arXiv research

Investigates the relationship between ResNets and Neural ODEs, quantifying their closeness and providing training methods.

This work presents a partitioned solution procedure to compute shape gradients in fluid-structure interaction (FSI) using black-box adjoint solvers. Special attention is paid to project the gradients onto the undeformed configuration. This is due to the mixed Lagrangian-Eulerian formulation of large-displacement FSI in…

Derives adjoint polynomials of torus knots in explicit form.

We describe a canonical form for linear differential operators that are formally self-adjoint or formally skew-adjoint.

Proves formal self-adjointness of certain differential operators.

Study of adjoint orbits in simplest non-trivial Lie algebra case.

Abstracts a construction of boundary triplets for self-adjoint elliptic problems.

Prove integrality of genus-$g$ indices with adjoint Reidemeister torsions for twist knots and meridians.

Quantizes Stäckel integrable systems into self-adjoint operators.

We give explicit descriptions of the adjoint group of the Coxeter quandle $Q_W$ associated with an arbitrary Coxeter group $W$. The adjoint group of $Q_W$ turns out to be an intermediate group between $W$ and the corresponding Artin group $A_W$, and fits into a central extension of $W$ by a finitely generated free abel…

Paper analyzes double twist knots using adjoint hyperbolic torsion polynomial.

Derives adjoint formulas for matrix operations and applies them to specific cases.

Explicit formula for Reidemeister torsion of two-bridge knots.

By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in p…

The paper explores self-adjointness of Laplace-Beltrami operator on special geometric manifolds.

Study extends Vogel's universality to torus knots in adjoint representation.

Extends adjoint representation concept to higher Lie groupoids.

New knot theory module shows torsion-ness in number theory.

We consider magnetic geodesic flows of the normal metrics on a class of homogeneous spaces, in particular (co)adjoint orbits of compact Lie groups. We give the proof of the non-commutative integrability of flows and show, in addition, for the case of (co)adjoint orbits, the usual Liouville integrability by means of ana…

The study confirms essential self-adjointness for certain differential operators on manifolds.

Paper proves index theorem for self-adjoint elliptic boundary problems.

Adjoint sampler targets infinite-dimensional function spaces for efficient sampling.

Let $Δ$ be a linear differential operator acting on the space of densities of a given weight $\lo$ on a manifold $M$. One can consider a pencil of operators $\hPi(Δ)=\{Δ_ł\}$ passing through the operator $Δ$ such that any $Δ_ł$ is a linear differential operator acting on densities of weight $ł$. This pencil can be iden…

We study the Gaffney Laplacian on a vector bundle equipped with a compatible metric and connection over a Riemannian manifold that is possibly geodesically incomplete. Under the hypothesis that the Cauchy boundary is polar, we demonstrate the self-adjointness of this Laplacian. Furthermore, we show that negligible boun…

I show that the adjoint variety of the complex special linear group is rigid to order three.

We give explicit formulas for the adjoint twisted Alexander polynomial and the nonabelian Reidemeister torsion of genus one two-bridge knots.

The study finds Lagrangian submanifolds in adjoint semisimple orbits for real forms.

Unified framework extends adjoint Schrödinger bridge sampler to discrete spaces.

Into this note we collect topics related to homogeneous vector bundles, elliptic adjoint orbits and so forth.

Let G be a real compact connected simple Lie group, and g its Lie algebra. We study the problem of determining, from root data, when a sum of adjoint orbits in g, or a product of conjugacy classes in G, contains an open set. Our general methods allow us to determine exactly which sums of adjoint orbits in su(m) and pro…

Study geodesics on $SL(n, \mathbb{R})$ adjoint orbits.

Proposes DAM for optimizing discrete generative models.

We study the hyperkaehler geometry of a regular semisimple adjoint orbit of SL(k,C) via the algebraic geometry of the corresponding reducible spectral curve.

Study modular class of Lie ∞-algebroids and their adjoint actions.

In this note we define the stabilizer group of any adjoint-invariant $l$-form on a complex simple Lie algebra. This result partially extend a previous result by Kable.

It is known that the Schrödinger flow on a complex Grassmann manifold is equivalent to the matrix non-linear Schrödinger equation and the Ferapontov flow on a principal Adjoint U(n)-orbit is equivalent to the $n$-wave equation. In this paper, we give a systematic method to construct integrable geometric curve flows on …

We prove a general essential self-adjointness criterion for sub-Laplacians on complete sub-Riemannian manifolds, defined with respect to singular measures. As a consequence, we show that the intrinsic sub-Laplacian (i.e. defined w.r.t. Popp's measure) is essentially self-adjoint on the equiregular connected components …

We consider first-order differential operators with locally bounded measurable coefficients on vector bundles with measurable coefficient metrics. Under a mild set of assumptions, we demonstrate the equivalence between the essential self-adjointness of such operators to a negligible boundary property. When the operator…

Adjoint SA speeds up bioprocess parameter learning.

Given a compact Lie group, endowed with a bi-invariant Riemannian metric, its complexification inherits a Kaehler structure having twice the kinetic energy of the metric as its potential, and Kaehler reduction with reference to the adjoint action yields a stratified Kaehler structure on the resulting adjoint quotient. …

The paper proves positivity preservation and self-adjointness for Schrödinger operators on incomplete Riemannian manifolds.

ASBS improves sampling from Boltzmann distributions without importance weighting.

Classifies local boundary conditions for Dirac-type operators on manifolds.

The paper defines and analyzes the adjoint Reidemeister torsion for connected sums of knots.

This paper develops an approach for describing centrally extended groups, as determining the adjoint groups associated with quandles. Furthermore, we explicitly describe such groups of some quandles. As a corollary, we determine some second quandle homologies.

It is shown that the multiplicative monoids of Brauer's centralizer algebras generated out of the basis are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself, and where, moreover, a kind of symmetry involving the self-adjoint functor is satisfied. As in a previous paper, of …

This expository article is an introduction to the adjoint orbits of complex semisimple groups, primarily in the algebro-geometric and Lie-theoretic contexts, and with a pronounced emphasis on the properties of semisimple and nilpotent orbits. It is intended to build a foundation for more specialized settings in which a…

The paper studies time-optimal problems on specific Lie groups, describing orbits and integrals.