Related papers: Characteristic foliations of material evolution: f…
Molino's description of Riemannian foliations on compact manifolds is generalized to the setting of compact equicontinuous foliated spaces, in the case where the leaves are dense. In particular, a structural local group is associated to…
We show that every source connected Lie groupoid always has global bisections through any given point. This bisection can be chosen to be the multiplication of some exponentials as close as possible to a prescribed curve. The existence of…
This article focuses on properties of monotone convolutions. A criterion for infinite divisibility and time evolution of convolution semigroups are mainly studied. In particular, we clarify that many analogues of the classical results of…
In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…
Attempts to consider evolution across space-time singularities often lead to quantum systems with time-dependent Hamiltonians developing an isolated singularity as a function of time. Examples include matrix theory in certain singular…
Regular Lie groups are infinite dimensional Lie groups with the property that smooth curves in the Lie algebra integrate to smooth curves in the group in a smooth way (an `evolution operator' exists). Up to now all known smooth Lie groups…
This paper develops the tools of formal algebraic geometry in the setting of noncommutative manifolds, roughly ringed spaces locally modeled on the free associative algebra. We define a notion of noncommutative coordinate system, which is a…
Deep Generative Models are frequently used to learn continuous representations of complex data distributions using a finite number of samples. For any generative model, including pre-trained foundation models with Diffusion or Transformer…
Most conspicuous organisms are multicellular and most multicellular organisms develop somatic cells to perform specific, non-reproductive tasks. The ubiquity of this division of labor suggests that it is highly advantageous. In this paper,…
Non-Euclidean method of the generalized geometry construction is considered. According to this approach any generalized geometry is obtained as a result of deformation of the proper Euclidean geometry. The method may be applied for…
Intriguing phenomena such as subrecoil laser cooling of atoms, or aging phenomenon in glasses, have in common that the systems considered do not reach a steady-state during the experiments, although the experimental time scales are very…
The evolution of various competing cell types in tissues, and the resulting persistent tissue population, is studied numerically and analytically in a particle-based model of active tissues. Mutations change the properties of cells in…
Presentations of smooth symmetry groups of differentiable stacks are studied within the framework of the weak 2-category of Lie groupoids, smooth principal bibundles, and smooth biequivariant maps. It is shown that principality of bibundles…
The relativistic time evolution of multi-layer spherically symmetric shell systems---consisting of infinitely thin shells separated by vacuum regions---is examined. Whenever two shells collide the evolution is continued with the assumption…
We study topology of leaves of 1-dimensional singular holomorphic foliations of Stein manifolds. We prove that for a generic foliation all leaves, except for at most countably many, are contractible, the rest are topological cylinders. We…
There exists a smooth foliation with 3 singular points on the two-dimensional torus such that any lifting of a leaf of this foliation on the universal covering of the torus is a dense subset of the covering.
A neural population responding to multiple appearances of a single object defines a manifold in the neural response space. The ability to classify such manifolds is of interest, as object recognition and other computational tasks require a…
Isoparametric submanifolds and hypersurfaces in space forms are geometric objects that have been studied since E. Cartan. Another important class of geometric objects is the orbits of a polar action on a Riemannian manifold,e.g., the orbits…
Model evolution is widely considered as a subject under research. Despite its role in research, common purpose concepts, approaches, solutions, and methodologies are missing. Limiting the scope to model libraries makes model evolution and…
We introduce Riemannian Lie algebroids as a generalization of Riemannian manifolds and we show that most of the classical tools and results known in Riemannian geometry can be stated in this setting. We give also some new results on the…