The classification and the conjugacy classes of the finite subgroups of the sphere braid groups

Let n >= 3. We classify the finite groups which are realised as subgroups of the sphere braid group B(n)(S(2)). Such groups must be of cohomological period 2 or 4. Depending on the value of n, we show that the following are the maximal finite subgroups of B(n)(S(2)): Z(2(n-1)); the dicyclic groups of order 4n and 4(n - 2); the binary tetrahedral group T*; the binary octahedral group O*; and the binary icosahedral group I(*). We give geometric as well as some explicit algebraic constructions of these groups in B(n)(S(2)) and determine the number of conjugacy classes of such finite subgroups. We also reprove Murasugi`s classification of the torsion elements of B(n)(S(2)) and explain how the finite subgroups of B(n)(S(2)) are related to this classification, as well as to the lower central and derived series of B(n)(S(2)).

Hopf solitons and area-preserving diffeomorphisms of the sphere

We consider a (3+1)-dimensional local field theory defined on the sphere S-2. The model possesses exact soliton solutions with nontrivial Hopf topological charges and an infinite number of local conserved currents. We show that the Poisson bracket algebra of the corresponding charges is isomorphic to that of the area-preserving diffeomorphisms of the sphere S-2. We also show that the conserved currents under consideration are the Noether currents associated to the invariance of the Lagrangian under that infinite group of diffeomorphisms. We indicate possible generalizations of the model.

Partial urethral obstruction of rabbit urinary bladder: stereological evidence that the increase in muscle content is mostly driven by changes in number, rather than size, of smooth muscle cells

The effects of partial urethral obstruction on the detrusor muscle of rabbit urinary bladder were investigated using stereological sampling and estimation tools. Twelve female Norfolk rabbits (2.5-3.0 kg body weight) were divided into four groups: 3, 7 and 12 weeks after surgical intervention to produce a standard partial obstruction and unobstructed controls. Following removal, bladder axes (craniocaudal, dorsoventral and laterolateral) and organ weights were recorded. Bladders were prepared for light microscopy by multistage random sampling procedures. Stereological methods were used to estimate the volume of muscle and the packing density and total number of myocyte nuclei in each bladder. We also estimated mean myocyte volume and the mean cross-sectional area and length of myocytes. Group comparisons were made by one-way analysis of variance. Changes in bladder axes were mainly laterolateral and craniocaudal. Mean bladder weight increased roughly six-fold by 3 weeks and 17-fold by 12 weeks and was accompanied, on average, by 12- and 33-fold increases in total muscle volume. These variables did not differ at 3 and 7 weeks post-obstruction. Increases in muscle content were not accompanied by changes in packing densities but were associated with increases in the total numbers of myocyte nuclei (13-fold by 3 weeks, 28-fold by 12 weeks). Mean myocyte volume did not vary significantly between groups but cells in obstructed groups were shorter and wider. These findings support the notion that partial outflow obstruction leads to an increase in the number, but not mean volume, of myocytes. If due solely to myocyte mitosis, the total of 43 x 10(8) cells found at 12 weeks could be generated by the original complement of 15 x 10(7) cells if an average of only 2.1 x 10(6) new cells was produced every hour. In reality, even this modest proliferation rate is unlikely to be achieved because myocyte proliferation rates are very low and it is possible that new myocytes can arise by differentiation of mesenchymal or other precursor cells.

Two matrix-based lattice construction techniques

Let m and n be integers greater than 1. Given lattices A and B of dimensions m and n, respectively, a technique for constructing a lattice from them of dimension m+n-1 is introduced. Furthermore, if A and B possess bases satisfying certain conditions, then a second technique yields a lattice of dimension m+n-2. The relevant parameters of the new lattices are given in terms of the respective parameters of A,B, and a lattice C isometric to a sublattice of A and B. Denser sphere packings than previously known ones in dimensions 52, 68, 84, 248, 520, and 4098 are obtained. © 2012 Elsevier Inc. All rights reserved.

A new number field construction of the lattice E8

Known number theoretical constructions of the lattice E8 use the cyclotomic fields Q(ζ15), Q(ζ20), and Q(ζ24). In this work, an infinite family of Abelian number fields yielding rotated versions of the lattice E 8 is exhibited. © 2012 The Managing Editors.

