Expected centre of mass for random embeddings is constant.
problem Understanding the expected centre of mass for random embeddings.
method Analyzing the Haar measure and Gaussian unitary ensemble on SL(N, C).
result The expectation of the centre of mass is a constant multiple of the identity matrix.
Adaptive HMC improves sampling efficiency by optimizing mass matrix.
problem Inefficient HMC performance due to mass matrix choice.
method Gradient-based adaptation of mass matrix to maximize proposal entropy.
result Adaptation method outperforms HMC variants by optimizing mass matrix.
Adaptive Bayesian sampling technique simplifies mass matrix learning.
problem Complexity in learning mass matrices for adaptive samplers.
method Monte Carlo EM framework with online learning of mass matrices.
result Comparable sampling accuracy to Riemannian samplers but faster.
Gradient flow solves optimal mass transport for covariance matrices.
problem Optimal mass transport for covariance matrices.
method Gradient flow on fiber bundle structure.
result Global convergence to polar decomposition.
QHMC improves HMC for sampling from complex distributions.
problem Inefficiency of HMC in sampling from spiky and multimodal distributions.
method Proposes QHMC, a quantum-inspired version of HMC with a random mass matrix.
result QHMC and QSGNHT achieve more stable and accurate sampling results.
SML improves pancreatic mass diagnosis accuracy using CT images.
problem Improving accuracy in pancreatic mass screening using CT imaging.
method Spectral machine learning method trained on 30,000 images, choosing fundamental images based on eigenvectors and removing irrelevant pixels.
result Achieved 94.6% test accuracy in diagnosing 113 patients.
Using the notion of vacuum pairs we show how the (square of the) mass matrix of the fermions can be considered geometrically as curvature. This curvature together with the curvature of space-time, defines the total curvature of the Clifford module bundle representing a ``free'' fermion within the geometrical setup of s…
Paper proposes a new approach to optimal transport for vector and matrix densities.
problem Optimal transport for vector and matrix densities with positivity and action transitivity constraints.
method Gauge-theoretic approach using semi-direct product groups of diffeomorphisms and gauge transformations.
result Bures-type metrics on semi-direct product groups relate to Wasserstein-type metrics on vector and matrix densities via Riemannian submersions.
Estimates matrix trace optimization with statistical learning theory.
problem Optimizing trace of parameter-dependent matrices.
method Monte Carlo estimator with bounds derived from epsilon nets and generic chaining.
result Predicts small sampling amount for matrices with small off-diagonal mass.
MASS Learning trains models to use minimal sufficient statistics, improving performance and uncertainty quantification.
problem Training deep networks to use minimal sufficient statistics for better performance and uncertainty quantification.
method MASS Learning trains models to produce minimal sufficient statistics with respect to a class of functions, using Conserved Differential Information (CDI).
result Deep networks trained with MASS Learning achieve competitive performance on supervised learning and uncertainty quantification benchmarks.
Novel concentration inequalities are obtained for the missing mass, i.e. the total probability mass of the outcomes not observed in the sample. We derive distribution-free deviation bounds with sublinear exponents in deviation size for missing mass and improve the results of Berend and Kontorovich (2013) and Yari Saeed…
New neural network enforces mass conservation for better ice flow predictions.
problem Reliably project future sea level rise by improving ice sheet model inputs.
method Proposes divergence-free neural networks (dfNNs) enforcing local mass conservation.
result dfNNs yield more reliable ice flux estimates compared to other models.
Efficient federated algorithm for calculating transportation barycenter.
problem Efficiently calculating the free-support transportation barycenter in a federated setting.
method Single-loop dual decomposition algorithm that uses only aggregated information.
result Significantly scalable and low-complexity algorithm for federated computation.
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.
Microbial identification is a central issue in microbiology, in particular in the fields of infectious diseases diagnosis and industrial quality control. The concept of species is tightly linked to the concept of biological and clinical classification where the proximity between species is generally measured in terms o…
New algorithm detects anomalies by forcing samples to displace mass in low-density regions.
problem Detecting anomalies in datasets.
method Mass Repulsing Optimal Transport (MROT) approach.
result Our algorithm improves anomaly detection over existing methods.
Two masses on surfaces with boundary converge to ADM mass.
problem Evaluating quasi-local masses on surfaces with boundaries.
method Hawking mass and Huisken's isoperimetric mass on surfaces with boundary, convergence to ADM mass.
result Convergence of Hawking and Huisken's masses to ADM mass.
Deep learning predicts mass from images with sparse ground truth.
problem Accurately estimating mass from images with limited ground truth.
method Semi-supervised deep learning with gradient aggregation and sparse ground truth.
result Deep neural network accurately predicts mass from images.
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.
