Related papers: Anti-Invariant Holomorphic Statistical Submersions
In view of training increasingly complex learning architectures, we establish a nonsmooth implicit function theorem with an operational calculus. Our result applies to most practical problems (i.e., definable problems) provided that a…
In this article, we study the invariant differential forms which a correspondence of curves admits. We also try to classify the correspondences of $\mathbb{P}^1$ that admits such invariant differential forms.
In a polydiagonal subspace of the Euclidean space, certain components of the vectors are equal (synchrony) or opposite (anti-synchrony). Polydiagonal subspaces invariant under a matrix have many applications in graph theory and dynamical…
Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given…
We adapt the microcanonical framework of equilibrium statistical mechanics to predict the statistics of short waves in inhomogeneous moving media. For steady inhomogeneities and background flow, we compute the wave spectrum at any location…
In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the linear wave…
This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove smoothness of the invariant densities away from critical points and describe the asymptotics of the…
For a large class of nonuniformly expanding maps of $\Bbb R^m$, with indifferent fixed points and unbounded distorsion and non necessarily Markovian, we construct an absolutely continuous invariant measure. We extend to our case techniques…
In this note we prove certain necessary and sufficient conditions for the existence of an embedding of statistical manifolds. In particular, we prove that any compact smooth ($C^1$ resp.) statistical manifold can be embedded into the space…
In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…
We introduce holomorphic Riemannian maps between almost Hermitian manifolds as a generalization of holomorphic submanifolds and holomorphic submersions, give examples and obtain a geometric characterization of harmonic holomorphic…
We provide the first documented examples of immersions of closed oriented manifolds which are not homologous to embeddings, thus answering a question posed by Zhenhua Liu. In these examples we show that for any representing self-transverse…
\textit{Non-statistical dynamics} are those for which a set of points with positive measure (w.r.t. a reference probability measure which is in most examples the Lebesgue on a manifold) do not have a convergent sequence of empirical…
Conformal invariants of manifolds of non-positive scalar curvature are studied in association with growth in volume and fundamental group.
This paper presents an overview of physical ideas and mathematical methods for implementing non-smooth and discontinuous substitutions in dynamical systems. General purpose of such substitutions is to bring the differential equations of…
This paper introduces the notion of $k$-isoparametric hypersurface in an $(n+1)$-dimensional Riemannian manifold for $k=0,1,...,n$. Many fundamental and interesting results (towards the classification of homogeneous hypersurfaces among…
The objective of this work is to understand how the characteristics of relativistic MHD turbulence may differ from those of nonrelativistic MHD turbulence. We accomplish this by studying the ideal invariants in the relativistic case and…
Flow-based models typically define a latent space with dimensionality identical to the observational space. In many problems, however, the data does not populate the full ambient data space that they natively reside in, rather inhabiting a…
Upon a consistent topological statistical theory the application of structural statistics requires a quantification of the proximity structure of model spaces. An important tool to study these structures are Pseudo-Riemannian metrices,…
In this paper, invariant submanifolds of a generalized Kenmotsu manifold are studied. Necessary and sufficient conditions are given on a submanifold of a generalized Kenmotsu manifold to be an invariant submanifold.In this case, we…