Three new species of Lebiasina (Characiformes: Lebiasinidae) from the Brazilian shield border at Serra do Cachimbo, Pará, Brazil

Lebiasina marilynae n. sp., L. melanoguttata n. sp., and L. minuta n. sp. are described from the headwaters of the rio Curuá, in Serra do Cachimbo, Pará, Brazil, and represent the only members of the Lebiasininae in the Brazilian Shied, so far. A close relationship among these species is proposed based on: 1) the presence of a pair of foramina through which the ramus palatinus of the facial nerve passes, a modification unique in Lebiasinidae and apparently in the Characiformes, 2) the enlargement of the extrascapular bone, 3) the absence of the secondary stripe, and 4) the nearly equal length of caudal-fin lobes. Lebiasina marilynae additionally differs from all congeners in having the primary stripe extending from the tip of the snout to the distal border of the caudal-fin peduncle, the possession of two series of dark blotches parallel to the primary stripe, and a rounded dorsal surface of the mesethmoid. Lebiasina melanoguttata and Lebiasina minuta additionally differ from all congeners in the absence of the primary stripe and the caudal blotch, and the presence of three longitudinal series of dark blotches at the base of the scales of series 3-5. Lebiasina melanoguttata differs from Lebiasina minuta in the absence of a dark blotch at the base of the median rays of the dorsal fin, second infrapharyngobranchial bearing conical teeth, the reddish overall coloration of the eye and fins, and the dark blotches never coalescing (vs. dark dorsal-fin blotch present; the second infrapharyngobranchial being edentulous; dark, olive green eyes, and the yellowish overall color of body and fins; and the dark blotches of longitudinal series 3 and 4 coalescing where scales of adjacent longitudinal series overlap). The occurrence of species of the Lebiasininae on the Brazilian Shield is discussed, and the distribution pattern of the species described herein is compared to that of other endemic species of the Serra do Cachimbo, a highly biodiverse area isolated from the rest of the Amazon basin.

X-Ray studies of the physics of matter around super-massive black-holes in nearby Seyfert galaxies

