Characterizes critical points in convex double and triple bubbles.
problem Critical points of double and triple bubbles in convex shapes.
method Characterization through stationary varifolds in Rn and R3. result Characterization of critical points in convex shapes.
Paper develops estimates for Lagrangian phase changes in 2D.
problem Interior estimates for Lagrangian phase changes in 2D.
method Modified doubling technique to handle degenerate Jacobi inequalities.
result Interior Hessian and gradient estimates established for critical phase.
We reformulate the option framework as two parallel augmented MDPs. Under this novel formulation, all policy optimization algorithms can be used off the shelf to learn intra-option policies, option termination conditions, and a master policy over options. We apply an actor-critic algorithm on each augmented MDP, yieldi…
Existence of double bubbles with high constant mean curvatures in Riemannian manifolds.
problem Existence of double bubbles with high constant mean curvatures in Riemannian manifolds.
method Perturbations of geodesic standard double bubbles centered at critical points of the ambient scalar curvature and aligned along eigen-vectors of the ambient Ricci tensor, with general multiplicity results via Lusternik-Schnirelman theory.
result Existence of double bubbles with high constant mean curvatures in Riemannian manifolds.
Paper proves existence of minimal doublings on surfaces with specific properties.
problem Existence of minimal doublings on surfaces with given properties.
method Variational approach to finding nondegenerate critical points of a Coulomb-type energy.
result Proves existence of minimal doublings for surfaces of index one in a generic 3-manifold.
Geodesic nets on flat spheres are studied using Gauss-Bonnet theorem.
problem Existence and non-existence of specific geodesic nets on flat spheres.
method The theorem of Gauss-Bonnet is applied to demonstrate results.
result Existence and non-existence of geodesic nets on regular doubled polygons.
Reduces overestimation bias in multi-agent RL, improving performance.
problem Value function overestimation bias in multi-agent RL.
method Double centralized critics to reduce overestimation bias.
result Significant improvement in performance on mixed tasks.
Given a 3-manifold that can be written as the double of a compression body, we compute the Chern-Simons critical values for arbitrary compact connected structure groups. We also show that the moduli space of flat connections is connected when there are no reducibles.
A novel Q-learning variant reduces underestimation bias in deep actor-critic methods for reinforcement learning.
problem Underestimation bias in deep actor-critic methods for reinforcement learning.
method Introduces a parameter-free Q-learning variant that combines maximum and minimum operators to bound value estimates.
result Improves state-of-the-art performance on OpenAI Gym tasks.
Double descent found in DRL, improving generalization with model capacity.
problem Generalization in over-parameterized DRL models.
method Actor-Critic framework, Policy Entropy metric.
result Policy Entropy significantly reduces as model capacity increases, indicating improved generalization.
Researchers extend Godbillon-Vey functional to almost contact manifolds, finding critical structures.
problem Finding optimal almost contact manifolds using the Godbillon-Vey functional.
method Introduced a Godbillon-Vey type functional for 3D almost contact manifolds and found its Euler-Lagrange equations.
result Constructed critical 3D almost contact manifolds with double-twisted product structure.
Distance, normals, and double normals for real plane curves with singularities
problem Relation between normals and double normals and critical points of the squared distance function for real algebraic curves with singularities
method Investigate the topological discriminant of the distance function
result The topological discriminant consists of the evolute and distinguished normal lines at algebraic singular points
Study critical metrics on Riemannian manifolds, finding new minimizers and rigidity results.
problem Investigate critical metrics of higher-order curvature functionals on compact Riemannian manifolds.
method Develop variational framework using double forms and generalize Lanczos identity.
result Critical (2k)-Thorpe and (2k)-anti-Thorpe metrics are absolute minimizers of G2k in the critical dimension n=4k. Generalizes LD approach to create minimal surfaces and self-shrinkers.
problem Creating minimal surfaces and self-shrinkers using a generalized LD approach.
method Proves a theorem for constructing minimal surfaces using LD solutions and PDE gluing methods.
result Constructs new minimal surfaces and self-shrinkers via LD solutions and PDE gluing.
In value-based reinforcement learning methods such as deep Q-learning, function approximation errors are known to lead to overestimated value estimates and suboptimal policies. We show that this problem persists in an actor-critic setting and propose novel mechanisms to minimize its effects on both the actor and the cr…
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.