Neural network predicts electron-ionization mass spectra quickly.
problem Identifying unknown molecules not in existing libraries.
method Lightweight neural network model for predicting mass spectra.
result High accuracy predictions of small molecule mass spectra.
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.
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.
We are concerned with obtaining novel concentration inequalities for the missing mass, i.e. the total probability mass of the outcomes not observed in the sample. We not only derive - for the first time - distribution-free Bernstein-like deviation bounds with sublinear exponents in deviation size for missing mass, but …
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.
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
The paper establishes geometric inequalities for quasi-local masses.
problem Lower bounds for quasi-local masses in terms of charge, angular momentum, and horizon area.
method Hamiltonian approach to three quasi-local masses: Brown-York, Liu-Yau, and Wang-Yau.
result Geometric inequalities motivated by ADM mass, interpreted as localized versions.
Deep learning reduces noise in weak lensing mass maps using GANs.
problem Noise reduction in weak lensing mass maps.
method Generative adversarial networks (GANs) applied to Subaru Hyper Suprime-Cam data.
result GANs successfully reproduce non-Gaussian information in denoised maps, showing stronger cosmological dependence.
Study on Hawking and Bartnik masses for specific surfaces.
problem Analyzing the positivity and bounds of Hawking and Bartnik masses for constant mean curvature surfaces.
method Intrinsic conditions and estimates for the masses of constant mean curvature surfaces.
result Positivity and estimates of Hawking and Bartnik masses for surfaces with nonnegative scalar curvature.
Researchers calculate quasi-local mass on unit spheres at infinity.
problem Computing quasi-local mass on unit spheres at spatial infinity.
method Developed new techniques to evaluate quasi-local mass.
result Leading order term of quasi-local mass recovers stress-energy tensor for vacuum spacetime.
Study bounds outer surfaces in small mass geometrostatic manifolds.
problem Bounding outer surfaces in geometrostatic manifolds with small ADM mass.
method Proving Intrinsic Flat Stability of the Positive Mass Theorem.
result Stability of the Positive Mass Theorem in geometrostatic manifolds with small ADM mass.
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…
GT estimator shows convergence for Markov samples, improving i.i.d. results.
problem Estimating missing mass in Markov samples.
method Analyzed convergence of Good-Turing estimator for Markov samples, considering spectral properties of transition matrices.
result The convergence of the GT estimator for Markov samples depends on the spectral properties of the transition matrices, leading to a new minimax rate of 1/(nβ5) for rank-2 Markov chains. 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.
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.
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.
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
Computes quasi-local mass at null infinity using Bondi-Sachs coordinates.
problem Global properties of quasi-local mass at null infinity.
method Evaluation of Wang-Yau quasi-local mass on unit spheres in Bondi-Sachs coordinates.
result Quasi-local mass is related to the news function in Bondi-Sachs coordinates.
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.
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.
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.
This paper shows that one cannot learn the probability of rare events without imposing further structural assumptions. The event of interest is that of obtaining an outcome outside the coverage of an i.i.d. sample from a discrete distribution. The probability of this event is referred to as the "missing mass". The impo…
New theorem for spacetime mass in noncompact regions.
problem Mass in noncompact spacetime regions.
method Developed mass type invariant and boundary conditions; proof based on spinors.
result Proved positive mass theorem for noncompact boundaries.
New optimal transport method handles mass creation and destruction.
problem Optimal re-balancing of portfolios with mass creation or destruction.
method Formalizes an optimal transport problem with mass-change factor.
result Existence of optimal transport plans and maps established.
Study on residual Monge-Ampère mass for symmetric plurisubharmonic functions.
problem Estimating the residual Monge-Ampère mass of symmetric plurisubharmonic functions with isolated singularities.
method Utilized Sasakian geometry to derive estimates on the residual mass in relation to Lelong numbers.
result Partially resolved the zero mass conjecture by Guedj and Rashkovskii.
The paper connects mass, harmonic functions, and capacity in asymptotically flat 3-manifolds.
problem Connections among ADM mass, harmonic functions, and capacity in asymptotically flat 3-manifolds.
method New formulae for ADM mass via harmonic functions, monotone quantities, and geometric inequalities.
result The mass-to-capacity ratio is bounded below by 1 - sqrt(normalized Willmore functional of the boundary).
Study on residual Monge-Ampère mass for symmetric plurisubharmonic functions.
problem Analyzing the residual Monge-Ampère mass of symmetric plurisubharmonic functions.
method Proved zero mass for functions with zero Lelong number at origin and S1-invariance. result Zero mass conjecture answered for symmetric functions.
New mass definition linked to ADM mass for general metrics.
problem Defining mass for metrics with low regularity.
method Using isocapacitary inequality to define total mass.
result Inequality between new mass and ADM mass proved.