Seyfert galaxies are the closest active galactic nuclei. As such, we can use them to test the physical properties of the entire class of objects. To investigate their general properties, I took advantage of different methods of data analysis. In particular I used three different samples of objects, that, despite frequent overlaps, have been chosen to best tackle different topics: the heterogeneous BeppoS AX sample was thought to be optimized to test the average hard X-ray (E above 10 keV) properties of nearby Seyfert galaxies; the X-CfA was thought the be optimized to compare the properties of low-luminosity sources to the ones of higher luminosity and, thus, it was also used to test the emission mechanism models; finally, the XMM–Newton sample was extracted from the X-CfA sample so as to ensure a truly unbiased and well defined sample of objects to define the average properties of Seyfert galaxies. Taking advantage of the broad-band coverage of the BeppoS AX MECS and PDS instruments (between ~2-100 keV), I infer the average X-ray spectral propertiesof nearby Seyfert galaxies and in particular the photon index (~1.8), the high-energy cut-off (~290 keV), and the relative amount of cold reflection (~1.0). Moreover the unified scheme for active galactic nuclei was positively tested. The distribution of isotropic indicators used here (photon index, relative amount of reflection, high-energy cut-off and narrow FeK energy centroid) are similar in type I and type II objects while the absorbing column and the iron line equivalent width significantly differ between the two classes of sources with type II objects displaying larger absorbing columns. Taking advantage of the XMM–Newton and X–CfA samples I also deduced from measurements that 30 to 50% of type II Seyfert galaxies are Compton thick. Confirming previous results, the narrow FeK line is consistent, in Seyfert 2 galaxies, with being produced in the same matter responsible for the observed obscuration. These results support the basic picture of the unified model. Moreover, the presence of a X-ray Baldwin effect in type I sources has been measured using for the first time the 20-100 keV luminosity (EW proportional to L(20-100)^(−0.22±0.05)). This finding suggests that the torus covering factor may be a function of source luminosity, thereby suggesting a refinement of the baseline version of the unifed model itself. Using the BeppoSAX sample, it has been also recorded a possible correlation between the photon index and the amount of cold reflection in both type I and II sources. At a first glance this confirms the thermal Comptonization as the most likely origin of the high energy emission for the active galactic nuclei. This relation, in fact, naturally emerges supposing that the accretion disk penetrates, depending to the accretion rate, the central corona at different depths (Merloni et al. 2006): the higher accreting systems hosting disks down to the last stable orbit while the lower accreting systems hosting truncated disks. On the contrary, the study of the well defined X–C f A sample of Seyfert galaxies has proved that the intrinsic X-ray luminosity of nearby Seyfert galaxies can span values between 10^(38−43) erg s^−1, i.e. covering a huge range of accretion rates. The less efficient systems have been supposed to host ADAF systems without accretion disk. However, the study of the X–CfA sample has also proved the existence of correlations between optical emission lines and X-ray luminosity in the entire range of L_(X) covered by the sample. These relations are similar to the ones obtained if high-L objects are considered. Thus the emission mechanism must be similar in luminous and weak systems. A possible scenario to reconcile these somehow opposite indications is assuming that the ADAF and the two phase mechanism co-exist with different relative importance moving from low-to-high accretion systems (as suggested by the Gamma vs. R relation). The present data require that no abrupt transition between the two regimes is present. As mentioned above, the possible presence of an accretion disk has been tested using samples of nearby Seyfert galaxies. Here, to deeply investigate the flow patterns close to super-massive black-holes, three case study objects for which enough counts statistics is available have been analysed using deep X-ray observations taken with XMM–Newton. The obtained results have shown that the accretion flow can significantly differ between the objects when it is analyzed with the appropriate detail. For instance the accretion disk is well established down to the last stable orbit in a Kerr system for IRAS 13197-1627 where strong light bending effect have been measured. The accretion disk seems to be formed spiraling in the inner ~10-30 gravitational radii in NGC 3783 where time dependent and recursive modulation have been measured both in the continuum emission and in the broad emission line component. Finally, the accretion disk seems to be only weakly detectable in rk 509, with its weak broad emission line component. Finally, blueshifted resonant absorption lines have been detected in all three objects. This seems to demonstrate that, around super-massive black-holes, there is matter which is not confined in the accretion disk and moves along the line of sight with velocities as large as v~0.01-0.4c (whre c is the speed of light). Wether this matter forms winds or blobs is still matter of debate together with the assessment of the real statistical significance of the measured absorption lines. Nonetheless, if confirmed, these phenomena are of outstanding interest because they offer new potential probes for the dynamics of the innermost regions of accretion flows, to tackle the formation of ejecta/jets and to place constraints on the rate of kinetic energy injected by AGNs into the ISM and IGM. Future high energy missions (such as the planned Simbol-X and IXO) will likely allow an exciting step forward in our understanding of the flow dynamics around black holes and the formation of the highest velocity outflows.

Carl Gustav Jung a Eranos. Il contributo junghiano al Circolo di Eranos: ideazione, contributi e iniziative dal 1933 al 1952

The dissertation aims to explore the several forms in which the activity of the Swiss psychologist, Carl Gustav Jung (1875-1961) developed on the project and the realisation of the Eranos Conferences, founded in 1933 by Olga Fröbe-Kapteyn (1881-1962). The dissertation, in particular, focuses on the first twenty-year period (1933-1952) that determined the fundamental aspects and shaped the peculiar configuration of the Eranos Conferences as a “research laboratory” on the universal characteristics of the religious phenomenon. The dissertation contains the following chapters: 1) Aspects of C.G. Jung’s intellectual contribution to the religious hermeneutics proposed in the Eranos Conferences; 2) C.G. Jung’s conferences at Eranos: a historical examination; 3) C.G. Jung and the Eranos Archive for Research in Symbolism; 4) C.G. Jung and the hidden history of Eranos; 5) C.G. Jung’s commentary on Opicinus de Canistris’s Codex Palatinus Latinus 1993: fragments of a lost and rediscovered Eranos seminar.

