The operator algebra approach to quantum groups

A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory.

Cosmic microwave background theory

A long-standing goal of theorists has been to constrain cosmological parameters that define the structure formation theory from cosmic microwave background (CMB) anisotropy experiments and large-scale structure (LSS) observations. The status and future promise of this enterprise is described. Current band-powers in ℓ-space are consistent with a ΔT flat in frequency and broadly follow inflation-based expectations. That the levels are ∼(10−5)2 provides strong support for the gravitational instability theory, while the Far Infrared Absolute Spectrophotometer (FIRAS) constraints on energy injection rule out cosmic explosions as a dominant source of LSS. Band-powers at ℓ ≳ 100 suggest that the universe could not have re-ionized too early. To get the LSS of Cosmic Background Explorer (COBE)-normalized fluctuations right provides encouraging support that the initial fluctuation spectrum was not far off the scale invariant form that inflation models prefer: e.g., for tilted Λ cold dark matter sequences of fixed 13-Gyr age (with the Hubble constant H0 marginalized), ns = 1.17 ± 0.3 for Differential Microwave Radiometer (DMR) only; 1.15 ± 0.08 for DMR plus the SK95 experiment; 1.00 ± 0.04 for DMR plus all smaller angle experiments; 1.00 ± 0.05 when LSS constraints are included as well. The CMB alone currently gives weak constraints on Λ and moderate constraints on Ωtot, but theoretical forecasts of future long duration balloon and satellite experiments are shown which predict percent-level accuracy among a large fraction of the 10+ parameters characterizing the cosmic structure formation theory, at least if it is an inflation variant.

Corneal collagen fibril structure in three dimensions: Structural insights into fibril assembly, mechanical properties, and tissue organization

The ability of the cornea to transmit light while being mechanically resilient is directly attributable to the formation of an extracellular matrix containing orthogonal sheets of collagen fibrils. The detailed structure of the fibrils and how this structure underpins the mechanical properties and organization of the cornea is understood poorly. In this study, we used automated electron tomography to study the three-dimensional organization of molecules in corneal collagen fibrils. The reconstructions show that the collagen molecules in the 36-nm diameter collagen fibrils are organized into microfibrils (≈4-nm diameter) that are tilted by ≈15° to the fibril long axis in a right-handed helix. An unexpected finding was that the microfibrils exhibit a constant-tilt angle independent of radial position within the fibril. This feature suggests that microfibrils in concentric layers are not always parallel to each other and cannot retain the same neighbors between layers. Analysis of the lateral structure shows that the microfibrils exhibit regions of order and disorder within the 67-nm axial repeat of collagen fibrils. Furthermore, the microfibrils are ordered at three specific regions of the axial repeat of collagen fibrils that correspond to the N- and C-telopeptides and the d-band of the gap zone. The reconstructions also show macromolecules binding to the fibril surface at sites that correspond precisely to where the microfibrils are most orderly.

Three-dimensional cryoelectron microscopy of dimeric kinesin and ncd motor domains on microtubules.

Kinesin and ncd motor proteins are homologous in sequence yet move in opposite directions along microtubules. We have previously shown that monomeric kinesin and ncd bind in the same orientation on equivalent sites relative to the ends of tubulin sheets of known polarity. We now report cryoelectron microscope images of 16-protofilament microtubules decorated with both single- and double-headed kinesin and double-headed ncd. Three-dimensional density maps and difference maps show that, in adenosine 5'-[beta,gamma-imido]triphosphate, both dimeric motors bind tightly to microtubules via one head, leaving the other free, though apparently in a fixed position. The attached heads of dimers bind to tubulin in the same way as single kinesin heads. The second heads are connected to the tops of the first but, whereas the second kinesin head is closely associated with the first, pairs of ncd heads are splayed apart. There is also a distinct difference in orientation: the second kinesin head is tilted toward the microtubule plus end, while the second head of ncd points toward the minus end.

Projection structure of frog rhodopsin in two crystal forms.

Rhodopsin is the G protein-coupled receptor that upon light activation triggers the visual transduction cascade. Rod cell outer segment disc membranes were isolated from dark-adapted frog retinas and were extracted with Tween detergents to obtain two-dimensional rhodopsin crystals for electron crystallography. When Tween 80 was used, tubular structures with a p2 lattice (a = 32 A, b = 83 A, gamma = 91 degrees) were formed. The use of a Tween 80/Tween 20 mixture favored the formation of larger p22(1)2(1) lattices (a = 40 A, b = 146 A, gamma = 90 degrees). Micrographs from frozen hydrated frog rhodopsin crystals were processed, and projection structures to 7-A resolution for the p22(1)2(1) form and to 6-A resolution for the p2 form were calculated. The maps of frog rhodopsin in both crystal forms are very similar to the 9-A map obtained previously for bovine rhodopsin and show that the arrangement of the helices is the same. In a tentative topographic model, helices 4, 6, and 7 are nearly perpendicular to the plane of the membrane. In the higher-resolution projection maps of frog rhodopsin, helix 5 looks more tilted than it appeared previously. The quality of the two frog rhodopsin crystals suggests that they would be suitable to obtain a three-dimensional structure in which all helices would be resolved.

