Related papers: A p-adic approach to local analytic dynamics: anal…
Meaning can be generated when information is related at a systemic level. Such a system can be an observer, but also a discourse, for example, operationalized as a set of documents. The measurement of semantics as similarity in patterns…
In this article, we develop a version of Sen theory for equivariant vector bundles on the Fargues-Fontaine curve. We show that every equivariant vector bundle canonically descends to a locally analytic vector bundle. A comparison with the…
The dominant theme of this thesis is that random matrix valued analytic functions, generalizing both random matrices and random analytic functions, for many purposes can (and perhaps should) be effectively studied in that level of…
Normalizing flow-based sampling methods have been successful in tackling computational challenges traditionally associated with simulating lattice quantum field theories. Further works have incorporated gauge and translational invariance of…
We generalize Tutte's integer flows and the $d$-dimensional Euclidean flows of Mattiolo, Mazzuoccolo, Rajn\'{i}k, and Tabarelli to \emph{$d$-dimensional $p$-normed nowhere-zero flows} and define the corresponding flow index $\phi_{d,p}(G)$…
Topological transforms have been very useful in statistical analysis of shapes or surfaces without restrictions that the shapes are diffeomorphic and requiring the estimation of correspondence maps. In this paper we introduce two…
Let $M$ and $N$ be Nash manifolds, and $f$ and $g$ Nash maps from $M$ to $N$. If $M$ and $N$ are compact and if $f$ and $g$ are analytically R-L equivalent, then they are Nash R-L equivalent. In the local case, $C^infty$ R-L equivalence of…
In this paper we show that the non-analyticity locus of an arc-analytic function is arc-symmetric. Recall that a function is called arc-analytic if it is real analytic on each real analytic arc. By a result of Bierstone and Milman a big…
Local analytic germs can be simultaneously deformed equivariantly for the flow if there is one holomorphic solution whose degree is high compared to local discrepancy.
Self-similar symmetric $\alpha$-stable, $\alpha\in(0,2)$, mixed moving averages can be related to nonsingular flows. By using this relation and the structure of the underlying flows, one can decompose self-similar mixed moving averages into…
We adapt the "royal road" method used to simplify automatic analyticity theorems in noncommutative function theory to several complex variables. We show that certain families of functions must be real analytic if they have certain nice…
We give a criterion of integrality of an one-dimensional formal group law in terms of congruences satisfied by the coefficients of the canonical invariant differential. For an integral formal group law a p-adic analytic formula for the…
Cartograms are maps that rescale geographic regions (e.g., countries, districts) such that their areas are proportional to quantitative demographic data (e.g., population size, gross domestic product). Unlike conventional bar or pie charts,…
We continue our study on infinitesimal lifting properties of maps between locally noetherian formal schemes started in math.AG/0604241. In this paper, we focus on some properties which arise specifically in the formal context. In this vein,…
Let $p$ be a prime. We discuss methods of solution of congruences modulo $p^n$ using $p$-adic numbers; these methods are similar to computations with real numbers (local methods). Examples of relations between local and global methods are…
In this article, we define the l-adic homology for a morphism of schemes satisfying certain finiteness conditions. This homology has these functors similar to the Chow groups: proper push-forward, flat pull-back, base change, cap-product,…
We show that there exists a strong connection between the generic formal neighborhood at a rational arc lying in the Nash set associated with a toric divisorial valuation on a toric variety and the formal neighborhood at the generic point…
We study the Bowen topological entropy of generic and irregular points for certain dynamical systems. We define the topological entropy of noncompact sets for flows, analogous to Bowen's definition. We show that this entropy coincides with…
We study the definable topological dynamics $(G,S_G(M))$ of a definable group acting on its type space, where $M$ is a structure and $G$ is a group definable in $M$. In \cite{Newelski-I}, Newelski raised a question of whether weakly generic…
It was already known that a p-adic, locally Lipschitz continuous semi-algebraic function is piecewise Lipschitz continuous, where the pieces can be taken semi-algebraic. We prove that if the function has locally Lipschitz constant 1, then…