A formula for the coincidence Reidemeister trace of selfmaps on bouquets of circles

We give a formula for the coincidence Reidemeister trace of selfmaps on bouquets of circles in terms of the Fox calculus. Our formula reduces the problem of computing the coincidence Reidemeister trace to the problem of distinguishing doubly twisted conjugacy classes in free groups.Comment: 17 pages, 4 figure

Constructing balleans

A ballean is a set endowed with a coarse structure. We introduce and explore three constructions of balleans from a pregiven family of balleans: bornological products, bouquets and combs. We analyze the smallest and the largest coarse structures on a set $X$ compatible with a given bornology on $X$.Comment: Ballean, coarse structure, bornology, bornological product, fan, attachmen

Semiconjugacies, pinched Cantor bouquets and hyperbolic orbifolds

Let f be a transcendental entire map that is subhyperbolic, i.e., the intersection of the Fatou set F(f) and the postsingular set P(f) is compact and the intersection of the Julia set J(f) and P(f) is finite. Assume that no asymptotic value of f belongs to J(f) and that the local degree of f at all points in J(f) is bounded by some finite constant. We prove that there is a hyperbolic map g (of the form g(z)=f(bz) for some complex number b) with connected Fatou set such that f and g are semiconjugate on their Julia sets. Furthermore, we show that this semiconjugacy is a conjugacy when restricted to the escaping set I(g) of g. In the case where f can be written as a finite composition of maps of finite order, our theorem, together with recent results on Julia sets of hyperbolic maps, implies that J(f) is a pinched Cantor bouquet, consisting of dynamic rays and their endpoints. Our result also seems to give the first complete description of topological dynamics of an entire transcendental map whose Julia set is the whole complex plane.Comment: 32 pages, 3 figure

Consumer Acceptability in Flower Chains: How Can We Determine What the Final Customers Really Want?

When we look at the ornamental supply chain in the Netherlands as a Value Chain (Porter, 1998) it strikes us that most actors in the chain are obsessed by the product and have no idea how the value of these products is developed throughout the entire production and supply chain. Any value chain starts with the value a group of consumers attributes to the product. So it all starts with finding out what consumers want and then finding the most cost effective way of delivering that product with the desired attributes to these consumers. In the USA the South American producers expected to be able to compete with the local production by offering the product (cut flowers) at a lower price (Reid, 2002). In the first instance this worked very well and the local production virtually disappeared. However the quality of the imported product was a dismal failure and while imports surged, total flower consumption plummeted in the 90s. In the UK the retail chains such as Sainsbury’s and Tesco wanted to improve their ornamental categories. They invented the ‘Vase Life Guarantee’ and improved their quality considerably. This resulted in an increase in market share from 18 to 60% over 15 years, while the total flower consumption in the UK doubled in the past 15 years. A research will be shown on the response of stakeholders in the ornamental industry and consumers on the question whether they would see the ‘Vase Life Guarantee’ as a value addition in the supply chain. This research was done in the UK and the Netherlands (where no vase life guarantee was used explicitly in the retail) at the turn of the millennium. It clearly shows the difference between the judgements of the stakeholders versus the opinions of the consumers. If we want to create Value Added Chains in the ornamental industry it is about time to find out what the consumer really wants

Striosome–dendron bouquets highlight a unique striatonigral circuit targeting dopamine-containing neurons

The dopamine systems of the brain powerfully influence movement and motivation. We demonstrate that striatonigral fibers originating in striosomes form highly unusual bouquet-like arborizations that target bundles of ventrally extending dopamine-containing dendrites and clusters of their parent nigral cell bodies. Retrograde tracing showed that these clustered cell bodies in turn project to the striatum as part of the classic nigrostriatal pathway. Thus, these striosome-dendron formations, here termed "striosome-dendron bouquets," likely represent subsystems with the nigro-striato-nigral loop that are affected in human disorders including Parkinson's disease. Within the bouquets, expansion microscopy resolved many individual striosomal fibers tightly intertwined with the dopamine-containing dendrites and also with afferents labeled by glutamatergic, GABAergic, and cholinergic markers and markers for astrocytic cells and fibers and connexin 43 puncta. We suggest that the striosome-dendron bouquets form specialized integrative units within the dopamine-containing nigral system. Given evidence that striosomes receive input from cortical regions related to the control of mood and motivation and that they link functionally to reinforcement and decision-making, the striosome-dendron bouquets could be critical to dopamine-related function in health and disease