Same homology via different sign assignments in link Floer theory.
problem Comparing sign assignments in link Floer homology.
method Comparison of sign assignments from two different constructions.
result Small modification of sign convention results in identical chain complexes.
We lift the characteristic-2 totally twisted Khovanov homology of Roberts and Jaeger to a theory with integer coefficients. The result is a complex computing reduced odd Khovanov homology for knots. This complex is equivalent to a spanning-tree complex whose differential is explicit modulo a sign ambiguity coming from …
Adapts scanning algorithm for odd Khovanov homology.
problem Computing odd Khovanov homology efficiently.
method Uses mapping cone construction instead of tensor product.
result Determines odd Khovanov homology of 3-strand torus links.
For knots in S^3, the bi-graded hat version of knot Floer homology is defined over Z; however, for a link L in S^3 with #|L|=l>1, there are 2^{l-1} bi-graded hat versions of link Floer homology defined over Z, the multi-graded hat version of link Floer homology is only defined over F_2 from holomorphic considerations, …
We provide an intergral lift of the combinatorial definition of Heegaard Floer homology for nice diagrams, and show that the proof of independence using convenient diagrams adapts to this setting.
Researchers analyze sign choices for O-planes in orientifolds, proving stabilisation and deriving topological constraints.
problem Assigning sign choices to O-planes in orientifolds of type II string theory.
method Investigating sequences of invariant p-gerbes and coboundary maps to derive sign choices and topological constraints.
result Sign choice homomorphisms stabilise with the dimension of the orientifold and topological constraints on sign configurations are derived.
New method combines randomization tests and flexible models for valid inference without splitting data.
problem Valid inference in randomized panel experiments with complex effect heterogeneity.
method Model-assisted randomization tests that estimate unsigned CATE from residualized outcomes.
result CATE-assisted tests control Type I error and achieve higher power than alternatives.
We compute the reduced Khovanov homology of 3-stranded pretzel links. The coefficients are the integers with the "even" sign assignment. In particular, we show that the only homologically thin, non-quasi-alternating 3-stranded pretzels are P(-p,p,r) with p an odd integer and r greater than or equal to p (these were sho…
We present very efficient active learning algorithms for link classification in signed networks. Our algorithms are motivated by a stochastic model in which edge labels are obtained through perturbations of a initial sign assignment consistent with a two-clustering of the nodes. We provide a theoretical analysis within…
Grid homology invariant proved for lens space links.
problem Proving combinatorial invariance of grid homology for lens space links.
method Combining combinatorial methods with sign assignments to prove invariance.
result Grid homology is a link invariant for lens space links.
The paper defines grid homologies for singular links in lens spaces and constructs a resolution cube for knot Floer homology.
problem Defining and constructing a resolution cube for knot Floer homology of singular links in lens spaces.
method Defining grid homologies for singular links in lens spaces and using them to construct a resolution cube.
result A complete description of singular knot theory in lens spaces and a signed combinatorial resolution cube for knot Floer homology.
DCIts interprets complex time series data with interpretable coefficients.
problem Interpreting nonlinear multivariate time series data.
method Deep convolutional architecture with a Focuser and Modeler components.
result DCIts provides interpretable coefficients and interaction patterns.
We consider the signed density of the extremal points of (two-dimensional) scalar fields with a Gaussian distribution. We assign a positive unit charge to the maxima and minima of the function and a negative one to its saddles. At first, we compute the average density for a field in half-space with Dirichlet boundary c…
Computes homology of an obstruction chain complex in grid homology.
problem Computing the homology of an obstruction chain complex in grid homology.
method Defined and computed the homology of the obstruction chain complex of the full grid.
result Results about the existence of sign assignments in grid homology.
A new method improves graph-based semi-supervised classification by removing noise and mixed signs.
problem Inaccurate soft labels and noise in graph-based semi-supervised classification.
method Triple-matrix-recovery-based robust auto-weighted label propagation framework (ALP-TMR).
result Improved robustness to noise and outliers in label estimation.
