A note on syndeticity, recognizable sets and Cobham's theorem

In this note, we give an alternative proof of the following result. Let p, q >= 2 be two multiplicatively independent integers. If an infinite set of integers is both p- and q-recognizable, then it is syndetic. Notice that this result is needed in the classical proof of the celebrated Cobham?s theorem. Therefore the aim of this paper is to complete [13] and [1] to obtain an accessible proof of Cobham?s theorem

Avoiding 2-binomial squares and cubes

Two finite words $u,v$ are 2-binomially equivalent if, for all words $x$ of length at most 2, the number of occurrences of $x$ as a (scattered) subword of $u$ is equal to the number of occurrences of $x$ in $v$. This notion is a refinement of the usual abelian equivalence. A 2-binomial square is a word $uv$ where $u$ and $v$ are 2-binomially equivalent. In this paper, considering pure morphic words, we prove that 2-binomial squares (resp. cubes) are avoidable over a 3-letter (resp. 2-letter) alphabet. The sizes of the alphabets are optimal

Breadth-first serialisation of trees and rational languages

We present here the notion of breadth-first signature and its relationship with numeration system theory. It is the serialisation into an infinite word of an ordered infinite tree of finite degree. We study which class of languages corresponds to which class of words and,more specifically, using a known construction from numeration system theory, we prove that the signature of rational languages are substitutive sequences.Comment: 15 page

El règim jurídic dels topònims de les Illes Balears

Abstract not availabl

Superconductivity as a Bose-Einstein condensation?

Bose-Einstein condensation (BEC) in two dimensions (2D) (e.g., to describe the quasi-2D cuprates) is suggested as the possible mechanism widely believed to underlie superconductivity in general. A crucial role is played by nonzero center-of-mass momentum Cooper pairs (CPs) usually neglected in BCS theory. Also vital is the unique {\it linear} dispersion relation appropriate to weakly-coupled "bosonic" CPs moving in the Fermi sea--rather than in vacuum where the dispersion would be quadratic but only for very strong coupling, and for which BEC is known to be impossible in 2D.Comment: 6 pages included 3 figure

A prospective longitudinal study of perceived infant outcomes at 18-24 months: Neural and psychological correlates of parental thoughts and actions assessed during the first month postpartum

The first postpartum months constitute a critical period for parents to establish an emotional bond with their infants. Neural responses to infant-related stimuli have been associated with parental sensitivity. However, the associations among these neural responses, parenting, and later infant outcomes for mothers and fathers are unknown. In the current longitudinal study, we investigated the relationships between parental thoughts/actions and neural activation in mothers and fathers in the neonatal period with infant outcomes at the toddler stage. At the first month postpartum, mothers (n=21) and fathers (n=19) underwent a neuroimaging session during which they listened to their own and unfamiliar baby’s cry. Parenting-related thoughts/behaviors were assessed by interview twice at the first month and 3-4 months postpartum and infants’ socioemotional outcomes were reported by mothers and fathers at 18-24 months postpartum. In mothers, higher levels of anxious thoughts/actions about parenting at the first month postpartum, but not at 3-4 months postpartum, were associated with infant’s low socioemotional competencies at 18-24 months. Anxious thoughts/actions were also associated with heightened responses in the motor cortex and reduced responses in the substantia nigra to own infant cry sounds. On the other hand, in fathers, higher levels of positive perception of being a parent at the first month postpartum, but not at 3-4 months postpartum, were associated with higher infant socioemotional competencies at 18-24 months. Positive thoughts were associated with heightened responses in the auditory cortex and caudate to own infant cry sounds. The current study provides evidence that parental thoughts are related to concurrent neural responses to their infants at the first month postpartum as well as their infant’s future socioemotional outcome at 18-24 months. Parent differences suggest that anxious thoughts in mothers and positive thoughts in fathers may be the targets for parenting-focused interventions very early postpartum

From quantum trajectories to classical orbits

Recently it has been shown that the evolution of open quantum systems may be ``unraveled'' into individual ``trajectories,'' providing powerful numerical and conceptual tools. In this letter we use quantum trajectories to study mesoscopic systems and their classical limit. We show that in this limit, Quantum Jump (QJ) trajectories approach a diffusive limit very similar to the Quantum State Diffusion (QSD) unraveling. The latter follows classical trajectories in the classical limit. Hence, both unravelings show the rise of classical orbits. This is true for both regular and chaotic systems (which exhibit strange attractors).Comment: 7 pages RevTeX 3.0 + 2 figures (postscript). Submitted to Physical Review Letter