184 research outputs found
Making connections: Using skill theory to recognize how students build and rebuild understanding
In this companion to Marc Schwartz and Kurt Fischer's article, Patricia King and JoNes VanHecke describe how student affairs educators can help students become sophisticated thinkers.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/50666/1/155_ftp.pd
Connes-Lott model building on the two-sphere
In this work we examine generalized Connes-Lott models on the two-sphere. The
Hilbert space of the continuum spectral triple is taken as the space of
sections of a twisted spinor bundle, allowing for nontrivial topological
structure (magnetic monopoles). The finitely generated projective module over
the full algebra is also taken as topologically non-trivial, which is possible
over . We also construct a real spectral triple enlarging this Hilbert
space to include "particle" and "anti-particle" fields.Comment: 57 pages, LATE
The Connes-Lott program on the sphere
We describe the classical Schwinger model as a study of the projective
modules over the algebra of complex-valued functions on the sphere. On these
modules, classified by , we construct hermitian connections with
values in the universal differential envelope which leads us to the Schwinger
model on the sphere. The Connes-Lott program is then applied using the Hilbert
space of complexified inhomogeneous forms with its Atiyah-Kaehler structure. It
splits in two minimal left ideals of the Clifford algebra preserved by the
Dirac-Kaehler operator D=i(d-delta). The induced representation of the
universal differential envelope, in order to recover its differential
structure, is divided by the unwanted differential ideal and the obtained
quotient is the usual complexified de Rham exterior algebra over the sphere
with Clifford action on the "spinors" of the Hilbert space. The subsequent
steps of the Connes-Lott program allow to define a matter action, and the field
action is obtained using the Dixmier trace which reduces to the integral of the
curvature squared.Comment: 34 pages, Latex, submitted for publicatio
Liberal arts student learning outcomes: An integrated approach
Researchers completing a study of liberal arts education sought to identify learning outcomes associated with both wisdom and citizenship. They have synthesized these themes into seven outcomes that facilitate effective student learning and development.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57388/1/222_ftp.pd
Carnot-Caratheodory metric and gauge fluctuation in Noncommutative Geometry
Gauge fields have a natural metric interpretation in terms of horizontal
distance. The latest, also called Carnot-Caratheodory or subriemannian
distance, is by definition the length of the shortest horizontal path between
points, that is to say the shortest path whose tangent vector is everywhere
horizontal with respect to the gauge connection. In noncommutative geometry all
the metric information is encoded within the Dirac operator D. In the classical
case, i.e. commutative, Connes's distance formula allows to extract from D the
geodesic distance on a riemannian spin manifold. In the case of a gauge theory
with a gauge field A, the geometry of the associated U(n)-vector bundle is
described by the covariant Dirac operator D+A. What is the distance encoded
within this operator ? It was expected that the noncommutative geometry
distance d defined by a covariant Dirac operator was intimately linked to the
Carnot-Caratheodory distance dh defined by A. In this paper we precise this
link, showing that the equality of d and dh strongly depends on the holonomy of
the connection. Quite interestingly we exhibit an elementary example, based on
a 2 torus, in which the noncommutative distance has a very simple expression
and simultaneously avoids the main drawbacks of the riemannian metric (no
discontinuity of the derivative of the distance function at the cut-locus) and
of the subriemannian one (memory of the structure of the fiber).Comment: published version with additional figures to make the proof more
readable. Typos corrected in this ultimate versio
Non-commutative Quantum Mechanics in Three Dimensions and Rotational Symmetry
We generalize the formulation of non-commutative quantum mechanics to three
dimensional non-commutative space. Particular attention is paid to the
identification of the quantum Hilbert space in which the physical states of the
system are to be represented, the construction of the representation of the
rotation group on this space, the deformation of the Leibnitz rule accompanying
this representation and the implied necessity of deforming the co-product to
restore the rotation symmetry automorphism. This also implies the breaking of
rotational invariance on the level of the Schroedinger action and equation as
well as the Hamiltonian, even for rotational invariant potentials. For
rotational invariant potentials the symmetry breaking results purely from the
deformation in the sense that the commutator of the Hamiltonian and angular
momentum is proportional to the deformation.Comment: 21 page
Screening of human gene promoter activities using transfected-cell arrays
Promoters are the best characterized transcriptional regulatory sequences in complex genomes because of their predictable location immediately upstream of transcription start sites. Despite a substantial body of literature describing transcriptional promoters, the identification of true start sites for all human transcripts is far from complete. The same is true of the key structural and functional elements responsible for promoter action in different cell types. In order to identify elements responsible for promoter activity, we applied transfected-cell array technology to functionally evaluate promoters for genes involved in inflammatory bowel disease. Seventy-four promoters were examined by reverse transfection of a promoter-fluorescent reporter constructs into a human embryonic kidney cell line (HEK293T). Sixteen (21.6%) promoters were found to be active in HEK293 T cells. Correlations between promoter activity and endogenous transcript level were calculated, and 75% of active promoters were found to be associated with transcriptional activity of their gene counterparts. These results provide experimental evidence of promoter activity, which may aid in understanding the regulation of gene expression. Moreover, this is the first large-scale functional study of regulatory sequences to use a high-throughput transfected-cell array technique
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