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.
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.
Improved node classification in signed social networks using diffuse interface methods.
problem Classifying nodes in signed social networks (positive and negative interactions).
method Diffuse interface methods based on Ginzburg-Landau functional and extended graph Laplacian.
result Performance improvement in real signed social networks, outperforming state of the art.
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.
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.
New approach uses graphs for sign language recognition.
problem Challenges in recognizing sign language for deaf individuals.
method Spatial-Temporal Graph Convolutional Network.
result Improved sign language recognition using human skeletal movements.
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.
New method clusters signed graphs using matrix power means.
problem Clustering signed graphs with positive and negative relations.
method Signed Power Mean Laplacian, defined as matrix power mean of normalized standard and signless Laplacians.
result Signed power mean Laplacian captures ground truth clusters under reasonable settings.
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.
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.
GANs generate new traffic sign images to improve recognition accuracy.
problem Lack of data limits SqueezeNet's performance in traffic sign recognition.
method Applied pix2pix GANs to translate symbolic sign images to real ones for data augmentation.
result Data augmentation with GANs increased classification accuracy for traffic signs.
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.
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…
Method predicts which high-dimensional correlation signs will change in the future.
problem Predicting which correlation matrix coefficients will change signs in high-dimensional data.
method Stability of correlation signs depends on three-by-three relationships, inspired by Heider social cohesion theory.
result The method accurately predicts the stability of correlation signs in high-dimensional data.
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.
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.
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.
Study develops sign recognition system for DHH users.
problem Accessibility of voice-controlled devices for Deaf and Hard-of-Hearing users.
method Multimodal data (RGB video and skeletal data) for sign language recognition using deep learning.
result Validation on GMUASL51 dataset of 12 users and 13107 samples across 51 signs.
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.
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.
A new method learns node embeddings for signed directed networks by capturing both first-order and high-order topologies.
problem Learning representative node embeddings for signed directed networks considering both first-order and high-order topologies.
method Proposes a decoupled variational embedding (DVE) method that leverages a specially designed auto-encoder structure to capture both first-order and high-order topologies.
result Extensive experiments on real-world datasets show the effectiveness of DVE in link sign prediction and node recommendation tasks.
DiagNet uses adversarial learning and signed graph regularization for better mammography diagnosis.
problem Inadequate data and similarity between benign and cancerous masses in mammography.
method Adversarial learning to generate positive and negative mammograms, signed similarity graph, deep convolutional neural network training.
result DiagNet outperforms state-of-the-art in breast mass diagnosis.
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.
It is well-known that the Jones polynomial of an alternating knot is closely related to the Tutte polynomial of a special graph obtained from a regular projection of the knot. Relying on the results of Bollobás and Riordan, we introduce a generalization of Kauffman's Tutte polynomial of signed graphs for which describi…
We present a method for learning the parameters of a Bayesian network with prior knowledge about the signs of influences between variables. Our method accommodates not just the standard signs, but provides for context-specific signs as well. We show how the various signs translate into order constraints on the network …
New risk measures for incomplete markets without lattice structures.
problem Risk measures on incomplete markets without lattice structures.
method Study of risk measures without lattice structures, focusing on tractable dual representations and solid superspaces.
result Existence of a tractable dual representation equivalent to a Fatou-like property, and extension theorems under certain conditions.
Study on blow-up behavior of sign-changing solutions for Yamabe equation.
problem Blow-up behavior of sign-changing solutions for Yamabe equation.
method Construction of a smooth metric on space forms to prove blow-up at lowest energy level.
result Blow-up occurs at the lowest energy level for sign-changing solutions in dimensions 11 to 24.
New nodal domain theorems for symmetric matrices via signed graphs.
problem Establish nodal domain theorems for symmetric matrices.
method Explore signed graph structure to define nodal domains for any function.
result Improved lower bound estimates for the number of strong nodal domains.