Calicheamicin-DNA complexes: warhead alignment and saccharide recognition of the minor groove.

The solution structures of calicheamicin gamma 1I, its cycloaromatized analog (calicheamicin epsilon), and its aryl tetrasaccharide complexed to a common DNA hairpin duplex have been determined by NMR and distance-refined molecular dynamics computations. Sequence specificity is associated with carbohydrate-DNA recognition that places the aryl tetrasaccharide component of all three ligands in similar orientations in the minor groove at the d(T-C-C-T).d(A-G-G-A) segment. The complementary fit of the ligands and the DNA minor groove binding site creates numerous van der Waals contacts as well as hydrogen bonding interactions. Notable are the iodine and sulfur atoms of calicheamicin that hydrogen bond with the exposed amino proton of the 5'- and 3'-guanines, respectively, of the d(A-G-G-A) segment. The sequence-specific carbohydrate binding orients the enediyne aglycone of calicheamicin gamma 1I such that its C3 and C6 proradical centers are adjacent to the cleavage sites. While the enediyne aglycone of calicheamicin gamma 1I is tilted relative to the helix axis and spans the minor groove, the cycloaromatized aglycone is aligned approximately parallel to the helix axis in the respective complexes. Specific localized conformational perturbations in the DNA have been identified from imino proton complexation shifts and changes in specific sugar pucker patterns on complex formation. The helical parameters for the carbohydrate binding site are comparable with corresponding values in B-DNA fibers while a widening of the groove is observed at the adjacent aglycone binding site.

The structure of Ascaris hemoglobin domain I at 2.2 A resolution: molecular features of oxygen avidity.

The perienteric hemoglobin of the parasitic nematode Ascaris has an exceptionally high affinity for oxygen. It is an octameric protein containing two similar heme-binding domains per subunit, but recombinant constructs expressing a single, monomeric heme-binding domain (domain 1; D1) retain full oxygen avidity. We have solved the crystal structure of D1 at 2.2 A resolution. Analysis of the structure reveals a characteristic globin fold and illuminates molecular features involved in oxygen avidity of Ascaris perienteric hemoglobin. A strong hydrogen bond between tyrosine at position 10 in the B helix (tyrosine-B10) and the distal oxygen of the ligand, combined with a weak hydrogen bond between glutamine-E7 and the proximal oxygen, grips the ligand in the binding pocket. A third hydrogen bond between these two amino acids appears to stabilize the structure. The B helix of D1 is displaced laterally by 2.5 A when compared with sperm whale myoglobin. This shifts the tyrosine-B10 hydroxyl far enough from liganded oxygen to form a strong hydrogen bond without steric hindrance. Changes in the F helix compared with myoglobin contribute to a tilted heme that may also be important for oxygen affinity.

Equações de onda generalizadas e quantização funtorial para teorias de campo escalar livre

Nesta dissertação apresentamos um método de quantização matemática e conceitualmente rigoroso para o campo escalar livre de interações. Trazemos de início alguns aspéctos importantes da Teoria de Distribuições e colocamos alguns pontos de geometria Lorentziana. O restante do trabalho é dividido em duas partes: na primeira, estudamos equações de onda em variedades Lorentzianas globalmente hiperbólicas e apresentamos o conceito de soluções fundamentais no contexto de equações locais. Em seguida, progressivamente construímos soluções fundamentais para o operador de onda a partir da distribuição de Riesz. Uma vez estabelecida uma solução para a equação de onda em uma vizinhança de um ponto da variedade, tratamos de construir uma solução global a partir da extensão do problema de Cauchy a toda a variedade, donde as soluções fundamentais dão lugar aos operadores de Green a partir da introdução de uma condição de contorno. Na última parte do trabalho, apresentamos um mínimo da Teoria de Categorias e Funtores para utilizar esse formalismo na contrução de um funtor de segunda quantização entre a categoria de variedades Lorentzianas globalmente hiperbólicas e a categoria de redes de álgebras C* satisfazendo os axiomas de Haag-Kastler. Ao fim, retomamos o caso particular do campo escalar quântico livre.

Divided but United: European Trade Policy & EC-U.S. Agricultural Negotiations in the Uruguay Round. CES Germany & Europe Working Papers, No. 07.3, 1996

How has the integration of trade policy and negotiating authority in Europe affected the external bargaining capabilities of the European Community (EC)? This paper analyzes the bargaining constraints and opportunities for the EC created by the obligation to negotiate as a single entity. The nature of demands in external~ the voting rules at the EC level, and the amount of autonomy exercised by EC negotiators contribute to explaining, this paper argues, whether the EC gains some external bargaining clout from its internal divisions and whether the final international agreement reflects the position of the median or the extreme countries in the Community. The Uruguay Round agricultural negotiations illustrate the consequences of the EC's institutional structure on its external bargaining capabilities. Negotiations between the EC and the U.S. were deadlocked for six years because the wide gap among the positions of the member states at the start of the Uruguay Round had prevented the EC from making sufficient concessions. The combination of a weakened unanimity rule and greater autonomy seized by Commission negotiators after the May 1992 reform of the Common Agricultural Policy made possible the conclusion of an EC-U.S. agricultural agreement. Although the majority of member states supported the Blair House agreement, the reinstating of the veto power in the EC and the tighter member states' control over the Commission eventually resulted in a renegotiation of the U.S.-EC agreement tilted in favor of France, the most recalcitrant country.

