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.
Paper solves curvature prescription on unit ball with sign-changing functions.
problem Prescribing mean curvature on the unit ball with sign-changing functions.
method Negative gradient flow method to realize f as mean curvature. result Proves that a sign-changing function f can be realized as the boundary mean curvature of a conformal metric. New method uses geometric mean of Laplacians for better clustering of signed networks.
problem Existing spectral clustering methods for signed networks fail in noisy conditions.
method Proposes using geometric mean of Laplacians of positive and negative networks.
result Geometric mean outperforms arithmetic mean in recovering ground truth clustering.
Researchers solve the negative Yamabe case for scalar curvature prescription.
problem Prescribing scalar curvature on manifolds with negative Yamabe invariant.
method A new variational approach to the problem.
result Existence of solutions for sign-changing scalar curvature functions, but not uniqueness.
Researchers propose a method to simulate quantum annealing with non-stoquastic Hamiltonians.
problem Negative sign problem in quantum Monte Carlo simulation of non-stoquastic Hamiltonians.
method Alternative approach using Suzuki--Trotter decomposition to avoid negative sign problem.
result Demonstrated method's validity through application to a simple problem.
Better spectral partitioning of signed graphs using standard Laplacian.
problem Meaningless partitioning using signed Laplacian eigenvectors.
method Use standard graph Laplacian for spectral partitioning.
result Fiedler vector of standard Laplacian is easier to compute and more beneficial.
Signed network models reduce portfolio risk by considering negative edges in financial markets.
problem Tackles portfolio optimization in financial markets by exploiting negative edges in network representations.
method Proposes a discrete optimization scheme to reduce asset selection, building time series of signed networks from asset returns.
result Empirical results show that signed network portfolios perform similarly to classical mean-variance optimization and equally weighted benchmarks.
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.
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.
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.
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.
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.
We perform an analysis of fractal properties of the positive and the negative changes of the German DAX30 index separately using Multifractal Detrended Fluctuation Analysis (MFDFA). By calculating the singularity spectra f(α) we show that returns of both signs reveal multiscaling. Curiously, these spectra display a s…
A new method clusters signed networks using a modified MBO scheme.
problem Clustering signed networks with mixed positive and negative edge weights.
method Adapted MBO scheme for graph-based diffuse interface model.
result Method outperforms state-of-the-art approaches on various datasets.
The paper solves a problem related to curvature in complex geometry.
problem Resolving the prescribed Chern scalar curvature problem.
method Divided into three cases based on the sign of the Gauduchon degree, analyzed separately.
result Proves that certain functions are Chern scalar curvatures of conformal metrics.
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.
Consider a random vector with finite second moments. If its precision matrix is an M-matrix, then all partial correlations are non-negative. If that random vector is additionally Gaussian, the corresponding Markov random field (GMRF) is called attractive. We study estimation of M-matrices taking the role of inverse sec…
Copulas reveal strong positive dependencies in stock demand fluctuations due to volume imbalances.
problem Analyzing dependencies of stock demands using local volume fluctuations.
method Copula analysis of empirical data to model dependence structures.
result Large local fluctuations of signed traded volumes increase positive dependencies in demand but slightly lower negative ones.
New black hole solutions with positive and negative masses in 4 and 5 dimensions.
problem Constructing static vacuum black hole solutions with signed masses.
method Axisymmetric and bi-axisymmetric solutions in 4 and 5 dimensions, using Weyl-Papapetrou coordinates.
result Signed mass black holes can be superposed, with specific topologies in 5 dimensions.
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.
Study finds least-energy nodal solutions to the Yamabe problem on manifolds with boundary.
problem Existence of sign-changing solutions to the Yamabe problem on manifolds with boundary.
method Variational approach, analysis of conformal invariants, and sharp energy estimates.
result Existence of least-energy nodal solutions when the manifold is positive and the boundary has non-negative constant mean curvature.
Study on prescribing curvature on specific manifolds with negative Gauduchon degree.
problem Prescribing Chern scalar curvatures on compact Hermitian manifolds with negative Gauduchon degree.
method Analysis of geometric flow convergence to obtain existence results.
result Existence results for curvature functions that are nonzero and nonpositive, and sign-changing cases.
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.
SPONGE clusters signed graphs by solving a generalized eigenproblem.
problem Clustering signed graphs where affinity can be positive or negative.
method Generalized eigenproblem inspired by social balance theory.
result The method provides theoretical guarantees and outperforms existing methods.
New regularization method corrects over-shrinkage in small data regression.
problem Over-shrinkage in small data regression leading to underfitting.
method Negative-capable ridge family that permits negative regularization.
result Negative regularization acts as controlled anti-shrinkage, increasing effective complexity.
The main purpose of this short note is to point out that the negative gradient flow for the prescribed Q-curvature problem on Sn can be extended to handle the case that the Q-curvature candidate f may change signs.
A new method using negative-shifted gradient descent improves overparameterized linear regression by avoiding structural limitations of negative ridge endpoints.
problem Structural limitations of negative ridge endpoints in overparameterized linear regression.
method Negative-shifted gradient descent, which avoids the pole constraint of negative ridge endpoints.
result The method improves over all admissible endpoints by a polynomial factor in risk under explicit conditions.
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.
