increase the Perron eigenvalue of tree Ricci matrices.
No minimizer exists for certain spherical metrics with edge-cones.
problem Existence of Yamabe minimizers on singular spheres.
method Analyzing standard edge-cone spherical metrics of cone angles greater than or equal to 4π. result No minimizer exists for the specified spherical metrics.
The paper examines how edge subdivisions affect the vanishing of L2-homology in Coxeter groups.
problem The vanishing of L2-homology in Coxeter groups under edge subdivisions. method Investigates conditions for the vanishing of L2-homology to be preserved under edge subdivisions of flag triangulations. result Conditions are given to preserve the vanishing of L2-homology under edge subdivisions, and counterexamples are constructed for a torsion growth analogue of Singer's conjecture. FoSR adds edges to graphs to prevent oversquashing and oversmoothing in GNNs.
problem Oversquashing and oversmoothing in graph neural networks (GNNs).
method First-order spectral rewiring to add edges based on spectral expansion, combined with a relational architecture.
result Our algorithm outperforms existing graph rewiring methods in graph classification tasks.
We study the geometry of cuspidal Sk singularities in R3 obtained by folding generically a cuspidal edge. In particular we study the geometry of the cuspidal cross-cap M, i.e. the cuspidal S0 singularity. We study geometrical invariants associated to M and show that they determine it up to order 5.…
First-passage percolation affects graph properties like curvature and geodesics.
problem Effect of first-passage percolation on graph curvature and geodesics.
method Randomly perturbs the metric of a graph by assigning random edge lengths.
result Non-positive curvature and geodesic properties are not preserved by first-passage percolation.
TransNet improves community detection on target networks using privacy-preserved source networks.
problem Community detection on sensitive network data with privacy constraints.
method Spectral clustering framework leveraging locally distributed privacy-preserved auxiliary networks via randomized response and adaptive weighting.
result TransNet delivers strong gains in community detection across various privacy levels and heterogeneity patterns.
Paper develops a federated learning method to protect privacy without sacrificing model utility.
problem Privacy leakage in federated learning due to information exchange between edge devices and server.
method Combines local gradient perturbation, secure aggregation, and zCDP for privacy protection.
result Demonstrates superior trade-off between privacy and model utility through extensive experiments.
FPP preserves sublinear Morse boundaries in geodesic graphs.
problem Preserving sublinear Morse boundaries in FPP.
method First passage percolation on geodesic graphs with i.i.d. passage times.
result Sublinear Morse boundaries are invariant under FPP.
POET enables large neural network training on tiny devices with reduced energy.
problem Training large neural networks on memory-limited edge devices.
method Jointly optimizes rematerialization and paging for memory reduction, formulating an MILP for energy-efficient training.
result POET trains ResNet-18 and BERT within Cortex-M memory constraints, outperforming current methods in energy efficiency.
We study infinitesimal conformal deformations of a triangulated surface in Euclidean space and investigate the change in its extrinsic geometry. A deformation of vertices is conformal if it preserves length cross-ratios. On one hand, conformal deformations generalize deformations preserving edge lengths. On the other h…
New curvature concept preserves graph distances under operations.
problem Preserving graph distances under graph operations.
method Characterization of distance matrix and its null space.
result Linear system Dx=1 may not have a solution. The paper proposes a novel Kernelized image segmentation scheme for noisy images that utilizes the concept of Smallest Univalue Segment Assimilating Nucleus (SUSAN) and incorporates spatial constraints by computing circular colour map induced weights. Fuzzy damping coefficients are obtained for each nucleus or center p…
Sherpa.ai framework combines federated learning and differential privacy for edge AI services.
problem Protecting data privacy in edge AI services.
method Holistic federated learning and differential privacy approach with methodological guidelines.
result Demonstrated through classification and regression use cases.
Rectangular mosaics extend virtual knot studies to larger polygons.
problem Studying virtual knots using mosaic techniques.
method Introduced rectangular mosaics, modified mosaic moves, and provided invariants.
result Developed algorithms for computing virtual knot invariants.
A triangulation of a surface with fixed topological type is called irreducible if no edge can be contracted to a vertex while remaining in the category of simplicial complexes and preserving the topology of the surface. A complete list of combinatorial structures of irreducible triangulations is made by hand for the on…
This paper addresses questions of quasi-isometric rigidity and classification for fundamental groups of finite graphs of groups, under the assumption that the Bass-Serre tree of the graph of groups has finite depth. The main example of a finite depth graph of groups is one whose vertex and edge groups are coarse Poinca…
iGCL preserves graph semantics in latent space augmentations.
problem Manual tuning of augmentation ratios and unexpected graph changes.
method iGCL uses a Variational Graph Auto-Encoder to learn augmentations in the latent space, optimizing an upper bound for contrastive loss.
result iGCL achieves state-of-the-art performance on graph-level and node-level tasks.
This paper presents a new approach for filter design based on stochastic distances and tests between distributions. A window is defined around each pixel, overlapping samples are compared and only those which pass a goodness-of-fit test are used to compute the filtered value. The technique is applied to intensity SAR d…