Polynomial-sized Semidefinite Representations of Derivative Relaxations of Spectrahedral Cones

We give explicit polynomial-sized (in $n$ and $k$) semidefinite representations of the hyperbolicity cones associated with the elementary symmetric polynomials of degree $k$ in $n$ variables. These convex cones form a family of non-polyhedral outer approximations of the non-negative orthant that preserve low-dimensional faces while successively discarding high-dimensional faces. More generally we construct explicit semidefinite representations (polynomial-sized in $k,m$, and $n$) of the hyperbolicity cones associated with $k$th directional derivatives of polynomials of the form $p(x) = \det(\sum_{i=1}^{n}A_i x_i)$ where the $A_i$ are $m\times m$ symmetric matrices. These convex cones form an analogous family of outer approximations to any spectrahedral cone. Our representations allow us to use semidefinite programming to solve the linear cone programs associated with these convex cones as well as their (less well understood) dual cones.Comment: 20 pages, 1 figure. Minor changes, expanded proof of Lemma

The Effects of Seed Size on Hybrids Formed between Oilseed Rape (Brassica napus) and Wild Brown Mustard (B. juncea)

Background : Seed size has significant implications in ecology, because of its effects on plant fitness. The hybrid seeds that result from crosses between crops and their wild relatives are often small, and the consequences of this have been poorly investigated. Here we report on plant performance of hybrid and its parental transgenic oilseed rape (Brassica napus) and wild B. juncea, all grown from seeds sorted into three seed-size categories.[br/] Methodology/Principal Findings : Three seed-size categories were sorted by seed diameter for transgenic B. napus, wild B. juncea and their transgenic and non-transgenic hybrids. The seeds were sown in a field at various plant densities. Globally, small-seeded plants had delayed flowering, lower biomass, fewer flowers and seeds, and a lower thousand-seed weight. The seed-size effect varied among plant types but was not affected by plant density. There was no negative effect of seed size in hybrids, but it was correlated with reduced growth for both parents.[br/] Conclusions : Our results imply that the risk of further gene flow would probably not be mitigated by the small size of transgenic hybrid seeds. No fitness cost was detected to be associated with the Bt-transgene in this study

Mice deficient in CD38 develop an attenuated form of collagen type II-induced arthritis

CD38, a type II transmembrane glycoprotein expressed in many cells of the immune system, is involved in cell signaling, migration and differentiation. Studies in CD38 deficient mice (CD38 KO mice) indicate that this molecule controls inflammatory immune responses, although its involvement in these responses depends on the disease model analyzed. Here, we explored the role of CD38 in the control of autoimmune responses using chicken collagen type II (col II) immunized C57BL/6-CD38 KO mice as a model of collagen-induced arthritis (CIA). We demonstrate that CD38 KO mice develop an attenuated CIA that is accompanied by a limited joint induction of IL-1β and IL-6 expression, by the lack of induction of IFNγ expression in the joints and by a reduction in the percentages of invariant NKT (iNKT) cells in the spleen. Immunized CD38 KO mice produce high levels of circulating IgG1 and low of IgG2a anti-col II antibodies in association with reduced percentages of Th1 cells in the draining lymph nodes. Altogether, our results show that CD38 participates in the pathogenesis of CIA controlling the number of iNKT cells and promoting Th1 inflammatory responses

GABAergic inhibition is weakened or converted into excitation in the oxytocin and vasopressin neurons of the lactating rat

