38,622 research outputs found
Grappling with Issues of Learning Science from Everyday Experiences: An Illustrative Case Study
There are different perceptions among researchers with regard to the infusion of everyday experience in the teaching of science: 1) it hinders the learning of science concepts; or, 2) it increases the participation and motivation of students in science learning. This article attempts to contemplate those different perspectives of everyday knowledge in science classrooms by using everyday contexts to teach grade 3 science in Singapore. In this study, two groups of grade 3 students were presented with a scenario that required them to apply the concept of properties of materials to design a shoe. Subsequently, the transcripts of classroom discussions and interactions were analyzed using the framework of sociocultural learning and an interpretative analytic lens. Our analysis suggests that providing an authentic everyday context is insufficient to move young learners of science from their everyday knowledge to scientific knowledge. Further, group interactions among young learners of science to solve an everyday issue need to be scaffolded to ensure meaningful, focused, and sustained learning. Implications for research in science learning among younger students are discussed
Scaling Exponent and Moderate Deviations Asymptotics of Polar Codes for the AWGN Channel
This paper investigates polar codes for the additive white Gaussian noise
(AWGN) channel. The scaling exponent of polar codes for a memoryless
channel with capacity characterizes the closest gap
between the capacity and non-asymptotic achievable rates in the following way:
For a fixed , the gap between the capacity
and the maximum non-asymptotic rate achieved by a length- polar code
with average error probability scales as , i.e.,
.
It is well known that the scaling exponent for any binary-input
memoryless channel (BMC) with is bounded above by ,
which was shown by an explicit construction of polar codes. Our main result
shows that remains to be a valid upper bound on the scaling exponent
for the AWGN channel. Our proof technique involves the following two ideas: (i)
The capacity of the AWGN channel can be achieved within a gap of
by using an input alphabet consisting of
constellations and restricting the input distribution to be uniform; (ii) The
capacity of a multiple access channel (MAC) with an input alphabet consisting
of constellations can be achieved within a gap of by
using a superposition of binary-input polar codes. In addition, we
investigate the performance of polar codes in the moderate deviations regime
where both the gap to capacity and the error probability vanish as grows.
An explicit construction of polar codes is proposed to obey a certain tradeoff
between the gap to capacity and the decay rate of the error probability for the
AWGN channel.Comment: 24 page
Strong Converse Theorems for Classes of Multimessage Multicast Networks: A R\'enyi Divergence Approach
This paper establishes that the strong converse holds for some classes of
discrete memoryless multimessage multicast networks (DM-MMNs) whose
corresponding cut-set bounds are tight, i.e., coincide with the set of
achievable rate tuples. The strong converse for these classes of DM-MMNs
implies that all sequences of codes with rate tuples belonging to the exterior
of the cut-set bound have average error probabilities that necessarily tend to
one (and are not simply bounded away from zero). Examples in the classes of
DM-MMNs include wireless erasure networks, DM-MMNs consisting of independent
discrete memoryless channels (DMCs) as well as single-destination DM-MMNs
consisting of independent DMCs with destination feedback. Our elementary proof
technique leverages properties of the R\'enyi divergence.Comment: Submitted to IEEE Transactions on Information Theory, Jul 18, 2014.
Revised on Jul 31, 201
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