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>

Finitely fibered Rosenthal compacta and trees

We study some topological properties of trees with the interval topology. In particular, we characterize trees which admit a 2-fibered compactification and we present two examples of trees whose one-point compactifications are Rosenthal compact with certain renorming properties of their spaces of continuous functions.Comment: Small changes, mainly in the introduction and in final remark

Boolean Rings that are Baire Spaces

∗ The present article was originally submitted for the second volume of Murcia Seminar on Functional Analysis (1989). Unfortunately it has been not possible to continue with Murcia Seminar publication anymore. For historical reasons the present vesion correspond with the original one.Weak completeness properties of Boolean rings are related to the property of being a Baire space (when suitably topologised) and to renorming properties of the Banach spaces of continuous functions on the corresponding Stone spaces

A fundamental test for stellar feedback recipes in galaxy simulations

Direct comparisons between galaxy simulations and observations that both reach scales < 100 pc are strong tools to investigate the cloud-scale physics of star formation and feedback in nearby galaxies. Here we carry out such a comparison for hydrodynamical simulations of a Milky Way-like galaxy, including stochastic star formation, HII region and supernova feedback, and chemical post-processing at 8 pc resolution. Our simulation shows excellent agreement with almost all kpc-scale and larger observables, including total star formation rates, radial profiles of CO, HI, and star formation through the galactic disc, mass ratios of the ISM components, both whole-galaxy and resolved Kennicutt-Schmidt relations, and giant molecular cloud properties. However, we find that our simulation does not reproduce the observed de-correlation between tracers of gas and star formation on < 100 pc scales, known as the star formation 'uncertainty principle', which indicates that observed clouds undergo rapid evolutionary lifecycles. We conclude that the discrepancy is driven by insufficiently-strong pre-supernova feedback in our simulation, which does not disperse the surrounding gas completely, leaving star formation tracer emission too strongly associated with molecular gas tracer emission, inconsistent with observations. This result implies that the cloud-scale de-correlation of gas and star formation is a fundamental test for feedback prescriptions in galaxy simulations, one that can fail even in simulations that reproduce all other macroscopic properties of star-forming galaxies.Comment: 13 pages, 10 figures, accepted for publication in MNRA

One health: a concept led by Africa, with global benefits

Titus Mlengeya Kamani and others argue that Africa is well positioned and equipped to conduct and benefit from an integrated approac

Plasticity in transmission strategies of the malaria parasite, Plasmodium chabaudi : environmental and genetic effects

Parasites may alter their behaviour to cope with changes in the within-host environment. In particular, investment in transmission may alter in response to the availability of parasite resources or host immune responses. However, experimental and theoretical studies have drawn conflicting conclusions regarding parasites' optimal (adaptive) responses to deterioration in habitat quality. We analyse data from acute infections with six genotypes of the rodent malaria species to quantify how investment in transmission (gametocytes) is influenced by the within-host environment. Using a minimum of modelling assumptions, we find that proportional investment in gametocytogenesis increases sharply with host anaemia and also increases at low parasite densities. Further, stronger dependence of investment on parasite density is associated with greater virulence of the parasite genotype. Our study provides a robust quantitative framework for studying parasites' responses to the host environment and whether these responses are adaptive, which is crucial for predicting the short-term and evolutionary impact of transmission-blocking treatments for parasitic diseases

Integrating serological and genetic data to quantify cross-species transmission: brucellosis as a case study

Epidemiological data are often fragmented, partial, and/or ambiguous and unable to yield the desired level of understanding of infectious disease dynamics to adequately inform control measures. Here, we show how the information contained in widely available serology data can be enhanced by integration with less common type-specific data, to improve the understanding of the transmission dynamics of complex multi-species pathogens and host communities. Using brucellosis in Northern Tanzania as a case-study, we developed a latent process model based on serology data obtained from the field, to reconstruct Brucella transmission dynamics. We were able to identify sheep and goats as a more likely source of human and animal infection than cattle; however, the highly cross-reactive nature of Brucella spp. meant that it was not possible to determine which Brucella species (B. abortus or B. melitensis) is responsible for human infection. We extended our model to integrate simulated serology and typing data, and show that although serology alone can identify the host source of human infection under certain restrictive conditions, the integration of even small amounts (5%) of typing data can improve understanding of complex epidemiological dynamics. We show that data integration will often be essential when more than one pathogen is present and when the distinction between exposed and infectious individuals is not clear from serology data. With increasing epidemiological complexity, serology data become less informative. However, we show how this weakness can be mitigated by integrating such data with typing data, thereby enhancing the inference from these data and improving understanding of the underlying dynamics

The impact of host species and vector control measures on the fitness of African malaria vectors

Many malaria vector mosquitoes in Africa have an extreme preference for feeding on humans. This specialization allows them to sustain much higher levels of transmission than elsewhere, but there is little understanding of the evolutionary forces that drive this behaviour. In Tanzania, we used a semi-field system to test whether the well-documented preferences of the vectors An. arabiensis and An. gambiae s.s. for cattle and humans respectively are predicted by the fitness they obtain from host-seeking on these species relative to other available hosts. Mosquito fitness was contrasted when humans were fully exposed, and when they were protected by a typical bednet. The fitness of both vectors varied between host species. The predicted relationship between host preference and fitness was confirmed in An. arabiensis, but not in An. gambiae s.s. whose fitness was similar on humans and other mammals. Use of typical, imperfect bednets generated only minor reductions in An. gambiae s.s. feeding success and fitness on humans, but was predicted to generate a significant reduction in the lifetime reproductive success of An. arabiensis on human relative to cows. This supports the hypothesis that such human-protective measures could additionally benefit malaria control by increasing selection for zoophily in vectors

Cryptosporidium cuniculus - new records in human and kangaroo in Australia

BACKGROUND: To date, Cryptosporidium cuniculus has been found exclusively in rabbits and humans. The present study provides the first published molecular evidence for C. cuniculus in an Australian human patient as well as a kangaroo. FINDINGS: Using PCR-based sequencing of regions in the actin, 60 kDa glycoprotein (gp60) and small subunit of ribosomal RNA (SSU) genes, we identified a new and unique C. cuniculus genotype (akin to VbA25) from a human, and C. cuniculus genotype VbA26 from an Eastern grey kangaroo (Macropus giganteus) in Australia. CONCLUSIONS: The characterisation of these genotypes raises questions as to their potential to infect humans and/or other animals in Australia, given that C. cuniculus has been reported to cause cryptosporidiosis outbreaks in Europe