New formula for spherical polygon area via prequantization.
problem Traditional area formula for spherical polygons requires measuring angles.
method Uses prequantization to create a new formula that doesn't require angle measurement.
result New formula applicable to a wider range of degenerate curves and polygons.
Minimal cylinders in Heisenberg group characterized using loop group method.
problem Characterizing minimal cylinders in the Heisenberg group.
method Generalized Weierstrass type representation and loop group method.
result Characterization of all non-vertical minimal cylinders in terms of pairs of closed plane curves.
New method uses path signatures for causal discovery in time series data.
problem Challenges in understanding causal structure from observational time series data.
method Path signatures and signed areas for model-free causal discovery.
result Confidence sequence regions help identify lag/lead causal relationships.
Gradient flow method solves isoperimetric inequality for maps.
problem Finding maps with optimal enclosed area.
method Sobolev gradient flow for area-normalised Dirichlet energy.
result Solutions converge to a circle as time goes to infinity.
Study calculates the renormalized area of catenoids in hyperbolic spaces.
problem Calculating the renormalized area of catenoids in hyperbolic spaces.
method Variational characterization and Chern--Gauss--Bonnet formulas for locally conformally flat manifolds.
result Renormalized area of catenoids varies continuously from negative infinity to twice the area of totally geodesic hypersurfaces.
A flag area measure on an n-dimensional euclidean vector space is a continuous translation-invariant valuation with values in the space of signed measures on the flag manifold consisting of a unit vector v and a (p+1)-dimensional linear subspace containing v with 0≤p≤n−1. Using local parallel sets, …
Paper studies existence of Toda systems with sign-changing functions.
problem Existence of Toda systems with prescribed sign-changing functions.
method Variational method and blowup analysis.
result Blowup can only occur at points where h1 is positive. The Riemannian Penrose inequality (RPI) bounds from below the ADM mass of asymptotically flat manifolds of nonnegative scalar curvature in terms of the total area of all outermost compact minimal surfaces. The general form of the RPI is currently known for manifolds of dimension up to seven. In the present work, we pro…
In online social networks people often express attitudes towards others, which forms massive sentiment links among users. Predicting the sign of sentiment links is a fundamental task in many areas such as personal advertising and public opinion analysis. Previous works mainly focus on textual sentiment classification, …
Nowadays autonomous technologies are a very heavily explored area and particularly computer vision as the main component of vehicle perception. The quality of the whole vision system based on neural networks relies on the dataset it was trained on. It is extremely difficult to find traffic sign datasets from most of th…
GRU-D detects age-specific missing patterns in vital signs.
problem Temporal missingness in clinical time series data.
method Gated recurrent unit with decay mechanisms (GRU-D) trained on MIMIC-IV vital signs.
result GRU-D achieves AUROC 0.780 and AUPRC 0.810 on bootstrapped data.
New pseudometrics defined on knot spaces based on curve thickness and length.
problem Rigidity and non-degeneracy of knot spaces under isotopies.
method Swept-area pseudometrics on ropelength-filtered knot spaces.
result Proved non-degeneracy on polygonal strata and exact distance formulas.
The coarea formula is proven for Heisenberg group maps, addressing open questions.
problem Proving the coarea formula for Lipschitz maps from the Heisenberg group to Euclidean space.
method Introducing a new integral to define symplectic area of curves and proving convergence conditions.
result The coarea formula is established for CH1 maps from the Heisenberg group to R2n. Theory proves existence of hypersurfaces with prescribed curvature.
problem Existence of hypersurfaces with prescribed mean curvature in noncompact manifolds.
method Developed min-max theory for noncompact manifolds.
result Proved existence of closed and finite area hypersurfaces.
Intensive care clinicians are presented with large quantities of patient information and measurements from a multitude of monitoring systems. The limited ability of humans to process such complex information hinders physicians to readily recognize and act on early signs of patient deterioration. We used machine learnin…
In this paper we study properties of the area evolute (AE) and the center symmetry set (CSS) of a convex planar curve γ. The main tool is to define a Minkowski plane where γ becomes a constant width curve. In this Minkowski plane, the CSS is the evolute of γ and the AE is an involute of the CSS. We prove that the…
Paper extends LME models to allow sign constraints on coefficients with SDTN random effects.
problem Inference with sign constraints on random effects in LME models.
method Proposes SDTN distribution for random effects and develops likelihood-based approaches for estimation.
result Proposed constrained model improves real-world interpretations and achieves satisfactory performance.
