On Linearizing Systems of Diffusion Equations

We consider systems of diffusion equations that have considerable interest in Soil Science and Mathematical Biology and focus upon the problem of finding those forms of this class that can be linearized. In particular we use the equivalence transformations of the second generation potential system to derive forms of this system that can be linearized. In turn, these transformations lead to nonlocal mappings that linearize the original system.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Exploration of Sensemaking in the Education of Novices to the Complex Cognitive Work Domain of Air Traffic Control

Many current complex business and industry jobs consist primarily of cognitive work; however, current approaches to training may be inadequate for this type of work (Hoffman, Feltovich, Fiore, Klein, & Ziebell, 2009). To try and improve training and education for cognitive work, Klein and Baxter (2006) have proposed cognitive transformation theory (CTT), a learning theory that claims that sensemaking activities are essential for acquiring expertise that is adaptive and thus well suited for cognitive work domains. In the present research, cognitive task analysis methods were used to identify and assess sensemaking support in the instruction and learning of complex concepts by two experienced air traffic control professors and seven of their students. The goal of this research was to compare instructional strategies used in an academic setting with the predictions of CTT to gain insight into strategies for the application of CTT. Cognitive task analysis methods employed included course observation, artifact examination, and knowledge elicitation sessions with two professors and seven of their students. Knowledge elicitation transcriptions were coded using categories derived from CTT and the data/frame theory of sensemaking (e.g. Klein, Moon, & Hoffman, 2006; Sieck, Klein, Peluso, Smith, & Harris-Thompson, 2007) to assess theoretical and applied implications for learning and instruction in a complex domain. Findings are represented by synthesizing theory driven predictions with grounded training strategies and technologies. In addition, recommendations are advanced for applying CTT to training and educational systems in order to provide sensemaking support during early phases of learning from which expertise may be developed

Fractal Bubble Cosmology: A concordant cosmological model?

The Fractal Bubble model has been proposed as a viable cosmology that does not require dark energy to account for cosmic acceleration, but rather attributes its observational signature to the formation of structure. In this paper it is demonstrated that, in contrast to previous findings, this model is not a good fit to cosmological supernovae data; there is significant tension in the best fit parameters obtained from different samples, whereas LCDM is able to fit all datasets consistently. Furthermore, the concordance between galaxy clustering scales and data from the cosmic microwave background is not achieved with the most recent supernova compilations. The validity of the FB formalism as a sound cosmological model is further challenged as it is shown that previous studies of this model achieve concordance by requiring a value for the present day Hubble constant that is derived from supernovae data containing an arbitrary distance normalisation.Comment: 6 pages, 3 figures, revised version published in MNRAS letter

Imaging the Near Field

In an earlier paper we introduced the concept of the perfect lens which focuses both near and far electromagnetic fields, hence attaining perfect resolution. Here we consider refinements of the original prescription designed to overcome the limitations of imperfect materials. In particular we show that a multi-layer stack of positive and negative refractive media is less sensitive to imperfections. It has the novel property of behaving like a fibre-optic bundle but one that acts on the near field, not just the radiative component. The effects of retardation are included and minimized by making the slabs thinner. Absorption then dominates image resolution in the near-field. The deleterious effects of absorption in the metal are reduced for thinner layers.Comment: RevTeX, (9 pages, 8 figures

Robertson-Walker fluid sources endowed with rotation characterised by quadratic terms in angular velocity parameter

Einstein's equations for a Robertson-Walker fluid source endowed with rotation Einstein's equations for a Robertson-Walker fluid source endowed with rotation are presented upto and including quadratic terms in angular velocity parameter. A family of analytic solutions are obtained for the case in which the source angular velocity is purely time-dependent. A subclass of solutions is presented which merge smoothly to homogeneous rotating and non-rotating central sources. The particular solution for dust endowed with rotation is presented. In all cases explicit expressions, depending sinusoidally on polar angle, are given for the density and internal supporting pressure of the rotating source. In addition to the non-zero axial velocity of the fluid particles it is shown that there is also a radial component of velocity which vanishes only at the poles. The velocity four-vector has a zero component between poles

Collaborative Creativity:Information-Driven Coordination Dynamics and Prediction in Movement and Musical Improvisation

Humans collaborate with a large number of people in order to create and accomplish incredible feats. We argue that rich coordination dynamics underpin our capacity for collaborative creativity. These dynamics characterize the ways in which people are able to covary their thoughts, actions, behavior, etc. for functional purposes. We investigated the coordination dynamics of improvisation as a special case of collaborative creativity using two openly available data sets: a movement-based mirror game and jazz piano improvisation. By focusing on improvisation, the tasks elicit the need for real-time adaptation and mutual prediction based on information exchange between interacting individuals, with the creative ‘product’ being the behavioral performance itself. For each data set, we performed a transfer entropy analysis as well as an estimate of prediction decay. The combination of these two methods allows us to understand the dynamics as information-driven coordination flow and to differentiate unidirectional influence from mutual influence as well as the predictability of signals exhibited during collaborative creativity. We observed that for the mirror game, experts and novices exhibited unidirectional and bidirectional influence on each other’s movements largely independent of their improvisational experience level. Further, movement improvisation signals generated by experts were generally more predictable than those of novices. In terms of the jazz improvisation, our results showed evidence of bidirectional influence between the onset densities of coupled and one-way improvisational dyads, and the predictability of the signal did not vary systematically across these conditions. We discuss these findings in terms of differences between improvisational contexts, methodical challenges, and future directions

