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.

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.

The ischial spine sign: does pelvic tilt and rotation matter?

Although the ischial spine sign (ISS) has been advocated to detect acetabular retroversion, it is unknown whether the sign is valid on anteroposterior (AP) pelvic radiographs with tilted or rotated pelves. We therefore evaluated reliability of the ISS as a tool for diagnosing acetabular retroversion in the presence of considerable pelvic tilt and/or malrotation. We obtained radiographs of 20 cadaver pelves in 19 different malorientations resulting in 380 pelvis images (760 hips) for evaluation. In addition, 129 clinical radiographs of patients' hips that had varying pelvis orientations were reviewed. We found an overall sensitivity of 81% (90%), specificity of 70% (71%), positive predictive value of 77% (80.7%), and negative predictive value of 75% (85%) in the cadaver (patient) hips. Our data suggest the ISS is a valid tool for diagnosing acetabular retroversion on plain radiographs taken using a standardized technique regardless of the degree of pelvic tilt and rotation.

Line focusing for soft x-ray laser-plasma lasing

A computational study of line-focus generation was done using a self-written ray-tracing code and compared to experimental data. Two line-focusing geometries were compared, i.e., either exploiting the sagittal astigmatism of a tilted spherical mirror or using the spherical aberration of an off-axis- illuminated spherical mirror. Line focusing by means of astigmatism or spherical aberration showed identical results as expected for the equivalence of the two frames of reference. The variation of the incidence angle on the target affects the line-focus length, which affects the amplification length such that as long as the irradiance is above the amplification threshold, it is advantageous to have a longer line focus. The amplification threshold is physically dependent on operating parameters and plasma-column conditions and in the present study addresses four possible cases.

Dystonic movement disorders and spinal degenerative disease

The occurrence of degenerative spinal disease subsequent to dystonic movement disorders has been neglected and has received more attention only recently. Spinal surgery is challenging with regard to continuous mechanical stress when treatment of the underlying movement disorder is insufficient. To characterize better the particular features of degenerative spinal disease in patients with dystonia and to analyze operative strategies, we reviewed the available published data. Epidemiologic studies reveal that degenerative spinal disorders in patients with dystonia and choreoathetosis occur much earlier than in the physiological aging process. Dystonic movement disorders more often affect the spine at higher cervical levels (C(2-5)), in contrast to spinal degeneration with age which manifests more frequently at the middle and lower cervical spine (C(5-7)). Degenerative changes of the cervical spine are more likely to occur on the side where the chin is rotated or tilted to. Various operative approaches for treatment of spinal pathologies have been advocated in patients with dystonic movement disorders. The available data do not allow making firm statements regarding the superiority of one approach over the other. Posterior approaches were first used for decompression, but additional anterior fusion became necessary in many instances. Anterior approaches with or without instrumented fusion yielded more favorable results, but drawbacks are pseudarthrosis and adjacent-level disease. Parallel to the development of posterior fusion techniques, circumferential surgery was suggested to provide a maximum degree of cord decompression and a higher fusion rate. Perioperative local injections of botulinum toxin were used initially to enhance patient comfort with halo immobilization, but they are also applied in patients without external fixation nowadays. Treatment algorithms directed at the underlying movement disorder itself, taking advantage of new techniques of functional neurosurgery, combined with spinal surgery have recently been introduced and show promising results.

Projection structure of a member of the amino acid/polyamine/organocation transporter superfamily

The L-arginine/agmatine antiporter AdiC is a key component of the arginine-dependent extreme acid resistance system of Escherichia coli. Phylogenetic analysis indicated that AdiC belongs to the amino acid/polyamine/organocation (APC) transporter superfamily having sequence identities of 15-17% to eukaryotic and human APC transporters. For functional and structural characterization, we cloned, overexpressed, and purified wild-type AdiC and the point mutant AdiC-W293L, which is unable to bind and consequently transport L-arginine. Purified detergent-solubilized AdiC particles were dimeric. Reconstitution experiments yielded two-dimensional crystals of AdiC-W293L diffracting beyond 6 angstroms resolution from which we determined the projection structure at 6.5 angstroms resolution. The projection map showed 10-12 density peaks per monomer and suggested mainly tilted helices with the exception of one distinct perpendicular membrane spanning alpha-helix. Comparison of AdiC-W293L with the projection map of the oxalate/formate antiporter from Oxalobacter formigenes, a member from the major facilitator superfamily, indicated different structures. Thus, two-dimensional crystals of AdiC-W293L yielded the first detailed view of a transport protein from the APC superfamily at sub-nanometer resolution.