Related papers: Space filling positionality and the Spiroformer
A special approach to examine spinor structure of 3-space is proposed. It is based on the use of the concept of a spatial spinor defined through taking the square root of a real-valued 3-vector. Two sorts of spatial spinor according to…
Many representation systems on the sphere have been proposed in the past, such as spherical harmonics, wavelets, or curvelets. Each of these data representations is designed to extract a specific set of features, and choosing the best fixed…
Shape formation is a basic distributed problem for systems of computational mobile entities. Intensively studied for systems of autonomous mobile robots, it has recently been investigated in the realm of programmable matter. Namely, it has…
We study one and two point functions of conformal field theories on spaces of maximal symmetry with and without boundaries and investigate their spectral representations. Integral transforms are found, relating the spectral decomposition to…
In this article we study polyharmonic curves of constant curvature where we mostly focus on the case of curves on the sphere. We classify polyharmonic curves of constant curvature in three-dimensional space forms and derive an explicit…
In this work, we present Point Transformer, a deep neural network that operates directly on unordered and unstructured point sets. We design Point Transformer to extract local and global features and relate both representations by…
The paper is continuation of [6] where we have discussed some classical and quantization problems of rigid bodies of infinitesimal size moving in Riemannian spaces. Strictly speaking, we have considered oscillatory dynamical models on…
Similar to sperm, where individuals self-organize in space while also striving for coherence in their tail swinging, several natural and engineered systems exhibit the emergence of swarming and synchronization. The arising and interplay of…
New variables of separation for few integrable systems on the two-dimensional sphere with higher order integrals of motion are considered in detail. We explicitly describe canonical transformations of initial physical variables to the…
In the first work of this series [physics/0204035] it was shown that the conformational space of a molecule could be described to a fair degree of accuracy by means of a central hyperplane arrangement. The hyperplanes divide the espace into…
We prove, for a class of contact manifolds, that the universal cover of the group of contact diffeomorphisms carries a natural partial order. It leads to a new viewpoint on geometry and dynamics of contactomorphisms. It gives rise to…
We study the simplicial volume of manifolds obtained from Davis' reflection group trick, the goal being characterizing those having positive simplicial volume. In particular, we focus on checking whether manifolds in this class with nonzero…
In our previous paper we have discussed Poisson properties of cluster algebras of geometric type for the case of a nondegenerate matrix of transition exponents. In this paper we consider the case of a general matrix of transition exponents.…
Scattering transforms are a new type of summary statistics recently developed for the study of highly non-Gaussian processes, which have been shown to be very promising for astrophysical studies. In particular, they allow one to build…
Metamorphism is a recently introduced integral transform, which is useful in solving partial differential equations. Basic properties of metamorphism can be verified by direct calculations. In this paper we present metamorphism as a sort of…
Transformers are effective and efficient at modeling complex relationships and learning patterns from structured data in many applications. The main aim of this paper is to propose and design NLAFormer, which is a transformer-based…
Transformers are built upon multi-head scaled dot-product attention and positional encoding, which aim to learn the feature representations and token dependencies. In this work, we focus on enhancing the distinctive representation by…
``Rubber'' coated rolling bodies satisfy a no-twist in addition to the no slip satisfied by ``marble'' coated bodies. Rubber rolling has an interesting differential geometric appeal because the geodesic curvatures of the curves on the…
Higher-order accurate solution to electromagnetic scattering problems are obtained at reduced computational cost in a {\it p}-variable finite volume time domain method. Spatial operators of lower, including first-order accuracy, are…
Vision Transformers are very popular nowadays due to their state-of-the-art performance in several computer vision tasks, such as image classification and action recognition. Although their performance has been greatly enhanced through…