arXiv research

Paper classifies bifurcations of Minkowski symmetry sets for plane curves.

The investigation of 3D euclidean symmetry sets (SS) and medial axis is an important area, due in particular to their various important applications. The pre-symmetry set of a surface M in 3-space (resp. smooth closed curve in 2D) is the set of pairs of points which contribute to the symmetry set, that is, the closure …

Study on geodesics in a specific sub-Riemannian structure with two types of behavior.

The paper examines the geometry of a curve's centre symmetry set.

Study shows instability of certain MOTSs with continuous symmetry.

Develops non-parametric tests for group symmetry in data.

Origami patterns are classified based on their symmetry groups.

New findings on hidden symmetries in ReLU networks.

Invariants found for tau-symmetric bihamiltonian systems.

The generalized Feix--Kaledin construction shows that c-projective $2n$-manifolds with curvature of type $(1,1)$ are precisely the submanifolds of quaternionic $4n$-manifolds which are fixed points set of a special type of quaternionic $S^1$ action $v$. In this paper, we consider this construction in the presence of in…

Invariant kernels reduce rank and improve generalization across dimensions.

Study spectral settings of generalized Laplacians on homogeneous spaces.

Study connects symmetries in dynamical systems to phase plane representations.

Study on symmetry defects of complete intersections in complex space.

We fully develop the concept of causal symmetry introduced in Class. Quant. Grav. 20 (2003) L139. A causal symmetry is a transformation of a Lorentzian manifold (V,g) which maps every future-directed vector onto a future-directed vector. We prove that the set of all causal symmetries is not a group under the usual comp…

Unified framework for enforcing, discovering, and promoting symmetry in machine learning.

Paper proves non-compact inaudibility of symmetry and commutativity.

Study of intrinsic symmetry groups of links, finding counterexamples.

The Regge symmetry is a set of remarkable relations between two tetrahedra whose edge lengths are related in a simple fashion. It was first discovered as a consequence of an asymptotic formula in mathematical physics. Here we give a simple geometric proof of Regge symmetries in Euclidean, spherical, and hyperbolic geom…

This work extends PAC-Bayesian learning guarantees to non-compact symmetries and non-invariant data.

Part I. We prove a one-to-one correspondence between differential symmetry breaking operators for equivariant vector bundles over two homogeneous spaces and certain homomorphisms for representations of two Lie algebras, in connection with branching problems of the restriction of representations. We develop a new method…

Study symmetries in smoothed polygonal links.

Abstract: Generalized reduction methods for symmetries in graded geometry.

We show that the distribution of symmetry of a naturally reductive nilpotent Lie group coincides with the invariant distribution induced by the set of fixed vectors of the isotropy. This extends a known result on compact naturally reductive spaces. We also address the study of the quotient by the foliation of symmetry.

Study of symmetries in 2D Yang-Mills theory, including orbifolds and higher forms.

The paper defines symmetries in no-arbitrage markets.

The paper simplifies symmetries in complex geometric structures.

Study invariant Lipschitz bandits, improving regret bounds.

Study symmetric linear bandits with hidden symmetry, achieving improved regret bounds.

In this paper, we present the point symmetry group of three-dimensional homogeneous Helmholtz equation, when we consider the cylindrical coordinate system. In continuation, we present a complete set of functionally independent invariants of the equation along with the form of the general solution provided by these inva…

This work relaxes GNN symmetries to approximate automorphisms, improving model performance.

Based on the recent work \cite{PII} we put forward a new type of transformation for Lorentzian manifolds characterized by mapping every causal future-directed vector onto a causal future-directed vector. The set of all such transformations, which we call causal symmetries, has the structure of a submonoid which contain…

Study of 4D flows with nilpotent symmetry, showing immortal solutions and blowdown limits.

Bayesian framework detects symmetries in chaotic dynamical systems.

Let P and Q be convex polyhedra in E3 with face lattices F(P) and F(Q) and symmetry groups G(P) and G(Q), respectively. Then, P and Q are called face equivalent if there is a lattice isomorphism between F(P) and F(Q); P and Q are called symmetry equivalent if the action of G(P) on F(P) is equivalent to the action of G(…

We define a new type of transformation for Lorentzian manifolds characterized by mapping every causal future-directed vector onto a causal future-directed vector. The set of all such transformations, which we call causal symmetries, has the structure of a submonoid. Some of their properties are investigated and we give…

New method produces reflections with nonseparating fixed points.

We show that the space of algebraic covariant derivative curvature tensors R' is generated by Young symmetrized tensor products W*U or U*W, where W and U are covariant tensors of order 2 and 3 whose symmetry classes are irreducible and characterized by the following pairs of partitions: {(2),(3)}, {(2),(2 1)} or {(1 1)…

Study on MHD equilibria on curved spaces without symmetries.

Hidden symmetry of a G'-space X is defined by an extension of the G'-action on X to that of a group G containing G' as a subgroup. In this setting, we study the relationship between the three objects: (A) global analysis on X by using representations of G (hidden symmetry); (B) global analysis on X by using representat…

Study of sub-Riemannian problem on specific Lie groups, revealing symmetries and bounds.

Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. "Structure" can be understood as symmetry and a range of symmetries are expressed by hierarchy. Such symmetries directly point to invariants, that pinpoint intrinsic properties of the data and of the …

Since the foundational work of Chenciner and Montgomery in 2000 there has been a great deal of interest in choreographic solutions of the n-body problem: periodic motions where the n bodies all follow one another at regular intervals along a closed path. The principal approach combines variational methods with symmetry…

Given a pair of planar curves, one can define its generalized area distance, a concept that generalizes the area distance of a single curve. In this paper, we show that the generalized area distance of a pair of planar curves is an improper indefinite affine spheres with singularities, and, reciprocally, every indefini…

New triangulations of octonionic projective plane found with restricted symmetry groups.

Study examines stability of MOTS in symmetric initial data sets.

The symmetries of paths in a manifold $M$ are classified with respect to a given pointwise proper action of a Lie group $G$ on $M$. Here, paths are embeddings of a compact interval into $M$. There are at least two types of symmetries: Firstly, paths that are parts of an integral curve of a fundamental vector field on $…

Study nearly parallel G2-structures with torus symmetry using multi-moment maps.