Introduces central U(1)-extensions of double Lie groupoids.
problem No specific problem stated; focuses on new mathematical concept.
method Defines a central U(1)-extension and shows it as a cocycle in a triple complex.
result Establishes a mathematical structure for U(1)-extensions of double Lie groupoids.
We find contact integrable extensions and coverings for the r-th double modified dispersionless Kadomtsev--Petviashvili equation.
Unified approach to decomposing commutative n-ary superalgebras with skew-symmetric forms.
problem Decomposing commutative n-ary superalgebras with skew-symmetric invariant forms.
method Unified approach using derived bracket formalism and inductive orthogonal sums and generalized double extensions.
result Any commutative n-ary superalgebra with a skew-symmetric invariant form can be obtained by inductive orthogonal sums and generalized double extensions.
Defines and extends flat pseudo-Riemannian F-Lie algebras.
problem Generating weakly flat Lorentzian non-abelian bi-nilpotent F-Lie algebras.
method Constructs double extensions of flat pseudo-Riemannian F-Lie algebras.
result Provides a framework for generating all weakly flat Lorentzian non-abelian bi-nilpotent F-Lie algebras.
Paper shows certain algebra types are not differentially smooth.
problem Characterizing smoothness in double extension regular algebras.
method Analyzing algebra type (14641) for differential smoothness.
result Double extension regular algebras of type (14641) are not differentially smooth.
Finite subgraphs of extension graph are found within a sequence of induced subgraphs.
problem Identifying all finite subgraphs within the extension graph.
method Inductively define a sequence of induced subgraphs through 'doubling along a star'.
result Every finite induced subgraph of the extension graph is isomorphic to an induced subgraph of some Γi. Classifies solvable symplectic Lie algebras via extensions and proves structural theorems.
problem Characterizing solvable symplectic Lie algebras.
method Symplectic double extension process.
result Classifies Lie algebras of dimensions up to 6 and proves structural theorems.
Derives equations for interacting Lie-Poisson systems using 2-cocycle extensions.
problem Understanding collective motion of interacting Lie-Poisson systems.
method Derives equations on dual space of extended structure, including 2-cocycle terms.
result Provides most general realization of Lie-Poisson system coupling.
A Margulis spacetime is a complete flat affine Lorentzian 3-manifold with free fundamental group. Associated to M is a noncompact complete hyperbolic surface Σ. We study double extensions of π1(M)≅π1(Σ) when Σ is homeomorphic to a projective plane minus two discs. We classify proper actions of this do…
A new algebraic structure extends Drinfel'd double for U-duality applications.
problem Constructing generalized frame fields for U-duality.
method Proposing a family of algebras En and using generalized Lie derivative to realize these algebras. result Generalized frame fields include a twist by a Nambu-Poisson tensor.
We give a simple characterization of Mackenzie's double Lie algebroids in terms of homological vector fields. Application to the `Drinfeld double' of Lie bialgebroids is given and an extension to the multiple case is suggested.
We study quadratic Lie algebras over a field K of null characteristic which admit, at the same time, a symplectic structure. We see that if K is algebraically closed every such Lie algebra may be constructed as the T*-extension of a nilpotent algebra admitting an invertiblederivation and also as the double extension of…
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…
New examples of Lie algebras with ad-invariant metrics found.
problem Finding ad-invariant metrics on nonnice nilpotent Lie algebras.
method Introducing single extension method to construct Lie algebras with ad-invariant metrics.
result Explicit examples of nonnice nilpotent Lie algebras with ad-invariant metrics for dimensions > 10 and steps > 2.
Extends Khovanov homology to surfaces with singularities.
problem Computing invariants for surfaces with singularities.
method Functorial extension of Khovanov homology to surfaces with double points.
result Induces a map between Khovanov homology groups of boundary links.
Constructs special Kähler structures on Lie groups.
problem Creating special Kähler structures on Lie groups.
method Introducing twisted cartesian product and double extension process.
result Characterizes left invariant flat special Kähler structures.
We describe a natural q-deformation of Fock and Goncharov's canonical basis for the algebra of regular functions on a cluster variety associated to a quiver of type A. We then describe an extension of this construction involving a cluster variety called the symplectic double.
This paper extends Q(σ) to Q(σ, λ) and Double Q(σ), improving reinforcement learning control.
problem Improving reinforcement learning control methods.
method Extends Q(σ) to Q(σ, λ) using eligibility traces and introduces Double Q(σ).
result The new Q(σ, λ) algorithm outperforms classical TD control methods.
