4,939 research outputs found
Having a Heart for ALL Students
The student body in today’s general educational classrooms continues to increase in diversity, with many of the students being English language learners. This growth in the number of non-English speaking students brings challenges to educators. Students’ test scores are the measurement of success for educators, resulting in a decrease of caring about students as individuals. This article addresses the importance and responsibility for Christian educators to reach out to non-English speaking students
Observational Learning with Position Uncertainty
Observational learning is typically examined when agents have precise information about their position in the sequence of play. We present a model in which agents are uncertain about their positions. Agents are allowed to have arbitrary ex-ante beliefs about their positions: they may observe their position perfectly, imperfectly, or not at all. Agents sample the decisions of past individuals and receive a private signal about the state of the world. We show that social learning is robust to position uncertainty. Under any sampling rule satisfying a stationarity assumption, learning is complete if signal strength is unbounded. In cases with bounded signal strength, we show that agents achieve what we define as constrained efficient learning: individuals do at least as well as the most informed agent would do in isolation.social learning; information aggregation; herds; position uncertainty; observational learning
Invisibility and PT Symmetry: A Simple Geometrical Viewpoint
We give a simplified account of the properties of the transfer matrix for a
complex one-dimensional potential, paying special attention to the particular
instance of unidirectional invisibility. In appropriate variables, invisible
potentials appear as performing null rotations, which lead to the
helicity-gauge symmetry of massless particles. In hyperbolic geometry, this can
be interpreted, via M\"{o}bius transformations, as parallel displacements, a
geometric action that has no Euclidean analogy.Comment: 13 pages. No figure. Accepted for publication in Symmetr
Sliderule-like property of Wigner's little groups and cyclic S-matrices for multilayer optics
It is noted that two-by-two S-matrices in multilayer optics can be
represented by the Sp(2) group whose algebraic property is the same as the
group of Lorentz transformations applicable to two space-like and one time-like
dimensions. It is noted also that Wigner's little groups have a sliderule-like
property which allows us to perform multiplications by additions. It is shown
that these two mathematical properties lead to a cyclic representation of the
S-matrix for multilayer optics, as in the case of ABCD matrices for laser
cavities. It is therefore possible to write the N-layer S-matrix as a
multiplication of the N single-layer S-matrices resulting in the same
mathematical expression with one of the parameters multiplied by N. In
addition, it is noted, as in the case of lens optics, multilayer optics can
serve as an analogue computer for the contraction of Wigner's little groups for
internal space-time symmetries of relativistic particles.Comment: RevTex 13 pages, Secs. IV and V revised and expande
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