Power law distributions in pattern dynamics of attacker-defender dyads in the team sport of Rugby Union : phenomena in a region of self-organized criticality?

In the region of self-organized criticality (SOC) interdependency between multi-agent system components exists and slight changes in near-neighbor interactions can break the balance of equally poised options leading to transitions in system order. In this region, frequency of events of differing magnitudes exhibits a power law distribution. The aim of this paper was to investigate whether a power law distribution characterized attacker-defender interactions in team sports. For this purpose we observed attacker and defender in a dyadic sub-phase of rugby union near the try line. Videogrammetry was used to capture players’ motion over time as player locations were digitized. Power laws were calculated for the rate of change of players’ relative position. Data revealed that three emergent patterns from dyadic system interactions (i.e., try; unsuccessful tackle; effective tackle) displayed a power law distribution. Results suggested that pattern forming dynamics dyads in rugby union exhibited SOC. It was concluded that rugby union dyads evolve in SOC regions suggesting that players’ decisions and actions are governed by local interactions rules.

Dynamics of pattern writing and erasure in photorefractive lithium niobate for data storage applications

The present rate of technological advance continues to place significant demands on data storage devices. The sheer amount of digital data being generated each year along with consumer expectations, fuels these demands. At present, most digital data is stored magnetically, in the form of hard disk drives or on magnetic tape. The increase in areal density (AD) of magnetic hard disk drives over the past 50 years has been of the order of 100 million times, and current devices are storing data at ADs of the order of hundreds of gigabits per square inch. However, it has been known for some time that the progress in this form of data storage is approaching fundamental limits. The main limitation relates to the lower size limit that an individual bit can have for stable storage. Various techniques for overcoming these fundamental limits are currently the focus of considerable research effort. Most attempt to improve current data storage methods, or modify these slightly for higher density storage. Alternatively, three dimensional optical data storage is a promising field for the information storage needs of the future, offering very high density, high speed memory. There are two ways in which data may be recorded in a three dimensional optical medium; either bit-by-bit (similar in principle to an optical disc medium such as CD or DVD) or by using pages of bit data. Bit-by-bit techniques for three dimensional storage offer high density but are inherently slow due to the serial nature of data access. Page-based techniques, where a two-dimensional page of data bits is written in one write operation, can offer significantly higher data rates, due to their parallel nature. Holographic Data Storage (HDS) is one such page-oriented optical memory technique. This field of research has been active for several decades, but with few commercial products presently available. Another page-oriented optical memory technique involves recording pages of data as phase masks in a photorefractive medium. A photorefractive material is one by which the refractive index can be modified by light of the appropriate wavelength and intensity, and this property can be used to store information in these materials. In phase mask storage, two dimensional pages of data are recorded into a photorefractive crystal, as refractive index changes in the medium. A low-intensity readout beam propagating through the medium will have its intensity profile modified by these refractive index changes and a CCD camera can be used to monitor the readout beam, and thus read the stored data. The main aim of this research was to investigate data storage using phase masks in the photorefractive crystal, lithium niobate (LiNbO3). Firstly the experimental methods for storing the two dimensional pages of data (a set of vertical stripes of varying lengths) in the medium are presented. The laser beam used for writing, whose intensity profile is modified by an amplitudemask which contains a pattern of the information to be stored, illuminates the lithium niobate crystal and the photorefractive effect causes the patterns to be stored as refractive index changes in the medium. These patterns are read out non-destructively using a low intensity probe beam and a CCD camera. A common complication of information storage in photorefractive crystals is the issue of destructive readout. This is a problem particularly for holographic data storage, where the readout beam should be at the same wavelength as the beam used for writing. Since the charge carriers in the medium are still sensitive to the read light field, the readout beam erases the stored information. A method to avoid this is by using thermal fixing. Here the photorefractive medium is heated to temperatures above 150�C; this process forms an ionic grating in the medium. This ionic grating is insensitive to the readout beam and therefore the information is not erased during readout. A non-contact method for determining temperature change in a lithium niobate crystal is presented in this thesis. The temperature-dependent birefringent properties of the medium cause intensity oscillations to be observed for a beam propagating through the medium during a change in temperature. It is shown that each oscillation corresponds to a particular temperature change, and by counting the number of oscillations observed, the temperature change of the medium can be deduced. The presented technique for measuring temperature change could easily be applied to a situation where thermal fixing of data in a photorefractive medium is required. Furthermore, by using an expanded beam and monitoring the intensity oscillations over a wide region, it is shown that the temperature in various locations of the crystal can be monitored simultaneously. This technique could be used to deduce temperature gradients in the medium. It is shown that the three dimensional nature of the recording medium causes interesting degradation effects to occur when the patterns are written for a longer-than-optimal time. This degradation results in the splitting of the vertical stripes in the data pattern, and for long writing exposure times this process can result in the complete deterioration of the information in the medium. It is shown in that simply by using incoherent illumination, the original pattern can be recovered from the degraded state. The reason for the recovery is that the refractive index changes causing the degradation are of a smaller magnitude since they are induced by the write field components scattered from the written structures. During incoherent erasure, the lower magnitude refractive index changes are neutralised first, allowing the original pattern to be recovered. The degradation process is shown to be reversed during the recovery process, and a simple relationship is found relating the time at which particular features appear during degradation and recovery. A further outcome of this work is that the minimum stripe width of 30 ìm is required for accurate storage and recovery of the information in the medium, any size smaller than this results in incomplete recovery. The degradation and recovery process could be applied to an application in image scrambling or cryptography for optical information storage. A two dimensional numerical model based on the finite-difference beam propagation method (FD-BPM) is presented and used to gain insight into the pattern storage process. The model shows that the degradation of the patterns is due to the complicated path taken by the write beam as it propagates through the crystal, and in particular the scattering of this beam from the induced refractive index structures in the medium. The model indicates that the highest quality pattern storage would be achieved with a thin 0.5 mm medium; however this type of medium would also remove the degradation property of the patterns and the subsequent recovery process. To overcome the simplistic treatment of the refractive index change in the FD-BPM model, a fully three dimensional photorefractive model developed by Devaux is presented. This model shows significant insight into the pattern storage, particularly for the degradation and recovery process, and confirms the theory that the recovery of the degraded patterns is possible since the refractive index changes responsible for the degradation are of a smaller magnitude. Finally, detailed analysis of the pattern formation and degradation dynamics for periodic patterns of various periodicities is presented. It is shown that stripe widths in the write beam of greater than 150 ìm result in the formation of different types of refractive index changes, compared with the stripes of smaller widths. As a result, it is shown that the pattern storage method discussed in this thesis has an upper feature size limit of 150 ìm, for accurate and reliable pattern storage.

