Knots and links in lens spaces

The aim of this dissertation is to improve the knowledge of knots and links in lens spaces. If the lens space L(p,q) is defined as a 3-ball with suitable boundary identifications, then a link in L(p,q) can be represented by a disk diagram, i.e. a regular projection of the link on a disk. In this contest, we obtain a complete finite set of Reidemeister-type moves establishing equivalence, up to ambient isotopy. Moreover, the connections of this new diagram with both grid and band diagrams for links in lens spaces are shown. A Wirtinger-type presentation for the group of the link and a diagrammatic method giving the first homology group are described. A class of twisted Alexander polynomials for links in lens spaces is computed, showing its correlation with Reidemeister torsion. One of the most important geometric invariants of links in lens spaces is the lift in 3-sphere of a link L in L(p,q), that is the counterimage of L under the universal covering of L(p,q). Starting from the disk diagram of the link, we obtain a diagram of the lift in the 3-sphere. Using this construction it is possible to find different knots and links in L(p,q) having equivalent lifts, hence we cannot distinguish different links in lens spaces only from their lift. The two final chapters investigate whether several existing invariants for links in lens spaces are essential, i.e. whether they may assume different values on links with equivalent lift. Namely, we consider the fundamental quandle, the group of the link, the twisted Alexander polynomials, the Kauffman Bracket Skein Module and an HOMFLY-PT-type invariant.

Minimalinvasive Osteosynthese der distalen extraartikulären Radiusfraktur : XSCREW und DorsalNailPlate im biomechanischen Vergleich

Gegenstand der Arbeit: Die distale Radiusfraktur ist der häufigste Bruch des Menschen. Neben etablierten Verfahren wie der dorsalen und palmaren Plattenosteosynthese gibt es seit Kurzem neuartige minimalinvasive Osteosynthesesysteme. Gegenstand der vorliegenden Arbeit ist die Untersuchung der biomechanischen Stabilität von zwei neuartigen Implantaten für die distale extraartikuläre Radiusfraktur. rnMethodik: Es handelt sich einerseits um das System XSCREW (Zimmer, Freiburg i. Br., Deutschland), eine kanülierte Schraube, die über den Processus styloideus eingeführt wird und mit bis zu neun Bohrdrähten im Knochen fixiert werden kann. Das Vergleichsimplantat DorsalNailPlate (HandInnovations, Miami, Florida, USA) ist ein Hybrid aus einer dorsalen Platte und einem Marknagel. Beide Systeme wurden an 8 paarigen frischen unfixierten Leichenradii unter Axialbelastung bis 100 N und Torsionsbelastung bis 1,5 Nm getestet. Die A3-Fraktur wurde durch eine standardisierte Keilosteotomie simuliert. Das Biomaterial wurde prä- und postinterventionell sowie nach einem Dauerbelastungstest unter 1000 Zyklen in Rotation mit 0,5 Hz untersucht. Ein Versagenstest mit steigendem Drehmoment beendete das Experiment. rnErgebnisse: Die XSCREW erreichte eine Axialsteifigkeit von 136 N/mm und eine Torsionssteifigkeit von 0,16 Nm/°. Die DNP erzielte hingegen axial 70 N/mm und torsional 0,06 Nm/°. Der Unterschied zwischen beiden Verfahren war nur für die Torsion eindeutig statistisch auffällig (p=0,012), jedoch nicht für die Axialsteifigkeit (p=0,054). Die ursprüngliche Axial- und Torsionssteifigkeit wurde durch die XSCREW signifikant besser wiederhergestellt als durch die DNP (p=0,012). Beide Verfahren erzielten nach der Intervention signifikant niedrigere Steifigkeiten als die intakten Knochen (p=0,012). Ein Präparat der DNP-Gruppe und vier Präparate der XSCREW-Gruppe überstanden den Dauerbelastungstest. Das Drehmoment bei Versagen war mit der XSCREW höher als mit der DNP, der Unterschied zwischen den Verfahren war signifikant (p=0,043). Die Schwachstellen beider Systeme lagen vorwiegend in der proximalen Verankerung im Knochen. Kirschner-Drähte bzw. Verriegelungsschrauben führten unter andauernder Belastung zu einer Spaltung der Kortikalis im Schaftbereich. Bedingt durch die Ausrichtung der distalen Verriegelungen können mit beiden Implantaten Schäden an der radiocarpalen bzw. radioulnaren Gelenkfläche entstehen. rnZusammenfassung: Die XSCREW ermöglicht insgesamt eine höhere mechanische Stabilität als die DNP. Beide Verfahren sind jedoch einer winkelstabilen palmaren Plattenosteosynthese insbesondere unter rotatorischer Dauerbelastung unterlegen und erreichen nicht die Stabilität eines anderen neuartigen minimalinvasiven Systems.