Von nichtkommutativen Geometrien, ihren Symmetrien und etwas Hochenergiephysik

In den letzten fünf Jahren hat sich mit dem Begriff desspektralen Tripels eine Möglichkeit zur Beschreibungdes an Spinoren gekoppelten Gravitationsfeldes auf(euklidischen) nichtkommutativen Räumen etabliert. Die Dynamik dieses Gravitationsfeldes ist dabei durch diesogenannte spektrale Wirkung, dieSpur einer geeigneten Funktion des Dirac-Operators,bestimmt. Erstaunlicherweise kann man die vollständige Lagrange-Dichtedes (an das Gravitationsfeld gekoppelten) Standardmodellsder Elementarteilchenphysik, also insbesondere auch denmassegebenden Higgs-Sektor, als spektrale Wirkungeines entsprechenden spektralen Tripels ableiten. Diesesspektrale Tripel ist als Produkt des spektralenTripels der (kommutativen) Raumzeit mit einem speziellendiskreten spektralen Tripel gegeben. In der Arbeitwerden solche diskreten spektralen Tripel, die bis vorKurzem neben dem nichtkommutativen Torus die einzigen,bekannten nichtkommutativen Beispiele waren, klassifiziert. Damit kannnun auch untersucht werden, inwiefern sich dasStandardmodell durch diese Eigenschaft gegenüber anderenYang-Mills-Higgs-Theorien auszeichnet. Es zeigt sichallerdings, dasses - trotz mancher Einschränkung - eine sehr große Zahl vonModellen gibt, die mit Hilfe von spektralen Tripelnabgeleitet werden können. Es wäre aber auch denkbar, dass sich das spektrale Tripeldes Standardmodells durch zusätzliche Strukturen,zum Beispiel durch eine darauf ``isometrisch'' wirkendeHopf-Algebra, auszeichnet. In der Arbeit werden, um dieseFrage untersuchen zu können, sogenannte H-symmetrischespektrale Tripel, welche solche Hopf-Isometrien aufweisen,definiert.Dabei ergibt sich auch eine Möglichkeit, neue(H-symmetrische) spektrale Tripel mit Hilfe ihrerzusätzlichen Symmetrienzu konstruieren. Dieser Algorithmus wird an den Beispielender kommutativen Sphäre, deren Spin-Geometrie hier zumersten Mal vollständig in der globalen, algebraischen Sprache der NichtkommutativenGeometrie beschrieben wird, sowie dem nichtkommutativenTorus illustriert.Als Anwendung werden einige neue Beipiele konstruiert. Eswird gezeigt, dass sich für Yang-Mills Higgs-Theorien, diemit Hilfe von H-symmetrischen spektralen Tripeln abgeleitetwerden, aus den zusätzlichen Isometrien Einschränkungen andiefermionischen Massenmatrizen ergeben. Im letzten Abschnitt der Arbeit wird kurz auf dieQuantisierung der spektralen Wirkung für diskrete spektraleTripel eingegangen.Außerdem wird mit dem Begriff des spektralen Quadrupels einKonzept für die nichtkommutative Verallgemeinerungvon lorentzschen Spin-Mannigfaltigkeiten vorgestellt.

Algebraische Beschreibung von Symmetrien: das Modell der Nichtkommutativen Multi-Tori

In der Nichtkommutativen Geometrie werden Räume und Strukturen durch Algebren beschrieben. Insbesondere werden hierbei klassische Symmetrien durch Hopf-Algebren und Quantengruppen ausgedrückt bzw. verallgemeinert. Wir zeigen in dieser Arbeit, daß der bekannte Quantendoppeltorus, der die Summe aus einem kommutativen und einem nichtkommutativen 2-Torus ist, nur den Spezialfall einer allgemeineren Konstruktion darstellt, die der Summe aus einem kommutativen und mehreren nichtkommutativen n-Tori eine Hopf-Algebren-Struktur zuordnet. Diese Konstruktion führt zur Definition der Nichtkommutativen Multi-Tori. Die Duale dieser Multi-Tori ist eine Kreuzproduktalgebra, die als Quantisierung von Gruppenorbits interpretiert werden kann. Für den Fall von Wurzeln der Eins erhält man wichtige Klassen von endlich-dimensionalen Kac-Algebren, insbesondere die 8-dim. Kac-Paljutkin-Algebra. Ebenfalls für Wurzeln der Eins kann man die Nichtkommutativen Multi-Tori als Hopf-Galois-Erweiterungen des kommutativen Torus interpretieren, wobei die Rolle der typischen Faser von einer endlich-dimensionalen Hopf-Algebra gespielt wird. Der Nichtkommutative 2-Torus besitzt bekanntlich eine u(1)xu(1)-Symmetrie. Wir zeigen, daß er eine größere Quantengruppen-Symmetrie besitzt, die allerdings nicht auf die Spektralen Tripel des Nichtkommutativen Torus fortgesetzt werden kann.