Mathematical modelling of intramembranous bone formation during fracture healing

During fracture healing, many complex and cryptic interactions occur between cells and bio-chemical molecules to bring about repair of damaged bone. In this thesis two mathematical models were developed, concerning the cellular differentiation of osteoblasts (bone forming cells) and the mineralisation of new bone tissue, allowing new insights into these processes. These models were mathematically analysed and simulated numerically, yielding results consistent with experimental data and highlighting the underlying pattern formation structure in these aspects of fracture healing.

A four-variable model for the pattern-forming mechanism in Hydra

A generalized Gierer-Meinhardt model has been used to account for the transplantation experiments in Hydra. In this model, a cross inhibition between the two organizing centres (namely, head and foot) are assumed to be the only mode of interaction in setting up a stable morphogen distribution for the pattern formation in Hydra.

The influencing factors on the macroporous formation in polymer films by water droplet templating

Regular micrometer-size porous polystyrene film is prepared by water droplet templating, i.e. breath figures are stabilized by the polymer in solution and thermocapillary flow arranges them into ordered packing. The influences of polystyrene molecular weight, solvent properties, and the relative humidity of atmosphere on the pattern formation and hole sizes are investigated. Two different kinds of hole packing fashion are also observed and their formation mechanisms are discussed.

How to form regular polymer microstructures by surface-pattern-directed dewetting

The substrates with regular patterns of self-assembly monolayers (SAMs) produced by microcontact printing with octadecyltrichlorosilane (OTS) was employed to direct thin polystyrene dewetting to fabricate ordered micrometer scale pattern. The pattern sizes and pattern fashion can be manipulated by controlling the experimental parameters. The pattern formation mechanisms have been discussed. The dewetting pattern can be transferred to form PDMS stamp for future microfabrication process.

Towards a unifying framework for pattern transformation in swarm systems

This paper identifies the major challenges in the area of pattern formation. The work is also motivated by the need for development of a single framework to surmount these challenges. A framework based on the control of macroscopic parameters is proposed. The issue of transformation of patterns is specifically considered. A definition for transformation and four special cases, namely elementary and geometrical transformations by repositioning all or some robots in the pattern are provided. Two feasible tools for pattern transformation namely, a macroscopic parameter method and a mathematical tool - Moebius transformation also known as the linear fractional transformation are introduced. The realization of the unifying framework considering planning and communication is reported.

A swarm pattern transformation method based on macroscopic parameter operations

The work reported in this paper is motivated by biomimetic inspiration - the transformation of patterns. The major issue addressed is the development of feasible methods for transformation based on a macroscopic tool. The general requirement for the feasibility of the transformation method is determined by classifying pattern formation approaches an their characteristics. A formal definition for pattern transformation is provided and four special cases namely, elementary and geometric transformation based on repositioning all and some robotic agents are introduced. A feasible method for transforming patterns geometrically, based on the macroscopic parameter operation of a swarm is considered. The transformation method is applied to a swarm model which lends itself to the transformation technique. Simulation studies are developed to validate the feasibility of the approach, and do indeed confirm the approach.

