Related papers: Minimal Diffeomorphisms cannot satisfy Generalized…
We work out the theory of fractional isomorphism of graphons as a generalization to the classical theory of fractional isomorphism of finite graphs. The generalization is given in terms of homomorphism densities of finite trees and it is…
We provide a geometric interpretation for a normalized version of the minimal denominator function, $$q_{\min}(x,\delta)=\min\left\{q\in \mathbb{N}: \text{ there exists } p\in\mathbb{Z} \text{ such that } \frac{p}{q}\in…
Nowadays, huge amounts of data are naturally collected in distributed sites due to different facts and moving these data through the network for extracting useful knowledge is almost unfeasible for either technical reasons or policies.…
A resolution of the intersection of a finite number of subgroups of an abelian group by means of their sums is constructed, provided the lattice generated by these subgroups is distributive. This is used for detecting singularities of…
In this note we prove that the factorization theorem for dominated polynomials previously proved by the authors is equivalent to an alternative factorization scheme that uses classical linear techniques and a linearization process. However,…
Let $M$ be the circle or a compact interval, and let $\alpha=k+\tau\ge1$ be a real number such that $k=\lfloor \alpha\rfloor$. We write $\mathrm{Diff}_+^{\alpha}(M)$ for the group of $C^k$ diffeomorphisms of $M$ whose $k^{th}$ derivatives…
Let X be a normal variety such that $K_X$ is Q-Cartier, and let $f: X \rightarrow X$ be a finite surjective morphism of degree at least two. We establish a close relation between the irreducible components of the locus of singularities that…
We prove generic differentiability in $P$-minimal theories, strengthening an earlier result of Kuijpers and Leenknegt. Using this, we prove Onshuus and Pillay's $P$-minimal analogue of Pillay's conjectures on o-minimal groups. Specifically,…
This article explains and extends semialgebraic homotopy theory (developed by H. Delfs and M. Knebusch) to o-minimal homotopy theory (over a field). The homotopy category of definable CW-complexes is equivalent to the homotopy category of…
A set $Q$ in $\mathbb{Z}_+^d$ is a lower set if $(k_1,\dots,k_d)\in Q$ implies $(l_1,\dots,l_d)\in Q$ whenever $0\le l_i\le k_i$ for all $i$. We derive new and refine known results regarding the cardinality of the lower sets of size $n$ in…
{\em Partial domination problem} is a generalization of the {\em minimum dominating set problem} on graphs. Here, instead of dominating all the nodes, one asks to dominate at least a fraction of the nodes of the given graph by choosing a…
Recent works related to Palis conjecture of J. Yang, S. Crovisier, M. Sambarino and D. Yang showed that any aperiodic class of a $C^1$-generic diffeomorphism far away from homoclinic bifurcations (or homoclinic tangencies) is partially…
We study a geometric variational problem for sets in the plane in which the perimeter and a regularized dipolar interaction compete under a mass constraint. In contrast to previously studied nonlocal isoperimetric problems, here the…
Hyperbolicity and dominated splitting are two of the most important concepts in the global analysis of differentiable dynamics. In this paper we give several equivalent characterizations of the dominated splitting and in particular we show…
Let $\widehat G \subseteq G$ be complex reductive algebraic groups. The branching problem that aims to study $G$-modules as $\widehat G$-modules is encoded by a collection of branching multiplicities parameterised by pairs of dominant…
The properties of uniform hyperbolicity and dominated splitting have been introduced to study the stability of the dynamics of diffeomorphisms. One meets difficulties when one tries to extend these definitions to vector fields and Shantao…
Let $X$ be a normal projective variety. A surjective endomorphism $f:X\to X$ is int-amplified if $f^\ast L - L =H$ for some ample Cartier divisors $L$ and $H$. This is a generalization of the so-called polarized endomorphism which requires…
Our basic element is a $C^1$ mapping $f:X\to Y$, with $X,Y$ Banach spaces, and with derivative everywhere invertible. So $f$ is a local diffeomorphism at every point. The aim of this paper is to find a sufficient condition for $f$ to be…
We show that in any $\mathbb{Q}$-Gorenstein flat family of klt singularities, normalized volumes are lower semicontinuous with respect to the Zariski topology. A quick consequence is that smooth points have the largest normalized volume…
We address the problem of computing a Minimal Dominating Set in highly dynamic distributed systems. We assume weak connectivity, i.e., the network may be disconnected at each time instant and topological changes are unpredictable. We make…