Vertex-algebraic structure of the principal subspaces of certain A_1^(1)-modules, I: level one case

This is the first in a series of papers in which we study vertex-algebraic structure of Feigin-Stoyanovsky's principal subspaces associated to standard modules for both untwisted and twisted affine Lie algebras. A key idea is to prove suitable presentations of principal subspaces, without using bases or even ``small'' spanning sets of these spaces. In this paper we prove presentations of the principal subspaces of the basic A_1^(1)-modules. These convenient presentations were previously used in work of Capparelli-Lepowsky-Milas for the purpose of obtaining the classical Rogers-Ramanujan recursion for the graded dimensions of the principal subspaces.Comment: 20 pages. To appear in International J. of Mat

Multiple mechanisms of growth hormone-regulated gene transcription

Diverse physiological actions of growth hormone (GH) are mediated by changes in gene transcription. Transcription can be regulated at several levels, including post-translational modification of transcription factors, and formation of multiprotein complexes involving transcription factors, co-regulators and additional nuclear proteins; these serve as targets for regulation by hormones and signaling pathways. Evidence that GH regulates transcription at multiple levels is exemplified by analysis of the proto-oncogene c-fos. Among the GH-regulated transcription factors on c-fos, C/EBPbeta appears to be key, since depletion of C/EBPbeta by RNA interference blocks the stimulation of c-fos by GH. The phosphorylation state of C/EBPbeta and its ability to activate transcription are regulated by GH through MAPK and PI3K/Akt-mediated signaling cascades. The acetylation of C/EBPbeta also contributes to its ability to activate c-fos transcription. These and other post-translational modifications of C/EBPbeta appear to be integrated for regulation of transcription by GH. The formation of nuclear proteins into complexes associated with DNA-bound transcription factors is also regulated by GH. Both C/EBPbeta and the co-activator p300 are recruited to c-fos in response to GH, altering c-fos promoter activation. In addition, GH rapidly induces spatio-temporal re-localization of C/EBPbeta within the nucleus. Thus, GH-regulated gene transcription mediated by C/EBPbeta reflects the integration of diverse mechanisms including post-translational modifications, modulation of protein complexes associated with DNA and re-localization of gene regulatory proteins. Similar integration involving other transcription factors, including Stats, appears to be a feature of regulation by GH of other gene targets.Fil: Ceseña, Teresa I.. University of Michigan; Estados UnidosFil: Cui, Tracy Xiao. University of Michigan; Estados UnidosFil: Piwien Pilipuk, Graciela. Fundación Instituto Leloir; ArgentinaFil: Kaplani, Julianne. University of Michigan; Estados UnidosFil: Calinescu, Anda Alexandra. Michigan State University; Estados UnidosFil: Huo, Jeffrey S.. University of Michigan; Estados UnidosFil: Iñiguez Lluhí, Jorge A.. University of Michigan; Estados UnidosFil: Kwok, Roland. University of Michigan; Estados UnidosFil: Schwartz, Jessica. University of Michigan; Estados Unido

Rehabilitation Intervention to Restore the Functionality of the Shoulder With Scapular Fracture – Case Report

This report presents an individualized physical therapy program and the therapeutic results for a 36-year-old man with a posttraumatic left scapular body fracture with minimal displacement and without ribs fractures scapular fracture. Because the glenoid fossa was intact, conservative treatment was recommended. The patient reports arm activities dysfunctions. The rehabilitation was conducted in an outpatient physical therapy clinic from Craiova under direct supervision for 12 weeks. At the end of the follow-up period, the level of pain was considerably decreased. Despite the functional deficit from the beginning of the rehabilitation program, normal function was restored. The patient was fully involved and cooperative during the physical therapy session

Stochastic Vehicle Routing with Recourse

We study the classic Vehicle Routing Problem in the setting of stochastic optimization with recourse. StochVRP is a two-stage optimization problem, where demand is satisfied using two routes: fixed and recourse. The fixed route is computed using only a demand distribution. Then after observing the demand instantiations, a recourse route is computed -- but costs here become more expensive by a factor lambda. We present an O(log^2 n log(n lambda))-approximation algorithm for this stochastic routing problem, under arbitrary distributions. The main idea in this result is relating StochVRP to a special case of submodular orienteering, called knapsack rank-function orienteering. We also give a better approximation ratio for knapsack rank-function orienteering than what follows from prior work. Finally, we provide a Unique Games Conjecture based omega(1) hardness of approximation for StochVRP, even on star-like metrics on which our algorithm achieves a logarithmic approximation.Comment: 20 Pages, 1 figure Revision corrects the statement and proof of Theorem 1.

Maximum gradient embeddings and monotone clustering

Let (X,d_X) be an n-point metric space. We show that there exists a distribution D over non-contractive embeddings into trees f:X-->T such that for every x in X, the expectation with respect to D of the maximum over y in X of the ratio d_T(f(x),f(y)) / d_X(x,y) is at most C (log n)^2, where C is a universal constant. Conversely we show that the above quadratic dependence on log n cannot be improved in general. Such embeddings, which we call maximum gradient embeddings, yield a framework for the design of approximation algorithms for a wide range of clustering problems with monotone costs, including fault-tolerant versions of k-median and facility location.Comment: 25 pages, 2 figures. Final version, minor revision of the previous one. To appear in "Combinatorica

Utilization of dielectric properties assessment to evaluate the catalytic activity and rate of deactivation of heterogeneous catalysts

The use of dielectric property assessment to gauge the catalytic activity and rate of deactivation of heterogeneous catalysts is reported. Four supported catalysts containing a combination of Fe and Ni active sites and γ-Al₂O₃, ZSM-5, MCM-41, and SBA-15 supports were synthesized, characterized, and utilized to catalyze a Fischer–Tropsch process over a temperature range of 250–400 °C that was specifically directed toward the production of lower olefins. While the highest conversion was obtained from ZSM-5 and MCM-41 supports containing Fe and Ni as active sites at 350 °C, all these catalysts were observed to be deactivated by the formation of carbon on their surface. The dielectric properties of the fresh, used catalysts and supports were evaluated and correlated with their catalytic activity and structural/textural properties. It was clearly shown that the dielectric property measurement could demonstrate both the presence and magnitude of carbon deposits on the catalyst via the differences in the values of fresh and used catalysts. Furthermore, the ability to differentiate between the levels of the carbon deposition observed was shown to be independent of the morphology exhibited by the carbon deposit demonstrating that this is a method that can be generally applied