Transverse instability for non-normal parameters

We consider the behaviour of attractors near invariant subspaces on varying a parameter that does not preserve the dynamics in the invariant subspace but is otherwise generic, in a smooth dynamical system. We refer to such a parameter as ``non-normal''. If there is chaos in the invariant subspace that is not structurally stable, this has the effect of ``blurring out'' blowout bifurcations over a range of parameter values that we show can have positive measure in parameter space. Associated with such blowout bifurcations are bifurcations to attractors displaying a new type of intermittency that is phenomenologically similar to on-off intermittency, but where the intersection of the attractor by the invariant subspace is larger than a minimal attractor. The presence of distinct repelling and attracting invariant sets leads us to refer to this as ``in-out'' intermittency. Such behaviour cannot appear in systems where the transverse dynamics is a skew product over the system on the invariant subspace. We characterise in-out intermittency in terms of its structure in phase space and in terms of invariants of the dynamics obtained from a Markov model of the attractor. This model predicts a scaling of the length of laminar phases that is similar to that for on-off intermittency but which has some differences.Comment: 15 figures, submitted to Nonlinearity, the full paper available at http://www.maths.qmw.ac.uk/~eo

The Mental Demands and Coping Strategies of Professional Motocross Riders: A Qualitative Investigation

Professional motocross is one of the most physically and mentally demanding of sports. Riders often have to simultaneously execute various motor and cognitive tasks while remaining in a calm and focused state. The only published study suggests that detailed pre-performance planning and mental rehearsal are essential when developing motocross athlete’s performance (Collins, Doherty, & Talbot, 1993). While there has been a good deal of information regarding how elite athletes in other sports like figure skating (Gould, Jackson, & Finch, 1993b), wrestling (Gould, Eklund, & Jackson, 1992), and the decathlon (Dale, 2000) deal with the mental demands of their sport, there has been no opportunity for motocross athletes to articulate the mental factors they experience both on and off the track. Therefore, the purpose of this study was to gain an in-depth, comprehensive understanding of professional motocross riders’ experience of the mental demands and coping strategies of their sport. More specifically, an attempt was made to gain a greater understanding of how professional motocross riders view the word “mental demands” as well as how this perspective influences their mindset during practice, competition, around teammates and friends and family. To achieve this purpose, the following questions guided the research: (a) what do they think are some of the mental demands related to being a professional motocross rider?; (b) at what times/when do they experience these mental demands?; and (c) how to they cope with the mental demands that they experience, both on and off the motocross track? Answers to these questions were obtained from seven professional motocross riders who participated in semi-structured interview sessions. Four themes were derived from the interpretive analysis dealing with the athletes’ mental demands. They included: (a) the racing environment; (b) the nature of the sport; (c) expectations; and (d) relationship with others. Three themes representing coping strategies used by the professional motocross riders also emerged. They included: (a) thought control; (b) staying focused; and (c) emotional control. Discussion centered on the consistency of the results with the current sport literature. Finally, implications for sport psychology consultants, riders, and researchers are offered

Chimera states in networks of phase oscillators: the case of two small populations

Chimera states are dynamical patterns in networks of coupled oscillators in which regions of synchronous and asynchronous oscillation coexist. Although these states are typically observed in large ensembles of oscillators and analyzed in the continuum limit, chimeras may also occur in systems with finite (and small) numbers of oscillators. Focusing on networks of $2N$ phase oscillators that are organized in two groups, we find that chimera states, corresponding to attracting periodic orbits, appear with as few as two oscillators per group and demonstrate that for $N>2$ the bifurcations that create them are analogous to those observed in the continuum limit. These findings suggest that chimeras, which bear striking similarities to dynamical patterns in nature, are observable and robust in small networks that are relevant to a variety of real-world systems.Comment: 13 pages, 16 figure

The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability

We study the dynamics arising when two identical oscillators are coupled near a Hopf bifurcation where we assume a parameter $\epsilon$ uncouples the system at $\epsilon=0$. Using a normal form for $N=2$ identical systems undergoing Hopf bifurcation, we explore the dynamical properties. Matching the normal form coefficients to a coupled Wilson-Cowan oscillator network gives an understanding of different types of behaviour that arise in a model of perceptual bistability. Notably, we find bistability between in-phase and anti-phase solutions that demonstrates the feasibility for synchronisation to act as the mechanism by which periodic inputs can be segregated (rather than via strong inhibitory coupling, as in existing models). Using numerical continuation we confirm our theoretical analysis for small coupling strength and explore the bifurcation diagrams for large coupling strength, where the normal form approximation breaks down

Optimal Radiometric Calibration for Camera-Display Communication

We present a novel method for communicating between a camera and display by embedding and recovering hidden and dynamic information within a displayed image. A handheld camera pointed at the display can receive not only the display image, but also the underlying message. These active scenes are fundamentally different from traditional passive scenes like QR codes because image formation is based on display emittance, not surface reflectance. Detecting and decoding the message requires careful photometric modeling for computational message recovery. Unlike standard watermarking and steganography methods that lie outside the domain of computer vision, our message recovery algorithm uses illumination to optically communicate hidden messages in real world scenes. The key innovation of our approach is an algorithm that performs simultaneous radiometric calibration and message recovery in one convex optimization problem. By modeling the photometry of the system using a camera-display transfer function (CDTF), we derive a physics-based kernel function for support vector machine classification. We demonstrate that our method of optimal online radiometric calibration (OORC) leads to an efficient and robust algorithm for computational messaging between nine commercial cameras and displays.Comment: 10 pages, Submitted to CVPR 201