Derives new orthogonal coordinates for evolving surfaces and curves.
problem Accounting for geometric effects in boundary layer asymptotics.
method Elementary derivation of orthogonal signed-distance coordinates.
result Provides vector calculus identities for these coordinates.
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…
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.
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…
New algorithm eliminates sign function in PGD attacks, improving performance.
problem Improving robustness of neural networks against adversarial attacks.
method Proposes a new raw gradient descent (RGD) algorithm that eliminates the sign function in PGD attacks.
result The RGD algorithm outperforms PGD and other competitors in various settings.
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.
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.
Study finds infinite sign-changing solutions for a specific equation on manifolds.
problem Existence of sign-changing solutions for a Yamabe-type equation on manifolds.
method Analyzes a specific Yamabe-type equation on manifolds with proper isoparametric functions and positive focal submanifolds.
result Proves the existence of infinite sign-changing solutions for the equation when 1<q<q∗. Study on compact Kähler surfaces for sign-changing curvatures.
problem Prescribing sign-changing Chern scalar curvatures on compact Kähler surfaces.
method Established a Chen-Li type existence theorem and provided an alternative proof.
result Alternative proof of Ding-Liu's theorem on sign-changing Gaussian curvatures.
The classical Sturm-Hurwitz-Kellogg theorem asserts that a function, orthogonal to an n-dimensional Chebyshev system on a circle, has at least n+1 sign changes. We prove the converse: given an n-dimensional Chebyshev system on a circle and a function with at least n+1 sign changes, there exists an orientation preservin…
In this paper, we consider the problem of prescribing scalar curvature on n-sphere. Assume that the candidate curvature function f, which is allowed to change sign, satisfies some kind of Morse index or symmetry condition. By studying the well-known scalar curvature flow, we are able to prove that the flow converges …
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.
Sign-RIP improves robust low-rank matrix recovery by preserving norms even with corrupted measurements.
problem Robust low-rank matrix recovery in the presence of corrupted measurements.
method Proposed Sign-RIP, a robust restricted isometry property.
result Sign-RIP guarantees uniform convergence of subdifferentials in robust low-rank matrix recovery.
For the London Stock Exchange we demonstrate that the signs of orders obey a long-memory process. The autocorrelation function decays roughly as τ−α with α≈0.6, corresponding to a Hurst exponent H≈0.7. This implies that the signs of future orders are quite predictable from the signs of past orde…
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. 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.
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.
Ancient Ricci flows are identified without curvature sign condition.
problem Identifying type II ancient Ricci flows and their backward limits.
method Using a size condition of the sharp log Sobolev functional near infinity.
result Rigidity result for ancient Ricci flows without sign condition on curvatures.
The paper proves the existence of infinite sign-changing solutions to a Hardy-Sobolev equation on Riemannian manifolds.
problem Existence of solutions to a specific type of Hardy-Sobolev equation on Riemannian manifolds.
method Addressed using the properties of isoparametric functions and focusing on the distance function from a submanifold.
result Proves the existence of infinite sign-changing solutions to the Hardy-Sobolev equation.
Standard ChIP-seq peak calling pipelines seek to differentiate biochemically reproducible signals of individual genomic elements from background noise. However, reproducibility alone does not imply functional regulation (e.g., enhancer activation, alternative splicing). Here we present a general-purpose, interpretable …
We construct a price impact model between stocks in a correlated market. For the price change of a given stock induced by the short-run liquidity of this stock itself and of the information about other stocks, we introduce a self- and a cross-impact function of the time lag. We model the average cross-response function…
Two methods find at least two solutions to Kazdan-Warner's problem on surfaces.
problem Finding solutions to Kazdan-Warner's problem on two-dimensional surfaces.
method Direct method on convex sets and variational method of mountain pass.
result At least two solutions to the Kazdan-Warner's problem are found.
Develops a new nonparametric trace regression model for high-dimensional data.
problem Violation of known functional form and global low-rank structure assumptions in trace regression.
method Structured sign series representations for nonparametric trace regression models.
result Establishes excess risk bounds and sample complexities for the proposed model.
DKMD is a fast signed statistic for comparing univariate distributions.
problem Comparing univariate distributions, especially preserving directionality.
method DKMD integrates kernel mean embeddings against an odd weighting function.
result DKMD preserves directionality and is robust to outliers.
