Vanishing Twist in the Hamiltonian Hopf Bifurcation

The Hamiltonian Hopf bifurcation has an integrable normal form that describes the passage of the eigenvalues of an equilibrium through the 1: -1 resonance. At the bifurcation the pure imaginary eigenvalues of the elliptic equilibrium turn into a complex quadruplet of eigenvalues and the equilibrium becomes a linearly unstable focus-focus point. We explicitly calculate the frequency map of the integrable normal form, in particular we obtain the rotation number as a function on the image of the energy-momentum map in the case where the fibres are compact. We prove that the isoenergetic non-degeneracy condition of the KAM theorem is violated on a curve passing through the focus-focus point in the image of the energy-momentum map. This is equivalent to the vanishing of twist in a Poincar\'e map for each energy near that of the focus-focus point. In addition we show that in a family of periodic orbits (the non-linear normal modes) the twist also vanishes. These results imply the existence of all the unusual dynamical phenomena associated to non-twist maps near the Hamiltonian Hopf bifurcation.Comment: 18 pages, 4 figure

Normal Forms for Symplectic Maps with Twist Singularities

We derive a normal form for a near-integrable, four-dimensional symplectic map with a fold or cusp singularity in its frequency mapping. The normal form is obtained for when the frequency is near a resonance and the mapping is approximately given by the time-$T$ mapping of a two-degree-of freedom Hamiltonian flow. Consequently there is an energy-like invariant. The fold Hamiltonian is similar to the well-studied, one-degree-of freedom case but is essentially nonintegrable when the direction of the singular curve in action does not coincide with curves of the resonance module. We show that many familiar features, such as multiple island chains and reconnecting invariant manifolds, are retained even in this case. The cusp Hamiltonian has an essential coupling between its two degrees of freedom even when the singular set is aligned with the resonance module. Using averaging, we approximately reduced this case to one degree of freedom as well. The resulting Hamiltonian and its perturbation with small cusp-angle is analyzed in detail.Comment: LaTex, 27 pages, 21 figure

Reward, learning and games

The link between reward and learning has chiefly been studied scientifically in the context of reinforcement learning. This type of learning, which relies upon midbrain dopaminergic response, differs greatly from the learning valued by educators, which typically involves declarative memory formation. However, with recent insights regarding the modulation of hippocampal function by midbrain dopamine, scientific understanding of the midbrain response to reward may be becoming more relevant to education. Here, we consider the potential for our current understanding of reward to inform educational learning, and consider its implications for game-like interventions in the classroom

Surgical versus nonsurgical therapy for lumbar spinal stenosis.

BACKGROUND: Surgery for spinal stenosis is widely performed, but its effectiveness as compared with nonsurgical treatment has not been shown in controlled trials. METHODS: Surgical candidates with a history of at least 12 weeks of symptoms and spinal stenosis without spondylolisthesis (as confirmed on imaging) were enrolled in either a randomized cohort or an observational cohort at 13 U.S. spine clinics. Treatment was decompressive surgery or usual nonsurgical care. The primary outcomes were measures of bodily pain and physical function on the Medical Outcomes Study 36-item Short-Form General Health Survey (SF-36) and the modified Oswestry Disability Index at 6 weeks, 3 months, 6 months, and 1 and 2 years. RESULTS: A total of 289 patients were enrolled in the randomized cohort, and 365 patients were enrolled in the observational cohort. At 2 years, 67% of patients who were randomly assigned to surgery had undergone surgery, whereas 43% of those who were randomly assigned to receive nonsurgical care had also undergone surgery. Despite the high level of nonadherence, the intention-to-treat analysis of the randomized cohort showed a significant treatment effect favoring surgery on the SF-36 scale for bodily pain, with a mean difference in change from baseline of 7.8 (95% confidence interval, 1.5 to 14.1); however, there was no significant difference in scores on physical function or on the Oswestry Disability Index. The as-treated analysis, which combined both cohorts and was adjusted for potential confounders, showed a significant advantage for surgery by 3 months for all primary outcomes; these changes remained significant at 2 years. CONCLUSIONS: In the combined as-treated analysis, patients who underwent surgery showed significantly more improvement in all primary outcomes than did patients who were treated nonsurgically. (ClinicalTrials.gov number, NCT00000411 [ClinicalTrials.gov].)

