Connected Choice and the Brouwer Fixed Point Theorem

We study the computational content of the Brouwer Fixed Point Theorem in the Weihrauch lattice. Connected choice is the operation that finds a point in a non-empty connected closed set given by negative information. One of our main results is that for any fixed dimension the Brouwer Fixed Point Theorem of that dimension is computably equivalent to connected choice of the Euclidean unit cube of the same dimension. Another main result is that connected choice is complete for dimension greater than or equal to two in the sense that it is computably equivalent to Weak K\H{o}nig's Lemma. While we can present two independent proofs for dimension three and upwards that are either based on a simple geometric construction or a combinatorial argument, the proof for dimension two is based on a more involved inverse limit construction. The connected choice operation in dimension one is known to be equivalent to the Intermediate Value Theorem; we prove that this problem is not idempotent in contrast to the case of dimension two and upwards. We also prove that Lipschitz continuity with Lipschitz constants strictly larger than one does not simplify finding fixed points. Finally, we prove that finding a connectedness component of a closed subset of the Euclidean unit cube of any dimension greater or equal to one is equivalent to Weak K\H{o}nig's Lemma. In order to describe these results, we introduce a representation of closed subsets of the unit cube by trees of rational complexes.Comment: 36 page

XTH acts at the microfibril-matrix interface during cell elongation

Sulphorhodamine-labelled oligosaccharides of xyloglucan are incorporated into the cell wall of Arabidopsis and tobacco roots, and of cultured Nicotiana tabacum cells by the transglucosylase (XET) action of XTHs. In the cell wall of diffusely growing cells, the subcellular pattern of XET action revealed a 'fibrillar' pattern, different from the xyloglucan localization. The fibrillar fluorescence pattern had no net orientation in spherical cultured cells. It changed to transverse to the long axis when the cells started to elongate, a feature mirroring the rearrangements of cortical microtubules and the accompanying cellulose deposition. Interference with the polymerization of microtubules and with cellulose deposition inhibited this strong and 'fibrillar'-organized XET-action, whereas interference with actin-polymerization only decreased the intensity of enzyme action. Epidermal cells of a mutant with reduced cellulose synthesis also had low XET action. Root hairs (tip-growing cells) exhibited high XET-action over all their length, but lacked the specific parallel pattern. In both diffuse- and tip-growing cell types extraction of the incorporated fluorescent xyloglucans by a xyloglucan-specific endoglucanase reduced the fluorescence, but the 'fibrillar' appearance in diffuse growing cells was not eliminated. These results show that XTHs act on the xyloglucans attached to cellulose microfibrils. After incorporation of the fluorescent oligosaccharides, the xyloglucans decorate the cellulose microfibrils and become inaccessible to hydrolytic enzymes

Theoretical study of the charge transport through C60-based single-molecule junctions

We present a theoretical study of the conductance and thermopower of single-molecule junctions based on C60 and C60-terminated molecules. We first analyze the transport properties of gold-C60-gold junctions and show that these junctions can be highly conductive (with conductances above 0.1G0, where G0 is the quantum of conductance). Moreover, we find that the thermopower in these junctions is negative due to the fact that the LUMO dominates the charge transport, and its magnitude can reach several tens of micro-V/K, depending on the contact geometry. On the other hand, we study the suitability of C60 as an anchoring group in single-molecule junctions. For this purpose, we analyze the transport through several dumbbell derivatives using C60 as anchors, and we compare the results with those obtained with thiol and amine groups. Our results show that the conductance of C60-terminated molecules is rather sensitive to the binding geometry. Moreover, the conductance of the molecules is typically reduced by the presence of the C60 anchors, which in turn makes the junctions more sensitive to the functionalization of the molecular core with appropriate side groups.Comment: 9 pages, 7 figure

Growth, mortality and recruitment of commercially important fishes and penaeid shrimps in Indonesian waters

Population dynamics, Stock assessment, Commercial species, Shrimp fisheries, Arafura Sea, Indonesia, Penaeus merguiensis

Insurance loss coverage under restricted risk classification: The case of iso-elastic demand

This paper investigates equilibrium in an insurance market where risk classification is restricted. Insurance demand is characterised by an iso-elastic function with a single elasticity parameter. We characterise the equilibrium by three quantities: equilibrium premium; level of adverse selection (in the economist’s sense); and “loss coverage”, defined as the expected population losses compensated by insurance. We consider both equal elasticities for high and low risk-groups, and then different elasticities. In the equal elasticities case, adverse selection is always higher under pooling than under risk-differentiated premiums, while loss coverage first increases and then decreases with demand elasticity. We argue that loss coverage represents the efficacy of insurance for the whole population; and therefore that if demand elasticity is sufficiently low, adverse selection is not always a bad thing

A duality for Spin Verlinde spaces and Prym Theta functions

The paper proves canonical isomorphisms between Spin Verlinde spaces, that is, spaces of global sections of a determinant line bundle over the moduli space of semistable Spinn-bundles over a smooth projective curve C, and the dual spaces of theta functions over Prym varieties of unramified double covers of C