Energy

Resource /Energy Economics and Policy,

The Internet and Civic Engagement

Based on a survey, analyzes how socioeconomic status and other demographics correlate with online and offline political and civic engagement. Explores suggestions that younger generations' political use of social media may alter such patterns

Pushing fillings in right-angled Artin groups

We construct "pushing maps" on the cube complexes that model right-angled Artin groups (RAAGs) in order to study filling problems in certain subsets of these cube complexes. We use radial pushing to obtain upper bounds on higher divergence functions, finding that the k-dimensional divergence of a RAAG is bounded by r^{2k+2}. These divergence functions, previously defined for Hadamard manifolds to measure isoperimetric properties "at infinity," are defined here as a family of quasi-isometry invariants of groups; thus, these results give new information about the QI classification of RAAGs. By pushing along the height gradient, we also show that the k-th order Dehn function of a Bestvina-Brady group is bounded by V^{(2k+2)/k}. We construct a class of RAAGs called "orthoplex groups" which show that each of these upper bounds is sharp.Comment: The result on the Dehn function at infinity in mapping class groups has been moved to the note "Filling loops at infinity in the mapping class group.

Filling loops at infinity in the mapping class group

We study the Dehn function at infinity in the mapping class group, finding a polynomial upper bound of degree four. This is the same upper bound that holds for arbitrary right-angled Artin groups.Comment: 7 pages, 2 figures; this note presents a result which was contained in an earlier version of "Pushing fillings in right-angled Artin groups" (arXiv:1004.4253) but is independent of the techniques in that pape

Pathologic Complete Response After Neoadjuvant Chemoradiation in a Patient with Gastric Neuroendocrine Cancer

Neuroendocrine tumors are about 0.5% of all malignancies. Specifically, for gastrointestinal (GI) malignancies, neuroendocrine tumor incidence is approximately 1%-2% per year. Gastric neuroendocrine neoplasms are rare and consist of various tumor types with differing histomorphology, pathogenesis, and biological behavior. Following surgery, post-operative chemotherapy is generally considered the standard of care. Our case report demonstrates the potential benefit of neoadjuvant concurrent chemoradiotherapy prior to surgery for a malignant gastric neuroendocrine tumor. While radiotherapy has been demonstrated to possibly provide a survival benefit in the treatment of GI neuroendocrine tumors, its use in treatment, particularly neoadjuvantly, needs to be further assessed.Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Homological and homotopical Dehn functions are different

The homological and homotopical Dehn functions are different ways of measuring the difficulty of filling a closed curve inside a group or a space. The homological Dehn function measures fillings of cycles by chains, while the homotopical Dehn function measures fillings of curves by disks. Since the two definitions involve different sorts of boundaries and fillings, there is no a priori relationship between the two functions, but prior to this work there were no known examples of finitely-presented groups for which the two functions differ. This paper gives the first such examples, constructed by amalgamating a free-by-cyclic group with several Bestvina-Brady groups.Comment: (17 pages

Pushing fillings in right-angled Artin groups

We obtain bounds on the higher divergence functions of right-angled Artin groups (RAAGs), finding that the k-dimensional divergence of a RAAG is bounded above by r2k+2. These divergence functions, previously defined for Hadamard manifolds to measure isoperimetric properties at infinity, are defined here as a family of quasi-isometry invariants of groups. We also show that the kth order Dehn function of a Bestvina-Brady group is bounded above by V (2k+2)/k and construct a class of RAAGs called orthoplex groups which show that each of these upper bounds is sharp. © 2013 London Mathematical Society