Dynamical Systems

"Given a compact group G, a standard construction of a Z^2 Markov shift Sigma_G with alphabet G is described. The cardinality of G (if G is finite) or the topological dimension of G (if G is a torus) is shown to be an invariant of measurable isomorphism for Sigma_G. We show that if G is sufficiently non-abelian (for instance A_5, PSL_2(F_7), or a Suzuki simple group) and H is any abelian group with |H| = |G|, then Sigma_G and Sigma_H are not isomorphic. Thus the cardinality of G is seen to be necessary but not sufficient to determine the measurable structure of Sigma_G.
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We studied the spatio-temporal characteristics of cortical activity in early visual areas and the fusiform gyri (FG) by means of magnetoencephalography (MEG) while subjects performed a visual classification task. Letters and visually similar pseudo-letters were presented in different surrounds and under different task demands. The stimuli appeared in a cued half of the visual field (VF). We observed pre-stimulus effects on amplitudes in V1 and Cuneus relating to VF and task demands, suggesting a combination of active anticipation and specialized routing of activity in visual processing. Amplitudes in the right FG between 150 and 350 ms after stimulus onset reflected task demands, while those in the left FG between 300 and 400 ms showed selectivity for graphemes. The contrasting stimulus-evoked effects in the right and left FG show that the former area is sensitive to task demands irrespective of stimulus content, whereas the left FG is sensitive to stimulus content irrespectively of task demand.

Mobility issues are the typical sequelae of “tunnel vision” (severe peripheral visual field loss), and manifest in the difficulty patients have detecting and avoiding obstacles during locomotion. We examined the behavior of seven patients with tunnel vision (6 ̊-27 ̊ visual fields) and six normally sighted individuals as they walked toward a visible goal in a virtual environment with or without an obstacle present. Each obstacle was a pole 1.8m tall and either stationary or moving across the path of the participant. Stationary obstacles appeared at a distance of 4 or 6m and an angle of 1 ̊ from the path to the goal. The moving obstacles crossed the participant’s path at 4 or 6m while moving at a constant speed (50%, 70% or 90% of the participant’s preferred walking speed). All obstacles appeared after participants walked 1m, and participants pressed a button when they detected an obstacle. Based on detection rates for short 1.2m obstacles (Kiefer et al., 2012), the patients were divided into two subgroups: (1) a low-detection group and (2) a high-detection group. We simulated individual locomotor trajectories using Fajen & Warren’s (2003) steering dynamics model. RMSE between the model and human heading time series revealed no significant differences between the normally sighted (M = 0.28 ̊ +/- 0.01 ̊), low-detection (M = 0.36 ̊ +/- 0.04 ̊) and high-detection (M = 0.30 ̊ +/- 0.03 ̊) groups with stationary obstacles; simulations with moving obstacles are ongoing. There was a trend toward greater variability in RMSE for both patient groups compared to the normally sighted group. The results indicate that tunnel vision patients have different detection strategies (Kiefer et al.), but once an obstacle is detected their locomotor behavior is similar to normally sighted pedestrians. Patients appear to exhibit noisier trajectories, perhaps due to difficulty tracking the obstacle as they fixate and steer toward the goal.

"We present a novel synchronization scheme for secure communication with two chaotic unidirectionally coupled Rössler circuits. The circuits are synchronized via one of the
variables, while a signal is transmitted through another variable. We show that this scheme allows more stable communications. The system dynamics is studied numerically and experimentally in a wide range of a control parameter. The possibility of secure
communications with an audio signal is demonstrated."

The article first describes characteristics of major infrastructure projects. Second, it documents a much neglected topic in economics: that ex ante estimates of costs and benefits are often very different from actual ex post costs and benefits. For large infrastructure projects the consequences are cost overruns, benefit shortfalls, and the systematic underestimation of risks. Third, implications for cost–benefit analysis are described, including that such analysis is not to be trusted for major infrastructure projects. Fourth, the article uncovers the causes of this state of affairs in terms of perverse incentives that encourage promoters to underestimate costs and overestimate benefits in the business cases for their projects. But the projects that are made to look best on paper are the projects that amass the highest cost overruns and benefit shortfalls in reality. The article depicts this situation as ‘survival of the unfittest’. Fifth, the article sets out to explain how the problem may be solved, with a view to arriving at more efficient and more democratic projects, and avoiding the scandals that often accompany major infrastructure investments. Finally, the article identifies current trends in major infrastructure development. It is argued that a rapid increase in stimulus spending, combined with more investments in emerging economies, combined with more spending on information technology is catapulting infrastructure investment from the frying pan into the fire.