Statistical mechanics of protein complexed and condensed DNA

In this thesis I treat various biophysical questions arising in the context of complexed / ”protein-packed” DNA and DNA in confined geometries (like in viruses or toroidal DNA condensates). Using diverse theoretical methods I consider the statistical mechanics as well as the dynamics of DNA under these conditions. In the first part of the thesis (chapter 2) I derive for the first time the single molecule ”equation of state”, i.e. the force-extension relation of a looped DNA (Eq. 2.94) by using the path integral formalism. Generalizing these results I show that the presence of elastic substructures like loops or deflections caused by anchoring boundary conditions (e.g. at the AFM tip or the mica substrate) gives rise to a significant renormalization of the apparent persistence length as extracted from single molecule experiments (Eqs. 2.39 and 2.98). As I show the experimentally observed apparent persistence length reduction by a factor of 10 or more is naturally explained by this theory. In chapter 3 I theoretically consider the thermal motion of nucleosomes along a DNA template. After an extensive analysis of available experimental data and theoretical modelling of two possible mechanisms I conclude that the ”corkscrew-motion” mechanism most consistently explains this biologically important process. In chapter 4 I demonstrate that DNA-spools (architectures in which DNA circumferentially winds on a cylindrical surface, or onto itself) show a remarkable ”kinetic inertness” that protects them from tension-induced disruption on experimentally and biologically relevant timescales (cf. Fig. 4.1 and Eq. 4.18). I show that the underlying model establishes a connection between the seemingly unrelated and previously unexplained force peaks in single molecule nucleosome and DNA-toroid stretching experiments. Finally in chapter 5 I show that toroidally confined DNA (found in viruses, DNAcondensates or sperm chromatin) undergoes a transition to a twisted, highly entangled state provided that the aspect ratio of the underlying torus crosses a certain critical value (cf. Eq. 5.6 and the phase diagram in Fig. 5.4). The presented mechanism could rationalize several experimental mysteries, ranging from entangled and supercoiled toroids released from virus capsids to the unexpectedly short cholesteric pitch in the (toroidaly wound) sperm chromatin. I propose that the ”topological encapsulation” resulting from our model may have some practical implications for the gene-therapeutic DNA delivery process.

Topologically correct intersection curves of tori and natural quadrics

This thesis provides efficient and robust algorithms for the computation of the intersection curve between a torus and a simple surface (e.g. a plane, a natural quadric or another torus), based on algebraic and numeric methods. The algebraic part includes the classification of the topological type of the intersection curve and the detection of degenerate situations like embedded conic sections and singularities. Moreover, reference points for each connected intersection curve component are determined. The required computations are realised efficiently by solving quartic polynomials at most and exactly by using exact arithmetic. The numeric part includes algorithms for the tracing of each intersection curve component, starting from the previously computed reference points. Using interval arithmetic, accidental incorrectness like jumping between branches or the skipping of parts are prevented. Furthermore, the environments of singularities are correctly treated. Our algorithms are complete in the sense that any kind of input can be handled including degenerate and singular configurations. They are verified, since the results are topologically correct and approximate the real intersection curve up to any arbitrary given error bound. The algorithms are robust, since no human intervention is required and they are efficient in the way that the treatment of algebraic equations of high degree is avoided.