COINCIDENCES OF FIBREWISE MAPS BETWEEN SPHERE BUNDLES OVER THE CIRCLE

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Two-Dimensional Bin Packing Problem with Guillotine Restrictions

This thesis, after presenting recent advances obtained for the two-dimensional bin packing problem, focuses on the case where guillotine restrictions are imposed. A mathematical characterization of non-guillotine patterns is provided and the relation between the solution value of the two-dimensional problem with guillotine restrictions and the two-dimensional problem unrestricted is being studied from a worst-case perspective. Finally it presents a new heuristic algorithm, for the two-dimensional problem with guillotine restrictions, based on partial enumeration, and computationally evaluates its performance on a large set of instances from the literature. Computational experiments show that the algorithm is able to produce proven optimal solutions for a large number of problems, and gives a tight approximation of the optimum in the remaining cases.

Packing a trunk : a physically based approach with full motional freedom

Geometric packing problems may be formulated mathematically as constrained optimization problems. But finding a good solution is a challenging task. The more complicated the geometry of the container or the objects to be packed, the more complex the non-penetration constraints become. In this work we propose the use of a physics engine that simulates a system of colliding rigid bodies. It is a tool to resolve interpenetration conflicts and to optimize configurations locally. We develop an efficient and easy-to-implement physics engine that is specialized for collision detection and contact handling. In succession of the development of this engine a number of novel algorithms for distance calculation and intersection volume were designed and imple- mented, which are presented in this work. They are highly specialized to pro- vide fast responses for cuboids and triangles as input geometry whereas the concepts they are based on can easily be extended to other convex shapes. Especially noteworthy in this context is our ε-distance algorithm - a novel application that is not only very robust and fast but also compact in its im- plementation. Several state-of-the-art third party implementations are being presented and we show that our implementations beat them in runtime and robustness. The packing algorithm that lies on top of the physics engine is a Monte Carlo based approach implemented for packing cuboids into a container described by a triangle soup. We give an implementation for the SAE J1100 variant of the trunk packing problem. We compare this implementation to several established approaches and we show that it gives better results in faster time than these existing implementations.

Experimentelle Untersuchung von Phasenübergängen im kolloidalen Modellsystem harter Kugeln

