80 research outputs found
Simplicial presheaves of coalgebras
The category of simplicial R-coalgebras over a presheaf of commutative unital
rings on a small Grothendieck site is endowed with a left proper, simplicial,
cofibrantly generated model category structure where the weak equivalences are
the local weak equivalences of the underlying simplicial presheaves. This model
category is naturally linked to the R-local homotopy theory of simplicial
presheaves and the homotopy theory of simplicial R-modules by Quillen
adjunctions. We study the comparison with the R-local homotopy category of
simplicial presheaves in the special case where R is a presheaf of
algebraically closed (or perfect) fields. If R is a presheaf of algebraically
closed fields, we show that the R-local homotopy category of simplicial
presheaves embeds fully faithfully in the homotopy category of simplicial
R-coalgebras.Comment: 24 page
Separable Functors and Formal Smoothness
The natural problem we approach in the present paper is to show how the
notion of formally smooth (co)algebra inside monoidal categories can substitute
that of (co)separable (co)algebra in the study of splitting bialgebra
homomorphisms. This is performed investigating the relation between formal
smoothness and separability of certain functors and led to other results
related to Hopf algebra theory. Between them we prove that the existence of
-(co)invariant integrals for a Hopf algebra is equivalent to the
separability of some forgetful functors. In the finite dimensional case, this
is also equivalent to the separability of the Drinfeld Double over .
Hopf algebras which are formally smooth as (co)algebras are characterized. We
prove that given a bialgebra surjection with nilpotent kernel
such that is a Hopf algebra which is formally smooth as a -algebra, then
has a section which is a right -colinear algebra homomorphism.
Moreover, if is also endowed with an -invariant integral, then this
section can be chosen to be -bicolinear. We also deal with the dual case
Characteristic classes for cohomology of split Hopf algebra extensions
We introduce characteristic classes for the spectral sequence associated to a
split short exact sequence of Hopf algebras. We show that these characteristic
classes can be seen as obstructions for the vanishing of differentials in the
spectral sequence and prove a decomposition theorem. We also interpret our
results in the settings of group and Lie algebra extensions and prove some
interesting corollaries concerning the collapse of the
(Lyndon-)Hochschild-Serre spectral sequence and the order of characteristic
classes.Comment: 22 page
Sharing the Power: Training Consumer Health Information Center Volunteers Online
Introduction
Tutorial created through cooperative efforts of the
WHIC manager, volunteer coordinator, two Health
Sciences Librarians, a graduate student, and a
graduate intern.
19 months of iterative development
Goals
Reduce time required train volunteers
Prepare volunteers to provide health information to
consumers
Track learning through built-in self assessment tools
Learning Objectives
WHIC's mission and procedures
Using information resources
Guiding customers to appropriate resources
When and where to refer information request
Weak Localization Effect in Superconductors by Radiation Damage
Large reductions of the superconducting transition temperature and
the accompanying loss of the thermal electrical resistivity (electron-phonon
interaction) due to radiation damage have been observed for several A15
compounds, Chevrel phase and Ternary superconductors, and in
the high fluence regime. We examine these behaviors based on the recent theory
of weak localization effect in superconductors. We find a good fitting to the
experimental data. In particular, weak localization correction to the
phonon-mediated interaction is derived from the density correlation function.
It is shown that weak localization has a strong influence on both the
phonon-mediated interaction and the electron-phonon interaction, which leads to
the universal correlation of and resistance ratio.Comment: 16 pages plus 3 figures, revtex, 76 references, For more information,
Plesse see http://www.fen.bilkent.edu.tr/~yjki
Classification of Children's Handwriting Errors for the Design of an Educational Co-writer Robotic Peer
In this paper, we propose a taxonomy of handwriting errors exhibited by children as a way to build adequate strategies for integration with a co-writing peer. The exploration includes the collection of letters written by children in an initial study, which were then revised in a second study. The second study also analyses the "peer-learning" (PL) and "peer-tutoring" (PT) learning methods in an educational scenario, where a pair of children perform a collaborative writing activity in the presence of a robot facilitator. The data obtained in the first two studies allowed us to create a "taxonomy of handwriting errors". A set of writing errors were selected and implemented in an educational activity for validation. This activity constituted a third study, wherein we systematically induced the errors into a Nao robot's handwriting using the {PT} method - A teacher-child corrects the handwriting errors of the learner-robot. The preliminary results suggest that the children in general showed awareness to the writing errors and were able to perceive the writing abilities of the robot
Pointed Hopf Algebras with Triangular Decomposition: A Characterization of Multiparameter Quantum Groups
© 2016, The Author(s). In this paper, we present an approach to the definition of multiparameter quantum groups by studying Hopf algebras with triangular decomposition. Classifying all of these Hopf algebras which are of what we call weakly separable type over a group, we obtain a class of pointed Hopf algebras which can be viewed as natural generalizations of multiparameter deformations of universal enveloping algebras of Lie algebras. These Hopf algebras are instances of a new version of braided Drinfeld doubles, which we call asymmetric braided Drinfeld doubles. This is a generalization of an earlier result by Benkart and Witherspoon (Algebr. Represent. Theory 7(3) ? BC) who showed that two-parameter quantum groups are Drinfeld doubles. It is possible to recover a Lie algebra from these doubles in the case where the group is free abelian and the parameters are generic. The Lie algebras arising are generated by Lie subalgebras isomorphic to sl2
Hopf algebras and Markov chains: Two examples and a theory
The operation of squaring (coproduct followed by product) in a combinatorial
Hopf algebra is shown to induce a Markov chain in natural bases. Chains
constructed in this way include widely studied methods of card shuffling, a
natural "rock-breaking" process, and Markov chains on simplicial complexes.
Many of these chains can be explictly diagonalized using the primitive elements
of the algebra and the combinatorics of the free Lie algebra. For card
shuffling, this gives an explicit description of the eigenvectors. For
rock-breaking, an explicit description of the quasi-stationary distribution and
sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes
will only appear on the version on Amy Pang's website, the arXiv version will
not be updated.
Genome-Wide Analyses Reveal a Role for Peptide Hormones in Planarian Germline Development
Genomic/peptidomic analyses of the planarian Schmidtea mediterranea identifies >200 neuropeptides and uncovers a conserved neuropeptide required for proper maturation and maintenance of the reproductive system
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