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 $S^2$. 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 $\pi_2(S^2)$, 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