A new metric invariant for Banach spaces

We show that if the Szlenk index of a Banach space $X$ is larger than the first infinite ordinal $\omega$ or if the Szlenk index of its dual is larger than $\omega$, then the tree of all finite sequences of integers equipped with the hyperbolic distance metrically embeds into $X$. We show that the converse is true when $X$ is assumed to be reflexive. As an application, we exhibit new classes of Banach spaces that are stable under coarse-Lipschitz embeddings and therefore under uniform homeomorphisms.Comment: 22 page

Asymptotic geometry of Banach spaces and uniform quotient maps

Recently, Lima and Randrianarivony pointed out the role of the property $(\beta)$ of Rolewicz in nonlinear quotient problems, and answered a ten-year-old question of Bates, Johnson, Lindenstrauss, Preiss and Schechtman. In the present paper, we prove that the modulus of asymptotic uniform smoothness of the range space of a uniform quotient map can be compared with the modulus of $(\beta)$ of the domain space. We also provide conditions under which this comparison can be improved

Tsetse and human trypanosomiasis challenge in south eastern Uganda

Pièges pyramidaux (8000) ont été mis en place contre #Glossina fuscipes fuscipes afin de lutter contre la maladie du sommeil à #Trypanosoma rhodésiense dans le Busoga. Dans le but de comprendre les modalités du contact homme/mouche, la récolte des données sur la densité, la distribution spatiale et la mobilité des mouches, ont été mis en relation avec la dynamique de la transmission de la trypanosomiase humaine dans le Bugosa. Comme pour #T. gambiense$, peu de corrélations entre la densité globale de mouche et l'incidence de la maladie ont été trouvées. Cependant, des observations de terrain avec un enregistrement daté des mouvements saisonniers des hommes et des animaux dans des habitats favorables aux mouches demeure la clé de la compréhension de la transmission de la maladie. (Résumé d'auteur

Shift invariant preduals of ℓ₁(ℤ)

The Banach space ℓ<sub>1</sub>(ℤ) admits many non-isomorphic preduals, for example, C(K) for any compact countable space K, along with many more exotic Banach spaces. In this paper, we impose an extra condition: the predual must make the bilateral shift on ℓ<sub>1</sub>(ℤ) weak<sup>*</sup>-continuous. This is equivalent to making the natural convolution multiplication on ℓ<sub>1</sub>(ℤ) separately weak*-continuous and so turning ℓ<sub>1</sub>(ℤ) into a dual Banach algebra. We call such preduals <i>shift-invariant</i>. It is known that the only shift-invariant predual arising from the standard duality between C<sub>0</sub>(K) (for countable locally compact K) and ℓ<sub>1</sub>(ℤ) is c<sub>0</sub>(ℤ). We provide an explicit construction of an uncountable family of distinct preduals which do make the bilateral shift weak<sup>*</sup>-continuous. Using Szlenk index arguments, we show that merely as Banach spaces, these are all isomorphic to c<sub>0</sub>. We then build some theory to study such preduals, showing that they arise from certain semigroup compactifications of ℤ. This allows us to produce a large number of other examples, including non-isometric preduals, and preduals which are not Banach space isomorphic to c<sub>0</sub>

Improving the Cost-Effectiveness of Artificial Visual Baits for Controlling the Tsetse Fly Glossina fuscipes fuscipes

Tsetse flies, which transmit sleeping sickness to humans and nagana to cattle, are commonly controlled by stationary artificial baits consisting of traps or insecticide-treated screens known as targets. In Kenya the use of electrocuting sampling devices showed that the numbers of Glossina fuscipes fuscipes (Newstead) visiting a biconical trap were nearly double those visiting a black target of 100 cm×100 cm. However, only 40% of the males and 21% of the females entered the trap, whereas 71% and 34%, respectively, alighted on the target. The greater number visiting the trap appeared to be due to its being largely blue, rather than being three-dimensional or raised above the ground. Through a series of variations of target design we show that a blue-and-black panel of cloth (0.06 m2) flanked by a panel (0.06 m2) of fine black netting, placed at ground level, would be about ten times more cost-effective than traps or large targets in control campaigns. This finding has important implications for controlling all subspecies of G. fuscipes, which are currently responsible for more than 90% of sleeping sickness cases