This paper bounds the volume of singular and critical sets for elliptic equations with Hölder coefficients.
problem Bounding the volume of singular and critical sets for elliptic equations with Hölder coefficients.
method Proves explicit bounds for (n−2)-dimensional Minkowski estimates of singular and critical sets using Hölder continuity and new almost monotonicity formula. result Optimal improvement on Cheeger-Naber-Valtorta's volume estimates on each quantitative stratum.
Study Neumann problem for special Lagrangian type equations.
problem Neumann problem for special Lagrangian type equations.
method Uniform a priori estimates, continuity method, direct proof of boundary double normal derivative estimates.
result Existence result for Neumann problem of special Lagrangian type equations.
The main result of this paper is a construction of solutions to the reverse Yang-Mills-Higgs flow converging in the C∞ topology to a critical point. The construction uses only the complex gauge group action, which leads to an algebraic classification of the isomorphism classes of points in the unstable set of a…
Researchers compute Khovanov polynomials for satellite knots.
problem Computing Khovanov polynomials for satellite knots.
method Explicit computation using a computer program for two families of satellite knots.
result Khovanov polynomials can be expressed as a linear combination of pattern and companion invariants, with a jump at a critical point.
Double machine learning improves causal effect estimation by relaxing assumptions.
problem Estimating causal effects with observational data.
method Double/debiased machine learning (DML) framework.
result DML improves adjustment for nonlinear confounding relationships.
In this paper we study perpetual American call and put options in an exponential Lévy model. We consider a negative effective discount rate which arises in a number of financial applications including stock loans and real options, where the strike price can potentially grow at a higher rate than the original discount f…
In earlier work of NK new closed embedded smooth minimal surfaces in the round three-sphere S3(1) were constructed, each resembling two parallel copies of the equatorial two-sphere Seq2 joined by small catenoidal bridges, with the catenoidal bridges concentrating along two parallel circles, o…
The paper introduces Morse theory for Lie groupoids and proves inequalities.
problem Defining Morse theory for Lie groupoids and studying their properties.
method Introducing Morse Lie groupoid morphisms and proving their Morita invariance.
result Established Morse theory for Lie groupoids and proved Morse inequalities.
In this paper we study equivariant constrained Willmore tori in the 3-sphere. These tori admit a 1-parameter group of Möbius symmetries and are critical points of the Willmore energy under conformal variations. We show that the associated spectral curve of an equivariant torus is given by a double covering of $\mathbb …
This study shows ESG ratings reduce equity crash risk during market downturns.
problem Decoupling of alpha from tail risk resilience in traditional models.
method Double Machine Learning for structural deconfounding, state-dependent analysis.
result High ESG ratings reduce crash incidence during systemic drawdowns.
Let k be a knot in S3. In [8], H.N. Howards and J. Schultens introduced a method to construct a manifold decomposition of double branched cover of (S3, k) from a thin position of k. In this article, we will prove that if a thin position of k induces a thin decomposition of double branched cover of (S3,k) by Howards and…
Statistical mechanics reveals phase transitions in ε-SVR error.
problem Understanding task precision in neural representations with variability.
method Statistical mechanics applied to ε-SVR. result Double-descent phenomenon in generalization error due to ε. Research tackles investor confusion in ESG rankings, offering tailored strategies.
problem Widespread confusion among investors regarding ESG rankings.
method Developed ESG ensemble strategies, integrated ESG scores into RL model, proposed Double-Mean-Variance model, introduced ESG-adjusted CAPMs.
result Optimized portfolios that balance financial returns and ESG-focused outcomes.
Curious hierarchical reinforcement learning improves learning performance.
problem Combining hierarchical abstraction and curiosity-driven exploration in reinforcement learning.
method Developed a method that combines hierarchical reinforcement learning with curiosity.
result Curiosity can more than double learning performance and success rates.
Multi-label classification is a type of supervised learning where an instance may belong to multiple labels simultaneously. Predicting each label independently has been criticized for not exploiting any correlation between labels. In this paper we propose a novel approach, Nearest Labelset using Double Distances (NLDD)…
Smooth tori in S^4 are topologically unknotted.
problem Tackling the topological unknottedness of smooth tori in S^4.
method Analyzing the intersection forms and critical points of tori to prove topological unknottedness.
result Certain smooth tori in S^4 are topologically unknotted.