Collaborative Creativity:Information-Driven Coordination Dynamics and Prediction in Movement and Musical Improvisation

Humans collaborate with a large number of people in order to create and accomplish incredible feats. We argue that rich coordination dynamics underpin our capacity for collaborative creativity. These dynamics characterize the ways in which people are able to covary their thoughts, actions, behavior, etc. for functional purposes. We investigated the coordination dynamics of improvisation as a special case of collaborative creativity using two openly available data sets: a movement-based mirror game and jazz piano improvisation. By focusing on improvisation, the tasks elicit the need for real-time adaptation and mutual prediction based on information exchange between interacting individuals, with the creative ‘product’ being the behavioral performance itself. For each data set, we performed a transfer entropy analysis as well as an estimate of prediction decay. The combination of these two methods allows us to understand the dynamics as information-driven coordination flow and to differentiate unidirectional influence from mutual influence as well as the predictability of signals exhibited during collaborative creativity. We observed that for the mirror game, experts and novices exhibited unidirectional and bidirectional influence on each other’s movements largely independent of their improvisational experience level. Further, movement improvisation signals generated by experts were generally more predictable than those of novices. In terms of the jazz improvisation, our results showed evidence of bidirectional influence between the onset densities of coupled and one-way improvisational dyads, and the predictability of the signal did not vary systematically across these conditions. We discuss these findings in terms of differences between improvisational contexts, methodical challenges, and future directions

Charged Dilaton Black Holes with a Cosmological Constant

The properties of static spherically symmetric black holes, which are either electrically or magnetically charged, and which are coupled to the dilaton in the presence of a cosmological constant, are considered. It is shown that such solutions do not exist if the cosmological constant is positive (in arbitrary spacetime dimension >= 4). However, asymptotically anti-de Sitter black hole solutions with a single horizon do exist if the cosmological constant is negative. These solutions are studied numerically in four dimensions and the thermodynamic properties of the solutions are derived. The extreme solutions are found to have zero entropy and infinite temperature for all non-zero values of the dilaton coupling constant.Comment: 12 pages, epsf, phyzzx, 4 in-text figures incl. (minor typos fixed, 1 reference added

Team Interaction Dynamics during Collaborative Problem Solving

The need for better understanding collaborative problem solving (CPS) is rising in prominence as many organizations are increasingly addressing complex problems requiring the combination of diverse sets of individual expertise to address novel situations. This research draws from theoretical and empirical work that describes the knowledge coordination arising from team communications during CPS and builds from this by incorporating methods to study interaction dynamics. Interaction between team members in such contexts is inherently dynamic and exhibits nonlinear patterns not accounted for by extant research methods. To redress this gap, the present study draws from methods designed to study social and team interaction as a nonlinear dynamical system. CPS was examined by studying knowledge building and interaction processes of 43 dyads working to solve NASA’s Moonbase Alpha simulation. Specifically, frame-differencing, an automated video analysis technique, was used to capture the bodily movements of participants and content coding was applied to the teams’ communications to characterize their CPS processes. A combination of linear and nonlinear analytic and modeling techniques were applied to quantify and predict CPS performance based on the observed interaction dynamics and other individual differences. We hypothesized that teams exhibiting synchronization in their bodily movements and complementarity in their communications would produce better problem solving outcomes. The present research advances theory and empirical knowledge on effective team interaction during CPS and provides practical guidance on methods that can be used to observe and quantify interaction dynamics during CPS in complex work domains

Dynamical coherent states and physical solutions of quantum cosmological bounces

A new model is studied which describes the quantum behavior of transitions through an isotropic quantum cosmological bounce in loop quantum cosmology sourced by a free and massless scalar field. As an exactly solvable model even at the quantum level, it illustrates properties of dynamical coherent states and provides the basis for a systematic perturbation theory of loop quantum gravity. The detailed analysis is remarkably different from what is known for harmonic oscillator coherent states. Results are evaluated with regard to their implications in cosmology, including a demonstration that in general quantum fluctuations before and after the bounce are unrelated. Thus, even within this solvable model the condition of classicality at late times does not imply classicality at early times before the bounce without further assumptions. Nevertheless, the quantum state does evolve deterministically through the bounce.Comment: 30 pages, 3 figure