arXiv research

Characterizes higher rank model geometries using antipodal sets.

Eisermann and Lamm introduced a notion of symmetric equivalence among symmetric union diagrams and studied it using a refined form of the Jones polynomial. We introduced invariants of symmetric equivalence via refined versions of topological spin models and provided a partial answer to a question left open by Eisermann…

New neural networks respect symmetries in symmetric tensors, improving efficiency and generalization.

Paper proves March's criterion for transience on symmetric manifolds.

An open question akin to the slice-ribbon conjecture asks whether every ribbon knot can be represented as a symmetric union. Next to this basic existence question sits the question of uniqueness of such representations. Eisermann and Lamm investigated the latter question by introducing a notion of symmetric equivalence…

The paper introduces exponential-wrapped distributions on symmetric spaces for better data modeling.

In this article, we first propose the modified Hannan-Rissanen Method for estimating the parameters of the autoregressive moving average (ARMA) process with symmetric stable noise and symmetric stable generalized autoregressive conditional heteroskedastic (GARCH) noise. Next, we propose the modified empirical character…

New infinite families of flat spaces found from symmetric spaces.

The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant subspaces that corresponds to considering an important class of harmonic maps into symmetric and $k$-symmetric spaces. In parti…

Paper introduces symmetric divergence link models for probability distributions.

Efficient diffusion model for symmetric manifolds reduces training and computation costs.

Local equivalence found between maximally symmetric rolling and flat Cartan distributions.

The theory of the vortex filament in three-dimensional fluid dynamics, consisting mainly of the models up to the third-order approximation, is an attractive subject in both physics and mathematics. Many efforts have been devoted to the extension of the theory to higher-dimensional symmetric Lie algebras. However, such …

Study of 4D symmetric spaces with (2,2) signature.

We obtain Ricci flat Kähler metrics on complex symmetric spaces of rank two by using an explicit asymptotic model whose geometry at infinity is interpreted in the wonderful compactification of the symmetric space. We recover the metrics of Biquard-Gauduchon in the Hermitian case and obtain in addition several new metri…

New algorithm for online optimization over symmetric cones, unifying previous methods.

It is well-known that sigma-models with symmetric target spaces are classically integrable. At the example of the model with target space the flag manifold U(3)/U(1)^3 -- a non-symmetric space -- we show that the introduction of torsion allows to cast the equations of motion in the form of a zero-curvature condition fo…

The paper classifies symmetric triads with multiplicities and their applications.

We define symmetric spaces in arbitrary dimension and over arbitrary non-discrete topological fields $\K$, and we construct manifolds and symmetric spaces associated to topological continuous quasi-inverse Jordan pairs and -triple systems. This class of spaces, called smooth generalized projective geometries, generaliz…

We find all Ricci semi-symmetric as well as all conformally semi-symmetric spacetimes. Neither of these properties implies the other. We verify that only conformally flat spacetimes can be Ricci semi-symmetric without being conformally semi-symmetric and show that only vacuum spacetimes and spacetimes with just a $Λ$-t…

We establish a new symmetrization procedure for the isoperimetric problem in symmetric spaces of noncompact type. This symmetrization generalizes the well known Steiner symmetrization in euclidean space. In contrast to the classical construction the symmetrized domain is obtained by solving a nonlinear elliptic equatio…

Study on totally symmetric sets with group applications.

In this article, we summarize the results on symmetric conformal geometries. We review the results following from the general theory of symmetric parabolic geometries and prove several new results for symmetric conformal geometries. In particular, we show that each symmetric conformal geometry is either locally flat or…

The paper analyzes tensor recovery from symmetric rank-one measurements using information theory.

The object of the present paper is to study locally $φ$-symmetric LP-Sasakian manifolds admitting semi-symmetric metric connection and obtain a necessary and sufficient condition for a locally $φ$-symmetric LP-Sasakian manifold with respect to semi-symmetric metric connection to be locally $φ$-symmetric LP-Sasakian man…

The study proves strong cosmic censorship violation for spherically symmetric dust clouds.

Bayesian networks are simplified for categorical variables using staged trees and asymmetry-labeled DAGs.

In this note, we discuss symmetric brackets on skew-symmetric algebroids associated with a metric structure. Given a pseudo-Riemannian metric structure, we describe symmetric brackets induced by connections with totally skew-symmetric torsion in the language of Lie derivatives and differentials of functions. In particu…

Symmetric Poisson structures linked to geodesic foliations and Jordan algebras.

In a previous paper, we obtained a cohomological obstruction to the existence of compact manifolds locally modelled on a homogeneous space. In this paper, we give a classification of the semisimple symmetric spaces to which this obstruction is applicable.

There are two different approaches to exhibit submaximal symmetric rank 2 distributions in 5D via Monge equations. In this note we establish precise relations between these models, find auto-equivalences of one family, and treat two special equations.

Complete classification of quaternionic skew-Hermitian symmetric spaces found.

We construct zero-curvature representations for the equations of motion of a class of sigma-models with complex homogeneous target spaces, not necessarily symmetric. We show that in the symmetric case the proposed flat connection is gauge-equivalent to the conventional one.

Symmetric quandles provide new insights into link colorings.

Study curvature and symplectic properties of symmetric products of surfaces.

Study para-Sasakian φ-symmetric spaces using Boothby-Wang fibration.

Formulae for non-symmetric connections derived from covariant derivatives.

New (co)homology theory for symmetric quandles developed.

New neural network models learn symmetric functions of varying input sizes.

Paper introduces capillary Schwarz symmetrization in half-space.

New proof for symmetric spaces with rectangular lattices.

In this paper, we introduce the notion of a left-symmetric bialgebroid as a geometric generalization of a left-symmetric bialgebra and construct a left-symmetric bialgebroid from a pseudo-Hessian manifold. We also introduce the notion of a Manin triple for left-symmetric algebroids, which is equivalent to a left-symmet…

Determinantal point processes (DPPs) have attracted substantial attention as an elegant probabilistic model that captures the balance between quality and diversity within sets. DPPs are conventionally parameterized by a positive semi-definite kernel matrix, and this symmetric kernel encodes only repulsive interactions …

Framework uncovers symmetric and asymmetric species associations from data.

We construct and identify star representations canonically associated with holonomy reducible simple symplectic symmetric spaces. This leads the a non-commutative geometric realization of the correspondence between causal symmetric spaces of Cayley type and Hermitian symmetric spaces of tube type.

Develops symmetric Cartan calculus linking to Patterson-Walker metric.

The study characterizes and verifies equivariant embeddings of symmetric Kählerian manifolds.

Defines semi-symmetric metric connection on super warped products.