Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.

Social motility of African trypanosomes is a property of a distinct life-cycle stage that occurs early in tsetse fly transmission

The protozoan pathogen Trypanosoma brucei is transmitted between mammals by tsetse flies. The first compartment colonised by trypanosomes after a blood meal is the fly midgut lumen. Trypanosomes present in the lumen-designated as early procyclic forms-express the stage-specific surface glycoproteins EP and GPEET procyclin. When the trypanosomes establish a mature infection and colonise the ectoperitrophic space, GPEET is down-regulated, and EP becomes the major surface protein of late procyclic forms. A few years ago, it was discovered that procyclic form trypanosomes exhibit social motility (SoMo) when inoculated on a semi-solid surface. We demonstrate that SoMo is a feature of early procyclic forms, and that late procyclic forms are invariably SoMo-negative. In addition, we show that, apart from GPEET, other markers are differentially expressed in these two life-cycle stages, both in culture and in tsetse flies, indicating that they have different biological properties and should be considered distinct stages of the life cycle. Differentially expressed genes include two closely related adenylate cyclases, both hexokinases and calflagins. These findings link the phenomenon of SoMo in vitro to the parasite forms found during the first 4-7 days of a midgut infection. We postulate that ordered group movement on plates reflects the migration of parasites from the midgut lumen into the ectoperitrophic space within the tsetse fly. Moreover, the process can be uncoupled from colonisation of the salivary glands. Although they are the major surface proteins of procyclic forms, EP and GPEET are not essential for SoMo, nor, as shown previously, are they required for near normal colonisation of the fly midgut.

The Social Life of African Trypanosomes

The unicellular parasite Trypanosoma brucei shuttles between its definitive host, the tsetse fly, and various mammals including humans. In the fly digestive tract, T. brucei must first migrate to the ectoperitrophic space, establish a persistent infection of the midgut and then migrate to the salivary glands before being transmitted to a new mammalian host. In 2010, it was shown that insect stages of the parasite (procyclic forms) exhibit social motility (SoMo) when cultured on a semi-solid surface, and it was postulated that this behaviour might reflect a migration step in the tsetse fly. Now, almost 5 years after the initial report, several new publications shed some light on the biological function of SoMo and provide insights into the underlying signalling pathways.

Nonverbal synchrony in social interactions of patients with schizophrenia indicates socio-communicative deficits

Background Disordered interpersonal communication can be a serious problem in schizophrenia. Recent advances in computer-based measures allow reliable and objective quantification of nonverbal behavior. Research using these novel measures has shown that objective amounts of body and head movement in patients with schizophrenia during social interactions are closely related to the symptom profiles of these patients. In addition to and above mere amounts of movement, the degree of synchrony, or imitation, between patients and normal interactants may be indicative of core deficits underlying various problems in domains related to interpersonal communication, such as symptoms, social competence, and social functioning. Methods Nonverbal synchrony was assessed objectively using Motion Energy Analysis (MEA) in 378 brief, videotaped role-play scenes involving 27 stabilized outpatients diagnosed with paranoid-type schizophrenia. Results Low nonverbal synchrony was indicative of symptoms, low social competence, impaired social functioning, and low self-evaluation of competence. These relationships remained largely significant when correcting for the amounts of patients‘ movement. When patients showed reduced imitation of their interactants’ movements, negative symptoms were likely to be prominent. Conversely, positive symptoms were more prominent in patients when their interaction partners’ imitation of their movements was reduced. Conclusions Nonverbal synchrony can be an objective and sensitive indicator of the severity of patients’ problems. Furthermore, quantitative analysis of nonverbal synchrony may provide novel insights into specific relationships between symptoms, cognition, and core communicative problems in schizophrenia.

The Social Geography of Education: Neighborhood, Class Composition, and the Educational Achievement of Elementary School Students in Zurich, Switzerland

Despite an impressive amount of research and policy intervention no robust pattern of neighborhood effects on educational attainment has previously been identified. Adequate theoretical modeling and the sensitivity of the results to the method of the study are the major challenges in this area of research. This paper elaborates the social mechanisms of neighborhood effects and applies various methodological approaches to test them. Using data from Switzerland, the research reported here has detected heterogeneous effects of neighborhood on elementary school students’ educational achievement in Zurich. Although modest in comparison with the effects of classroom composition, these effects appear to be mediated primarily through social integration into a local peer network and are differentiated according to students’ gender and their social origin.

No scope for social modulation of steroid levels in a year-round territorial damselfish.

Both latitude and mating system have been proposed to shape relationships between steroid hormone levels and social behavior. Recently it has been postulated that species with long lasting non-seasonal territorial behavior have low androgen responsiveness. Tropical damselfishes are an ideal family to test this proposition because they show a large variety in mating systems. Here we contribute to the comparative dataset by measuring the response in steroid levels after social modulation in the banded sergeant, Abudefduf septemfasciatus, a species with non-seasonal territoriality. In highly territorial and brooding males, we found low androgen and cortisol levels that did not increase after experimental intraspecific simulated territorial intrusions (STI tests). No relationship was found between the variation in steroid hormone levels and territorial responses to naturally occurring territorial intrusions. Although steroid levels were low, male A. septemfasciatus were highly territorial both to STI challenges and to fishes that passed the territory. They often chased intruders for several meters away from the territory. This indicates that during nest defence in a non-seasonal territorial damselfish species, territorial behaviors are shown independent of variation in androgen and cortisol levels.