Die vorliegende Arbeit behandelt den fluid-kristallinen Phasenübergang sowie den Glasübergang anhand von kolloidalen Hart-Kugel(HK)-Modellsystemen. Die Untersuchungen erfolgen dabei im Wesentlichen mit unterschiedlichen Lichtstreumethoden und daher im reziproken Raum. rnDie Analyse der Kristallisationskinetik zeigt, dass es bei der Kristallisation zu signifikanten Abweichungen vom Bild der klassischen Nukleationstheorie (CNT) kommt. Diese geht von einem einstufigen Nukleationsprozess aus, wohingegen bei den hier durchgeführten Experimenten ein mehrstufiger Prozess beobachtet wird. Vor der eigentlichen Kristallisation kommt es zunächst zur Nukleation einer metastabilen Zwischenphase, sogenannter Precursor. In einer zweiten Stufe erfolgt innerhalb der Precursor die eigentliche Nukleation der Kristallite. rnDurch weitere Analyse und den Vergleich des Kristallisations- und Verglasungsszenarios konnte das Konzept der Precursornukleation auf den Vorgang der Verglasung erweitert werden. Während die Kristallnukleation oberhalb des Glasübergangspunktes zum Erliegen kommt, bleibt der Prozess der Precursornukleation auch bei verglasenden Proben erhalten. Ein Glas erstarrt somit in einem amorphen Zustand mit lokalen Precursorstrukturen. Die Korrelation der gemessenen zeitlichen Entwicklung der strukturellen sowie der dynamischen Eigenschaften zeigt darüber hinaus, dass das bisher unverstandene Ageing-Phänomen von HK-Gläsern mit der Nukleation von Precursorn zusammenhängt.rnEin solches mehrstufiges Szenario wurde bereits in früheren Veröffentlichungen beobachtet. Die im Rahmen dieser Arbeit durchgeführten Messungen ermöglichten erstmals die Bestimmung von Kristallnukleationsratendichten (Kristall-NRD) und Ratendichten für die Precursornukleation bis über den Glasübergangspunkt hinaus. Die Kristall-NRD bestätigen die Resultate aus anderen experimentellen Arbeiten. Die weiteren Analysen der Kristall-NRD belegen, dass die fluid-kristalline Grenzflächenspannung bei der Nukleation entgegen den Annahmen der CNT nicht konstant ist, sondern mit ansteigendem Volumenbruch linear zunimmt. Die Erweiterung der CNT um eine linear zunehmende Grenzflächenspannung ermöglichte eine quantitative Beschreibung der gemessenen Kristall- sowie der Precursor-NRD, was den Schluss zulässt, dass es sich in beiden Fällen um einen Boltzmann-aktivierten Prozess handelt. rnUm die beobachteten Abweichungen des Nukleationsprozesses vom Bild der CNT näher zu untersuchen, wurden die kollektiven Partikeldynamiken in stabilen Fluiden und metastabilen Schmelzen analysiert. Im klassischen Bild wird angenommen, dass die kollektive Partikeldynamik beim Vorgang der Nukleation keine Rolle spielt. Anhand der Resultate zeigen sich Abweichungen in der Dynamik stabiler Fluide und metastabiler Schmelzen. Während die kollektive Partikeldynamik in der stabilen Schmelze von der Struktur entkoppelt ist, tritt oberhalb des Phasenübergangspunktes eine Kopplung von Struktur und Dynamik auf. Dabei treten die Abweichungen zunächst in der Umgebung des ersten Strukturfaktormaximums und somit bei den am stärksten besetzten Moden auf. Mit steigender Unterkühlung nehmen die Anzahl der abweichenden Moden sowie die Stärke der Abweichungen zu. Dieses Phänomen könnte einen signifikanten Einfluss auf den Nukleationsprozess und somit auf die Kristallisationskinetik haben. Die Analyse der Dynamik im stabilen Fluid zeigt darüber hinaus Hinweise auf eine Singularität bei Annäherung an den fluid-kristallinen Phasenübergangspunkt.rnDes Weiteren wurden im Rahmen der vorliegenden Arbeit erstmals Ratendichten für die heterogene Nukleation eines HK-Systems an einer flachen Wand mittels statischer Lichtstreuung (SLS) bestimmt. Die Ergebnisse der Messung zeigen, dass die Nukleationsbarriere der heterogenen Nukleation annähernd Null ist und folglich eine vollständige Benetzung der Wand mit einer kristallinen Monolage vorliegt. Die Erweiterung der Untersuchungen auf gekrümmte Oberflächen in Form von sphärischen Partikeln (Seeds) stellt die erste experimentelle Arbeit dar, die den Einfluss eines Ensembles von Seeds auf die Kristallisationskinetik in HK-Systemen untersucht. Die Kristallisationskinetik und die Mikrostruktur werden abhängig von Größe und Anzahldichte der Seed-Partikel signifikant beeinflusst. In Übereinstimmung mit konfokalmikroskopischen Experimenten und Simulationen spielt dabei das Radienverhältnis der Majoritäts- zur Minoritätskomponente eine entscheidende Rolle.

Plants growing near the cargo packing station, and seed occurrence in cargo and luggage destined for Gough and Marion Island and the Antarctic

Globalization has resulted in unprecedented movements of people, goods, and alien species across the planet. Although the impacts of biological invasions are widely appreciated, a bias exists in research effort to post-dispersal processes because of the difficulties of measuring propagule pressure. The Antarctic provides an ideal model system in which to investigate propagule movements because of the region's isolation and small number of entry routes. Here we investigated the logistics operations of the South African National Antarctic Programme (SANAP) and quantified the initial dispersal of alien species into the region. we found that over 1400 seeds from 99 taxa are transported into the Antarctic each field season in association with SANAP passenger luggage and cargo. The first ever assessment of propagule drop-off indicated that 30-50% of these propagules will enter the recipient environment. Many of the taxa include cosmopolitan weeds and known aliens in the Antarctic, indicating that logistics operations form part of a globally self-perpetuating cycle moving alien species between areas of human disturbance. in addition, propagules of some taxa native to the Antarctic region were also found, suggesting that human movements may be facilitating intra-regional homogenization. Several relatively simple changes in biosecurity policy that could significantly reduce the threat of introduction of nonnative species are suggested.

Characterization of a Right Angle Transfer Point in a Fruit Packing Line

Characteristics of the impacts su!ered by the fruit on a transfer point of an experimental fruit packing line were analysed. The transfer is made up by two transporting belts at di!erent heights forming an angle of 903. These transfer points are very common in fruit packing lines, in which fruits receive two impacts: the "rst onto the belt base and the second into the lateral plate. Diferent tests were carried out to study the e!ect of transfer height, velocity, belt structure and padding on the acceleration values recorded by an instrumental sphere (IS 100). Results showed that transfer height and belt structure a!ect mainly impact values on the belt base, and padding a!ects mainly impact values registered for lateral contact. The elect of belt velocity in both impacts is less important when compared to the rest of the variables. Additionally, two powered transfer decelerators were tested at the same point with the aim of decreasing impacts su!ered by the fruit. Comparing impacts registered using these decelerators to those analysed in the first part of the study without decelerators, a high reduction of the impact values was observed.

