Splittings of knot groups

Let K be a knot of genus g. If K is fibered, then it is well known that the knot group pi(K) splits only over a free group of rank 2g. We show that if K is not fibered, then pi(K) splits over non-free groups of arbitrarily large rank. Furthermore, if K is not fibered, then pi(K) splits over every free group of rank at least 2g. However, pi(K) cannot split over a group of rank less than 2g. The last statement is proved using the recent results of Agol, Przytycki-Wise and Wise.Comment: 28 pages, 2 figure

Hidden Translation and Translating Coset in Quantum Computing

We give efficient quantum algorithms for the problems of Hidden Translation and Hidden Subgroup in a large class of non-abelian solvable groups including solvable groups of constant exponent and of constant length derived series. Our algorithms are recursive. For the base case, we solve efficiently Hidden Translation in $\Z_{p}^{n}$, whenever $p$ is a fixed prime. For the induction step, we introduce the problem Translating Coset generalizing both Hidden Translation and Hidden Subgroup, and prove a powerful self-reducibility result: Translating Coset in a finite solvable group $G$ is reducible to instances of Translating Coset in $G/N$ and $N$, for appropriate normal subgroups $N$ of $G$. Our self-reducibility framework combined with Kuperberg's subexponential quantum algorithm for solving Hidden Translation in any abelian group, leads to subexponential quantum algorithms for Hidden Translation and Hidden Subgroup in any solvable group.Comment: Journal version: change of title and several minor update

Multi-scale analysis and modelling of collective migration in biological systems

Collective migration has become a paradigm for emergent behaviour in systems of moving and interacting individual units resulting in coherent motion. In biology, these units are cells or organisms. Collective cell migration is important in embryonic development, where it underlies tissue and organ formation, as well as pathological processes, such as cancer invasion and metastasis. In animal groups, collective movements may enhance individuals' decisions and facilitate navigation through complex environments and access to food resources. Mathematical models can extract unifying principles behind the diverse manifestations of collective migration. In biology, with a few exceptions, collective migration typically occurs at a 'mesoscopic scale' where the number of units ranges from only a few dozen to a few thousands, in contrast to the large systems treated by statistical mechanics. Recent developments in multi-scale analysis have allowed linkage of mesoscopic to micro- and macroscopic scales, and for different biological systems. The articles in this theme issue on 'Multi-scale analysis and modelling of collective migration' compile a range of mathematical modelling ideas and multi-scale methods for the analysis of collective migration. These approaches (i) uncover new unifying organization principles of collective behaviour, (ii) shed light on the transition from single to collective migration, and (iii) allow us to define similarities and differences of collective behaviour in groups of cells and organisms. As a common theme, self-organized collective migration is the result of ecological and evolutionary constraints both at the cell and organismic levels. Thereby, the rules governing physiological collective behaviours also underlie pathological processes, albeit with different upstream inputs and consequences for the group. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'

Frequency Shifts and Linewidth Changes of Infrared-Active Phonons in Double-Layered High-Temperature Superconductors

We calculate frequency shifts and changes in linewidths of infrared-active phonons within a shell model for the bare phononic system coupled to an electronic double-layer structure with inter-layer charge transfer. The theoretical concept is applied to YBaCuO yielding a good description of experimental results in the normal state as well as at the transition to the superconducting state.Comment: 8 pages, LaTex, SISSA-CM-93-00

The Turaev and Thurston norms

In 1986, W. Thurston introduced a (possibly degenerate) norm on the first cohomology group of a 3-manifold. Inspired by this definition, Turaev introduced in 2002 a analogous norm on the first cohomology group of a finite 2-complex. We show that if N is the exterior of a link in a rational homology sphere, then the Thurston norm agrees with a suitable variation of Turaev's norm defined on any 2-skeleton of N.Comment: 17 pages. V2: We deleted one direction of Lemma 4.5 since the proof was incorrect. This does not affect any of the other results of the pape