The study characterizes flat pseudo-Euclidean Lie algebras and their properties.
problem Characterizing flat pseudo-Euclidean Lie algebras and their properties.
method Using the double extension process and analyzing the center of the Lie algebras.
result All flat pseudo-Euclidean nilpotent Lie algebras of signature (2,n−2) can be obtained by the double extension process from flat Lorentzian nilpotent Lie algebras. Uncountably many contractible 3-manifolds with double 3-space property and those without are identified.
problem Characterizing contractible 3-manifolds with specific topological properties.
method Generalizations of the Whitehead Link and interlacing theory.
result Existence of uncountably many contractible 3-manifolds with and without the double 3-space property.
Study shows double and triple descent in unsupervised autoencoders, improving performance in various tasks.
problem Exploring the phenomenon of double descent in unsupervised learning.
method Analytical demonstration and extensive experiments on synthetic and real datasets.
result Over-parameterized unsupervised autoencoders exhibit double and triple descent, enhancing performance in downstream tasks.
We give an extension of Fox's formula of the Alexander polynomial for double branched covers over the three-sphere. Our formula provides the Reidemeister torsion of a double branched cover along a knot for a non-trivial one dimensional representation by the product of two factors derived from the knot group. One of the…
Extends Double Field Theory with new kinematical structure.
problem Formalizing Double Field Theory on para-Hermitian manifolds.
method Constructing a canonical connection and generalised Lie derivative for a Leibniz algebroid.
result Integrability conditions for symmetry algebra closure under non-flat and non-constant η and ω. Study indefinite bi-invariant metrics and their conformal properties.
problem Characterize indefinite bi-invariant metrics and their conformal relationships.
method Analyzes Lie algebras under different cases and structures.
result Conformally Einstein properties for various Lie algebras are determined.
Research decouples Lie algebroids using bicocycle double cross product theory.
problem Understanding decoupling and coupling phenomena in Lie algebroids.
method Bicocycle double cross product realization method.
result Unified product, double cross product, semi-direct product, and cocycle extension frameworks are instances of the general method.
Introduces fat Lie theory for Lie groupoids and algebroids.
problem Representation theory of Lie groupoids and algebroids.
method Introduces fat extensions and abstract 2-term representations up to homotopy (ruths). Establishes correspondences and equivalences.
result One-to-one correspondence between fat extensions and abstract 2-term representations up to homotopy.
Paper addresses underestimation bias in double Q-learning, proposing a method to improve learning performance.
problem Underestimation bias in double Q-learning leading to non-optimal fixed points.
method Proposes a simple approach using approximate dynamic programming to bound the target value.
result Significant improvement in learning performance over baseline algorithms in Atari benchmark tasks.
Study on pseudo-Riemannian metrics on Lie groups, finding new non-Einstein examples.
problem Characterizing and finding non-Einstein pseudo-Riemannian metrics on Lie groups.
method Analyzing left invariant metrics, using double extension process, and constructing examples.
result Construction of infinitely many new explicit examples of non-Einstein pseudo-Riemannian metrics on Lie groups.
Extends double linear policy with time-varying weights and proves robust positive expectation.
problem Ensuring robustness in policy optimization with time-varying parameters.
method Employed a novel elementary symmetric polynomials characterization approach to prove robust positive expectation (RPE). Derived explicit expressions for expected cumulative gain-loss and variance.
result Proved the robust positive expectation property holds for the extended double linear policy.
Paper proposes algorithms for active learning of reject option classifiers.
problem Active learning of reject option classifiers is unaddressed in machine learning.
method Developed novel algorithms using double ramp and double sigmoid loss functions.
result Proposed algorithms efficiently reduce the number of labeled examples required.
The study examines extensions of Lie algebras with specific geometric structures.
problem Conditions for preserving geometric structures in Lie algebra extensions.
method Analyzes extensions of Sasakian and Frobenius-Kähler Lie algebras.
result Conditions for maintaining Sasakian or Frobenius-Kähler structures after extensions.
Generalizes double transgression formulas on complex manifolds.
problem Currential double transgression formulas on complex manifolds.
method General framework using Bott-Chern Duality.
result Complements existing transgression formulas and provides new applications.