Characterization of a 90° Transfer Point in a Fruit Packing Line.

Characteristics of the impacts suffered by the fruit on a transfer point of an experimental fruit packing line were analysed. The transfer is made up by two transporting belts at different heights forming an angle of 90°. These transfer points are very common in fruit packing lines, in which fruits receive two impacts: the first onto the belt base and the second into the lateral plate. Different tests were earned out to study the effect of transfer height, velocity, belt structure and padding on tire acceleration values recorded by an instrumental sphere (IS 100). Results showed that transfer height and belt structure affect mainly impact values on the belt base, and padding affects mainly impact values registered in lateral impact. The effect of belt velocity in both impacts is less important when compared to the rest of the variables. Additionally, two powered transfer decelerators were tested at the same point with the aim of decreasing impacts suffered by the fruit. Comparing impacts registered using these decelerators to those analysed in the first part of the study without decelerators a high reduction of the impact values was observed.

A procedure for testing padding materials in fruit packing lines.

Padding materials are commonly used in fruit packing lines with the objective of diminishing impact damage in postharvest handling. Two sensors, instrumented sphere IS 100 and impact tester, have been compared to analyze the performance of six different padding materials used in Spanish fruit packing lines. Padding materials tested have been classified according to their capability to decrease impact intensities inflicted to fruit in packing lines. A procedure to test padding materials has been developed for "Golden" apples. Its basis is a logistic regression to predict bruise probability in fruit. The model combines two kinds of parameters: padding material parameters measured with IS, and fruit properties.

A general method for determining helix packing in membrane proteins in situ: Helices I and II are close to helix VII in the lactose permease of Escherichia coli

It was previously shown that coexpression of the lactose permease of Escherichia coli in two contiguous fragments leads to functional complementation. We demonstrate here that site-directed thiol crosslinking of coexpressed permease fragments can be used to determine helix proximity in situ without the necessity of purifying the permease. After coexpression of the six N-terminal (N6) and six C-terminal (C6) transmembrane helices, each with a single Cys residue, crosslinking was carried out in native membranes and assessed by the mobility of anti-C-terminal-reactive polypeptides on immunoblots. A Cys residue at position 242 or 245 (helix VII) forms a disulfide with a Cys residue at either position 28 or 29 (helix I), but not with a Cys residue at position 27, which is on the opposite face of helix I, thereby indicating that the face of helix I containing Pro-28 and Phe-29 is close to helix VII. Similarly, a Cys residue at position 242 or 245 (helix VII) forms a disulfide with a Cys residue at either position 52 or 53 (helix II), but not with a Cys residue at position 54. Furthermore, low-efficiency crosslinking is observed between a Cys residue at position 52 or 53 and a Cys residue at position 361 (helix XI). The results indicate that helix VII lies in close proximity to both helices I and II and that helix II is also close to helix XI. The method should be applicable to a number of different polytopic membrane proteins.

A loop-loop "kissing" complex is the essential part of the dimer linkage of genomic HIV-1 RNA.

RNA-RNA interactions govern a number of biological processes. Several RNAs, including natural sense and antisense RNAs, interact by means of a two-step mechanism: recognition is mediated by a loop-loop complex, which is then stabilized by formation of an extended intermolecular duplex. It was proposed that the same mechanism holds for dimerization of the genomic RNA of human immunodeficiency virus type 1 (HIV-1), an event thought to control crucial steps of HIV-1 replication. However, whereas interaction between the partially self-complementary loop of the dimerization initiation site (DIS) of each monomer is well established, formation of the extended duplex remained speculative. Here we first show that in vitro dimerization of HIV-1 RNA is a specific process, not resulting from simple annealing of denatured molecules. Next we used mutants of the DIS to test the formation of the extended duplex. Four pairs of transcomplementary mutants were designed in such a way that all pairs can form the loop-loop "kissing" complex, but only two of them can potentially form the extended duplex. All pairs of mutants form heterodimers whose thermal stability, dissociation constant, and dynamics were analyzed. Taken together, our results indicate that, in contrast with the interactions between natural sense and antisense RNAs, no extended duplex is formed during dimerization of HIV-1 RNA. We also showed that 55-mer sense RNAs containing the DIS are able to interfere with the preformed HIV-1 RNA dimer.