Computer-aided breast cancer diagnosis in mammography is limited by inadequate data and the similarity between benign and cancerous masses. To address this, we propose a signed graph regularized deep neural network with adversarial augmentation, named \textsc{DiagNet}. Firstly, we use adversarial learning to generate p…
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.
Study examines Kähler immersions of ALE Kähler metrics into complex space forms.
problem Kähler immersions of ALE Kähler metrics into complex space forms.
method Investigation of the relationship between Kähler immersions and the mass of ALE Kähler metrics.
result ALE Kähler metrics with positive mass do not admit a Kähler immersion into complex Euclidean space.
Geometric framework for signed multivariate tail-dependence compatibility at various thresholds.
problem Modeling and analyzing signed multivariate tail-dependence across different thresholds.
method Developed a geometric witness framework to represent and invert signed tail families, identifying nonnegative weights and normalized masses.
result Characterization and synthesis of signed multivariate tail-dependence at finite thresholds, preserving the complete signed tail family throughout.
AI model identifies chemical agents in MCI with high accuracy.
problem Identifying chemical agents in mass casualty incidents.
method Reverse engineered signs/symptoms, trained using ANN, BDT, and WISER.
result WISER outperformed ANN and BDT in identifying chemical agents.
We show that the limit at infinity of the vector-valued Brown-York-type quasi-local mass along any coordinate exhaustion of an asymptotically hyperbolic 3-manifold satisfying the relevant energy condition on the scalar curvature has the conjectured causal character. Our proof uses spinors and relies on a Witten-type …
We use an idea of Wang and Yau to give a new definition of quasi-local mass for a topological sphere in an initial date set. The new definition modifies Brown-York's definition by using certain spinor norm as lapse function. And it requires mean curvature of the topological sphere satisfies apparent horizon conditions,…
Closed and broken electromagnetic orbits in Kerr-Newman spacetime
problem Constructing closed and broken electromagnetic orbits in the Kerr-Newman spacetime
method Constructing smooth closed electromagnetic orbits tangent to the axial Killing field and proving the existence of spherical electromagnetic orbits
result Proving the existence of spherical electromagnetic orbits and constructing closed broken electromagnetic orbits
We quantify conditions that ensure that a signed measure on a Riemannian manifold has a well defined centre of mass. We then use this result to quantify the extent of a neighbourhood on which the Riemannian barycentric coordinates of a set of n+1 points on an n-manifold provide a true coordinate chart, i.e., the ba…
Signed Evidence Flow (SEF) combines fitted prediction with signed feature attributions to measure evidence conflict and stability.
problem Modern data analysis lacks mechanisms to show the clarity, conflict, or stability of evidence behind predictions.
method Signed Evidence Flow (SEF) combines fitted prediction with signed feature attributions.
result SEF measures conflict and stability, and shows that conflict can improve loss prediction beyond confidence.
Ricci flow preserves ALF structure on high-dimensional manifolds.
problem Preserving ALF structure under Ricci flow on high-dimensional manifolds.
method Developed a weighted Fredholm framework and a renormalized functional λ_ALF.
result Ricci flow preserves ALF structure on ALF n-manifolds with n≥4.
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…
Method shows existence of conformal metrics with constant Q-curvature on manifolds.
problem Existence of conformal metrics with constant Q-curvature on manifolds. method Bahri-Coron barycenter method applied to GJMS operator.
result Existence of positive solutions for the 2k-th order Q-curvature equation. Constructs fill-ins with scalar curvature lower bounds for geometric applications.
problem Realizing (n−1)-dimensional manifolds as boundaries of higher-dimensional ones with controlled scalar curvature. method Variations of an argument by Miao and the author, constructing fill-ins with different scalar curvature lower bounds.
result Illustrates applications to geometric inequalities in general relativity, including mass bounds and Penrose inequalities.
Let (M,g) be a two dimensional compact Riemannian manifold of genus g(M)>1. Let f be a smooth function on M such that f≥0,f≡0,minMf=0. Let p1,…,pn be any set of points at which f(pi)=0 and D2f(pi) is non-singular. We prove that for all sufficiently small $λ>…
Algorithm finds best Dirac mass approximation of target measure.
problem Finding optimal Dirac mass approximation of target measure.
method Minimizes statistical distance between original measure and quantized version using Huber-energy kernel.
result HEMQ algorithm robust and versatile, matches intuitive behavior.
