Search results for "R1"
showing 10 items of 1016 documents
The Long-Term Patterns of Regional Income Inequality in Spain, 1860–2000
2013
This paper studies the evolution of Spanish regional inequality from 1860 to 2000. The results point to the coexistence of two basic forces behind changes in regional economic inequality: differences in economic structure and labor productivity across regions. In the Spanish case, the initial expansion of industrialization during the period 1860-1900, in a context of growing economic integration of regions, promoted the spatial concentration of manufacturing in certain regions, which also benefited from the greatest advances in terms of labor productivity. Since 1900 and until 1985, the diffusion of manufacturing and services production to a greater number of locations generated the emulati…
R&D Offshoring and the Productivity Growth of European Regions
2013
The recent increase in R&D offshoring have raised fears that knowledge and competitiveness in advanced countries may be at risk of `hollowing out\'. At the same time, economic research has stressed that this process is also likely to allow some reverse technology transfer and foster growth at home. This paper addresses this issue by investigating the extent to which R&D offshoring is associated with productivity dynamics of European regions. We find that offshoring regions have higher productivity growth, but this positive effect fades down with the number of investment projects carried out abroad. A large and positive correlation emerge between the extent of R&D offshoring and the home reg…
Neuronal FGFR1 transactivation by inducing FGFR1/5-HT1A heteroreceptor complexes formation
2011
There are no clear data on the molecular mechanism by which the hippocampal 5-HT transmission contributes to the neuroprotective and antidepressant effects of 5-HT uptake blockers. Previously, we revealed that a 5-HT1A agonist may induce phosphorylation of FGFR1 and ERK1/2 in rat hippocampus independent of FGF-2, suggesting transactivation of FGFR1 tyrosine kinase in the absence of neurotrophic factor binding. As extension of previous work, using BRET analysis and coimmunoprecipitation in cellular models, FGFR1-5-HT1A heteroreceptor complexes have been demonstrated and agonist modulation characterized. In vitro assays on ERK1/2 phosphorylation in HEK cells and primary hippocampal cultures h…
On the Number of Closed Factors in a Word
2015
A closed word (a.k.a. periodic-like word or complete first return) is a word whose longest border does not have internal occurrences, or, equivalently, whose longest repeated prefix is not right special. We investigate the structure of closed factors of words. We show that a word of length $n$ contains at least $n+1$ distinct closed factors, and characterize those words having exactly $n+1$ closed factors. Furthermore, we show that a word of length $n$ can contain $\Theta(n^{2})$ many distinct closed factors.
Cyclic Complexity of Words
2014
We introduce and study a complexity function on words $c_x(n),$ called \emph{cyclic complexity}, which counts the number of conjugacy classes of factors of length $n$ of an infinite word $x.$ We extend the well-known Morse-Hedlund theorem to the setting of cyclic complexity by showing that a word is ultimately periodic if and only if it has bounded cyclic complexity. Unlike most complexity functions, cyclic complexity distinguishes between Sturmian words of different slopes. We prove that if $x$ is a Sturmian word and $y$ is a word having the same cyclic complexity of $x,$ then up to renaming letters, $x$ and $y$ have the same set of factors. In particular, $y$ is also Sturmian of slope equ…
Anti-powers in infinite words
2018
In combinatorics of words, a concatenation of $k$ consecutive equal blocks is called a power of order $k$. In this paper we take a different point of view and define an anti-power of order $k$ as a concatenation of $k$ consecutive pairwise distinct blocks of the same length. As a main result, we show that every infinite word contains powers of any order or anti-powers of any order. That is, the existence of powers or anti-powers is an unavoidable regularity. Indeed, we prove a stronger result, which relates the density of anti-powers to the existence of a factor that occurs with arbitrary exponent. As a consequence, we show that in every aperiodic uniformly recurrent word, anti-powers of ev…
Factorizations of the Fibonacci Infinite Word
2015
The aim of this note is to survey the factorizations of the Fibonacci infinite word that make use of the Fibonacci words and other related words, and to show that all these factorizations can be easily derived in sequence starting from elementary properties of the Fibonacci numbers.
The sequence of open and closed prefixes of a Sturmian word
2017
A finite word is closed if it contains a factor that occurs both as a prefix and as a suffix but does not have internal occurrences, otherwise it is open. We are interested in the {\it oc-sequence} of a word, which is the binary sequence whose $n$-th element is $0$ if the prefix of length $n$ of the word is open, or $1$ if it is closed. We exhibit results showing that this sequence is deeply related to the combinatorial and periodic structure of a word. In the case of Sturmian words, we show that these are uniquely determined (up to renaming letters) by their oc-sequence. Moreover, we prove that the class of finite Sturmian words is a maximal element with this property in the class of binar…
Abelian combinatorics on words: A survey
2022
We survey known results and open problems in abelian combinatorics on words. Abelian combinatorics on words is the extension to the commutative setting of the classical theory of combinatorics on words. The extension is based on \emph{abelian equivalence}, which is the equivalence relation defined in the set of words by having the same Parikh vector, that is, the same number of occurrences of each letter of the alphabet. In the past few years, there was a lot of research on abelian analogues of classical definitions and properties in combinatorics on words. This survey aims to gather these results.
Abelian Repetitions in Sturmian Words
2012
We investigate abelian repetitions in Sturmian words. We exploit a bijection between factors of Sturmian words and subintervals of the unitary segment that allows us to study the periods of abelian repetitions by using classical results of elementary Number Theory. We prove that in any Sturmian word the superior limit of the ratio between the maximal exponent of an abelian repetition of period $m$ and $m$ is a number $\geq\sqrt{5}$, and the equality holds for the Fibonacci infinite word. We further prove that the longest prefix of the Fibonacci infinite word that is an abelian repetition of period $F_j$, $j>1$, has length $F_j(F_{j+1}+F_{j-1} +1)-2$ if $j$ is even or $F_j(F_{j+1}+F_{j-1}…