A Klein surface is a surface with a dianalytic structure. A double of a Klein surface X is a Klein surface Y such that there is a degree two morphism (of Klein surfaces) Y→X. There are many doubles of a given Klein surface and among them the so-called natural doubles which are: the complex double, the …
Efficient exploration improves large language model performance with fewer queries.
problem Improving large language model performance with fewer human feedback queries.
method Sequentially generates queries, fits a reward model to feedback, uses double Thompson sampling with epistemic neural network uncertainty.
result Efficient exploration enables high performance with far fewer queries.
In a recent comment (Johansen A 2003 An alternative view, Quant. Finance 3: C6-C7, cond-mat/0302141), Anders Johansen has criticized our methodology and has questioned several of our results published in [Sornette D and Zhou W-X 2002 The US 2000-2002 market descent: how much longer and deeper? Quant. Finance 2: 468-81,…
We define a general notion of abstract double Lie algebroid. We show (1) that the double Lie algebroid of a double Lie groupoid is a double Lie algebroid in this sense; (2) that the double cotangent constructed from Lie algebroid structures on a vector bundle A and its dual A* is a double Lie algebroid if and only if (…
Discover conservation laws from trajectories using a neural network.
problem Finding invariants and conservation laws from large-scale data without prior knowledge.
method ConservNet, a neural network trained with noise-variance loss to discover hidden invariants in grouped multi-dimensional observables.
result Successfully discovers underlying invariants from simulated and real-world systems.
The word `double' was used by Ehresmann to mean `an object X in the category of all X'. Double categories, double groupoids and double vector bundles are instances, but the notion of Lie algebroid cannot readily be doubled in the Ehresmann sense, since a Lie algebroid bracket cannot be defined diagrammatically. In this…
Maximum entropy deep reinforcement learning (RL) methods have been demonstrated on a range of challenging continuous tasks. However, existing methods either suffer from severe instability when training on large off-policy data or cannot scale to tasks with very high state and action dimensionality such as 3D humanoid l…
We define double principal bundles (DPBs), for which the frame bundle of a double vector bundle, double Lie groups and double homogeneous spaces are basic examples. It is shown that a double vector bundle can be realized as the associated bundle of its frame bundle. Also dual structures, gauge transformations and conne…
Generalizes Hecke algebra for double torus, linking to skein algebra.
problem Understanding algebraic structures on double torus.
method Introducing Heegaard dual operators and Dehn twists.
result Established relationship between Hecke algebra and skein algebra.
Introduces Poisson double algebroids and their relation to Lie 2-bialgebras.
problem Developing Lie theory for Poisson double structures.
method Introducing Poisson double algebroids and double Lie bialgebroids, and relating them through differentiation and integration.
result Revisits Lie 2-bialgebras using Poisson double structures.
We prove a formula for the normal injectivity radius(thickness)i(K,M)for C^{1,1} compact submanifolds K^k of complete Riemannian manifolds M^n in terms of geometric focal distance and double critical points. We also prove the C^1 compactness of the set of all compact submanifolds K contained in a compact subset D of a …
Survey of global geometry for double field theory.
problem Global description of double field theory geometry.
method Review of Courant algebroids, metric algebroids, AKSZ construction, para-Hermitian geometry.
result Global description of doubled geometry and topological models.
New singularities and fibrations in non-orientable 4-manifolds.
problem Understanding singularities and fibrations in non-orientable 4-manifolds.
method Introducing M-singularities and M-fibrations, studying their handle decompositions and orientation double coverings. result Relations among crosscap transpositions give rise to M-fibrations on non-orientable 4-manifolds. Boosts Q-learning by using value function bounds.
problem Efficiently solving new tasks using past experience.
method Derives double-sided bounds on optimal value function and uses them to update Q-function.
result Boosted training performance through alternative Q-function update method.
This paper establishes an equivalence between transitive double Lie algebroids and core diagrams.
problem Understanding and characterizing transitive double Lie algebroids.
method Using core diagrams and equivalence of transitive core diagrams with transitive double Lie groupoids.
result Transitive double Lie algebroids are completely determined by their core diagrams.
We define an abstract notion of double Lie algebroid, which includes as particular cases: (1) the double Lie algebroid of a double Lie groupoid in the sense of the author, such as the iterated tangent bundle of an ordinary manifold, and various iterated tangent/cotangent constructions in symplectic and Poisson geometry…