The paper characterizes potential functions whose level sets are orbits in mechanical systems.
problem Characterizing smooth potential energy functions on the plane with specific level set properties.
method Analyzing inverse curvature flow and properties of level sets.
result Analytic or functions with totally path-disconnected critical sets must be radial, while every compact convex set is a critical set of a Levi potential.
Find conditions for starshapedness of level sets in Heisenberg group.
problem Ensure starshapedness of level sets of p-capacitary potentials. method Examine horizontally p-harmonic functions in the Heisenberg group. result Sharp conditions for strictly starshaped level sets.
Unified view of monotonicity formulas for inverse mean curvature flow and p-capacitary potentials.
problem Understanding monotonicity formulas for various geometric flows and potentials.
method Refined analysis of p-capacitary potentials and their level sets. result Strong convergence of p-capacitary potentials to inverse mean curvature flow and curvature varifolds. Proves Riemannian starshape of capacitary potential levels.
problem Proving starshape of capacitary potential levels in Riemannian warped products.
method Proved using Riemannian geometry and starshaped rings.
result Every level set of capacitary potential of starshaped rings is starshaped in Riemannian warped products.
The paper proves a geometric capacitary inequality for sub-static manifolds with harmonic potentials.
problem Proving a geometric capacitary inequality for sub-static manifolds with harmonic potentials.
method Introducing a one-parameter family of functions that are monotone along the level-set flow of the potential, up to the optimal threshold.
result Proves a geometric capacitary inequality where the capacity of the horizon plays the same role as the ADM mass in the celebrated Riemannian Penrose Inequality.
Paper proves extended Minkowski Inequality using nonlinear potential theory.
problem Proving an extended Minkowski Inequality for smooth bounded sets.
method Using monotonicity formulas derived from p-capacitary potentials and level set flow. result Stronger conclusions in dimensions n≥8 compared to previous methods. Computational Drug Repositioning (CDR) is the task of discovering potential new indications for existing drugs by mining large-scale heterogeneous drug-related data sources. Leveraging the patient-level temporal ordering information between numeric physiological measurements and various drug prescriptions provided in E…
Model predicts community health outcomes from social media language.
problem Linking social media language to community health outcomes.
method Sentence embeddings, regression model, clustering, without additional data.
result Predicts community-level medical outcomes from social media language.
New proof of Penrose inequality using potential theory.
problem Proving the Riemannian Penrose inequality for black holes.
method Establishing a monotonicity formula for the p-capacitary potential.
result A new proof of the Penrose inequality for black holes.
In this paper we present a new approach to the study of asymptotically flat static metrics arising in general relativity. In the case where the static potential is bounded, we introduce new quantities which are proven to be monotone along the level set flow of the potential function. We then show how to use these prope…
Modeling GDP growth rates using Lévy flights with confining potential.
problem Understanding the impact of firm size fluctuations on GDP.
method Combining microscopic firm growth rates with macroscopic GDP, using Lévy-stable fluctuations and a confining potential.
result The model accurately predicts 200 years of US GDP growth rates.
The paper finds optimal levels for traders in mean-reverting markets.
problem Determining optimal levels for traders in mean-reverting markets.
method Analytical framework using heat potentials.
result Developed an analytical solution for optimal levels.
The study examines constant weighted mean curvature hypersurfaces in shrinking Ricci solitons.
problem Characterizing constant weighted mean curvature hypersurfaces in shrinking Ricci solitons.
method Analyzing properties of hypersurfaces in specific ambient spaces (shrinking Ricci solitons).
result Conditions for a constant weighted mean curvature hypersurface to be a level set of the potential function.
The paper studies static manifolds with boundary and their properties.
problem Properties of static manifolds with boundary.
method Theorems relating topology and geometry, isoperimetric inequality, uniqueness theorems.
result Characterization of the round ball in Euclidean 3-space as the only scalar-flat static manifold with mean-convex boundary.
A new framework solves the causal frame problem using potential levels.
problem How to make decisions based on relevant information without considering irrelevant details.
method Introducing Potential Level (PL) and proposing a PL-based Inference Framework (PLIF).
result PLIF is consistent with causal judgment findings and makes testable predictions.
Study on gradient Ricci solitons with isoparametric potential functions.
problem Characterizing gradient Ricci solitons with isoparametric potential functions.
method Analyzes complete gradient Ricci solitons with isoparametric potential functions, proving theorems for steady and shrinking cases.
result Critical level sets of codimension greater than one for steady case, partial results for shrinking case.