The relevance of the silica metabolizing enzyme silicatein-alpha to biomineralization and the formation of biogenic silica in siliceous sponges

Die technische Silikatproduktion erfordert in der Regel hohe Temperaturen und extreme pH-Werte. In der Natur hingegen haben insbesondere Kieselschwämme die außergewöhnliche Fähigkeit, ihr Silikatskelett, das aus einzelnen sogenannten Spiculae besteht, enzymatisch mittels des Proteins Silicatein zu synthetisieren. rnIm Inneren der Spiculae, im zentralen Kanal, befindet sich das Axialfilament, welches hauptsächlich aus Silicatein-α aufgebaut ist. Mittels Antikörperfärbungen und Elektronenmikroskopischen Analysen konnte festgestellt werden, dass Silicatein in mit Kieselsäure-gefüllten Zellorganellen (silicasomes) nachzuweisen ist. Mittels dieser Vakuolen kann das Enzym und die Kieselsäure aus der Zelle zu den Spiculae im extrazellulären Raum befördert werden, wo diese ihre endgültige Länge und Dicke erreichen. Zum ersten Mal konnte nachgewiesen werden, dass rekombinant hergestelltes Silicatein-α sowohl als Siliciumdioxid-Polymerase als auch Siliciumdioxid-Esterase wirkt. Mittels Massenspektroskopie konnte die enzymatische Polymerisation von Kieselsäure nachverfolgt werden. Durch Spaltung der Esterbindung des künstlichen Substrates Bis(p-aminophenoxy)-dimethylsilan war es möglich kinetische Parameter der Siliciumdioxid-Esterase-Aktivität des rekombinanten Silicateins zu ermitteln.rnZu den größten biogenen Silikatstukuren auf der Erde gehören die Kieselnadeln der Schwammklasse Hexactinellida. Nadelextrakte aus den Schwammklassen Demospongien (S. domuncula) und Hexactinellida (M. chuni) wurden miteinander verglichen um die potentielle Existenz von Silicatein oder Silicatein-ähnliche Molekülen und die dazu gehörige proteolytischen Aktivität nachzuweisen. Biochemische Analysen zeigten, dass das 27 kDA große isolierte Polypeptid in Monoraphis mehrere gemeinsame Merkmale mit den Silicateinen der Demospongien teilt. Dazu gehören die Größe und die Proteinase-Aktivität. rnUm die Frage zu klären, ob das axiale Filament selbst zur Formbildung der Skelettelemente beiträgt, wurde ein neues mildes Extraktionsverfahren eingeführt. Dieses Verfahren ermöglichte die Solubilisierung des nativen Silicateins aus den Spiculae. Die isolierten Silicateine lagen als Monomere (24 kDa) vor, die Dimere durch nicht-kovalente Bindungen ausbildeten. Darüber hinaus konnten durch PAGE-Gelelektrophorese Tetramere (95 kDa) und Hexamere (135 kDa) nachgewiesen werden. Die Monomere zeigten eine beträchtliche proteolytische Aktivität, die sich während der Polymerisationsphase des Proteins weiter erhöhte. Mit Hilfe der Lichtmikroskopie und Elektronenmikroskopie (TEM) konnte die Assemblierung der Proteine zu filamentartigen Strukturen gezeigt werden. Die Selbstorganisation der Silicatein-α-Monomeren scheint eine Basis für Form- und Musterbildung der wachsenden Nadeln zu bilden.rn Um die Rolle des kürzlich entdeckten Proteins Silintaphin-1, ein starker Interaktionspartner des Silicatein-α, während der Biosilifizierung zu klären, wurden Assemblierungs-Experimente mit den rekombinanten Proteinen in vitro durchgeführt. Zusätzlich wurde deren Effekt auf die Biosilikatsynthese untersucht. Elektronenmikroskopische Analysen ergaben, dass rekombinantes Silicatein-α zufällig verteilte Aggregate bildet, während die Koinkubation beider Proteine (molekulares Verhältnis 4:1) über fraktal artige Strukturen zu Filamenten führt. Auch die enzymatische Aktivität der Silicatein-α-vermittelte Biosilikatsynthese erhöhte sich in Gegenwart von Silintaphin-1 um das 5,3-fache. rn

Mechano-Chemical Aspects of Organ Formation in Arabidopsis thaliana: The Relationship between Auxin and Pectin

