Sharp ABP estimate on metric spaces via optimal transport.
problem Sharp ABP estimate on metric measure spaces.
method Optimal transport theory.
result Established a sharp ABP estimate on metric measure spaces.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,786 papers · 148 categories
Trend · papers per month
31 results for “ABP”
ABPS improves RL training efficiency by sharing policies and evolving hyper-params.
problem Data inefficiency in training deep RL models for real-world applications.
method ABPS: adaptive behavior policy sharing; ABPS-PBT: hybridizing ABPS with PBT for evolving hyper-params.
result ABPS achieves superior performance and reduced variance compared to conventional hyper-parameter tuning.
Proves inequalities for tensor fields on submanifolds using ABP method.
problem Proving Michael-Simon inequalities for tensor fields.
method Alexandrov-Bakelman-Pucci (ABP) method
result Proved Michael-Simon inequalities for tensor fields.
Paper uses ABP method to prove logarithmic Sobolev inequalities on curved spaces.
problem Proving logarithmic Sobolev inequalities on manifolds with nonnegative curvature.
method Employing the ABP method developed by Brendle.
result Sharp and logarithmic Sobolev inequalities established.
Employing a notion of curvature for arbitrary closed sets we prove an ABP-type estimate for a class of singular submanifolds of arbitrary codimension and bounded mean curvature recently introduced by B. White. A weak-Harnack-type estimate is then derived using the ABP estimate. These results generalize analogous result…
Develop an ABP approach to Sobolev and Michael-Simon inequalities beyond Euclidean volume growth.
problem Developing an ABP approach to Sobolev and Michael-Simon inequalities under volume noncollapsing assumptions.
method Using a refinement of Brendle's contact-set argument to derive lower bounds for the volumes of geodesic balls.
result A Michael-Simon type inequality for immersed submanifolds with nonnegative sectional curvature and volume noncollapsing.
The ABP method is used to prove geometric inequalities for submanifolds and tensors.
problem Establishing geometric inequalities for submanifolds and tensors.
method Application of the Alexandrov-Bakelman-Pucci (ABP) method.
result Logarithmic Sobolev inequality and Sobolev-type inequality for submanifolds and tensors.
New estimate for complex Monge-Ampère equations improves previous results.
problem Improving estimates for complex Monge-Ampère equations.
method Using the ABP maximum principle to prove a new gradient estimate.
result Proves a new gradient estimate for complex Monge-Ampère equations.
New Sobolev inequalities found for curved spaces.
problem Sobolev inequalities in curved spaces with specific decay conditions.
method Used ABP method developed by Cabré and Brendle.
result Established Sobolev inequalities for compact domains and submanifolds.
Rare dense solutions clusters in asymmetric binary perceptrons -- local entropy via fully lifted RDTstat.ML
New method finds rare dense clusters in asymmetric binary perceptrons, resolving algorithmic hardness.
problem Resolving algorithmic hardness in asymmetric binary perceptrons.
method Fully lifted random duality theory (fl RDT) and large deviation upgrade (sfl LD RDT).
result Local entropy breaks down for constraint densities in (0.77, 0.78) interval, matching current solver limits.
Sharp inequalities for manifolds with nonnegative curvature.
problem Establishing inequalities for manifolds with nonnegative curvature.
method Using the ABP-method, generalizing previous work by Brendle.
result Sharp Sobolev and isoperimetric inequalities for compact domains and submanifolds.
Machine learning predicts phase behavior in active matter suspensions.
problem Predicting phase behavior in active matter systems using machine learning.
method Used deep learning techniques, including fully connected networks and graph neural networks, to predict motility-induced phase separation (MIPS) in ABP suspensions.
result Strong agreement between machine learning predictions and MIPS binodal from simulations, suggesting machine learning as an effective method for phase behavior determination.
Gradient estimate proved for Donaldson's equation on Kähler manifolds.
problem Proving gradient estimates for Donaldson's equation on compact Kähler manifolds.
method Using uniform upper bounds for and Alexandrov-Bakelman-Pucci (ABP) maximum principle.
result Gradient estimate for Donaldson's equation derived from uniform bounds.
The study analyzes weighted manifolds with curvature bounds, proving eigenvalue estimates and inequalities.
problem Analyzing geometric properties of weighted manifolds under Ricci curvature bounds.
method Develops geometric analysis techniques on weighted Riemannian manifolds with lower -weighted Ricci curvature bounds.
result Proves eigenvalue estimates for Steklov and ABP inequalities on weighted manifolds.
New insights into binary perceptron reveal phase transitions and algorithmic thresholds.
problem Understanding the statistical-computational gap in binary perceptron models.
method Application of fully lifted random duality theory (fl RDT) to uncover structural changes.
result Numerical estimates of constraint density thresholds align with theoretical predictions.