Analyzes Schouten square on specific Lie algebra extensions, revealing geometric and algebraic properties.
problem Analyzing Schouten square on specific Lie algebra extensions.
method Analyzes Schouten square on specific Lie algebra extensions $\g=\fb\oplus V\oplus\fb^{*}$, focusing on $\Rone$ and $\Rplus$.
result Schouten square splits orthogonally into radial and angular components, with radial component factoring through a moment map.
DoubleML implements machine learning for causal inference in R.
problem Estimating causal effects in regression models with high-dimensional data.
method Double machine learning framework with Neyman orthogonality and sample splitting.
result Valid inference on causal parameters using machine learning methods.
We show that certain classes of graphs of free groups contain surface subgroups, including groups with positive b2 obtained by doubling free groups along collections of subgroups, and groups obtained by "random" ascending HNN extensions of free groups. A special case is the HNN extension associated to the endomorphi…
The study of flat symplectic Lie algebras and groups.
problem Characterizing and understanding flat symplectic Lie algebras and groups.
method Analyzing the derived ideal, curvature, and double extension process.
result Every flat symplectic Lie algebra is obtained by a sequence of double extensions starting from the trivial algebra.
Double descent observed in tree-based models for genomic prediction.
problem Understanding the generalization behavior of tree-based models in machine learning.
method Systematic variation of model complexity in a genomic prediction task using whole-genome sequencing data.
result Double descent emerges only when complexity is scaled jointly across learner capacity and ensemble size.
Study assesses hyperparameter tuning for causal inference with DML.
problem Optimizing hyperparameters for causal inference with DML.
method Empirical simulation study using DML approach.
result Hyperparameter tuning crucial for causal estimation with DML.
New method for efficient pricing of double barrier options in Lévy models.
problem Difficulties in accurately and quickly calculating prices of double barrier options in jump models.
method GWR-SINH method based on Gaver-Wynn-Rho acceleration applied to Bromwich integral.
result Accurate and fast calculations of prices of double barrier options in jump models achieved.
Revisits superfields and geometry, offering new formulations and interpretations.
problem Exploring the connection between N=(2,2) superfields and geometry. method Combining different superfield formulations, using a doubled target space, and interpreting equations of motion geometrically.
result Shows that the doubled geometry is Donaldson's deformation of the original Kähler manifold.
The paper constructs Anosov representations for specific types of groups.
problem Constructing Anosov representations for certain groups.
method Analyzing uniform lattices and their extensions, proving existence of Anosov embeddings.
result Examples of one-ended hyperbolic groups admit Anosov embeddings into higher-rank Lie groups.
DoubleML is a Python library for causal inference using machine learning.
problem Estimating causal parameters in complex models with machine learning.
method Double machine learning framework for valid statistical inference.
result High flexibility and easy extension for various model specifications.
Paper estimates non-causal graphical models using covariance extension and transportation distance.
problem Estimating non-causal graphical models with smoothing relations.
method Proposes a covariance extension problem and uses transportation distance to minimize error with white noise.
result Solution is a double-sided autoregressive non-causal graphical model.
We give a geometric model for a tube category in terms of homotopy classes of oriented arcs in an annulus with marked points on its boundary. In particular, we interpret the dimensions of extension groups of degree 1 between indecomposable objects in terms of negative geometric intersection numbers between correspondin…
Researchers develop a method to measure treatment effects in settings with shared states.
problem Measuring treatment effects in settings with shared states like prices, recommendations, or social signals.
method Double machine learning (DML) theorem with conditions for efficient inference under shared-state interference.
result Efficient estimation of average direct effect (ADE) and global average treatment effect (GATE) in various models.
Paper uses DDQN for trading assets, showing better performance than market benchmarks.
problem Improving financial trading strategies using AI.
method Double Deep Q-Network (DDQN) algorithm for trading multiple assets.
result Trading agent outperformed market benchmarks and achieved higher net asset value.
New method improves robustness of double robust estimators under complete misspecification.
problem Improper performance of double robust estimators when all nuisance functions are misspecified.
method DR+ACC, an adaptive correction clipping method.
result DR+ACC ensures bounded error and maintains semiparametric efficiency.
In this note we show that for any hyperbolic surface S, the number of geodesics of length bounded above by L in the mapping class group orbit of a fixed closed geodesic with a single double point is asymptotic to L raised to the dimension of the Teichmuller space of S. Since closed geodesics with one double point fall …