1,199 research outputs found
The Effects of Early Technology Use on the Development of Young Children
With technology becoming a prevalent part of daily life, early childhood experts, teachers, and parents have concerns as to what is appropriate for young children to do and use. Research shows both benefits and potential risks associated with technology use. Benefits can include enhanced creativity and collaboration with peers and adults, literacy achievement gains, language and vocabulary development, and opportunities for independence. These benefits generally occur in purposeful situations with developmentally appropriate educational content alongside adult guidance and scaffolding. Risks include health factors, cognitive and behavioral challenges, displacement of traditional developmental activities, and fewer personal interactions. These risks are more prevalent when technology is used in passive manner, with violent or aggressive content, or with developmentally inappropriate requirements. Teachers and parents have a vast amount of research to educate themselves on best practices in the classroom and at home from experts in the medical and early childhood fields. However, in the grand scheme, technology is a fairly new topic to be researched and more time is needed to understand the long term effects
Computing the bounded subcomplex of an unbounded polyhedron
We study efficient combinatorial algorithms to produce the Hasse diagram of
the poset of bounded faces of an unbounded polyhedron, given vertex-facet
incidences. We also discuss the special case of simple polyhedra and present
computational results.Comment: 16 page
A Perturbative Approach to the Relativistic Harmonic Oscillator
A quantum realization of the Relativistic Harmonic Oscillator is realized in
terms of the spatial variable and {\d\over \d x} (the minimal canonical
representation). The eigenstates of the Hamiltonian operator are found (at
lower order) by using a perturbation expansion in the constant . Unlike
the Foldy-Wouthuysen transformed version of the relativistic hydrogen atom,
conventional perturbation theory cannot be applied and a perturbation of the
scalar product itself is required.Comment: 9 pages, latex, no figure
Nonlocality as a Benchmark for Universal Quantum Computation in Ising Anyon Topological Quantum Computers
An obstacle affecting any proposal for a topological quantum computer based
on Ising anyons is that quasiparticle braiding can only implement a finite
(non-universal) set of quantum operations. The computational power of this
restricted set of operations (often called stabilizer operations) has been
studied in quantum information theory, and it is known that no
quantum-computational advantage can be obtained without the help of an
additional non-stabilizer operation. Similarly, a bipartite two-qubit system
based on Ising anyons cannot exhibit non-locality (in the sense of violating a
Bell inequality) when only topologically protected stabilizer operations are
performed. To produce correlations that cannot be described by a local hidden
variable model again requires the use of a non-stabilizer operation. Using
geometric techniques, we relate the sets of operations that enable universal
quantum computing (UQC) with those that enable violation of a Bell inequality.
Motivated by the fact that non-stabilizer operations are expected to be highly
imperfect, our aim is to provide a benchmark for identifying UQC-enabling
operations that is both experimentally practical and conceptually simple. We
show that any (noisy) single-qubit non-stabilizer operation that, together with
perfect stabilizer operations, enables violation of the simplest two-qubit Bell
inequality can also be used to enable UQC. This benchmarking requires finding
the expectation values of two distinct Pauli measurements on each qubit of a
bipartite system.Comment: 12 pages, 2 figure
Bell inequalities stronger than the CHSH inequality for 3-level isotropic states
We show that some two-party Bell inequalities with two-valued observables are
stronger than the CHSH inequality for 3 \otimes 3 isotropic states in the sense
that they are violated by some isotropic states in the 3 \otimes 3 system that
do not violate the CHSH inequality. These Bell inequalities are obtained by
applying triangular elimination to the list of known facet inequalities of the
cut polytope on nine points. This gives a partial solution to an open problem
posed by Collins and Gisin. The results of numerical optimization suggest that
they are candidates for being stronger than the I_3322 Bell inequality for 3
\otimes 3 isotropic states. On the other hand, we found no Bell inequalities
stronger than the CHSH inequality for 2 \otimes 2 isotropic states. In
addition, we illustrate an inclusion relation among some Bell inequalities
derived by triangular elimination.Comment: 9 pages, 1 figure. v2: organization improved; less references to the
cut polytope to make the main results clear; references added; typos
corrected; typesetting style change
Spatial curvature at the sound horizon
The effect of spatial curvature on primordial perturbations is controlled by ΩK,0/cs2 , where ΩK,0 is today's fractional density of spatial curvature and cs is the speed of sound during inflation. Here we study these effects in the limit cs≪ 1 . First, we show that the standard cosmological soft theorems in flat universes are violated in curved universes and the soft limits of correlators can have non-universal contributions even in single-clock inflation. This is a consequence of the fact that, in the presence of spatial curvature, there is a gap between the spectrum of residual diffeomorphisms and that of physical modes. Second, there are curvature corrections to primordial correlators, which are not scale invariant. We provide explicit formulae for these corrections to the power spectrum and the bispectrum to linear order in curvature in single-clock inflation. We show that the large-scale CMB anisotropies could provide interesting new constraints on these curvature effects, and therefore on ΩK,0/cs2 , but it is necessary to go beyond our linear-order treatment
Spacetime structure of the global vortex
We analyse the spacetime structure of the global vortex and its maximal
analytic extension in an arbitrary number of spacetime dimensions. We find that
the vortex compactifies space on the scale of the Hubble expansion of its
worldvolume, in a manner reminiscent of that of the domain wall. We calculate
the effective volume of this compactification and remark on its relevance to
hierarchy resolution with extra dimensions. We also consider strongly
gravitating vortices and derive bounds on the existence of a global vortex
solution.Comment: 19 pages revtex, 2 figures, minor changes, references adde
Noise Thresholds for Higher Dimensional Systems using the Discrete Wigner Function
For a quantum computer acting on d-dimensional systems, we analyze the
computational power of circuits wherein stabilizer operations are perfect and
we allow access to imperfect non-stabilizer states or operations. If the noise
rate affecting the non-stabilizer resource is sufficiently high, then these
states and operations can become simulable in the sense of the Gottesman-Knill
theorem, reducing the overall power of the circuit to no better than classical.
In this paper we find the depolarizing noise rate at which this happens, and
consequently the most robust non-stabilizer states and non-Clifford gates. In
doing so, we make use of the discrete Wigner function and derive facets of the
so-called qudit Clifford polytope i.e. the inequalities defining the convex
hull of all qudit Clifford gates. Our results for robust states are provably
optimal. For robust gates we find a critical noise rate that, as dimension
increases, rapidly approaches the the theoretical optimum of 100%. Some
connections with the question of qudit magic state distillation are discussed.Comment: 14 pages, 1 table; Minor changes vs. version
Anti-de Sitter boundary in Poincare coordinates
We study the space-time boundary of a Poincare patch of Anti-de Sitter (AdS)
space. We map the Poincare AdS boundary to the global coordinate chart and show
why this boundary is not equivalent to the global AdS boundary. The Poincare
AdS boundary is shown to contain points of the bulk of the entire AdS space.
The Euclidean AdS space is also discussed. In this case one can define a
semi-global chart that divides the AdS space in the same way as the
corresponding Euclidean Poincare chart.Comment: In this revised version we add a discussion of the physical
consequences of the choice of a coordinate system for AdS space. We changed
figure 1 and added more references. Version to be published in Gen. Relat.
Grav
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