Researchers simplify Einstein-scalar field equations on specific manifolds.
problem Complexity of Einstein-scalar field conformal constraint equations.
method Study under harmonic manifold assumptions, reducing equations to a single nonlinear equation.
result Solutions exist on Euclidean and hyperbolic manifolds, nonexistence on spheres.
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…
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.
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 X-ADM mass is shown to be equivalent to the ADM mass, proving the X-positive mass theorem in all dimensions.
problem Proving the X-positive mass theorem for all dimensions.
method Conformal reduction argument.
result The X-ADM mass is equivalent to the ADM mass, proving the X-positive mass theorem in all dimensions.
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.
The paper studies nonlinear mass concepts in 3-manifolds with nonnegative scalar curvature.
problem Nonlinear isocapacitary mass in 3-manifolds with nonnegative scalar curvature.
method Derives positive mass theorems and shows mass coincides with ADM mass under mild conditions.
result Nonlinear masses coincide with ADM mass and prove the Penrose inequality.
Reformulates mod-two APS index using domain-wall fermion.
problem Non-local APS boundary condition and global anomalies.
method Physicist-friendly reformulation of APS index using domain-wall fermion.
result Equivalence between two formulations of APS index.
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…
Equivalence proven for isocapacitary mass notions.
problem Proving equivalence of isocapacitary mass notions.
method Proof of equivalence for G. Huisken's and J. L. Jauregui's isocapacitary mass.
result Equivalence of isocapacitary mass notions proven.
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 …
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.
The paper defines a new mass quantity for 3-manifolds and proves a positive mass theorem.
problem Proving the positive mass theorem for a new geometric quantity.
method Defining X-ADM mass and using a monotonicity formula. result Established a relative positive mass theorem for asymptotically flat 3-manifolds.
New algorithms for multivariate RL improve decision-making in complex systems.
problem Complex multi-objective decision-making in reinforcement learning.
method Oracle-free and computationally-tractable algorithms for multivariate distributional RL.
result Convergence rates match scalar reward settings and provide insights into reward dimensionality.
Introduce new boundary mass for asymptotically flat half-manifolds
problem Define boundary mass for asymptotically flat half-manifolds
method Introduce new boundary mass
result Define boundary mass for asymptotically flat half-manifolds
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 prove directly without using a density theorem that (i) the ADM mass defined in the usual way on an asymptotically flat manifold is equal to the mass defined intrinsically using Ricci tensor; (ii) the Hamiltonian formulation of center of mass and the center of mass defined intrinsically using Ricci tensor are the sa…
Continuous metrics on R^3 with specific properties have non-negative harmonic mass.
problem Proving non-negativity of mass for continuous metrics.
method Defining harmonic mass and using properties of approximating smooth metrics.
result The harmonic mass of continuous metrics is non-negative.
The paper examines mass aspects at future null infinity and limits of quasilocal mass.
problem Understanding mass aspects and limits of quasilocal mass at future null infinity.
method Review and extension of Bondi mass and mass loss formula in Bondi-Sachs coordinate system.
result New results about the limit of quasilocal mass of unit spheres at null infinity.
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.
Study the mass of flat 3-manifolds with boundary using specific methods.
problem Calculate the mass of asymptotically flat 3-manifolds with boundary.
method Use the method of Bray-Kazaras-Khuri-Stern to derive a mass formula.
result Derive sufficient conditions for the positivity of the mass.
Unified definition of mass aspect function for weakly regular hyperbolic manifolds.
problem Ambiguity in mass definition for asymptotically hyperbolic manifolds.
method Introduced an ADM-style mass aspect function for broad asymptotics and low regularity.
result Unified mass aspect function exhibits favorable covariance properties.
Local mass perspective on Bayesian inference
problem Measuring distributional discrepancy in Bayesian inference
method Introducing Mass Index and Regularised Extended KL
result Proving inequalities for comparing local small-ball masses
On asymptotically flat and asymptotically hyperbolic manifolds, by evaluating the total mass via the Ricci tensor, we show that the limits of certain Brown-York type and Hawking type quasi-local mass integrals equal the total mass of the manifold in all dimensions.
Simple proof for sphere mass calculation.
problem Computing the ADM mass of static sphere extensions.
method Uses mass formula for static asymptotically flat manifolds.
result Validated mass formula for small spheres.
New ADM mass definition for weakly regular manifolds.
problem Defining ADM mass for non-smooth manifolds.
method Proposed a new definition for metrics with local Sobolev regularity.
result Finite mass, invariance under coordinate changes, and agreement with smooth case.
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…