arXiv research

We find contact integrable extensions and coverings for the r-th double modified dispersionless Kadomtsev--Petviashvili equation.

In this paper, we introduce a notion of a central $U(1)$-extension of a double Lie groupoid and show that it defines a cocycle in the certain triple complex.

Paper shows certain algebra types are not differentially smooth.

Defines and extends flat pseudo-Riemannian F-Lie algebras.

The method of double extension, introduced by A.~Medina and Ph.~Revoy, is a procedure which decomposes a Lie algebra with an invariant symmetric form into elementary pieces. Such decompositions were developed for other algebras, for instance for Lie superalgebras and associative algebras, Filippov $n$-algebras and Jord…

Classifies solvable symplectic Lie algebras via extensions and proves structural theorems.

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 $π_1 (M) \cong π_1 (Σ)$ when $Σ$ is homeomorphic to a projective plane minus two discs. We classify proper actions of this do…

Derives equations for interacting Lie-Poisson systems using 2-cocycle extensions.

A new algebraic structure extends Drinfel'd double for U-duality applications.

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.

Extends Khovanov homology to surfaces with singularities.

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.

Constructs special Kähler structures on Lie groups.

An indecomposable Lie group with Riemannian bi-invariant metric is always simple and hence Einstein. For indefinite metrics this is no longer true, not even for simple Lie groups. We study the question of whether a semi-Riemannian bi-invariant metric is conformal to an Einstein metric. We obtain results for all three c…

Temporal-difference (TD) learning is an important field in reinforcement learning. Sarsa and Q-Learning are among the most used TD algorithms. The Q($σ$) algorithm (Sutton and Barto (2017)) unifies both. This paper extends the Q($σ$) algorithm to an online multi-step algorithm Q($σ, λ$) using eligibility traces and int…

Study shows double and triple descent in unsupervised autoencoders, improving performance in various 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…

Research decouples Lie algebroids using bicocycle double cross product theory.

Paper addresses underestimation bias in double Q-learning, proposing a method to improve learning performance.

Introduces fat Lie theory for Lie groupoids and algebroids.

Study on pseudo-Riemannian metrics on Lie groups, finding new non-Einstein examples.

Extends double linear policy with time-varying weights and proves robust positive expectation.

The study examines extensions of Lie algebras with specific geometric structures.

We formulate a kinematical extension of Double Field Theory on a $2d$-dimensional para-Hermitian manifold $(\mathcal{P},η,ω)$ where the $O(d,d)$ metric $η$ is supplemented by an almost symplectic two-form $ω$. Together $η$ and $ω$ define an almost bi-Lagrangian structure $K$ which provides a splitting of the tangent bu…

Let $Γ$ be a finite graph and let $Γ^{\mathrm{e}}$ be its extension graph. We inductively define a sequence $\{Γ_i\}$ of finite induced subgraphs of $Γ^{\mathrm{e}}$ through successive applications of an operation called "doubling along a star". Then we show that every finite induced subgraph of $Γ^{\mathrm{e}}$ is iso…

Generalizes double transgression formulas on complex manifolds.

DoubleML implements machine learning for causal inference in R.

We show that certain classes of graphs of free groups contain surface subgroups, including groups with positive $b_2$ 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…

Double descent observed in tree-based models for genomic prediction.

The study of flat symplectic Lie algebras and groups.

Study assesses hyperparameter tuning for causal inference with DML.

Gabai showed that the Whitehead manifold is the union of two submanifolds each of which is homeomorphic to $\mathbb R^3$ and whose intersection is again homeomorphic to $\mathbb R^3$. Using a family of generalizations of the Whitehead Link, we show that there are uncountably many contractible 3-manifolds with this doub…

New method for efficient pricing of double barrier options in Lévy models.

Revisits superfields and geometry, offering new formulations and interpretations.

The paper constructs Anosov representations for specific types of groups.

A flat pseudo-Euclidean Lie algebra is a real Lie algebra with a non degenerate symmetric bilinear form and a left symmetric product whose the commutator is the Lie bracket and such that the left multiplications are skew-symmetric. We show that the center of a flat pseudo-Euclidean nilpotent Lie algebra of signature $(…

DoubleML is a Python library for causal inference using machine learning.

Paper estimates non-causal graphical models using covariance extension and transportation distance.

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.

Paper uses DDQN for trading assets, showing better performance than market benchmarks.

New method improves robustness of double robust estimators under complete misspecification.

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 …

We extend the state models for Jones and Alexander polynomials of classical links to state models of 2-variable polynomials in the case of singular links. Moreover, we extend both of them to polynomials with d+1 variables for long singular knots with exactly d double points. These extensions can detect non-invertibilit…

This work merges 3-anchored bundles into 3-Lie algebroids.