Admissibility in Finitely Generated Quasivarieties

Checking the admissibility of quasiequations in a finitely generated (i.e., generated by a finite set of finite algebras) quasivariety Q amounts to checking validity in a suitable finite free algebra of the quasivariety, and is therefore decidable. However, since free algebras may be large even for small sets of small algebras and very few generators, this naive method for checking admissibility in Q is not computationally feasible. In this paper, algorithms are introduced that generate a minimal (with respect to a multiset well-ordering on their cardinalities) finite set of algebras such that the validity of a quasiequation in this set corresponds to admissibility of the quasiequation in Q. In particular, structural completeness (validity and admissibility coincide) and almost structural completeness (validity and admissibility coincide for quasiequations with unifiable premises) can be checked. The algorithms are illustrated with a selection of well-known finitely generated quasivarieties, and adapted to handle also admissibility of rules in finite-valued logics.

Amalgamation and interpolation in ordered algebras

The first part of this paper provides a comprehensive and self-contained account of the interrelationships between algebraic properties of varieties and properties of their free algebras and equational consequence relations. In particular, proofs are given of known equivalences between the amalgamation property and the Robinson property, the congruence extension property and the extension property, and the flat amalgamation property and the deductive interpolation property, as well as various dependencies between these properties. These relationships are then exploited in the second part of the paper in order to provide new proofs of amalgamation and deductive interpolation for the varieties of lattice-ordered abelian groups and MV-algebras, and to determine important subvarieties of residuated lattices where these properties hold or fail. In particular, a full description is given of all subvarieties of commutative GMV-algebras possessing the amalgamation property.

Epidemiology of Brucellosis and Q Fever in Linked Human and Animal Populations in Northern Togo

BACKGROUND: Although brucellosis (Brucella spp.) and Q Fever (Coxiella burnetii) are zoonoses of global importance, very little high quality data are available from West Africa. METHODS/PRINCIPAL FINDINGS: A serosurvey was conducted in Togo's main livestock-raising zone in 2011 in 25 randomly selected villages, including 683 people, 596 cattle, 465 sheep and 221 goats. Additionally, 464 transhumant cattle from Burkina Faso were sampled in 2012. The serological analyses performed were the Rose Bengal Test and ELISA for brucellosis and ELISA and the immunofluorescence assay (IFA) for Q Fever Brucellosis did not appear to pose a major human health problem in the study zone, with only 7 seropositive participants. B. abortus was isolated from 3 bovine hygroma samples, and is likely to be the predominant circulating strain. This may explain the observed seropositivity amongst village cattle (9.2%, 95%CI:4.3-18.6%) and transhumant cattle (7.3%, 95%CI:3.5-14.7%), with an absence of seropositive small ruminants. Exposure of livestock and people to C. burnetii was common, potentially influenced by cultural factors. People of Fulani ethnicity had greater livestock contact and a significantly higher seroprevalence than other ethnic groups (Fulani: 45.5%, 95%CI:37.7-53.6%; non-Fulani: 27.1%, 95%CI:20.6-34.7%). Appropriate diagnostic test cut-off values in endemic settings requires further investigation. Both brucellosis and Q Fever appeared to impact on livestock production. Seropositive cows were more likely to have aborted a foetus during the previous year than seronegative cows, when adjusted for age. This odds was 3.8 times higher (95%CI: 1.2-12.1) for brucellosis and 6.7 times higher (95%CI: 1.3-34.8) for Q Fever. CONCLUSIONS: This is the first epidemiological study of zoonoses in Togo in linked human and animal populations, providing much needed data for West Africa. Exposure to Brucella and C. burnetii is common but further research is needed into the clinical and economic impact.

Clinical signs of deformed wing virus infection are predictive markers for honey bee colony losses.

The ectoparasitic mite Varroa destructor acting as a virus vector constitutes a central mechanism for losses of managed honey bee, Apis mellifera, colonies. This creates demand for an easy, accurate and cheap diagnostic tool to estimate the impact of viruliferous mites in the field. Here we evaluated whether the clinical signs of the ubiquitous and mite-transmitted deformed wing virus (DWV) can be predictive markers of winter losses. In fall and winter 2007/2008, A.m. carnica workers with apparent wing deformities were counted daily in traps installed on 29 queenright colonies. The data show that colonies which later died had a significantly higher proportion of workers with wing deformities than did those which survived. There was a significant positive correlation between V. destructor infestation levels and the number of workers displaying DWV clinical signs, further supporting the mite's impact on virus infections at the colony level. A logistic regression model suggests that colony size, the number of workers with wing deformities and V. destructor infestation levels constitute predictive markers for winter colony losses in this order of importance and ease of evaluation.

Validation of targeting the ventrointermediate thalamic nucleus using Q-ball calculation in deep brain stimulation for tremor

Objective: Identification of the ventrointermediate thalamic nucleus (Vim) in modern 3T high-field MRI for image-based targeting in deep brain stimulation (DBS) is still challenging. To evaluate the usefulness and reliability of analyzing the connectivity with the cerebellum using Q-ball-calculation we performed a retrospective analysis. Method: 5 patients who underwent bilateral implantation of electrodes in the Vim for treatment of Essential Tremor between 2011 and 2012 received additional preoperative Q-ball imaging. Targeting was performed according to atlas coordinates and standard MRI. Additionally we performed a retrospective identification of the Vim by analyzing the connectivity of the thalamus with the dentate nucleus. The exact position of the active stimulation contact in the postoperative CT was correlated with the Vim as it was identified by Q-ball calculation. Results: Localization of the Vim by analysis of the connectivity between thalamus and cerebellum was successful in all 5 patients on both sides. The average position of the active contacts was 14.6 mm (SD 1.24) lateral, 5.37 mm (SD 0.094 posterior and 2.21 mm (SD 0.69) cranial of MC. The cranial portion of the dentato-rubro-thalamic tract was localized an average of 3.38 mm (SD 1.57) lateral and 1.5 mm (SD 1.22) posterior of the active contact. Conclusions: Connectivity analysis by Q-ball calculation provided direct visualization of the Vim in all cases. Our preliminary results suggest, that the target determined by connectivity analysis is valid and could possibly be used in addition to or even instead of atlas based targeting. Larger prospective calculations are needed to determine the robustness of this method in providing refined information useful for neurosurgical treatment of tremor.

The anisotropic λ -deformed SU(2) model is integrable

The all-loop anisotropic Thirring model interpolates between the WZW model and the non-Abelian T-dual of the anisotropic principal chiral model. We focus on the SU(2) case and we prove that it is classically integrable by providing its Lax pair formulation. We derive its underlying symmetry current algebra and use it to show that the Poisson brackets of the spatial part of the Lax pair, assume the Maillet form. In this way we procure the corresponding r and s matrices which provide non-trivial solutions to the modified Yang–Baxter equation.