Valutazione di un'attrezzatura per eseguire prove di torsione e/o flessione su una macchina assiale

Analisi di apparecchiature esistenti su macchina di prova assiale per l'esecuzione di prove differenti e sviluppo di una nuova attrezzatura per l'esecuzione di prove di torsione pura su macchina assiale.

Abnormal bone geometry at the metacarpal bone shaft of rheumatoid arthritis patients with maintained muscle-bone relationship

OBJECTIVES:: Metacarpal juxta-articular bone is altered in Rheumatoid Arthritis (RA). However, a detailed analysis of disease related geometrical adaptations of the metacarpal shaft is missing. The aim of the present study was to assess the role of RA disease, forearm muscle cross-sectional area (CSA), age and sex on bone geometry at the metacarpal shaft. METHODS:: In 64 RA patients and 128 control subjects geometric properties of the third metacarpal bone mid-shaft and forearm muscle CSA were measured by peripheral quantitative computed tomography (pQCT). Linear models were performed for cortical CSA, total bone CSA, polar stress-strain Index (polar SSI, a surrogate for bone's resistance to bending and torsion), cortical thickness and Metacarpal Index (MI=cortical CSA/total CSA) with explanatory variables muscle CSA, age, RA status and sex. RESULTS:: Forearm muscle CSA was associated with cortical and total metacarpal CSA, and polar SSI. RA group status was associated with all bone parameters except cortical CSA. There was a significant interaction between RA status and age, indicating that the RA group had a greater age-related decrease in cortical CSA, cortical thickness and MI. CONCLUSIONS:: Bone geometry of the metacarpal shaft is altered in RA patients compared to healthy controls. While bone mass of the metacarpal shaft is adapted to forearm muscle mass, cortical thickness and MI are reduced but outer bone shaft circumference and polar SSI increased in RA patients. These adaptations correspond to an enhanced aging pattern in RA patients.

Minimization of Intra-Operative Shaping of Orthopaedic Fixation Plates: A Population-Based Design

In this paper we present a new population-based method for the design of bone fixation plates. Standard pre-contoured plates are designed based on the mean shape of a certain population. We propose a computational process to design implants while reducing the amount of required intra-operative shaping, thus reducing the mechanical stresses applied to the plate. A bending and torsion model was used to measure and minimize the necessary intra-operative deformation. The method was applied and validated on a population of 200 femurs that was further augmented with a statistical shape model. The obtained results showed substantial reduction in the bending and torsion needed to shape the new design into any bone in the population when compared to the standard mean-based plates.

Quantum Mechnical Investion of Cyclic 3',5'- Adenosine Monophosphate, the Second Hormonal Messenger

Full geometry optimizations using the PM3, AM1, 3-21G∗/HF and 6-31G∗/HF levels of theory were conducted on the syn and anti conformations of cyclic3′,5′-adenosine monophosphate (cAMP). Comparison of the anti crystal structures with the semiempirical and ab initio results revealed that the ab initio results agree well with the experimental results. The results of semiempirical calculations are in qualitative agreement with experimental and ab initio values, with the exception of the glycosyl torsion angle for the anti conformer. Sugar puckering, which is not handled properly by semiempirical methods for unconstrained sugars, nucleosides, nucleotides and nucleotide base pairs, is modeled reasonably well by the semiempirical methods for cAMP. This improvement results from the constraints introduced by the cyclization of AMP to form the phosphodiester.

