Curvature and torsion in growing actin networks

Intracellular pathogens such as Listeria monocytogenes and Rickettsia rickettsii move within a host cell by polymerizing a comet-tail of actin fibers that ultimately pushes the cell forward. This dense network of cross-linked actin polymers typically exhibits a striking curvature that causes bacteria to move in gently looping paths. Theoretically, tail curvature has been linked to details of motility by considering force and torque balances from a finite number of polymerizing filaments. Here we track beads coated with a prokaryotic activator of actin polymerization in three dimensions to directly quantify the curvature and torsion of bead motility paths. We find that bead paths are more likely to have low rather than high curvature at any given time. Furthermore, path curvature changes very slowly in time, with an autocorrelation decay time of 200 seconds. Paths with a small radius of curvature, therefore, remain so for an extended period resulting in loops when confined to two dimensions. When allowed to explore a 3D space, path loops are less evident. Finally, we quantify the torsion in the bead paths and show that beads do not exhibit a significant left- or right-handed bias to their motion in 3D. These results suggest that paths of actin-propelled objects may be attributed to slow changes in curvature rather than a fixed torque

On asymptotic Teichmüller space

In this article we prove that for any hyperbolic Riemann surface M of infinite analytic type, the little Bers space Q0(M) is isomorphic to c0. As a consequence of this result, if M is such a Riemann surface, then its asymptotic Teichm¨uller space AT(M) is bi-Lipschitz equivalent to a bounded open subset of the Banach space l∞/c0. Further, if M and N are two such Riemann surfaces, their asymptotic Teichm¨uller spaces, AT(M) and AT(N), are locally bi-Lipschitz equivalen

Local rigidity of infinite-dimensional Teichmüller spaces

This paper presents a rigidity theorem for infinite-dimensional Bergman spaces of hyperbolic Riemann surfaces, which states that the Bergman space $A^{1}(M)$, for such a Riemann surface $M$, is isomorphic to the Banach space of summable sequence, $l^{1}$. This implies that whenever $M$ and $N$ are Riemann surfaces that are not analytically finite, and in particular are not necessarily homeomorphic, then $A^{1}(M)$ is isomorphic to $A^{1}(N)$. It is known from V. Markovic that if there is a linear isometry between $A^{1}(M)$ and $A^{1}(N)$, for two Riemann surfaces $M$ and $N$ of non-exceptional type, then this isometry is induced by a conformal mapping between $M$ and $N$. As a corollary to this rigidity theorem presented here, taking the Banach duals of $A^{1}(M)$ and $l^{1}$ shows that the space of holomorphic quadratic differentials on $M,\ Q(M)$, is isomorphic to the Banach space of bounded sequences, $l^{\infty }$. As a consequence of this theorem and the Bers embedding, the Teichmüller spaces of such Riemann surfaces are locally bi-Lipschitz equivalent

Exploring ‘events’ as an information systems research methodology

This paper builds upon existing research and commentary from a variety of disciplinary sources including Information Systems, Organisational and Management Studies, and the Social Sciences that focus upon the meaning, significance and impact of ‘events’ in both an organisational and a social sense. The aim of this paper is to define how the examination of the event is an appropriate, viable and useful Information Systems methodology. Our argument is that focusing on the ‘event’ enables the researcher to more clearly observe and capture the complexity, multiplicity and mundaneity of everyday lived experience. The use and notion of ‘event’ has the potential to reduce the methodological dilemmas associated with the micromanagement of the research process – an inherent danger of traditional and ‘virtual' ethnographic approaches. Similarly, this paper addresses the over-emphasis upon managerialist, structured and time-fixated praxis that is currently symptomatic of Information Systems research. All of these concerns are pivotal points of critique found within eventoriented literature. An examination of event-related theory within interpretative disciplines directs the focus of this paper towards the more specific realm of the ‘event scene’. The notion of the ‘event scene’ originated in the action based (and anti-academy) imperatives of the Situationists and emerged in an academic sense as critical situational analysis. Event scenes are a focus for contemporary critical theory where they are utilised as a means of representing theoried inquiry in order to loosen the restrictions that historical and temporally bound analysis imposes upon most interpretative approaches. The use of event scenes as the framework for critiquing established conceptual assumptions is exemplified by their use in CTheory. In this journal's version and articulation of the event scene poetry, commentary, multi-vocal narrative and other techniques are legitimated as academic forms. These various forms of multi-dimensional expression are drawn upon to enrich the understandings of the ‘event’, to extricate its meaning and to provide a sense of the moment from which the point of analysis stems. The objective of this paper is to advocate how Information Systems research can (or should) utilize an event scene oriented methodology