Eisenstein integrals and induction of relations

I give a survey of joint work with Henrik Schlichtkrull on the induction of certain relations among (partial) Eisenstein integrals for the minimal principal series of a reductive symmetric space. I explain the application of this principle of induction to the proofs of a Fourier inversion formula and a Paley-Wiener theorem. Finally, the relation with the Plancherel decomposition is discussed.Comment: Latex2e, 22 pp, Proc. Conf. `Analyse Harmonique Non Commutative (colloque en l'honneur de Jacques Carmona)' CIRM, Luminy, 20-24 Mai, 200

Pancyclicity of Hamiltonian line graphs

Let f(n) be the smallest integer such that for every graph G of order n with minimum degree 3(G)>f(n), the line graph L(G) of G is pancyclic whenever L(G) is hamiltonian. Results are proved showing that f(n) = ®(n 1/3)

Heat content and inradius for regions with a Brownian boundary

In this paper we consider $\beta[0; s]$, Brownian motion of time length $s > 0$, in $m$-dimensional Euclidean space $\mathbb R^m$ and on the $m$-dimensional torus $\mathbb T^m$. We compute the expectation of (i) the heat content at time $t$ of $\mathbb R^m\setminus \beta[0; s]$ for fixed $s$ and $m = 2,3$ in the limit $t \downarrow 0$, when $\beta[0; s]$ is kept at temperature 1 for all $t > 0$ and $\mathbb R^m\setminus \beta[0; s]$ has initial temperature 0, and (ii) the inradius of $\mathbb R^m\setminus \beta[0; s]$ for $m = 2,3,\cdots$ in the limit $s \rightarrow \infty$.Comment: 13 page

Structural selection in implicit learning of artificial grammars

In the contextual cueing paradigm, Endo and Takeda (in Percept Psychophys 66:293–302, 2004) provided evidence that implicit learning involves selection of the aspect of a structure that is most useful to one’s task. The present study attempted to replicate this finding in artificial grammar learning to investigate whether or not implicit learning commonly involves such a selection. Participants in Experiment 1 were presented with an induction task that could be facilitated by several characteristics of the exemplars. For some participants, those characteristics included a perfectly predictive feature. The results suggested that the aspect of the structure that was most useful to the induction task was selected and learned implicitly. Experiment 2 provided evidence that, although salience affected participants’ awareness of the perfectly predictive feature, selection for implicit learning was mainly based on usefulness

Functional agro biodiversity in Dutch arable farming: results of a three year pilot

A pilot on 400 ha of Dutch arable farms during 2004-2007 perennial grassy field margins and functional annual flower strips were created on potato and wheat fields. Monitoring information on pests and natural enemies was directly communicated to the farmers to support pest management decisions. Due to the increasing numbers of natural enemies and the gradually reducing peak densities of aphids, the farmers could refrain from insecticide applications against aphids in these crops. The pilot has yielded great public awareness on possibilities for functional agro biodiversity in arable crops

Quantum suppression of shot noise in atom-size metallic contacts

The transmission of conductance modes in atom-size gold contacts is investigated by simultaneously measuring conductance and shot noise. The results give unambiguous evidence that the current in the smallest gold contacts is mostly carried by nearly fully transmitted modes. In particular, for a single-atom contact the contribution of additional modes is only a few percent. In contrast, the trivalent metal aluminum does not show this property.Comment: Fig. 2 replaced, small errors correcte