We use a geometric construction to exhibit examples of autonomous Lagrangian systems admitting exactly two homoclinics emanating from a nondegenerate maximum of the potential energy and reaching a regular level of the potential having the same value of the maximum point. Similarly, we show examples of Hamiltonian syste…
We describe two-dimensional potential Schrodinger and Dirac operators which are finite-gap at one energy level and have singular spectral curves. It appears that the singularities can be rather complicated. Such Dirac operators appear as the spectral curves of tori immersed into the three-space.
Proposes efficient FOBO algorithms for global maxima of expensive functions.
problem Finding global maxima of expensive-to-evaluate functions.
method Uses gradient information from Gaussian process models to identify potential query points.
result Proposed algorithms outperform state-of-the-art FOBO algorithms.
Proposes a novel tensor-based approach for multi-level link prediction.
problem Inferring potential links from observed networks.
method Tensor-based joint network embedding capturing pairwise and hyperlinks.
result Improves hyperlink and pairwise link prediction accuracy.
Paper excludes the lowest energy level as an accumulation point for harmonic maps into analytic manifolds.
problem Analytic manifolds and their harmonic maps energy spectrum.
method Exclusion of the lowest energy level as an accumulation point using obstructions to the gluing of harmonic spheres and Lojasiewicz-estimates.
result Proves that the lowest energy level is not an accumulation point for generic 3-manifolds.
Study the limit of Calabi-Yau metrics with degenerate skeletons.
problem Understanding the behavior of Calabi-Yau metrics with degenerate skeletons.
method Using polarised degenerations and optimal transport problems.
result Describe the limiting behaviour of the Calabi-Yau potential.
New sigma models compute graviton scattering amplitudes from quaternionic geometry.
problem Computing graviton scattering amplitudes from quaternionic geometry.
method Introducing new twistor sigma models that encode finite non-linear perturbations of flat structures.
result Provides a first-principles derivation of Hodges' formula for MHV graviton amplitudes.
We consider self-similar solutions to mean curvature evolution of entire Lagrangian graphs. When the Hessian of the potential function u has eigenvalues strictly uniformly between -1 and 1, we show that on the potential level all the shrinking solitons are quadratic polynomials while the expanding solitons are in one…
Study potential computational gaps in symmetric binary perceptrons using fl-RDT.
problem Potential statistical-computational gaps in symmetric binary perceptrons.
method Parametric utilization of fully lifted random duality theory (fl-RDT).
result Observation of a computational gap SCG=αc−αa in SBP. In this paper we study some global properties of static potentials on asymptotically flat 3-manifolds (M,g) in the nonvacuum setting. Heuristically, a static potential f represents the (signed) length along M of an irrotational timelike Killing vector field, which can degenerate on surfaces corresponding to the…
This note is devoted to Keller-Lieb-Thirring spectral estimates for Schrödinger operators on infinite cylinders: the absolute value of the ground state level is bounded by a function of a norm of the potential. Optimal potentials with small norms are shown to depend on a single variable. The proof is a perturbation arg…
Generative model learns conditional distributions on collective variable levels.
problem Modeling conditional probability distributions on collective variable levels.
method General and efficient learning approach, data enrichment strategy.
result Effective generative models on different level-sets of collective variables.
New electromagnetic curvature defined via Jacobi-Maupertuis, showing positive curvature for non-zero magnetic force.
problem Defining and analyzing electromagnetic curvature.
method Using Jacobi-Maupertuis reparametrization and energy analysis.
result Positive electromagnetic Ricci curvature for non-zero magnetic force and small potential.
In this paper we prove the infinitesimal uniqueness theorem for the Newton potential of non simply connected bodies using the singularity theory approach. We consider the Newtonian potentials of the domains in Rn boundaries of which are the vanishing cycles on the level hypersurface of a holomorphic function w…
A new method boosts survival analysis by stratifying patients and removing noise covariates.
problem Weak detection of treatment differences in randomized clinical trials due to patient heterogeneity.
method 5-Step Stratified Testing and Amalgamation Routine (5-STAR) using elastic net Cox regression and conditional inference trees.
result The 5-STAR routine significantly improves power in detecting treatment effects compared to traditional methods.
Paper explores generalization of AID-based bi-level optimization methods.
problem Uncertainty in generalization properties of AID-based bi-level optimization methods.
method Uniform stability analysis and convergence study of AID-based methods.
result AID-based methods can achieve similar generalization as single-level nonconvex problems.