College Students’ Responses to Antismoking Messages: Denial, Defiance, and Other Boomerang Effects

Despite the success of antismoking campaigns that aim to prevent young teens from smoking, this qualitative study provides strong evidence that different initiatives are needed for college students, particularly those who already smoke. When asked for responses to current antismoking messages, nonsmokers generally championed the cause; however, smokers often responded with anger, defiance, denial, and other negative responses. Consumers who respond in this manner are not well served by existing strategies, and money used for such campaigns could be better spent. New strategies are offered in hopes that antismoking campaigns can communicate more effectively with one high-risk group—college student smokers

Gamification of learning deactivates the Default Mode Network

We hypothesised that embedding educational learning in a game would improve learning outcomes, with increased engagement and recruitment of cognitive resources evidenced by increased activation of working memory network (WMN) and deactivation of Default Mode Network (DMN) regions. In an fMRI study, we compared activity during periods of learning in three conditions that were increasingly game-like: Study-only (when periods of learning were followed by an exemplar question together with its correct answer), Self-quizzing (when periods of learning were followed by a multiple choice question in return for a fixed number of points) and Game-based (when, following each period of learning, participants competed with a peer to answer the question for escalating, uncertain rewards). DMN hubs deactivated as conditions became more game-like, alongside greater self-reported engagement and, in the Game-based condition, higher learning scores. These changes did not occur with any detectable increase in WMN activity. Additionally, ventral striatal activation was associated with responding to questions and receiving positive question feedback. Results support the significance of DMN deactivation for educational learning, and are aligned with recent evidence suggesting DMN and WMN activity may not always be anti-correlated

Getting It on Record: Issues and Strategies for Ethnographic Practice in Recording Studios

The recording studio has been somewhat neglected as a site for ethnographic fieldwork in the field of ethno-musicology and, moreover, the majority of published studies tend to overlook the specific concerns faced by the researcher within these contexts. Music recording studios can be places of creativity, artistry, and collaboration, but they often also involve challenging, intimidating, and fractious relations. Given that recording studios are, first and foremost, concerned with documenting musicians’ performances, we discuss the concerns of getting studio interactions “on record” in terms of access, social relations, and methods of data collection. This article reflects on some of the issues we faced when conducting our fieldwork within British music recording facilities and makes suggestions based on strategies that we employed to address these issues

Operational approach to open dynamics and quantifying initial correlations

A central aim of physics is to describe the dynamics of physical systems. Schrodinger's equation does this for isolated quantum systems. Describing the time evolution of a quantum system that interacts with its environment, in its most general form, has proved to be difficult because the dynamics is dependent on the state of the environment and the correlations with it. For discrete processes, such as quantum gates or chemical reactions, quantum process tomography provides the complete description of the dynamics, provided that the initial states of the system and the environment are independent of each other. However, many physical systems are correlated with the environment at the beginning of the experiment. Here, we give a prescription of quantum process tomography that yields the complete description of the dynamics of the system even when the initial correlations are present. Surprisingly, our method also gives quantitative expressions for the initial correlation.Comment: Completely re-written for clarity of presentation. 15 pages and 2 figure

Achieving the impossible : A review of magic-based interventions and their effects on wellbeing

Research has demonstrated that involvement with mainstream performing arts, such as music and dance, can boost wellbeing. This article extends this work by reviewing little-known research on whether learning magic tricks can have an equally beneficial effect. We first present an historic overview of several magic-based interventions created by magicians, psychologists and occupational therapists. We then identify the potential benefits of such interventions, and review studies that have attempted to systematically assess these interventions. The studies have mostly revealed beneficial outcomes, but much of the work is of poor methodological quality (involving small numbers of participants and no control group), and has tended to focus on clinical populations. Finally, we present guidelines for future research in the area, emphasizing the need for more systematic and better-controlled studies.Peer reviewe