Consider an asymptotically flat Riemannian manifold (M,g) of dimension n≥3 with nonempty compact boundary. We recall the harmonic conformal class [g]h of the metric, which consists of all conformal rescalings given by a harmonic function raised to an appropriate power. The geometric significance is that eve…
Extends Toda system existence results to negative functions.
problem Existence of solutions to Toda systems with sign-changing functions.
method Improved Moser-Trudinger inequality, Brezis-Merle type analyses, Pohozaev identities.
result Sufficient conditions for Toda system solutions remain valid with negative functions.
Refines d'Alembertian for signed Lorentz distance functions in metric measure spacetimes.
problem Exact representation and bounds of d'Alembertian for signed Lorentz distance functions.
method Metric geometry techniques, localization, Sobolev calculus.
result Distributional d'Alembertian is a signed measure with integration by parts formula.
Study on signed graphs with random signs, focusing on community detection.
problem Community detection in signed stochastic block models.
method Strong concentration inequalities for adjacency and Laplacian matrices, applied to signed Laplacian matrix.
result The sign of the first eigenvector of the Laplacian matrix defines a weakly consistent estimator for balanced community detection.
SELO model predicts link signs better than SDGNN using subgraph encoding and linear optimization.
problem Inferring the sign of links in signed networks with limited sign data.
method Subgraph Encoding via Linear Optimization (SELO) approach to learn edge embeddings.
result SELO model outperforms state-of-the-art methods on multiple real-world signed networks.
By a result of W.~P. Thurston, the moduli space of flat metrics on the sphere with n cone singularities of prescribed positive curvatures is a complex hyperbolic orbifold of dimension n−3. The Hermitian form comes from the area of the metric. Using geometry of Euclidean polyhedra, we observe that this space has a n…
We argue that the standard graph Laplacian is preferable for spectral partitioning of signed graphs compared to the signed Laplacian. Simple examples demonstrate that partitioning based on signs of components of the leading eigenvectors of the signed Laplacian may be meaningless, in contrast to partitioning based on th…
Novel GNN for signed and directed networks using magnetic signed Laplacian.
problem Efficiently modeling signed and directed networks for tasks like clustering and link prediction.
method Introduced a magnetic signed Laplacian for directed signed graphs, used it to construct a spectral GNN.
result Demonstrated effective performance on tasks involving signed and directional information.
Sign equivariant networks improve model expressiveness for spectral geometric learning.
problem Limited expressiveness of sign invariant models for tasks like graph link prediction.
method Developed sign equivariant neural network architectures based on new analytic sign equivariant polynomials.
result Sign equivariant models achieve theoretical benefits in spectral geometric learning tasks.
The paper proves reverse inequalities in various geometric settings using curvature radius data.
problem Proving reverse Alexandrov-Fenchel inequalities in different geometric settings.
method Using curvature radius data and associated evolute or focal maps.
result Sharp reverse Alexandrov-Fenchel estimates and inequalities in smooth convex curves and hypersurfaces.
Defines signed quasiregular curves and proves growth theorem.
problem Understanding growth of signed quasiregular curves.
method Proves weak reverse Hölder inequality and uses it to prove growth theorem.
result Proves growth theorem for signed quasiregular curves.
Signed networks contain both positive and negative kinds of interactions like friendship and enmity. The task of node classification in non-signed graphs has proven to be beneficial in many real world applications, yet extensions to signed networks remain largely unexplored. In this paper we introduce the first analysi…
In this short note, we compare the combinatorial sign assignment of Manolescu, Ozsvath, Szabo and Thurston for grid homology of knots and links in 3-sphere with the sign assignment coming from a coherent system of orientations on Whitney disks. Although these constructions produce different signs, a small modification …
Let M be a closed oriented surface endowed with a Riemannian metric g and let Ω be a 2-form. We show that the magnetic flow of the pair (g,Ω) has zero asymptotic Maslov index and zero Liouville action if and only g has constant Gaussian curvature, Ω is a constant multiple of the area form of g and the mag…
PyTorch Geometric Signed Directed fills the gap for GNNs on signed and directed graphs.
problem Lack of unified software packages for GNNs on signed and directed networks.
method Developed a software package with GNN models, synthetic and real-world data, and evaluation metrics.
result Demonstrates the effectiveness of the implemented methods through experiments.
