Proves mass-capacity inequalities for critical area-normalized capacitors, improving Schwarzschild metric uniqueness.
problem Proving mass-capacity inequalities for critical area-normalized capacitors.
method Analyzes asymptotically flat manifolds with boundary capacity potential satisfying an overdetermined problem.
result Improves Schwarzschild metric uniqueness and results for spin asymptotically flat spacetimes.
We create a flat end foliation by critical spheres solving a Laplace-Beltrami problem.
problem Foliation of an asymptotically flat end by critical hypersurfaces.
method Constructing hypersurfaces as critical points of a functional, solving an over-determined boundary value problem.
result Solutions to the Laplace-Beltrami operator over a foliation of critical spheres.
In this paper, we settle in the affirmative the Jakobson-Levitin-Nadirashvili-Nigam-Polterovich conjecture, stating that a certain singular metric on the Bolza surface, with area normalized, should maximize the first eigenvalue of the Laplacian.
Second paper applies Morse index to constrained optimization problems.
problem Optimization problems with constraints on capillary surfaces.
method Abstract Morse index formulation applied to capillary surfaces.
result Precise determination of indices with constraints for various examples.
USeMOC framework reduces expensive simulations for MO optimization with constraints.
problem Efficiently optimizing multi-objective problems with constraints using expensive function evaluations.
method USeMOC framework uses surrogate models to identify promising candidates and selects the best based on uncertainty.
result USeMOC achieves more than 90% reduction in function evaluations for circuit optimization.
The aim of this paper is to give a formulation of the dynamics of nonlinear RLC circuits as a geometric Birkhoffian system and to discuss in this context the concepts of regularity, conservativeness, dissipativeness. An RLC circuit, with no assumptions placed on its topology, will be described by a family of Birkhoffia…
We present a formulation of general nonlinear LC circuits within the framework of Birkhoffian dynamical systems on manifolds. We develop a systematic procedure which allows, under rather mild non-degeneracy conditions, to write the governing equations for the mathematical description of the dynamics of an LC circuit as…
Researchers prove existence of metrics maximizing Laplace eigenvalue on all closed surfaces.
problem Proving the existence of metrics maximizing the first Laplace eigenvalue on closed surfaces.
method By contradiction and refinement of techniques, proving strict monotonicity under surface modifications.
result Existence of metrics maximizing the area-normalized first eigenvalue on all closed surfaces.
User interfaces provide an interactive window between physical and virtual environments. A new concept in the field of human-computer interaction is a soft user interface; a compliant surface that facilitates touch interaction through deformation. Despite the potential of these interfaces, they currently lack a signal …
In [dLMu05], DeLellis and Müller proved a quantitative version of Codazzi's theorem, namely for a smooth embedded surface Σ⊆R3 with area normalized to H2(Σ)=4π, it was shown that ∥AΣ−id∥L2(Σ)≤C∥AΣ0∥L2(Σ) , and building on…
This paper presents a spatiotemporal unsupervised feature learning method for cause identification of electromagnetic transient events (EMTE) in power grids. The proposed method is formulated based on the availability of time-synchronized high-frequency measurement, and using the convolutional neural network (CNN) as t…
Recently, Hodgson and Kerckhoff found a small bound on Dehn surgered 3-manifolds from hyperbolic knots not admitting hyperbolic structures using deformations of hyperbolic cone-manifolds. They asked whether the area normalized meridian length squared of maximal tubular neighborhoods of the singular locus of the cone-ma…
In this paper, we are interested in short homologically and homotopically independent loops based at the same point on Riemannian surfaces and metric graphs. First, we show that for every closed Riemannian surface of genus g≥2 and area normalized to g, there are at least $\ceil{\log(2g)+1}$ homotopically indep…
New method maps global value chains at product level from trade data.
problem Lack of detailed product-level value chain information in existing datasets.
method Machine learning and trade theory applied to international trade data.
result Approximate product-level value chain information inferred from trade patterns.
Given a Riemannian surface, we consider a naturally embedded graph which captures part of the topology and geometry of the surface. By studying this graph, we obtain results in three different directions. First, we find bounds on the lengths of homologically independent curves on closed Riemannian surfaces. As a conseq…
Paper introduces a meta-critic for accelerating off-policy actor-critic learning.
problem Improving sample efficiency in continuous control tasks.
method Meta-critic that meta-learns an additional loss for the actor.
result Online meta-critic learning leads to improved performance in various continuous control environments.
