A combinatorial move on the set of Jenkins-Strebel differentials

We describe an elementary combinatorial move on the set of quadratic differentials with a horizontal one cylinder decom-position. Computer experiment suggests that the corresponding equivalent classes are in one-to-one correspondence with the con-nected component of the strata

Connected components of the strata of the moduli space of meromorphic differentials

In this paper, we study the translation surfaces corresponding to meromorphic differentials on compact Riemann surfaces. We compute the number of connected components of the corresponding strata of the moduli space. We show that in genus greater than or equal to two, one has up to three components with a similar description as the one of Kontsevich and Zorich for the moduli space of Abelian differentials. In genus one, one can obtain an arbitrarily large number of connected components that are easily distinghished by a simple topological invariant.Comment: Final version, to appear in Commentarii Mathematici Helvetic

Dynamics and geometry of the Rauzy-Veech induction for quadratic differentials

Interval exchange maps are related to geodesic flows on translation surfaces; they correspond to the first return maps of the vertical flow on a transverse segment. The Rauzy-Veech induction on the space of interval exchange maps provides a powerful tool to analyze the Teichmueller geodesic flow on the moduli space of Abelian differentials. Several major results have been proved using this renormalization. Danthony and Nogueira introduced in 1988 a natural generalization of interval exchange transformations, namely the linear involutions. These maps are related to general measured foliations on surfaces (orientable or not). In this paper we are interested by such maps related to geodesic flow on (orientable) flat surfaces with Z/2Z linear holonomy. We relate geometry and dynamics of such maps to the combinatorics of generalized permutations. We study an analogue of the Rauzy-Veech induction and give an efficient combinatorial characterization of its attractors. We establish a natural bijection between the extended Rauzy classes of generalized permutations and connected components of the strata of meromorphic quadratic differentials with at most simple poles, which allows, in particular, to classify the connected components of all exceptional strata.Comment: 50 pages, 16 figures. References added, minor corrections. Paper submitte

Ends of strata of the moduli space of quadratic differentials

Very few results are known about the topology of the strata of the moduli space of quadratic differentials. In this paper, we prove that any connected component of such strata has only one topological end. A typical flat surface in a neighborhood of the boundary is naturally split by a collection of parallel short saddle connections, but the discrete data associated to this splitting can be quite difficult to describe. In order to bypass these difficulties, we use the Veech zippered rectangles construction and the corresponding (extended) Rauzy classes.Comment: 18 pages, 8 pictures. Presentation improve

Configurations of saddle connections of quadratic differentials on CP1 and on hyperelliptic Riemann surfaces

34 pages, 12 figures, submitted, improved presentation and typography.International audienceConfigurations of rigid collections of saddle connections are connected component invariants for strata of the moduli space of quadratic differentials. They have been classified for strata of Abelian differentials by Eskin, Masur and Zorich. Similar work for strata of quadratic differentials has been done in Masur and Zorich, although in that case the connected components were not distinguished. We classify the configurations for quadratic differentials on the Riemann sphere and on hyperelliptic connected components of the moduli space of quadratic differentials. We show that, in genera greater than five, any configuration that appears in the hyperelliptic connected component of a stratum also appears in the non-hyperelliptic one

Do changes of pen and penmate affect the behaviour of heifers?

We wanted to investigate if relocation affects behaviour of dairy heifers. In the study 32 Holstein heifers were housed in pairs until they were 13 months old. 16 heifers stayed in the same pen with the same penmate (control). The pen and penmates of 16 heifers were changed 16 times between 11 and 13 months of age

Affect-Driven Attention Biases as Animal Welfare Indicators: Review and Methods.

Attention bias describes the differential allocation of attention towards one stimulus compared to others. In humans, this bias can be mediated by the observer's affective state and is implicated in the onset and maintenance of affective disorders such as anxiety. Affect-driven attention biases (ADABs) have also been identified in a few other species. Here, we review the literature on ADABs in animals and discuss their utility as welfare indicators. Despite a limited research effort, several studies have found that negative affective states modulate attention to negative (i.e., threatening) cues. ADABs influenced by positive-valence states have also been documented in animals. We discuss methods for measuring ADAB and conclude that looking time, dot-probe, and emotional spatial cueing paradigms are particularly promising. Research is needed to test them with a wider range of species, investigate attentional scope as an indicator of affect, and explore the possible causative role of attention biases in determining animal wellbeing. Finally, we argue that ADABs might not be best-utilized as indicators of general valence, but instead to reveal specific emotions, motivations, aversions, and preferences. Paying attention to the human literature could facilitate these advances