Graph Theory and Networks in Biology

In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of bio-molecular networks, as well as the application of centrality measures to interaction networks and research on the hierarchical structure of such networks and network motifs. Work on the link between structural network properties and dynamics is also described, with emphasis on synchronization and disease propagation.Comment: 52 pages, 5 figures, Survey Pape

On the parameterization of all admissible pairs in a class of CCF-ILC algorithms

This paper extends some recent results on the parameterization of all admissible pairs in a class of 2-parameter current-cycle-feedback ILC algorithms. In addition, a necessary and sufficient condition is given under which the associated set of equivalent controllers coincides with the set of all stabilizing controller

Global phase-locking in finite populations of phase-coupled oscillators

We present new necessary and sufficient conditions for the existence of fixed points in a finite system of coupled phase oscillators on a complete graph. We use these conditions to derive bounds on the critical coupling.Comment: 31 pages; to appear in SIAM journal of dynamical systems (SIADS

On equivalence classes in iterative learning control

This paper advocates a new approach to study the relation between causal iterative learning control (ILC) and conventional feedback control. Central to this approach is the introduction of the set of admissible pairs (of operators) defined with respect to a family of iterations. Considered are two problem settings: standard ILC, which does not include a current cycle feedback (CCF) term and CCF-ILC, which does. By defining an equivalence relation on the set of admissible pairs, it is shown that in the standard ILC problem there exists a bijective map between the induced equivalence classes and the set of all stabilizing controllers. This yields the well-known Youla parameterization as a corollary. These results do not extend in full generality to the case of CCF-ILC; though gain every admissible pair defines a stabilizing equivalent controller, the converse is no longer true in general

Ectopic cartilage in subglottic stenosis: Hamartoma or reaction to trauma?

In an experimental study in growing rabbits an endolaryngeal injury to the subglottis resulted in the development of a stenosis due to the formation of scar tissue containing ectopic cartilage. For comparison, biopsies taken from the subglottic stenosis in 8 children were studied histologically. In 6 cases ectopic cartilage was observed; all patients had a history of endotracheal intubation. In 3 children the diagnosis hamartoma was made. In the remaining 3 cases the formation of ectopic cartilage might have been a direct reaction to the endolaryngeal intubation. The observations suggest that the formation of ectopic cartilage in acquired subglottic stenosis is not always due to a developmental aberration such as a hamartoma

Correlation calculations for the reconstruction of the Si (100) surface

Ab initio multi-reference configuration interaction calculations are performed for the Si(100) surface using a cluster approach. The convergence with respect to the cluster size is checked and the final results are taken from a $Si_{32} H_{28}$ cluster which models two dimers and six bulk layers. We find for the ideal as well as for the p($1\times 2$) reconstruction a singlet ground state consisting of several configurations. The energy gain due to forming the symmetric dimer in the p($1\times 2$) structure is 1.75 eV, the bond length of the dimer is 2.35 \AA which is very close to the bulk value. In contradiction to the LDA results and in agreement with previous correlation calculations we do not find an asymmetric p($1\times 2$) structure.Comment: 6 pages, Revtex, 3 postscript figures, to appear in Surf. S

Macmillan, Verwoerd, and the 1960 `wind of change' speech

Just over fifty years ago, Prime Minister Macmillan made an extensive tour of Africa, culminating in his 'wind of change' speech in Cape Town. This article traces Macmillan's progress through Africa with particular emphasis on his intervention in South African politics. It offers a novel reading of the 1960 'wind of change' speech, arguing that the message was far more conciliatory with respect to white South African interests than is usually assumed. Pragmatism rather than principle was always the prime consideration. Far from being cowed by Macmillan's oratory or his message, Verwoerd stood up to Macmillan and, at least in the eyes of his supporters, gave as good as he got. The shock of the 'wind of change' speech was more evident in Britain and in British settler regions of Africa than in South Africa. Macmillan's advisers had an inflated view of the import of the speech and in many ways misread Verwoerd's brand of Afrikaner nationalism. One of the consequences of the speech was to embolden Verwoerd politically, and to prepare him for the declaration of republican status in 1961 and departure from the commonwealth