This paper reverses a construction by merging boundary critical points into an interior one.
problem Pushing interior critical points to the boundary and splitting them into two boundary points.
method Specific assumptions allow merging two boundary critical points into one interior critical point.
result Merging two boundary critical points into a single interior critical point.
The minimal number of critical points is studied for smooth functions on closed manifolds.
problem Determining the minimal number of critical points for smooth functions on closed manifolds.
method Investigates cylindrical ball neighborhoods and exotic critical points, proving the conjecture for certain types of critical points.
result The minimal number of critical points is the same for smooth functions without exotic critical points on closed manifolds of dimension at least 6.
The study confirms a conjecture about critical points of smooth functions.
problem Understanding isolated critical points of smooth functions.
method Investigated cone-like, reasonable, and Rothe H hypothesis critical points.
result The conjecture holds true for certain critical points.
We present the first provably convergent two-timescale off-policy actor-critic algorithm (COF-PAC) with function approximation. Key to COF-PAC is the introduction of a new critic, the emphasis critic, which is trained via Gradient Emphasis Learning (GEM), a novel combination of the key ideas of Gradient Temporal Differ…
Study critical points of Laplace eigenfunctions in polygons.
problem Characterize critical points of Laplace eigenfunctions in polygonal domains.
method Analyze components of the critical set with codimension 1.
result For simply connected polygons, if a second Neumann eigenfunction has infinitely many critical points, the polygon must be a rectangle.
Smaller actor-critic models lead to performance degradation and overfitting, highlighting the critic's role in value underestimation.
problem Performance degradation and overfitting in actor-critic models with smaller actors.
method Broad empirical investigations and analyses of asymmetric actor-critic setups, exploring techniques to mitigate value underestimation.
result Value underestimation is a key cause of performance degradation in smaller actor-critic models, and the critic plays a crucial role in mitigating this.
The paper analyzes an actor-critic algorithm with target networks for deep reinforcement learning.
problem Lack of theoretical understanding of target networks in actor-critic methods.
method Proposes a theoretical analysis of an online target-based actor-critic algorithm with linear function approximation.
result Establishes asymptotic convergence results and finite-time analysis for both critic and actor.
New PAC-Bayesian approach stabilizes actor-critic learning.
problem Training instability in actor-critic algorithms.
method Employing PAC-Bayesian bound as the critic training objective.
result Significant improvement in online learning performance.
Hard to approximate critical points for simple nonconvex functions.
problem Approximating critical points of nonconvex functions.
method Proving hardness results for polynomial-time approximation of critical points.
result Proving that approximating critical points is intractable for simple nonconvex functions.
We prove a version of symmetric criticality for ropelength-critical knots. Our theorem implies that a knot or link with a symmetric representative has a ropelength-critical configuration with the same symmetry. We use this to construct new examples of ropelength critical configurations for knots and links which are dif…
New method improves off-policy critic evaluation in reinforcement learning.
problem High variance and instability in off-policy policy evaluation.
method Doubly robust estimators applied to actor-critic algorithms.
result Doubly robust estimation significantly improves performance in continuous control tasks.
The paper studies critical points in overparameterized neural networks, identifying a star locus and degenerate critical points.
problem Understanding the geometry of loss functions in overparameterized neural networks.
method Identifying and analyzing components of the critical locus of the loss function L for overparameterized feedforward neural networks of depth ℓ≥4. result For very wide networks, all critical points are degenerate, and lower bounds on the number of zero eigenvalues of the Hessian are given.
WAVE improves stability in reinforcement learning by adaptively weighting critic's loss.
problem Inherent instability in actor-critic reinforcement learning algorithms.
method Wasserstein adaptive value estimation with Sinkhorn approximation.
result Achieves $\mathcal{O}\left(\frac{1}{k}
ight)$ convergence rate for critic's mean squared error.
Actor-critic methods solve reinforcement learning problems by updating a parameterized policy known as an actor in a direction that increases an estimate of the expected return known as a critic. However, existing actor-critic methods only use values or gradients of the critic to update the policy parameter. In this pa…
New findings on Chern flat metrics and their criticality.
problem Understanding critical Hermitian metrics on Chern flat manifolds.
method Analyzing Chern flat manifolds as compact quotients of complex Lie groups and studying their criticality.
result Chern flat metrics on semi-simple Lie groups are torsion-critical and vice versa.
