Related papers: Rationality in map and hypermap enumeration by gen…
A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the…
When studying families in the moduli space of dynamical systems, choosing an appropriate representative function for a conjugacy class can be a delicate task. The most delicate questions surround rationality of the conjugacy class compared…
If $R$ is a rational map, the Main Result is a uniformization Theorem for the space of decompositions of the iterates of $R$. Secondly, we show that Fatou conjecture holds for decomposable rational maps.
This paper introduces a differentiable semantic reasoner, where rules are presented as a relevant set of graph transformations. These rules can be written manually or inferred by a set of facts and goals presented as a training set. While…
We introduce bijections between families of rooted maps with unfixed genus and families of so-called blossoming trees endowed with an arbitrary forward matching of their leaves. We first focus on Eulerian maps with controlled vertex…
We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…
The moduli space of parabolic bundles with fixed determinant over a smooth curve of genus greater than one is proved to be rational whenever one of the multiplicities associated to the quasi-parabolic structure is equal to one. It follows…
Rational decision making in its linguistic description means making logical decisions. In essence, a rational agent optimally processes all relevant information to achieve its goal. Rationality has two elements and these are the use of…
In 2007, A.I.Aptekarev and his collaborators discovered a sequence of rational approximations to Euler's constant $\gamma$ defined by a linear recurrence. In this paper, we generalize this result and present an explicit construction of…
We consider the problem of approaching real numbers with rational numbers with prime denominator and with a single numerator allowed for each denominator. We then present a simple application, related to possible correlations between trace…
We show the existence of ``good'' approximations to a real number $\gamma$ using rationals with denominators formed by digits $0$ and $1$ in base $b$. We derive an elementary estimate and enhance this result by managing exponential sums.
To every automorphism w of an infinite rooted regular binary tree we associate a two variable generating function \Phi_w that encodes information on the orbit structure of w. We prove that this is a rational function if w can be described…
We formulate some problems and conjectures about semigroups of rational functions under composition. The considered problems arise in different contexts, but most of them are united by a certain relationship to the concept of amenability.
Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…
Functions with singularities are notoriously difficult to approximate with conventional approximation schemes. In computational applications, they are often resolved with low-order piecewise polynomials, multilevel schemes, or other types…
It is known that any rational abstract numeration system is faithfully, and effectively, represented by an N-rational series. A simple proof of this result is given which yields a representation of this series which in turn allows a simple…
Neural rationale models are popular for interpretable predictions of NLP tasks. In these, a selector extracts segments of the input text, called rationales, and passes these segments to a classifier for prediction. Since the rationale is…
The $\beta\gamma$ system is generalized by complex(rational) powers of the fields, which leads to a corresponding extension on the Fock space. Two different approaches to compute the Green functions of the physical operators are proposed.…
Let w: Map(X,Y;f) -> Y denote a general evaluation fibration. Working in the setting of rational homotopy theory via differential graded Lie algebras, we identify the long exact sequence induced on rational homotopy groups by w in terms of…
In this paper we present algorithmic considerations and theoretical results about the relation between the orders of certain groups associated to the components of a polynomial and the order of the group that corresponds to the polynomial,…