Hydrogen bonding of nucleotide base pairs: Application of the PM3 method

The ability of the pm3 semiempirical quantum mechanical method to reproduce hydrogen bonding in nucleotide base pairs was assessed. Results of pm3 calculations on the nucleotides 2′-deoxyadenosine 5′-monophosphate (pdA), 2′-deoxyguanosine 5′-monophosphate (pdG), 2′-deoxycytidine 5′-monophosphate (pdC), and 2′-deoxythymidine 5′-monophosphate (pdT) and the base pairs pdA–pdT, pdG–pdC, and pdG(syn)–pdC are presented and discussed. The pm3 method is the first of the parameterized nddo quantum mechanical models with any ability to reproduce hydrogen bonding between nucleotide base pairs. Intermolecular hydrogen bond lengths between nucleotides displaying Watson–Crick base pairing are 0.1–0.2 Å less than experimental results. Nucleotide bond distances, bond angles, and torsion angles about the glycosyl bond (χ), the C4′C5′ bond (γ), and the C5′O5′ bond (β) agree with experimental results. There are many possible conformations of nucleotides. pm3 calculations reveal that many of the most stable conformations are stabilized by intramolecular CHO hydrogen bonds. These interactions disrupt the usual sugar puckering. The stacking interactions of a dT–pdA duplex are examined at different levels of gradient optimization. The intramolecular hydrogen bonds found in the nucleotide base pairs disappear in the duplex, as a result of the additional constraints on the phosphate group when part of a DNA backbone. Sugar puckering is reproduced by the pm3 method for the four bases in the dT–pdA duplex. pm3 underestimates the attractive stacking interactions of base pairs in a B-DNA helical conformation. The performance of the pm3 method implemented in SPARTAN is contrasted with that implemented in MOPAC. At present, accurate ab initio calculations are too timeconsuming to be of practical use, and molecular mechanics methods cannot be used to determine quantum mechanical properties such as reaction-path calculations, transition-state structures, and activation energies. The pm3 method should be used with extreme caution for examination of small DNA systems. Future parameterizations of semiempirical methods should incorporate base stacking interactions into the parameterization data set to enhance the ability of these methods.

GROUPS THAT INVOLVE FINITELY MANY PRIMES AND HAVE ALL SUBGROUPS SUBNORMAL II

It is shown that if G is a hypercentral group with all subgroups subnormal, and if the torsion subgroup of G is a pi-group for some finite set pi of primes, then G is nilpotent. In the case where G is not hypercentral there is a section of G that is much like one of the well-known Heineken-Mohamed groups. It is also shown that if G is a residually nilpotent group with all subgroups subnormal whose torsion subgroup satisfies the above condition then G is nilpotent.

Conformationally Controlled Electron Delocalization in n-Type Rods: Synthesis, Structure, and Optical, Electrochemical, and Spectroelectrochemical Properties of Dicyanocyclophanes

A series of dicyanobiphenyl-cyclophanes 1-6 with various pi-backbone conformations and characteristic n-type semiconductor properties is presented. Their synthesis, optical, structural, electrochemical, spectroelectrochemical, and packing properties are investigated. The X-ray crystal structures of all n-type rods allow the systematic correlation of structural features with physical properties. In addition, the results are supported by quantum mechanical calculations based on density functional theory. A two-step reduction process is observed for all n-type rods, in which the first step is reversible. The potential gap between the reduction processes depends linearly on the cos(2) value of the torsion angle phi between the pi-systems. Similarly, optical absorption spectroscopy shows that the vertical excitation energy of the conjugation band correlates with the cos(2) value of the torsion angle phi. These correlations demonstrate that the fixed intramolecular torsion angle phi is the dominant factor determining the extent of electron delocalization in these model compounds, and that the angle phi measured in the solid-state structure is a good proxy for the molecular conformation in solution. Spectroelectrochemical investigations demonstrate that conformational rigidity is maintained even in the radical anion form. In particular, the absorption bands corresponding to the SOMO-LUMO+i transitions are shifted bathochromically, whereas the absorption bands corresponding to the HOMO-SOMO transition are shifted hypsochromically with increasing torsion angle phi.