How instructive signals are translated into robust and predictable changes in growth is a central question in developmental biology. Recently, much interest has centered on the feedback between chemical instructions and mechanical changes for pattern formation in development. In plants, the patterned arrangement of aerial organs, or phyllotaxis, is instructed by the phytohormone auxin; however, it still remains to be seen how auxin is linked, at the apex, to the biochemical and mechanical changes of the cell wall required for organ outgrowth. Here, using Atomic Force Microscopy, we demonstrate that auxin reduces tissue rigidity prior to organ outgrowth in the shoot apex of Arabidopsis thaliana, and that the de-methyl-esterification of pectin is necessary for this reduction. We further show that development of functional organs produced by pectin-mediated ectopic wall softening requires auxin signaling. Lastly, we demonstrate that coordinated localization of the auxin transport protein, PIN1, is disrupted in a naked-apex produced by increasing cell wall rigidity. Our data indicates that a feedback loop between the instructive chemical auxin and cell wall mechanics may play a crucial role in phyllotactic patterning.

Pattern and process: competition causes regular spacing of individuals within plant populations

1 We used simulated and experimental plant populations to analyse mortality-driven pattern formation under size-dependent competition. Larger plants had an advantage under size-asymmetric but not under symmetric competition. Initial patterns were random or clumped. 2 The simulations were individual-based and spatially explicit. Size-dependent competition was modelled with different rules to partition overlapping zones of influence. 3 The experiment used genotypes of Arabidopsis thaliana with different morphological plasticity and hence size-dependent competition. Compared with wild types, transgenic individuals over-expressed phytochrome A and had decreased plasticity because of disabled phytochrome-mediated shade avoidance. Therefore, competition among transgenics was more asymmetric compared with wild-types. 4 Density-dependent mortality under symmetric competition did not substantially change the initial spatial pattern. Conversely, simulations under asymmetric competition and experimental patterns of transgenic over-expressors showed patterns of survivors that deviated substantially from random mortality independent of initial patterns. 5 Small-scale initial patterns of wild types were regular rather than random or clumped. We hypothesize that this small-scale regularity may be explained by early shade avoidance of seedlings in their cotyledon stage. 6 Our experimental results support predictions from an individual-based simulation model and support the conclusion that regular spatial patterns of surviving individuals should be interpreted as evidence for strong, asymmetric competitive interactions and subsequent density-dependent mortality.

Complex formation between stage-specific oocyte factors and a Xenopus mRNA localization element

It is a long-standing proposal that localization of maternal factors in eggs can provide the basis for pattern formation in the early embryo. The localized information can be stored as RNA, one example being Vg1 RNA, which is localized exclusively to the vegetal hemisphere of Xenopus oocytes and eggs. Localization of Vg1 mRNA is directed by a 340-nt sequence element contained within its 3′ untranslated region. To understand the mechanism of localization, I have tested whether factors from the oocyte interact specifically with the RNA localization sequence. Results presented here show that a set of oocyte proteins form complexes with the localization element both in vitro and in vivo. These proteins are specifically enriched in the stages of oogenesis during which localization occurs and recognize sub-elements of the RNA localization element that are essential for localization in vivo. These data suggest that formation of a localization-specific RNA–protein complex may be the first step in directing Vg1 mRNA to its subcellular destination.

Pattern generation by dissipative parametric instability

Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems, ranging from biology to galaxy buildup. We propose a new instability mechanism leading to pattern formation in spatially extended nonlinear systems, which is based on a periodic antiphase modulation of spectrally dependent losses arranged in a zigzag way: an effective filtering is imposed at symmetrically located wave numbers k and -k in alternating order. The properties of the dissipative parametric instability differ from the features of both key classical concepts of modulation instabilities, i.e., the Benjamin-Feir instability and the Faraday instabiltyity. We demonstrate how the dissipative parametric instability can lead to the formation of stable patterns in one- and two-dimensional systems. The proposed instability mechanism is generic and can naturally occur or can be implemented in various physical systems.

Interpersonal coordination tendencies, decision-making and information governing dynamics in rugby union

In this chapter, ideas from ecological psychology and nonlinear dynamics are integrated to characterise decision-making as an emergent property of self-organisation processes in the interpersonal interactions that occur in sports teams. A conceptual model is proposed to capture constraints on dynamics of decisions and actions in dyadic systems, which has been empirically evaluated in simulations of interpersonal interactions in team sports. For this purpose, co-adaptive interpersonal dynamics in team sports such as rubgy union have been studied to reveal control parameter and collective variable relations in attacker-defender dyads. Although interpersonal dynamics of attackers and defenders in 1 vs 1 situations showed characteristics of chaotic attractors, the informational constraints of rugby union typically bounded dyadic systems into low dimensional attractors. Our work suggests that the dynamics of attacker-defender dyads can be characterised as an evolving sequence since players' positioning and movements are connected in diverse ways over time.