We establish regularity results for critical points to energies of immersed surfaces depending on the first and the second fundamental form exclusively. These results hold for a large class of intrinsic elliptic Lagrangians which are sub-critical or critical. They are derived using uniform ε−regularity estimates whic…
Critical surfaces are defined by Bachman as topological index 2 surfaces, generalizing incompressible surfaces and strongly irreducible surfaces. In this paper we give a condition to obtain critical Heegaard surfaces by amalgamation. As a special case, we obtain critical Heegaard surfaces by boundary stabilization. It …
Study on CR curves in 3-sphere, focusing on critical curves integration and existence.
problem Addressing the integration and existence of critical curves in the CR 3-sphere.
method Provided a procedure for the explicit integration of general critical curves and characterized closed curves.
result Existence of infinite countably many closed critical curves.
Single-timescale actor-critic finds globally optimal policy.
problem Finding globally optimal policy in reinforcement learning.
method Simultaneous actor and critic updates with linear or deep neural network approximations.
result Actor sequence converges to globally optimal policy at O(K−1/2) rate. This paper focuses on the problem of topological equivalence of functions with isolated critical points on the boundary of a compact surface M which are also isolated critical points of their restrictions to the boundary. This class of functions we denote by Ω(M). Firstly, we've obtained the topological classificat…
Symmetric critical points lead to symmetry breaking in neural networks.
problem Understanding symmetry in critical points of invariant functions.
method Analyzing the symmetry of critical points and their neighbors in invariant nonconvex functions.
result Symmetric critical points in invariant nonconvex functions are generically followed by symmetry breaking adjacent points.
Upper bounds found for systole function critical points on surface moduli space.
problem Finding upper bounds for systole function critical points.
method Analyzing the systole function on the surface moduli space.
result Upper bounds for critical points of systole function and their systole values.
Study classifies ruled surfaces critical to Dirichlet energy.
problem Identifying ruled surfaces critical to Dirichlet energy.
method Explicit parametrization of ruled surfaces.
result Classification of ruled surfaces as critical points of Dirichlet energy.
Study on critical faces convergence in a Poisson point process.
problem Convergence of point processes associated with critical faces in a Čech filtration.
method Established convergence in M0-topology for critical faces above vanishing threshold. result Obtained limit theorems for positive and negative critical faces.
Noninjective monodromy found in polynomial critical point tracking.
problem Tracking critical points in polynomials leads to noninjective monodromy.
method Monic squarefree complex polynomials with prescribed critical point multiplicities.
result Monodromy map is noninjective for polynomials with exactly two critical points.
New groups found with critical exponents close to but less than max.
problem Finding discrete isometry groups with critical exponents near maximum.
method Analyzing complex hyperbolic spaces to construct groups.
result Discrete isometry groups with critical exponents arbitrarily close to max but less.
Actor-critic methods can achieve incredible performance on difficult reinforcement learning problems, but they are also prone to instability. This is partly due to the interaction between the actor and critic during learning, e.g., an inaccurate step taken by one of them might adversely affect the other and destabilize…
Paper finds critical metrics with pinched curvature are geodesic balls.
problem Identifying critical metrics with specific curvature constraints.
method Proved isometry to geodesic balls in S^n and provided conditions for the gradient of the potential function.
result Critical metrics with pinched curvature are isometric to geodesic balls in S^n.
Critical hypersurfaces with boundary have unique shapes and properties.
problem Characterizing the shapes of hypersurfaces with boundary and zero fractional mean curvature.
method Analyzing critical points of fractional area in RN with boundary conditions. result Critical hypersurfaces with specific boundary conditions are not simple shapes like (N−1)-balls. The paper studies the smoothness of critical points of variational integrals on Hessian spaces.
problem The study focuses on the regularity of critical points of variational integrals defined on Hessian spaces.
method The approach involves solving a fourth order nonlinear equation and analyzing the Hessian of the critical points.
result Smooth critical points with bounded Hessian are shown to be smooth provided their Hessian has small BMO.
We give an alternative proof of that a critical knot of a Morse-Bott function f:S3→R is a graph knot where the critical set of f is a link in S3. Our proof inducts on the number of index-1 critical knots of f.
In this paper we investigate complete critical metrics of the L2-norm of the scalar curvature. We prove that any complete critical metric with positive scalar curvature has constant scalar curvature and we characterize critical metrics with nonnegative scalar curvature in dimension three and four.