4,410 research outputs found
Towards a more balanced understanding of motor control systems
Roberts's book provides a reasonably thorough guide to the physiology and biomechanics of balance, unfortunately the discussion of the neural and cognitive aspects of motor control is less satisfactory. We propose that Roberts's statement of the problem of balance control should be extended to include control of non-equilibrium states, and we discuss sensorimotor calibration and integration in the context of maturation of the organism.Peer reviewe
Spectral correlations in systems undergoing a transition from periodicity to disorder
We study the spectral statistics for extended yet finite quasi 1-d systems
which undergo a transition from periodicity to disorder. In particular we
compute the spectral two-point form factor, and the resulting expression
depends on the degree of disorder. It interpolates smoothly between the two
extreme limits -- the approach to Poissonian statistics in the (weakly)
disordered case, and the universal expressions derived for the periodic case.
The theoretical results agree very well with the spectral statistics obtained
numerically for chains of chaotic billiards and graphs.Comment: 16 pages, Late
Reduced Phase Space Quantization and Dirac Observables
In her recent work, Dittrich generalized Rovelli's idea of partial
observables to construct Dirac observables for constrained systems to the
general case of an arbitrary first class constraint algebra with structure
functions rather than structure constants. Here we use this framework and
propose a new way for how to implement explicitly a reduced phase space
quantization of a given system, at least in principle, without the need to
compute the gauge equivalence classes. The degree of practicality of this
programme depends on the choice of the partial observables involved. The
(multi-fingered) time evolution was shown to correspond to an automorphism on
the set of Dirac observables so generated and interesting representations of
the latter will be those for which a suitable preferred subgroup is realized
unitarily. We sketch how such a programme might look like for General
Relativity. We also observe that the ideas by Dittrich can be used in order to
generate constraints equivalent to those of the Hamiltonian constraints for
General Relativity such that they are spatially diffeomorphism invariant. This
has the important consequence that one can now quantize the new Hamiltonian
constraints on the partially reduced Hilbert space of spatially diffeomorphism
invariant states, just as for the recently proposed Master constraint
programme.Comment: 18 pages, no figure
Gauge invariant perturbations around symmetry reduced sectors of general relativity: applications to cosmology
We develop a gauge invariant canonical perturbation scheme for perturbations
around symmetry reduced sectors in generally covariant theories, such as
general relativity. The central objects of investigation are gauge invariant
observables which encode the dynamics of the system. We apply this scheme to
perturbations around a homogeneous and isotropic sector (cosmology) of general
relativity. The background variables of this homogeneous and isotropic sector
are treated fully dynamically which allows us to approximate the observables to
arbitrary high order in a self--consistent and fully gauge invariant manner.
Methods to compute these observables are given. The question of backreaction
effects of inhomogeneities onto a homogeneous and isotropic background can be
addressed in this framework. We illustrate the latter by considering
homogeneous but anisotropic Bianchi--I cosmologies as perturbations around a
homogeneous and isotropic sector.Comment: 39 pages, 1 figur
Holographic description of boundary gravitons in (3+1) dimensions
Gravity is uniquely situated in between classical topological field theories
and standard local field theories. This can be seen in the the quasi-local
nature of gravitational observables, but is nowhere more apparent than in
gravity's holographic formulation. Holography holds promise for simplifying
computations in quantum gravity. While holographic descriptions of
three-dimensional spacetimes and of spacetimes with a negative cosmological
constant are well-developed, a complete boundary description of zero curvature,
four-dimensional spacetime is not currently available. Building on previous
work in three-dimensions, we provide a new route to four-dimensional holography
and its boundary gravitons. Using Regge calculus linearized around a flat
Euclidean background with the topology of a solid hyper-torus, we obtain the
effective action for a dual boundary theory which describes the dynamics of the
boundary gravitons. Remarkably, in the continuum limit and at large radii this
boundary theory is local and closely analogous to the corresponding result in
three-dimensions. The boundary effective action has a degenerate kinetic term
that leads to singularities in the one-loop partition function that are
independent of the discretization. These results establish a rich boundary
dynamics for four-dimensional flat holography.Comment: 43 pages, 3 figures, 1 tabl
Curved planar quantum wires with Dirichlet and Neumann boundary conditions
We investigate the discrete spectrum of the Hamiltonian describing a quantum
particle living in the two-dimensional curved strip. We impose the Dirichlet
and Neumann boundary conditions on opposite sides of the strip. The existence
of the discrete eigenvalue below the essential spectrum threshold depends on
the sign of the total bending angle for the asymptotically straight strips.Comment: 7 page
From the discrete to the continuous - towards a cylindrically consistent dynamics
Discrete models usually represent approximations to continuum physics.
Cylindrical consistency provides a framework in which discretizations mirror
exactly the continuum limit. Being a standard tool for the kinematics of loop
quantum gravity we propose a coarse graining procedure that aims at
constructing a cylindrically consistent dynamics in the form of transition
amplitudes and Hamilton's principal functions. The coarse graining procedure,
which is motivated by tensor network renormalization methods, provides a
systematic approximation scheme towards this end. A crucial role in this coarse
graining scheme is played by embedding maps that allow the interpretation of
discrete boundary data as continuum configurations. These embedding maps should
be selected according to the dynamics of the system, as a choice of embedding
maps will determine a truncation of the renormalization flow.Comment: 22 page
Revisiting On-Line Discussion as Practice for Reflective Thinking in Three Sequential Classes
In a previous study, the authors questioned the potential of an on-line environment for increasing productive reflection in three sequential education classes. Of their findings, the issue of consistency stood out as particularly perplexing, namely, why did students exhibit high level reflections sometimes, but not all the time, in an on-line environment? In this follow-up study, the authors question whether in-class reflections coupled with on-line prompts could yield consistently high level pre-service teacher reflections, as measured by individual and class progress over time. This study also examines perceived relationships between the length of a student\u27s reflection and its productivity, as well as a student\u27s depth of focus and productivity. Using the same scoring approach as our previous study, our discussion of the results examines the usefulness of on-line environments for promoting consistently high level pre-service teacher reflection
A perturbative approach to Dirac observables and their space-time algebra
We introduce a general approximation scheme in order to calculate gauge
invariant observables in the canonical formulation of general relativity. Using
this scheme we will show how the observables and the dynamics of field theories
on a fixed background or equivalently the observables of the linearized theory
can be understood as an approximation to the observables in full general
relativity. Gauge invariant corrections can be calculated up to an arbitrary
high order and we will explicitly calculate the first non--trivial correction.
Furthermore we will make a first investigation into the Poisson algebra between
observables corresponding to fields at different space--time points and
consider the locality properties of the observables.Comment: 23 page
Using Technology to Develop Preservice Teachers\u27 Reflective Thinking
Developing high-level reflection skills proves troublesome for some preservice teachers. To examine the potential of an online environment for increasing productive reflection, students in three sequential undergraduate education classes responded to regular online prompts. We coded student comments for productive and unproductive reflection, knowledge integration, and analysis of the four aspects of teaching (learners and learning, subject matter knowledge, assessment and instruction ) as described by Davis, Bain, & Harrington (2001). We adapted a scoring approach recommended by Davis & Linn, (2000); Davis (2003) to analyze what aspects of teaching preservice teachers included, emphasized, and integrated when they reflected on their own beliefs about teaching. Discussion examines the utility of online environments for producing productive preservice teacher reflection
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