Proposes a privacy-preserving sign selection method for distributed systems.
problem Sign selection in distributed differentially private settings.
method Iterative peeling of stability function combined with exponential mechanism.
result Recovery of support and signs with optimal signal-to-noise ratio.
Estimates graph curvature and diameter using Laplacian eigenvalues.
problem Estimating graph curvature and diameter using Laplacian eigenvalues.
method Combination of gradient estimates and strong nodal domain walks.
result Li-Yau type eigenvalue-diameter estimate for signed graphs.
In this paper we study some global properties of static potentials on asymptotically flat 3-manifolds (M,g) in the nonvacuum setting. Heuristically, a static potential f represents the (signed) length along M of an irrotational timelike Killing vector field, which can degenerate on surfaces corresponding to the…
The paper discovers patterns in Maass forms' coefficients related to Fricke signs.
problem Identifying Fricke signs in Maass forms with unknown signs.
method Averaging Fourier coefficients, Linear Discriminant Analysis (LDA), neural networks.
result 96% accuracy in predicting Fricke signs for forms with even parity, 94% for odd parity.
Novel CNN array for sign language recognition using wearable IMUs.
problem Efficiently recognizing sign language from wearable IMU signals.
method Two-dimensional Convolutional Neural Network array architecture for Indian sign language recognition.
result Peak classification accuracies of 94.20% for general sentences and 95.00% for interrogative sentences achieved.
The recognition of sign language is a challenging task with an important role in society to facilitate the communication of deaf persons. We propose a new approach of Spatial-Temporal Graph Convolutional Network to sign language recognition based on the human skeletal movements. The method uses graphs to capture the si…
In this paper we use theory of embedded graphs on oriented and compact PL-surfaces to construct minimal realizations of signed Gauss paragraphs. We prove that the genus of the ambient surface of these minimal realizations can be seen as a function of the maximum number of Carter's circles. For the case of signed Gaus…
CSNE embeds signed networks by separating structural and fine-grained information.
problem Improving sign prediction in signed networks using inaccurate or incomplete balance theories.
method Conditional Signed Network Embedding (CSNE) models structural and fine-grained information separately, integrating them rigorously.
result CSNE outperforms state-of-the-art on sign prediction tasks, and MaxEnt priors are competitive in resource-constrained settings.
Signed seminorms linked to real tropical spaces and matroids.
problem Understanding signed seminorms and their real tropicalizations.
method Introducing signed Goldman-Iwahori space, identifying it as inverse limit of real tropicalizations, and giving matroid-theoretic description.
result Signed seminorms identified as inverse limit of real tropicalizations of projective space.
The paper finds sign-changing solutions for a specific type of elliptic equation.
problem Existence of sign-changing solutions for a Yamabe type equation.
method Investigates a critical elliptic equation with a Yamabe type operator on a compact manifold with boundary.
result Existence of sign-changing solutions assured under certain geometric conditions.
Unified sign-based compression for federated learning with faster convergence.
problem High communication cost in federated learning with large-scale models.
method Unified noisy perturbation scheme for sign-based compression.
result Achieves faster convergence rate than existing sign-based methods.
Signed graphs encode positive (attractive) and negative (repulsive) relations between nodes. We extend spectral clustering to signed graphs via the one-parameter family of Signed Power Mean Laplacians, defined as the matrix power mean of normalized standard and signless Laplacians of positive and negative edges. We pro…
Signed-permutation coordinate transport improves model alignment across checkpoints.
problem Improper alignment of coordinate-indexed objects across model checkpoints.
method Introduces sign-marginalized Hungarian matching and coordinate-preserving transport.
result Recovering signed-permutation gauge improves coordinate alignment and model performance.
New method estimates tensors from noisy data with missing entries.
problem Tensor estimation from noisy observations with missing entries.
method Sign series representation for tensor completion, addressing low- and high-rank signals.
result Excess risk bounds, estimation error rates, and sample complexities established.
Signed heights of knotoids are defined and studied.
problem Understanding the signed height of knotoids.
method Defined positive and negative parts of height, proved they determine unsigned height, provided lower bounds with polynomials, studied associated sequences.
result Positive and negative parts of height determine unsigned height.
Develops method for learning signed graphs from smooth signals.
problem Learning signed graphs from observed data, especially in contexts with both positive and negative interactions.
method Uses net Laplacian as graph shift operator and minimizes total variation of observed signals with ADMM.
result Theoretical proofs of convergence and estimation error bound provided.