Single-Molecule Junctions Based on Nitrile-Terminated Biphenyls: A Promising New Anchoring Group

We present a combined experimental and theoretical study of the electronic transport through single-molecule junctions based on nitrile-terminated biphenyl derivatives. Using a scanning tunneling microscope-based break-junction technique, we show that the nitrile-terminated compounds give rise to well-defined peaks in the conductance histograms resulting from the high selectivity of the N-Au binding. Ab initio calculations have revealed that the transport takes place through the tail of the LUMO. Furthermore, we have found both theoretically and experimentally that the conductance of the molecular junctions is roughly proportional to the square of the cosine of the torsion angle between the two benzene rings of the biphenyl core, which demonstrates the robustness of this structure-conductance relationship.

Intestinal atresia and ectopia in a bovine fetus

A 2-year-old Red Holstein cow was presented with uterine torsion at 235 days of pregnancy. The fetus extracted by cesarean section had weak vital signs and marked abdominal distention. An edematous pouch that contained tubular structures with peristaltic activity was associated with the umbilical cord. Because of poor prognosis, both dam and fetus were euthanized. At necropsy, the fetus had severe distention of the forestomachs, abomasum, and proximal small intestine; absence of distal small intestine, cecum, and proximal colon; atresia of the 2 blind ends of the intestine; and atrophy of distal colon and rectum. The tubular structures associated with the umbilical cord were identified as the segments of intestine that were absent in the fetus. Intestinal atresia combined with ectopia may be caused by local ischemia during temporary herniation and rotation of the fetal gut into the extraembryonic coelom. The close connection between ectopic intestine and amniotic sheath of the umbilical cord in this case may have facilitated vascularization and allowed development and viability of the ectopic intestine.

Hematometra presenting as an acute abdomen in a 13-year-old postmenarchal girl: a case report

Introduction Most underlying diseases for abdominal pain in children are not dangerous. However some require rapid diagnosis and treatment, such as acute ovarian torsion or appendicitis. Since reaching a diagnosis can be difficult, and delayed treatment of potentially dangerous diseases might have significant consequences, exploratory laparoscopy is a diagnostic and therapeutic option for patients who have unclear and potentially hazardous abdominal diseases. Here we describe a case where the anomaly could not be identified using a laparoscopy in an adolescent girl with acute abdomen. Case presentation A 13-year old postmenarchal caucasian female presented with an acute abdomen. Emergency sonography could not exclude ovarian torsion. Accurate diagnosis and treatment were achieved only after an initial laparoscopy followed by a laparotomy and after a magnetic resonance imaging scan a further laparotomy. The underlying disease was hematometra of the right uterine horn in a uterus didelphys in conjunction with an imperforate right cervix. Conclusion This report demonstrates that the usual approach for patients with acute abdominal pain may not be sufficient in emergency situations.

Static and Dynamic Error Correction of a Computer-Aided Mechanical Navigation Linkage for Arthroscopic Hip Surgery

While beneficially decreasing the necessary incision size, arthroscopic hip surgery increases the surgical complexity due to loss of joint visibility. To ease such difficulty, a computer-aided mechanical navigation system was developed to present the location of the surgical tool relative to the patient¿s hip joint. A preliminary study reduced the position error of the tracking linkage with limited static testing trials. In this study, a correction method, including a rotational correction factor and a length correction function, was developed through more in-depth static testing. The developed correction method was then applied to additional static and dynamic testing trials to evaluate its effectiveness. For static testing, the position error decreased from an average of 0.384 inches to 0.153 inches, with an error reduction of 60.5%. Three parameters utilized to quantify error reduction of dynamic testing did not show consistent results. The vertex coordinates achieved 29.4% of error reduction, yet with large variation in the upper vertex. The triangular area error was reduced by 5.37%, however inconsistent among all five dynamic trials. Error of vertex angles increased, indicating a shape torsion using the developed correction method. While the established correction method effectively and consistently reduced position error in static testing, it did not present consistent results in dynamic trials. More dynamic paramters should be explored to quantify error reduction of dynamic testing, and more in-depth dynamic testing methodology should be conducted to further improve the accuracy of the computer-aided nagivation system.