This work defines mean curvature in non-smooth spaces and proves sharp inequalities.
problem Defining and proving geometric inequalities in non-smooth metric spaces.
method Introducing mean curvature for level sets in non-smooth spaces and proving sharp inequalities.
result Mean curvature vectors in non-smooth spaces satisfy sharp Willmore inequalities.
Hierarchical framework for model evaluation on leaderboards
problem Uncertainty and variability in model performance across tasks
method Hierarchical framework with task-level and leaderboard-level rank prediction intervals
result Statistically valid and informative model rank intervals
Deep learning predicts stress levels from mouse hippocampus activity.
problem Stress level in mice under different environments.
method Deep learning combined with neuron decoding.
result Deep learning model accurately predicts stress levels.
Let M be a Kaehler manifold with a free, holomorphic and Hamiltonian action of the standard n-torus T. We give a simple, explicit and canonical formula for the Kaehler potential on the Kaehler reduction of M. As a consequence we can derive improvements of several classical results known for more general Hamiltonian red…
Investigates the cost-effectiveness of security features in smart card chips.
problem Costs of adding security features to smart card chips.
method Examines production phases, costs, and security features.
result Security features are worth the cost due to potential damages from attacks.
Generic potential primes have no self-intersections or intersections.
problem Finding non-degenerate periodic orbits without self-intersections.
method Generic convex Hamiltonian approach and Mañé genericity.
result Prime periodic orbits do not intersect or have self-intersections.
Graph Interplay (GIP) improves GSSL performance by enhancing graph-level communications.
problem Improving graph self-supervised learning performance without labeled data.
method Graph Interplay (GIP) introduces random inter-graph edges within standard batches to enhance GSSL methods.
result GIP significantly outperforms existing GSSL methods across multiple benchmarks.
Study uses Open Banking data to estimate customer value, showing potential 21% increase.
problem Limited CLV estimation using single-entity data.
method Introduces PCLV framework using Open Banking data for comprehensive customer value estimation.
result Open Banking data can estimate PCLV per competitor, showing a 21.06% increase over Actual CLV.
New algorithm speeds up user preference learning in conversational contexts.
problem Limited performance of existing conversational contextual bandit approaches.
method Proposes ConLinUCB framework and two algorithms, ConLinUCB-BS and ConLinUCB-MCR, with explorative key-term selection.
result Proves tighter regret bounds and achieves significant computational efficiency improvements.
Deep neural networks improve CMB lensing potential reconstruction for future cosmic microwave background experiments.
problem Low noise levels in upcoming CMB experiments require improved methods for extracting lensing potential.
method Deep convolutional neural networks (ResUNet) trained on simulated data without physical parametrization.
result ResUNets recover lensing potential with higher signal-to-noise ratio than quadratic estimator.
Unified algorithm for Bayesian optimization and level-set estimation.
problem Efficiently optimizing and estimating in settings with pointwise costs and heteroscedastic noise.
method Truncated Variance Reduction (TruVaR) algorithm that greedily shrinks a sum of truncated variances.
result Unified theoretical guarantee for TruVaR covering pointwise costs and heteroscedastic noise.
New framework for RL with opponents, improving learning outcomes.
problem Learning in RL with potential adversaries.
method Threatened Markov Decision Processes (TMDPs) and level-k thinking.
result Improved RL performance by accounting for adversaries.
Unified framework for imbalanced data resampling improves classification performance.
problem Data imbalance negatively impacts machine learning performance.
method Unified framework combining over- and undersampling with radial basis functions optimization.
result Potential Anchoring outperforms state-of-the-art resampling algorithms.
BiDVL improves EBLVMs for visual tasks by optimizing two variational distributions.
problem Training EBLVMs is challenging due to intractable distributions.
method Bi-level doubly variational learning with two tractable distributions.
result BiDVL achieves impressive image generation and reconstruction performance.
Biological systems are often modelled at different levels of abstraction depending on the particular aims/resources of a study. Such different models often provide qualitatively concordant predictions over specific parametrisations, but it is generally unclear whether model predictions are quantitatively in agreement, …
New algorithm tackles nested bi-level optimization problems for robust feature learning.
problem Nested compositional bi-level optimization problems in machine learning.
method Stochastic approximation algorithms for solving nested compositional bi-level optimization problems without matrix inversions.
result Achieves an ε-stationary solution with an oracle complexity of approximately O_T(1/ε^2).