Ab-initio study of hydrogen technology materials for hydrogen storage and proton conduction

This dissertation deals with two specific aspects of a potential hydrogen-based energy economy, namely the problems of energy storage and energy conversion. In order to contribute to the solution of these problems, the structural and dynamical properties of two promising materials for hydrogen storage (lithium imide/amide) and proton conduction (poly[vinyl phosphonic acid]) are modeled on an atomistic scale by means of first principles molecular dynamics simulation methods.rnrnrnIn the case of the hydrogen storage system lithium amide/imide (LiNH_2/Li_2NH), the focus was on the interplay of structural features and nuclear quantum effects. For these calculations, Path-Integral Molecular Dynamics (PIMD) simulations were used. The structures of these materials at room temperature were elucidated; in collaboration with an experimental group, a very good agreement between calculated and experimental solid-state 1H-NMR chemical shifts was observed. Specifically, the structure of Li_2NH features a disordered arrangement of the Li lattice, which was not reported in previous studies. In addition, a persistent precession of the NH bonds was observed in our simulations. We provide evidence that this precession is the consequence of a toroid-shaped effective potential, in which the protons in the material are immersed. This potential is essentially flat along the torus azimuthal angle, which might lead to important quantum delocalization effects of the protons over the torus.rnrnOn the energy conversion side, the dynamics of protons in a proton conducting polymer (poly[vinyl phosphonic acid], PVPA) was studied by means of a steered ab-initio Molecular Dynamics approach applied on a simplified polymer model. The focus was put on understanding the microscopic proton transport mechanism in polymer membranes, and on characterizing the relevance of the local environment. This covers particularly the effect of water molecules, which participate in the hydrogen bonding network in the material. The results indicate that these water molecules are essential for the effectiveness of proton conduction. A water-mediated Grotthuss mechanism is identified as the main contributor to proton conduction, which agrees with the experimentally observed decay on conductivity for the same material in the absence of water molecules.rnrnThe gain in understanding the microscopic processes and structures present in this materials can help the development of new materials with improved properties, thus contributing to the solution of problems in the implementation of fuel cells.

Die Microsauria des mitteleuropäischen Rotliegend

ZusammenfassungrnAlle bekannten Exemplare der Amphibien-Gruppe Microsauria des mitteleuropäischen Rotliegend wurden untersucht sowie – für die kladistische Untersuchung – ihre nächsten Verwandten. Im Saar-Nahe-Becken sind vier Arten aus zwei Microsauria-Gattungen nachzuweisen: Batropetes niederkirchensis n. sp., Batropetes palatinus n. sp., Batropetes appelensis n. sp. und Altenglanerpeton schroederi n. sp.. Aus dem Döhlen-Becken bei Dresden stammt Batropetes fritschi.rnDie Rekonstruktionen legen nahe, dass die in Seeablagerungen gefundenen Batropetes-Arten kleine, terrestrisch lebende Microsaurier waren, die sich von Insekten oder deren Larven ernährten. Ihre mittlere Gesamtlänge beträgt fast 8 cm, ihr Rumpf ist auffallend kurz mit je nach Art 17 oder 19 Präsakralwirbeln. Sie besitzen große von Wülsten umgebene Augenöffnungen, ein großes Pinealforamen, drei längs angeordnete Grübchen auf den Frontalia, dreispitzige Zähne, einen zahnlosen Gaumen und vier kurze kräftige Extremitäten. Becken- und Schultergürtel sind komplett verknöchert, außer den bei Batropetes appelensis und Batropetes fritschi knorpeligen Coracoid-Anteilen. Die Batropetes-Arten unterscheiden sich bezüglich Form, Proportionen bzw. Verknöcherungsgrad einiger Knochen im cranialen und postcranialen Skelett. rnDie kladistischen Untersuchungen ergeben für die Arten der monophyletische Gattung Batropetes, dass Batropetes appelensis den übrigen Arten gegenübersteht und Batropetes palatinus mit Batropetes fritschi eine Schwestergruppe zu Batropetes niederkirchensis bildet. Mit den etwas jüngeren texanischen Gattungen Carrolla und Quasicaecilia bildet Batropetes die monophyletische Familie Brachystelechidae. rnAltenglanerpeton schroederi, nur durch ein schlecht erhaltenes Exemplar überliefert, besitzt einen massiv gebauten Schädel, kaum länger als breit mit annähernd dreieckigem Umriss, ohne Anzeichen für Seitenlinien, mit kleiner rundlicher Orbita, sehr breiter Interorbitalregion und bis weit vor die Orbita reichendem Jugale. Sein langer Rumpf umfasst mindestens 30 lepospondyle Präsakralwirbel. Wegen der unvollkommenen Entwicklung der Gliedmaßen kann diese Art nicht auf vier Beinen gelaufen sein und lebte möglicherweise in der Laubschicht wühlend oder in Sümpfen. Altenglanerpeton ist keiner bestimmten Microsauria-Familie zuzuordnen und steht den Pantylidae, Gymnarthridae, Goniorhynchidae und Ostodolepidae am nächsten, wobei zu letzteren die meisten morphologischen Ähnlichkeiten bestehen.rnAußerdem sind mit isolierten Einzelknochen, insbesondere Wirbeln, Microsauria und andere Gruppen lepospondyler Amphibien ohne Bestimmung der Gattung und Art aus wenigen stratigraphischen Niveaus des Saar-Nahe-Beckens überliefert. rn