Kalman Filter approaches on crane swing

The purpose of this study is to explore a Kalman Filter approach to estimating swing of crane-suspended loads. Measuring real-time swing is needed to implement swing damping control strategies where crane joints are used to remove energy from a swinging load. The typical solution to measuring swing uses an inertial sensor attached to the hook block. Measured hook block twist is used to resolve the other two sensed body rates into tangential and radial swing. Uncertainty in the twist measurement leads to inaccurate tangential and radial swing calculations and ineffective swing damping. A typical mitigation approach is to bandpass the inertial sensor readings to remove low frequency drift and high frequency noise. The center frequency of the bandpass filter is usually designed to track the load length and the pass band width set to trade off performance with damping loop gain. The Kalman Filter approach developed here allows all swing motions (radial, tangential and twist) to be measured without the use of a bandpass filter. This provides an alternate solution for swing damping control implementation. After developing a Kalman Filter solution for a two-dimensional swing scenario, the three-dimensional system is considered where simplifying assumptions, suggested by the two-dimensional study, are exploited. One of the interesting aspects of the three-dimensional study is the hook block twist model. Unlike the mass-independence of a pendulum's natural frequency, the twist natural frequency depends both on the pendulum length and the load’s mass distribution. The linear Kalman Filter is applied to experimental data demonstrating the ability to extract the individual swing components for complex motions. It should be noted that the three-dimensional simplifying assumptions preclude the ability to measure two "secondary" hook block rotations. The ability to segregate these motions from the primary swing degrees of freedom was illustrated in the two-dimensional study and could be included into the three-dimensional solution if they were found to be important for a particular application.

Quantifying the periodicty of Inter Movement Intervals of Leg Movements

ims: Periodic leg movements in sleep (PLMS) are a frequent finding in polysomnography. Most patients with restless legs syndrome (RLS) display PLMS. However, since PLMS are also often recorded in healthy elderly subjects, the clinical significance of PLMS is still discussed controversially. Leg movements are seen concurrently with arousals in obstructive sleep apnoea (OSA) may also appear periodically. Quantitative assessment of the periodicity of LM/PLM as measured by inter movement intervals (IMI) is difficult. This is mainly due to influencing factors like sleep architecture and sleep stage, medication, inter and intra patient variability, the arbitrary amplitude and sequence criteria which tend to broaden the IMI distributions or make them even multi-modal. Methods: Here a statistical method is presented that enables eliminating such effects from the raw data before analysing the statistics of IMI. Rather than studying the absolute size of IMI (measured in seconds) we focus on the shape of their distribution (suitably normalized IMI). To this end we employ methods developed in Random Matrix Theory (RMT). Patients: The periodicity of leg movements (LM) of four patient groups (10 to 15 each) showing LM without PLMS (group 1), OSA without PLMS (group 2), PLMS and OSA (group 3) as well as PLMS without OSA (group 4) are compared. Results: The IMI of patients without PLMS (groups 1 and 2) and with PLMS (groups 3 and 4) are statistically different. In patients without PLMS the distribution of normalized IMI resembles closely the one of random events. In contrary IMI of PLMS patients show features of periodic systems (e.g. a pendulum) when studied in normalized manner. Conclusions: For quantifying PLMS periodicity proper normalization of the IMI is crucial. Without this procedure important features are hidden when grouping LM/PLM over whole nights or across patients. The clinical significance of PLMS might be eluded when properly separating random LM from LM that show features of periodic systems.