(Table 1) Paleomagnetic properties of specimens from DSDP Holes 69-504B and 70-504B

Paleomagnetic and rock magnetic measurements of basalt specimens from DSDP Hole 504B, associated with the Costa Rica Rift, have a mean natural remanence intensity (Jn) between 5 and 10 x 10**-3 gauss, consistent with the presence of a magnetized layer that is 0.5 to 1 km thick, which produces the observed magnetic anomalies. A mean Koenigsberger ratio (Qn) greater than 10 indicates that the remanence dominates the magnetic signal of the drilled section. The susceptibility (x) increases with depth, and the median demagnetizing field (MDF) decreases with increasing depth in Hole 504B, congruent with the downhole increase in the relative abundance of massive flow units. Hole 504B is composed of at least 12 units with distinct stable average inclinations (Is), which probably represent extrusion at times of different geomagnetic field directions and possibly also the effects of faulting. The thickness of basalt associated with these inclination units varies from less than 9 meters to possibly as much as 160 meters. Two relatively thick magnetic units (40 m and 45 m, separated by 100 m) have anomalously high Is values of -53° and -63°, in contrast with the near zero inclinations expected for the equatorial latitude of Site 504. For this reason and because the average inclination of all the magnetic units is skewed to a negative value, it might be that the entire section at Hole 504B was tilted by approximately 30°.

Chemical composition of rhyolites of ODP Site 103-639

Holes 639E and 639F were drilled along the western slope of a tilted fault block in an attempt to recover complete syn- and pre-rift stratigraphic sections and continental basement. Both holes ended in an apparent talus pile or conglomerate that includes cobbles of altered rhyolitic rock. Three small pieces of rhyolite (comprising about 20 cm of sample) were recovered from the bottoms of Holes 639E and 639F in the core catchers of the deepest cores. This note presents geochemical data from these rhyolitic rocks. Also recovered were quartz sandstones, graywackes, metasandstones, and quartz breccias. This assemblage of continentally derived 'basement' material was overlain by mudstones, limestones, and crystalline dolomites (see 'Site 639' chapter; Shipboard Scientific Party, 1987, doi:10.2973/odp.proc.ir.103.110.1987).

Sea-floor images from during POLARSTERN cruise ANT-XV/3 to the Weddell Sea, Antarctica

Transects of a Remotely Operated Vehicle (ROV) providing sea-bed videos and photographs were carried out during POLARSTERN expedition ANT-XV/3 focussing on the ecology of benthic assemblages on the Antarctic shelf in the South-Eastern Weddell Sea. The ROV-system sprint 103 was equiped with two video- and one still camera, lights, flash-lights, compass, and parallel lasers providing a scale in the images, a tether-management system (TMS), a winch, and the board units. All cameras used the same main lense and could be tilted. Videos were recorded in Betacam-format and (film-)slides were made by decision of the scientific pilot. The latter were mainly made under the aspect to improve the identification of organisms depicted in the videos because the still photographs have a much higher optical resolution than the videos. In the photographs species larger than 3 mm, in the videos larger than 1 cm are recognisable and countable. Under optimum conditions the transects were strait; the speed and direction of the ROV were determined by the drift of the ship in the coastal current, since both, the ship and the ROV were used as a drifting system; the option to operate the vehicle actively was only used to avoide obstacles and to reach at best a distance of only approximately 30 cm to the sea-floor. As a consequence the width of the photographs in the foreground is approximately 50 cm. Deviations from this strategy resulted mainly from difficult ice- and weather conditions but also from high current velocity and local up-welling close to the sea-bed. The sea-bed images provide insights into the general composition of key species, higher systematic groups and ecological guilds. Within interdisciplinary approaches distributions of assemblages can be attributed to environmental conditions such as bathymetry, sediment characteristics, water masses and current regimes. The images also contain valuable information on how benthic species are associated to each other. Along the transects, small- to intermediate-scaled disturbances, e.g. by grounding icebergs were analysed and further impact to the entire benthic system by local succession of recolonisation was studied. This information can be used for models predicting the impact of climate change to benthic life in the Southern Ocean. All these approaches contribute to a better understanding of the fiunctioning of the benthic system and related components of the entire Antarctic marine ecosystem. Despite their scientific value the imaging methods meet concerns about the protection of sensitive Antarctic benthic systems since they are non-invasive and they also provide valuable material for education and outreach purposes.

Rings of operators.

"Prepared with the assistance of a grant from the Research Corporation."

Linear operators and their spectra with applications to quantum mechanics.

From lectures given at the New York university Institute for mathematica and mechanics, by R. Cournat and others.

Analysis of edge detection algorithms on DIAL /

Mode of access: Internet.