Diagnosis of endometriosis with imaging: a review

Endometriosis corresponds to ectopic endometrial glands and stroma outside the uterine cavity. Clinical symptoms include dysmenorrhoea, dyspareunia, infertility, painful defecation or cyclic urinary symptoms. Pelvic ultrasound is the primary imaging modality to identify and differentiate locations to the ovary (endometriomas) and the bladder wall. Characteristic sonographic features of endometriomas are diffuse low-level internal echos, multilocularity and hyperchoic foci in the wall. Differential diagnoses include corpus luteum, teratoma, cystadenoma, fibroma, tubo-ovarian abscess and carcinoma. Repeated ultrasound is highly recommended for unilocular cysts with low-level internal echoes to differentiate functional corpus luteum from endometriomas. Posterior locations of endometriosis include utero-sacral ligaments, torus uterinus, vagina and recto-sigmoid. Sonographic and MRI features are discussed for each location. Although ultrasound is able to diagnose most locations, its limited sensitivity for posterior lesions does not allow management decision in all patients. MRI has shown high accuracies for both anterior and posterior endometriosis and enables complete lesion mapping before surgery. Posterior locations demonstrate abnormal T2-hypointense, nodules with occasional T1-hyperintense spots and are easier to identify when peristaltic inhibitors and intravenous contrast media are used. Anterior locations benefit from the possibility of MRI urography sequences within the same examination. Rare locations and possible transformation into malignancy are discussed.

Torque converter turbine noise and cavitation noise over varying speed ratio

These investigations will discuss the operational noise caused by automotive torque converters during speed ratio operation. Two specific cases of torque converter noise will be studied; cavitation, and a monotonic turbine induced noise. Cavitation occurs at or near stall, or zero turbine speed. The bubbles produced due to the extreme torques at low speed ratio operation, upon collapse, may cause a broadband noise that is unwanted by those who are occupying the vehicle as other portions of the vehicle drive train improve acoustically. Turbine induced noise, which occurs at high engine torque at around 0.5 speed ratio, is a narrow-band phenomenon that is audible to vehicle occupants currently. The solution to the turbine induced noise is known, however this study is to gain a better understanding of the mechanics behind this occurrence. The automated torque converter dynamometer test cell was utilized in these experiments to determine the effect of torque converter design parameters on the offset of cavitation and to employ the use a microwave telemetry system to directly measure pressures and structural motion on the turbine. Nearfield acoustics were used as a detection method for all phenomena while using a standardized speed ratio sweep test. Changes in filtered sound pressure levels enabled the ability to detect cavitation desinence. This, in turn, was utilized to determine the effects of various torque converter design parameters, including diameter, torus dimensions, and pump and stator blade designs on cavitation. The on turbine pressures and motion measured with the microwave telemetry were used to understand better the effects of a notched trailing edge turbine blade on the turbine induced noise.

Intact flagellar motor of Borrelia burgdorferi revealed by cryo-electron tomography: evidence for stator ring curvature and rotor/C-ring assembly flexion.

