Related papers: Transversality for critical relations of families …
We collect some classical results on the versal families of ordinary compact Riemann surfaces needed in `Versal Families of Compact Super Riemann Surfaces'.
Coupling probability measures lies at the core of many problems in statistics and machine learning, from domain adaptation to transfer learning and causal inference. Yet, even when restricted to deterministic transports, such couplings are…
We provide a partial classification of positive linear maps in matrix algebras which is based on a family of spectral conditions. This construction generalizes celebrated Choi example of a map which is positive but not completely positive.…
Hall's Theorem is a basic result in Combinatorics which states that the obvious necesssary condition for a finite family of sets to have a transversal is also sufficient. We present a sufficient (but not necessary) condition on the sizes of…
This paper is a systematic study about the syndetically proximal relation and the possible existence of syndetically scrambled sets for the dynamics of continuous self-maps of compact metric spaces. Especially we consider various classes of…
The hypothesis of self-organized criticality explains the existence of long-range `space-time' correlations, observed inseparably in many natural dynamical systems. A simple link between these correlations is yet unclear, particularly in…
An interval translation map (ITM) is a piece-wise translation $T \colon I \to I$ defined on a finite partition $I_1, \ldots, I_r$ of an interval $I$ into $r \ge 2$ subintervals. In contrast to classical interval exchange transformations…
We prove that any closed map between metrizable spaces can be extended to a closed map between completely metrizable spaces with the same extensional dimension.
We use the methods developed with M. Lyubich for proving complex bounds for real quadratics to extend E. De Faria's complex a priori bounds to all critical circle maps with an irrational rotation number. The contracting property for…
Let $f$ be a postcritically finite rational map. We prove that, as $n$ large enough, there exists an $f^n$-invariant (finite connected) graph on $\widehat{\mathbb{C}}$ such that it contains the postcritical set of $f$.
Motivated by problems arising in the relative trace formula and arithmetic invariant theory we prove the existence of rational points on orbits arising from certain infinitesimal symmetric spaces. As an application, we prove analogous…
An accessibility graph of a network contains a link, wherever there is a path of arbitrary length between two nodes. We generalize the concept of accessibility to temporal networks. Building an accessibility graph by consecutively adding…
In this note we obtain the surjectivity of smooth maps into Euclidean spaces under mild conditions. As application we give a new proof of the Fundamental Theorem of Algebra. We also observe that any $C^1$-map from a compact manifold into…
The notion of 'slope rational connectedness' is introduced in the context of smooth orbifold pairs. The main result parallels the characterization of the rational connectedness of projective manifolds in terms of either the non-existence of…
We formalize the general principle of significance with respect to binary relations which is a universal tool for description and analysis of various situations in and apart from mathematics. We derive the basic properties and focus on a…
There are presented sufficient conditions for existence of an infinite family of trajectories of an analytic gradient flow which converge to a critical point.
The chain relation, due to Conley, and the strong chain relation, due to Easton, are well studied for continuous maps on compact metric spaces. Following Fathi and Pageault, we use barrier functions to generalize the theory to general…
We characterize all translation invariant half planar maps satisfying a certain natural domain Markov property. For p-angulations with p \ge 3 where all faces are simple, we show that these form a one-parameter family of measures…
We give a short proof of the convergence to the boundary of Riemann maps on varying domains. Our proof provides a uniform approach to several ad-hoc constructions that have recently appeared in the literature.
A paper by Boros, Little, Moll, Mosteig, and Stanley relates properties of a map defined on the space of rational functions to Eulerian polynomials. We link their work to the carries Markov chain, giving a new proof and slight…