We prove some old and new isoperimetric inequalities with the best constant using the ABP method applied to an appropriate linear Neumann problem. More precisely, we obtain a new family of sharp isoperimetric inequalities with weights (also called densities) in open convex cones of . Our result applies to…
Sharp inequality outside ball proved using Neumann method.
problem Anisotropic isoperimetric inequality for domains outside an Euclidean ball.
method Applied ABP method to Neumann boundary value problem.
result Proved sharp anisotropic isoperimetric inequality.
Paper proves new isoperimetric inequality for minimal submanifolds with free boundary.
problem Proving a relative isoperimetric inequality for minimal submanifolds with free boundary.
method Generalized restricted normal cones, ABP method, Brendle's approach.
result Optimal relative isoperimetric inequality for minimal submanifolds with free boundary on convex surfaces.
Sobolev inequalities involving 2-tensor fields in manifolds with nonnegative sectional curvaturemath.DG
Log Sobolev and Michael Simon inequalities for tensor fields on curved manifolds.
problem Establishing inequalities for tensor fields on curved manifolds.
method Applying the ABP method to symmetric tensor fields on manifolds with nonnegative sectional curvature.
result Log Sobolev and Michael Simon inequalities for tensor fields.
New algorithm learns optimal policy with multi-step lookahead information.
problem Learning optimal policy in reinforcement learning with multi-step lookahead information is NP-hard.
method Adaptive batching policies that process lookahead in state-dependent chunks.
result Order-optimal regret bounds up to a constant factor of lookahead horizon.
New proofs and inequalities for capillarity problems quantify asymmetries.
problem Quantifying asymmetries in capillarity functionals.
method ABP-type technique, symmetrization, selection-type argument.
result Sharp quantitative inequalities for asymmetries in capillarity problems.
Isoperimetric and Michael-Simon inequalities on manifolds with asymptotically nonnegative curvaturemath.DG
The study proves inequalities on curved spaces without global curvature bounds.
problem Proving inequalities on manifolds with non-negative curvature outside compact sets.
method ABP method localized to regions of non-negative curvature, spectral properties of manifolds.
result Validated isoperimetric and Michael-Simon inequalities on manifolds with asymptotically non-negative curvature.
New Sobolev inequality found for mean convex spacelike submanifolds in Minkowski space.
problem Finding a Sobolev inequality for mean convex spacelike submanifolds in Minkowski space.
method Applying the ABP estimate method to spacelike submanifolds in .
result Obtained a Sobolev inequality without a mean curvature term for mean convex hypersurfaces.
Proves inequality for tensor fields on curved spaces.
problem Generalizing inequality for tensor fields on curved spaces.
method Alexandrov-Bakelman-Pucci (ABP) method
result Proves Michael-Simon-Sobolev inequality for tensor fields.
Asymptotically non-negative Ricci curvature, elliptic Kato constant and isoperimetric inequalitiesmath.DG
The paper proves isoperimetric inequalities in manifolds with small negative Ricci curvature.
problem Proving isoperimetric inequalities in manifolds with small negative Ricci curvature.
method Expanding on the ABP method, the paper uses the elliptic Kato constant to control the non-negativity of the Ricci-tensor and applies techniques from Li-Tam and Kasue.
result Sharp isoperimetric inequalities in the limit are proven in the presence of small negative curvature.
On a Riemannian metric-measure space, we establish an Alexandrov-Bakelman-Pucci type measure estimate connecting Bakry-Émery Ricci curvature lower bound, modified Laplacian and the measure of certain special sets. We apply this estimate to prove Harnack inequalities for the modified Laplacian operator and fully non-lin…
Gradient bounds and Liouville theorems for quasi-linear equations on manifolds with nonnegative Ricci curvature.
problem Establishing bounds and theorems for solutions to quasi-linear elliptic equations on compact manifolds with nonnegative Ricci curvature.
method Gradient bounds, Liouville-type theorems, local splitting theorem, Harnack-type inequality, ABP estimate.
result Gradient bounds and Liouville-type theorems for solutions to quasi-linear equations on compact manifolds with nonnegative Ricci curvature.
Estimates complex Hessian integral for complex Monge-Ampère equations.
problem Improving classical ABP estimate for complex settings.
method De Giorgi iteration method for complex Monge-Ampère equations.
result Sharp gradient estimates for complex Monge-Ampère equations.
Logarithmic Sobolev inequality proven for non-compact self-shrinkers.
problem Establishing a logarithmic Sobolev inequality for non-compact self-shrinkers.
method Using Alexandrov-Bakelman-Pucci (ABP) method to prove the inequality for Euclidean space, then applying this method to non-compact self-shrinkers.
result Optimal logarithmic Sobolev inequality for complete, non-compact, properly embedded self-shrinkers.
In this article we construct a family of genus two Lefschetz fibrations with , , and by applying a single lantern substitution to the twisted fiber sums of Matsumoto's genus two Lefschetz fibration over .…
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 in SBP.