We propose a general strategy for determining the minimal finite amplitude disturbance to trigger transition to turbulence in shear flows. This involves constructing a variational problem that searches over all disturbances of fixed initial amplitude, which respect the boundary conditions, incompressibility and the Navier--Stokes equations, to maximise a chosen functional over an asymptotically long time period. The functional must be selected such that it identifies turbulent velocity fields by taking significantly enhanced values compared to those for laminar fields. We illustrate this approach using the ratio of the final to initial perturbation kinetic energies (energy growth) as the functional and the energy norm to measure amplitudes in the context of pipe flow. Our results indicate that the variational problem yields a smooth converged solution providing the amplitude is below the threshold amplitude for transition. This optimal is the nonlinear analogue of the well-studied (linear) transient growth optimal. At and above this threshold, the optimising search naturally seeks out disturbances that trigger turbulence by the end of the period, and convergence is then practically impossible. The first disturbance found to trigger turbulence as the amplitude is increased identifies the `minimal seed' for the given geometry and forcing (Reynolds number). We conjecture that it may be possible to select a functional such that the converged optimal below threshold smoothly converges to the minimal seed at threshold.  This seems at least approximately true for our choice of energy growth functional and the pipe flow geometry chosen here.

"""Metacognition traditionally has been conceptualized as a form of higher-order thought that requires metarepresentation, logical reasoning, self-consciousness, and introspective access to
knowledge states. Thinking of metacognition along these lines precludes metacognition in nonhuman animals, preverbal human infants, and subjects with certain cognitive and neurophysiological impairments. Recent experimental evidence of implicit metacognitive skills in nonhuman primates, human infants, and human adults show the need for a broad concept of metacognition, based in what metacognition does, i.e., its operative function, instead of theoretical hypotheses about what it is, i.e., its nature. Such a concept would permit unbiased cross-disciplinary investigations of the evolution and development of metacognition. Presenting a new theoretical and conceptual framework for investigating implicit and perceptual forms of metacognition, the article explores the claim that metacognition has its developmental origin in primary intersubjectivity. The claim has implications for research on metacognition in comparative psychology, cognitive science, and related disciplines. It is argued that basic metacognitive skills start to develop from 2 months of age in episodes of turn-taking between infant and caregiver. Infants initially acquire the means for joint monitoring and control of the interaction with the caregiver. Later  metacognitive development is a function of the quality and quantity of the stimulation during this period. Turn-taking is
apt for scaffolding metacognitive growth because, first, monitoring and control of cognition is integral to it, second, it enables learning and training of epistemic actions that realize
monitoring and control functions, and third, feedback is immediate."""

Linguists tend to view language in terms of forms and their use. For historical reasons, speaking and listening have often often ascribed to knowledge of a language system. Language behavior is thus seen as the production and processing of forms. Others contrast language to man-made codes (see Kravchenko, 2007; Love, 2004). Instead of focusing on forms, language can be conceived of as action and, as such, both dynamic and symbolic (Raczaszek-Leonardi, 2009). History places us in a meshwork where public resources of language, among other things, contribute to games, mashing beans, and watching television. Speaking-while-hearing draws on cultural products (e.g., axes, social roles, pictures, and wordings). As we collaborate, we orient to wordings or repeated (and systematized) aspects of vocalizations that, within our community, carry historically derived information. Pursuing this view, it is argued that hearing “words” is like seeing “things” in pictures. This is described as taking a language stance. To defend the position, it is argued that, first, we learn to hear wordings and, later, to use “what we hear” as ways of constraining our actions. Far from depending on individual knowledge, orienting to wordings makes language irreducibly collective.

Overhead cranes are widely used in industry for transportation of heavy loads. The natural sway of crane payloads is detrimental to safe and efficient operation. However, the crane acceleration, required for motion, always induces undesirable load swing. This paper presents dynamic modelling of a 3-D overhead gantry crane system based on closed-form equations of motion. The Lagrangian method is used to derive the dynamic model of the system. A dynamic model of the system incorporating payload and rope length is developed. Then the effects of payload and rope length on the response of the system are discussed. Extensive results that validate the theoretical derivation are presented in the time and frequency domains.

Various results are presented here: First, a simple but formal measure-theoretic construction of the derivative is given, making it clear that it has a very concrete existence as a Lebesgue-Stieltjes measure, and thus is safe to manipulate in various familiar ways. Next, an exact result is given, expressing the measure as an infinite product of piece-wise continuous functions, with each piece being a Mobius transform of the form (ax+b)/(cx+d). This construction is then shown to be the Haar measure of a certain transfer operator. A general proof is given that any transfer operator can be understood to be nothing more nor less than a push-forward on a Banach space; such push-forwards induce an invariant measure, the Haar measure, of which the Minkowski measure can serve as a prototypical example. Some minor notes pertaining to it's relation to the Gauss-Kuzmin-Wirsing operator are made.