Recent successes in word embedding and document embedding have motivated researchers to explore similar representations for networks and to use such representations for tasks such as edge prediction, node label prediction, and community detection. Such network embedding methods are largely focused on finding distribute…
Regularized spectral methods improve clustering in signed graphs, especially for sparse data.
problem Clustering signed graphs with positive and negative edges.
method Developed regularized versions of SPONGE and Signed Laplacian methods for clustering signed graphs, especially for sparse data.
result Theoretical guarantees and empirical performance improvements for clustering signed graphs, especially in sparse regimes.
A new algorithm solves signed Fréchet regression on manifolds with bounded curvature.
problem Signed Fréchet regression on Riemannian manifolds with bounded curvature.
method Proximal DC algorithm (FRIDA) for computing signed Fréchet regression fits.
result Existence and interiority of minimizers, strong convexity of proximal subproblems, and convergence to stationary points.
New neural network architectures use signed permutation representations for finite groups, improving performance.
problem Designing and optimizing neural networks for finite groups with signed permutation representations.
method Introduces G-invariant deep neural networks with densely connected layers and signed permutation representations. result Signed permutation representations lead to significantly better performance in classification tasks.
New tests for high-dimensional data improve on existing methods.
problem Testing mean vectors in high-dimensional data.
method Generalized multivariate sign transformation, using different norm functions.
result Tests using generalized signs have higher power than existing tests.
Lowered regularity assumption for a phase-dependent Helfrich energy equation.
problem Analyzing the phase separation line of the Helfrich energy.
method Used a carefully chosen test function with a signed distance function.
result Regularity assumption lowered from C2 to C1,1 for the phase separation line. Mean field theory has been successfully used to analyze deep neural networks (DNN) in the infinite size limit. Given the finite size of realistic DNN, we utilize the large deviation theory and path integral analysis to study the deviation of functions represented by DNN from their typical mean field solutions. The para…
In latent Gaussian trees the pairwise correlation signs between the variables are intrinsically unrecoverable. Such information is vital since it completely determines the direction in which two variables are associated. In this work, we resort to information theoretical approaches to achieve two fundamental goals: Fir…
SLIM model predicts social network polarization using signed links.
problem Polarization and filter bubbles in social networks.
method Signed relational Latent dIstance Model (SLIM) using Skellam distribution.
result SLIM model accurately predicts friendships and animosity in social networks.
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…
Flow approach solves Toda system equations.
problem Solving the Toda system equations.
method Introducing Toda flow to study the system.
result Global existence and convergence conditions established.
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.
Unified signSGD and gradient descent analysis for neural networks.
problem Performance of sign-based optimization methods in neural networks.
method Unified analysis of separable smoothness and ℓ∞-smoothness, isolating geometric properties affecting performance. result Sign-based methods are preferable over gradient descent under specific Hessian properties in deep networks.
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.
Note on subgaussian bounds for sign-quantized linear maps.
problem Understanding subgaussian behavior of sign-quantized linear maps.
method Developed a dimension-independent subgaussian concentration bound for Gaussian vectors under nonlinear mappings.
result Answered a question about sign-quantized linear maps using a new subgaussian bound.
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 solutions found for Yamabe problem on spheres with foliations.
problem Yamabe problem on spheres with singular Riemannian foliations.
method Variational methods, symmetries from foliations, Sobolev embedding theorem, Principle of Symmetric Criticality.
result Existence of sign-changing and positive solutions with specific symmetries.
Novel metrics improve machine learning models for ICU patient care.
problem Predicting vital sign trajectories for early detection of adverse events.
method Developed novel performance metrics aligned with clinical contexts, validated on simulated and real datasets, and optimized neural networks using these metrics.
result Neural networks trained with these metrics excel in predicting clinically significant events.
By specifying model free preferences towards simple nested classes of lottery pairs, we develop the dual story to stand on equal footing with that of (primal) risk apportionment. The dual story provides an intuitive interpretation, and full characterization, of dual counterparts of such concepts as prudence and tempera…
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 …
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.
Fast Gradient Sign Method (FGSM) is a popular method to generate adversarial examples that make neural network models robust against perturbations. Despite its empirical success, its theoretical property is not well understood. This paper develops theory to explain the regularization effect of Generalized FGSM, a class…