34,981 research outputs found
What are Funds of Knowledge? A Collaborative Approach to Education
It is important as educators to have a holistic understanding of students’ identities as these experiences influence classroom dynamics. As noted by Dugan (2017), “…identity, knowledge, and power are influenced profoundly by ideology and hegemony and in turn play a role in shaping people’s stocks of knowledge” (p. 40). “Stocks of knowledge” are characterized by five principles: they are familiar, serve to help navigate the world, “shaped by lived experience, altered only through novel situations, and socially constructed based on identity” (Dugan, 2017, p. 34). These “stocks of knowledge” are also known as “funds of knowledge” by multicultural educators.https://digitalscholarship.unlv.edu/btp_expo/1052/thumbnail.jp
Pions: Experimental Tests of Chiral Symmetry Breaking
Based on the spontaneous breaking of chiral symmetry, chiral perturbation
theory (ChPT) is believed to approximate confinement scale QCD. Dedicated and
increasingly accurate experiments and improving lattice calculations are
confirming this belief, and we are entering a new era in which we can test
confinement scale QCD in some well chosen reactions. This is demonstrated with
an overview of low energy experimental tests of ChPT predictions of
scattering, pion properties, N scattering and electromagnetic pion
production. These predictions have been shown to be consistent with QCD in the
meson sector by increasingly accurate lattice calculations. At present there is
good agreement between experiment and ChPT calculations, including the
and N s wave scattering lengths and the lifetime. Recent,
accurate pionic atom data are in agreement with chiral calculations once
isospin breaking effects due to the mass difference of the up and down quarks
are taken into account, as was required to extract the scattering
lengths. In addition to tests of the theory, comparisons between and
N interactions based on general chiral principles are discussed. Lattice
calculations are now providing results for the fundamental, long and
inconclusively studied, N term and the contribution of the
strange quark to the mass of the proton. Increasingly accurate experiments in
electromagnetic pion production experiments from the proton which test ChPT
calculations (and their energy region of validity) are presented. These
experiments are also beginning to measure the final state N interaction.
This paper is based on the concluding remarks made at the Chiral Dynamics
Workshop CD12 held at Jefferson Lab in Aug. 2012.Comment: 13 pages, 8 fig
Dynamic Approximate All-Pairs Shortest Paths: Breaking the O(mn) Barrier and Derandomization
We study dynamic -approximation algorithms for the all-pairs
shortest paths problem in unweighted undirected -node -edge graphs under
edge deletions. The fastest algorithm for this problem is a randomized
algorithm with a total update time of and constant
query time by Roditty and Zwick [FOCS 2004]. The fastest deterministic
algorithm is from a 1981 paper by Even and Shiloach [JACM 1981]; it has a total
update time of and constant query time. We improve these results as
follows: (1) We present an algorithm with a total update time of and constant query time that has an additive error of
in addition to the multiplicative error. This beats the previous
time when . Note that the additive
error is unavoidable since, even in the static case, an -time
(a so-called truly subcubic) combinatorial algorithm with
multiplicative error cannot have an additive error less than ,
unless we make a major breakthrough for Boolean matrix multiplication [Dor et
al. FOCS 1996] and many other long-standing problems [Vassilevska Williams and
Williams FOCS 2010]. The algorithm can also be turned into a
-approximation algorithm (without an additive error) with the
same time guarantees, improving the recent -approximation
algorithm with running
time of Bernstein and Roditty [SODA 2011] in terms of both approximation and
time guarantees. (2) We present a deterministic algorithm with a total update
time of and a query time of . The
algorithm has a multiplicative error of and gives the first
improved deterministic algorithm since 1981. It also answers an open question
raised by Bernstein [STOC 2013].Comment: A preliminary version was presented at the 2013 IEEE 54th Annual
Symposium on Foundations of Computer Science (FOCS 2013
An on-line system for utilizing hand-printed input Progress report
Flow charts for recognizing hand printed characters on-line in real time operatio
Resampling images in Fourier domain
When simulating sky images, one often takes a galaxy image defined by
a set of pixelized samples and an interpolation kernel, and then wants to
produce a new sampled image representing this galaxy as it would appear with a
different point-spread function, a rotation, shearing, or magnification, and/or
a different pixel scale. These operations are sometimes only possible, or most
efficiently executed, as resamplings of the Fourier transform of
the image onto a -space grid that differs from the one produced by a
discrete Fourier transform (DFT) of the samples. In some applications it is
essential that the resampled image be accurate to better than 1 part in ,
so in this paper we first use standard Fourier techniques to show that
Fourier-domain interpolation with a wrapped sinc function yields the exact
value of in terms of the input samples and kernel. This operation
scales with image dimension as and can be prohibitively slow, so we next
investigate the errors accrued from approximating the sinc function with a
compact kernel. We show that these approximations produce a multiplicative
error plus a pair of ghost images (in each dimension) in the simulated image.
Standard Lanczos or cubic interpolators, when applied in Fourier domain,
produce unacceptable artifacts. We find that errors part in can be
obtained by (1) 4-fold zero-padding of the original image before executing the
DFT, followed by (2) resampling to the desired grid using
a 6-point, piecewise-quintic interpolant that we design expressly to minimize
the ghosts, then (3) executing the DFT back to domain.Comment: Typographical and one algebraic correction, to appear in PASP March
201
Upper Energy Limit of Heavy Baryon Chiral Perturbation Theory in Neutral Pion Photoproduction
With the availability of the new neutral pion photoproduction from the proton
data from the A2 and CB-TAPS Collaborations at Mainz it is mandatory to revisit
Heavy Baryon Chiral Perturbation Theory (HBChPT) and address the extraction of
the partial waves as well as other issues such as the value of the low-energy
constants, the energy range where the calculation provides a good agreement
with the data and the impact of unitarity. We find that, within the current
experimental status, HBChPT with the fitted LECs gives a good agreement with
the existing neutral pion photoproduction data up to 170 MeV and that
imposing unitarity does not improve this picture. Above this energy the data
call for further improvement in the theory such as the explicit inclusion of
the \Delta (1232). We also find that data and multipoles can be well described
up to 185 MeV with Taylor expansions in the partial waves up to first
order in pion energy.Comment: 6 pages, 5 figures, version to be published in Physics Letters
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