The bacterial flagellar motor is a remarkable nanomachine that provides motility through flagellar rotation. Prior structural studies have revealed the stunning complexity of the purified rotor and C-ring assemblies from flagellar motors. In this study, we used high-throughput cryo-electron tomography and image analysis of intact Borrelia burgdorferi to produce a three-dimensional (3-D) model of the in situ flagellar motor without imposing rotational symmetry. Structural details of B. burgdorferi, including a layer of outer surface proteins, were clearly visible in the resulting 3-D reconstructions. By averaging the 3-D images of approximately 1,280 flagellar motors, a approximately 3.5-nm-resolution model of the stator and rotor structures was obtained. flgI transposon mutants lacked a torus-shaped structure attached to the flagellar rod, establishing the structural location of the spirochetal P ring. Treatment of intact organisms with the nonionic detergent NP-40 resulted in dissolution of the outermost portion of the motor structure and the C ring, providing insight into the in situ arrangement of the stator and rotor structures. Structural elements associated with the stator followed the curvature of the cytoplasmic membrane. The rotor and the C ring also exhibited angular flexion, resulting in a slight narrowing of both structures in the direction perpendicular to the cell axis. These results indicate an inherent flexibility in the rotor-stator interaction. The FliG switching and energizing component likely provides much of the flexibility needed to maintain the interaction between the curved stator and the relatively symmetrical rotor/C-ring assembly during flagellar rotation.

Bipartite graphs and quasipositive surfaces

We present a simple combinatorial model for quasipositive surfaces and positive braids, based on embedded bipartite graphs. As a first application, we extend the well-known duality on standard diagrams of torus links to twisted torus links. We then introduce a combinatorial notion of adjacency for bipartite graph links and discuss its potential relation with the adjacency problem for plane curve singularities.

Superspace description of wagnerite-group minerals (Mg,Fe,Mn) 2 (PO 4 )(F,OH)

Reinvestigation of more than 40 samples of minerals belonging to the wagnerite group (Mg, Fe, Mn)2(PO4)(F,OH) from diverse geological environments worldwide, using single-crystal X-ray diffraction analysis, showed that most crystals have incommensurate structures and, as such, are not adequately described with known polytype models (2b), (3b), (5b), (7b) and (9b). Therefore, we present here a unified superspace model for the structural description of periodically and aperiodically modulated wagnerite with the (3+1)-dimensional superspace group C2/c(0[beta]0)s0 based on the average triplite structure with cell parameters a [asymptotically equal to] 12.8, b [asymptotically equal to] 6.4, c [asymptotically equal to] 9.6 Å, [beta] [asymptotically equal to] 117° and the modulation vectors q = [beta]b*. The superspace approach provides a way of simple modelling of the positional and occupational modulation of Mg/Fe and F/OH in wagnerite. This allows direct comparison of crystal properties.

From doubled Chern–Simons–Maxwell lattice gauge theory to extensions of the toric code

We regularize compact and non-compact Abelian Chern–Simons–Maxwell theories on a spatial lattice using the Hamiltonian formulation. We consider a doubled theory with gauge fields living on a lattice and its dual lattice. The Hilbert space of the theory is a product of local Hilbert spaces, each associated with a link and the corresponding dual link. The two electric field operators associated with the link-pair do not commute. In the non-compact case with gauge group R, each local Hilbert space is analogous to the one of a charged “particle” moving in the link-pair group space R2 in a constant “magnetic” background field. In the compact case, the link-pair group space is a torus U(1)2 threaded by k units of quantized “magnetic” flux, with k being the level of the Chern–Simons theory. The holonomies of the torus U(1)2 give rise to two self-adjoint extension parameters, which form two non-dynamical background lattice gauge fields that explicitly break the manifest gauge symmetry from U(1) to Z(k). The local Hilbert space of a link-pair then decomposes into representations of a magnetic translation group. In the pure Chern–Simons limit of a large “photon” mass, this results in a Z(k)-symmetric variant of Kitaev’s toric code, self-adjointly extended by the two non-dynamical background lattice gauge fields. Electric charges on the original lattice and on the dual lattice obey mutually anyonic statistics with the statistics angle . Non-Abelian U(k) Berry gauge fields that arise from the self-adjoint extension parameters may be interesting in the context of quantum information processing.