Modellering van het ontwerpproces:een proces-choreografie

Het vertrekpunt voor deze eindopdracht vormde de vraag wat het 'ontwerpen van het ontwerpproces' inhoudt. Gedurende het ontwerpproces wordt de vraag van de opdrachtgever geconcretiseerd en geleidelijk omgezet in een ontwerp. Aan dit ontwerp wordt door een groot aantal actoren gewerkt. Het bouwkundige ontwerp-proces is dus een samenwerkingsproces waar door vele actoren gewerkt wordt naar één eindresultaat.Bij de inrichting van dit proces wordt tegenwoordig veel aandacht besteed aan de ontwikkeling van het ontwerp. Dit gebeurt in de vorm van een nauwkeurige vastlegging van de wensen en eisen van de opdrachtgever die vervolgens vertaald worden in een ontwerp. Hierbij wordt ligt de nadruk op de afstemming van de verschillende activiteiten die door diverse actoren worden uitgevoerd. Hoe deze actoren samenwerken, wordt vastgelegd in een organisatiestructuur die onder meer de verdeling van taken, verantwoordelijkheden en bevoegdheden inhoudt.Vaak wordt er echter over het hoofd gezien dat ontwerpen door mensen wordt uitgevoerd en dat de diverse actoren die deel nemen in dit proces verschillen qua normen, waarden en werkwijzen. Ook is het proces niet slechts een probleem oplossingsproces maar ook een proces waarmee problemen boven tafel worden gehaald. Daarom wordt het proces ook gekenmerkt door grilligheid en een bepaalde mate aan onvoorspelbaarheid. In deze opdracht wordt naar een andere manier gezocht om het ontwerpproces in te kunnen richten. Hierbij staat het idee centraal dat voor een goed proces (en mede hierdoor ook voor een goed resultaat) de uitgangspunten en randvoor-waarden voor dit proces optimaal moeten zijn.Er wordt een innovatieve aanpak voorgesteld die de nadruk legt op het creëren van de juiste randvoorwaarden en uitgangspunten voor de inrichting van het ontwerp-proces.Hiervoor is eerst onderzocht wat de activiteit ontwerpen eigenlijk is en welke gevolgen hieruit ontstaan voor het ontwerpproces. Uitgaande van deze analyse is gekeken hoe ontwerpers tewerk gaan en welke actoren ontwerpactiviteiten uitvoeren in het proces. Vervolgens is geanalyseerd waar tegenwoordig de knelpunten liggen bij de inrichting van het ontwerpproces. Dit mondt uit in een beschrijving van de huidige aanpak. Uiteindelijk is een model opgesteld van een nieuwe innovatieve aanpak waarmee de problemen van de huidige aanpak voorkomen kunnen worden

Undifferentiated human mesenchymal stem cells (hMSCs) are highly sensitive to mechanical strain: transcriptionally controlled early osteo-chondrogenic response in vitro

SummaryObjectivePhysical cues play a crucial role in skeletogenesis and osteochondral regeneration. Although human mesenchymal stem cells (hMSCs) offer considerable therapeutic potential, little is known about the molecular mechanisms that control their differentiation. We hypothesized that mechanical strain might be an inherent stimulus for chondrogenic and/or osteogenic differentiation in undifferentiated hMSCs, where c-Fos (FOS) might play a major role in mechanotransduction.MethodhMSCs from 10 donors were intermittently stimulated by cyclic tensile strain (CTS) at 3000 μstrain for a period of 3 days. Differential gene expression of strained and unstrained hMSCs was analysed by real-time RT-PCR for several marker genes, including the transcription factors FOS, RUNX2, SOX9, and others. Additionally, alkaline phosphatase activity (ALP) was determined kinetically.ResultsThe application of CTS significantly stimulated the expression levels of the early chondrogenic and osteogenic marker genes (SOX9, LUM, DCN; RUNX2, SPARC, SPP1, ALPL); this was accompanied by stimulation of ALP activity (+38%±12 standard error of mean, P<0.05). Matrix analysis revealed that the osteo-chondrogenic response followed a coordinated expression pattern, in which FOS was attributed to early osteogenic but not chondrogenic differentiation.ConclusionUndifferentiated hMSCs are highly sensitive to mechanical strain with a transcriptionally controlled osteo-chondrogenic differentiation response in vitro

Polymorphismen im ICAM-1-Gen bei Psoriasis vulgaris

Es ist bekannt, daß bei Psoriatikern erhöhte Serumspiegel des solublen ICAM-1 im Vergleich zu Kontrollgruppen vorliegen (Kowalzick et al. 1993), (Hügle 1996). Um die Hypothese eines ICAM-1 generierten Entzündungsgeschehens bei Psoriasis zu überprüfen, wurde die Segregation zweier bereits beschriebener ICAM-1 Polymorphismen in 99 Trios untersucht. Alle Probanden wurden mittels Polymerase chain reaction (PCR) und Allel-spezifisches-Oligonukleotid (ASO) Techniken für die ICAM-1 Polymorphismen G/R bei Codon 241 (Exon 4) und E/K bei Codon 469 (Exon 6) genotypisiert. In dieser Arbeit konnte gezeigt werden, daß keines der untersuchten Allele eine signifikante Assoziation mit der Psoriasis aufweist. Ein ursächlicher Zusammenhang dieser beiden Allele mit der Psoriasis im hier untersuchten Kollektiv erscheint somit unwahrscheinlich

Glasspalace "Schunck" Heerlen:casestudy

The Glasspalace is built in 1935 in the centre of Heerlen and is designed as a department store by the architect F.P.J. Peutz. The building was originally surrounded by a façade of huge glass sheets mounted in thin steel profiles explaining its nickname "Glasspalace". It was quite revolutionary for that time. Currently the building occupies a position in the top 1000 list of the worlds most important architectural buildings. However during the transformation of the building into a shopping centre in 1972 most of its unique architectural qualities was lost. Because of poor maintenance in the 80's and 90's the situation got even worse. Nowadays the building is completely desolated and is a meeting place for drug-users. In 1997 the City of Heerlen decided to acquire the building and restore its original appearance to counteract the imminent deterioration of the city centre of Heerlen and to house a new set of users. Meanwhile a combination of architects has been commissioned to make a new design for the Glasspalace. However, the way the architects demand to work and the obliged regulations of the European Community are stipulating some specific conditions to the projects that brings in some complexities in the managerial context. This report will discuss the main bottlenecks of the existing process and will propose a new process design. The report is set up in two parts: the first part will deal with the existing process design; the second part is about the redesign proposed by the ADMS-group