Study relates Gaussian curvature signs to cuspidal edge types and geometric invariants.
problem Understanding the relationship between Gaussian curvature and singularities of Gauss maps of cuspidal edges.
method Analyzes geometric invariants and types of singularities of Gauss maps to define and characterize positivity/negativity of cusps.
result Defines and characterizes positivity/negativity of cusps of Gauss maps by geometric invariants of cuspidal edges, and shows relation between sign of cusps and Gaussian curvature.
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.
We introduce a geometric evolution equation for 3-manifolds with sectional curvature of one sign which is in some sense dual to the Ricci flow. On a closed 3-manifold with negative sectional curvature, we establish short time existence and a pair of monotonicity formulas for solutions to the flow. One of these formulas…
PPC learns binary codes from data similarities and dissimilarities.
problem Creating efficient binary codes from data similarities and dissimilarities.
method PPC learns binary codes by modeling attractive and repulsive forces in a signed graph.
result PPC achieves superior results in nearest-neighbor searches compared to spectral methods.
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.
LSQ+ improves quantization of neural nets with Swish activations, achieving state-of-the-art results.
problem Quantization of neural nets with Swish activations, especially negative activations, leads to significant performance loss.
method Introduces learnable scale and offset parameters for asymmetric quantization, and uses MSE-based initialization for quantization parameters.
result Significantly outperforms LSQ for low-bit quantization of neural nets with Swish activations, achieving up to 5.6% gain with W2A2 quantization of EfficientNet-B0.
Paper solves Gauduchon scalar curvature problem on almost Hermitian manifolds.
problem Prescribed Gauduchon scalar curvature problem on almost Hermitian manifolds.
method Reduced to solving a semi-linear partial differential equation with exponential nonlinearity using super and sub-solution method.
result Existence of solution depends on the sign of a constant associated to Gauduchon degree.
The discrete-time mean-variance portfolio selection formulation, a representative of general dynamic mean-risk portfolio selection problems, does not satisfy time consistency in efficiency (TCIE) in general, i.e., a truncated pre-committed efficient policy may become inefficient when considering the corresponding trunc…
Meta-analysis improves personalized treatment rules across multiple sites.
problem Lack of generalizability in learning individualized treatment rules across different medical sites.
method Developed a method for individual-level meta-analysis of ITRs, borrowing sign-coherency information between sites.
result Jointly learned site-specific ITRs with improved generalizability.
For all complex dimensions n>=2, we construct complete Kaehler manifolds of bounded curvature and non-negative Ricci curvature whose Kaehler--Ricci evolutions immediately acquire Ricci curvature of mixed sign.
A new method models financial returns by separating sign and magnitude, improving forecasting accuracy.
problem Capturing nonlinear predictability in financial return dynamics.
method Decomposes returns into sign and magnitude components, using a joint distribution model.
result Significantly outperforms traditional linear models in forecasting U.S. stock market returns.
The paper solves the Dirichlet problem at infinity for certain negatively curved 3-manifolds.
problem Solving the Dirichlet problem at infinity for negatively curved 3-manifolds with expansive ends.
method Based on a result that does not require explicit curvature assumptions, the paper presents an example of a metric on an end with indefinite curvature for which the Dirichlet Problem at Infinity is solvable.
result The Dirichlet problem at infinity is solvable for certain negatively curved 3-manifolds with expansive ends.
New method controls FDR for sparse GLMs, identifying positive and negative relationships.
problem Sparse GLMs with high-dimensional data and varying sample size.
method Debiased-Lasso estimator and CLIME method for precision matrix estimation.
result Asymptotically controls directional FDR and FDV for sparse GLMs.
New method handles structural uncertainty in graphs better than existing models.
problem Handling heterophily and structural noise in semi-supervised learning on graphs.
method Sparse signed message passing network that models a posterior distribution over signed adjacency matrices.
result Our method outperforms strong baseline models on heterophilic benchmarks under both synthetic and real-world structural noise.
This work shows MLPs can approximate monotonic functions without bounded activations.
problem Optimizing MLPs with monotonic constraints and bounded activations.
method Generalized theoretical results showing MLPs with non-negative weights and saturating activations are universal approximators.
result MLPs with non-negative weights and saturating activations are universal approximators for monotonic functions.
Novel neural likelihood ratio estimation for negative data in particle physics.
problem Estimating likelihood ratios with negative probability densities and weights.
method Introducing a novel loss function and a new model architecture based on signed mixture models.
result Demonstrated improved estimation on a real-world example from particle physics.
New method finds optimal learning rates for neural nets.
problem Finding optimal learning rates in stochastic neural networks.
method Gradient-only line searches using Non-negative Associative Gradient Projection Points (NN-GPPs).
result Learning rates can be reliably resolved as step sizes along search directions.
The results on the mean-variance hedging problem in Gouriéroux, Laurent and Pham (1998), Rheinländer and Schweizer (1997) and Arai (2005) are extended to discontinuous semimartingale models. When the numéraire method is used, we only assume the Radon-Nikodym derivative of the variance-optimal signed martingale measure …
We show that the Lagrangian of classical mechanics on a Riemannian manifold of bounded geometry carries a periodic solution of motion with rescribed energy, provided the potential satisfies an asymptotic growth condition, changes sign, and the negative set of the potential is non-trivial in the relative homology.
New proof shows Jacobian of certain homeomorphisms is non-negative.
problem Determining sign of Jacobian for Sobolev homeomorphisms.
method Analyzes Hölder continuity and uses Sobolev space properties.
result Jacobian of homeomorphisms is non-negative almost everywhere.