BACKGROUND: Increased secretion of oxytocin and arginine vasopressin (AVP) from hypothalamic magnocellular neurosecretory cells (MNCs) is a key physiological response to lactation. In the current study, we sought to test the hypothesis that the GABA(A) receptor-mediated inhibition of MNCs is altered in lactating rats. RESULTS: Gramicidin-perforated recordings in the rat supraoptic nucleus (SON) slices revealed that the reversal potential of GABA(A) receptor-mediated response (E(GABA)) of MNCs was significantly depolarized in the lactating rats as compared to virgin animals. The depolarizing E(GABA) shift was much larger in rats in third, than first, lactation such that GABA exerted an excitatory, instead of inhibitory, effect in most of the MNCs of these multiparous rats. Immunohistochemical analyses confirmed that GABAergic excitation was found in both AVP and oxytocin neurons within the MNC population. Pharmacological experiments indicated that the up-regulation of the Cl(−) importer Na(+)-K(+)-2Cl(−) cotransporter isotype 1 and the down-regulation of the Cl(−) extruder K(+)-Cl(−) cotransporter isotype 2 were responsible for the depolarizing shift of E(GABA) and the resultant emergence of GABAergic excitation in the MNCs of the multiparous rats. CONCLUSION: We conclude that, in primiparous rats, the GABAergic inhibition of MNCs is weakened during the period of lactation while, in multiparous females, GABA becomes excitatory in a majority of the cells. This reproductive experience-dependent alteration of GABAergic transmission may help to increase the secretion of oxytocin and AVP during the period of lactation

BARTHOLDI ZETA AND L-FUNCTIONS OF WEIGHTED DIGRAPHS, THEIR COVERINGS AND PRODUCTS

Since a zeta function of a regular graph was introduced by Ihara [Y. Ihara, On discrete subgroups of the two by two projective linear group over rho-adic fields, J. Math. Soc. Japan 19 (1966) 219-235], many kinds of zeta functions and L-functions of a graph or a digraph have been defined and investigated. Most of the works concerning zeta and L-functions of a graph contain the following: (1) defining a zeta function, (2) defining an L-function associated with a (regular) graph covering, (3) providing their determinant expressions, and (4) computing the zeta function of a graph covering and obtaining its decomposition formula as a product of L-functions. As a continuation of those works, we introduce a zeta function of a weighted digraph and an L-function associated with a weighted digraph bundle. A graph bundle is a notion containing a cartesian product of graphs and a (regular or irregular) graph covering. Also we provide determinant expressions of the zeta function and the L-function. Moreover, we compute the zeta function of a weighted digraph bundle and obtain its decomposition formula as a product of the L-functions. (c) 2007 Elsevier Inc. All rights reserved.X114sciescopu

Role of the equilibrium and perturbative central current density in sawtoothing and non-sawtoothing discharges in KSTAR

The experimental measurement [1,2] of the central current density before and after the sawtooth crash event puzzled the theoretical community for about two decades and has since largely been forgotten: the measurement confirmed that the q0 changes very little (i.e. from 0.75 to 0.8) whereas the theoretical community has believed that the q0 should return to ~1 from ~0.75 right after the crash to justify the m/n=1/1 kink instability believed to cause the crash. Note that there are experimental results contradicting with those two measurements. These days, many discharges are routinely operated with q0>1 and it is therefore rare to observe sawtoothing behaviors. Recent experimental and theoretical work on multiple mode structures (m/n=2/2, 3/3, etc.) in addition to the m/n=1/1 mode in the core of sawtoothing plasmas (q0<1) in KSTAR provided a new avenue to revisit this problem. A localized electron cyclotron heating/current drive (ECH/CD) inside the q~1 surface induced higher order modes right after the crash in the sawtoothing discharge and the time evolution of the higher order mode was studied using a 2D Electron Cyclotron imaging (ECEI) diagnostic system [3]. The time evolution of the higher order modes were compared with a reduced MHD simulation with an empirical source term for the radially localized current drive on a flat q-profile with q0~1 [4]. After each crash, the higher m/n mode transforms into the lower m/n mode and eventually merges into a single m/n=1/1 mode before the crash. In order to understand the observed time evolution of the multiple mode structures, the dependence of growth rates of the time evolving higher order modes for three different core equilibrium conditions are studied in detail using the M3D-C1[5] code in cylindrical geometry: (1) q0 changes from 0.8 to 0.75 (2) q0 changes from ~1 to 0.75 (3) q0 >1 as in non-sawtoothing H-mode plasmas

Crosstalk with cancer-associated fibroblasts induces resistance of non-small cell lung cancer cells to epidermal growth factor receptor tyrosine kinase inhibition

Chungyoul Choe,1,* Yong-Sung Shin,1,* Changhoon Kim,2 So-Jung Choi,1 Jinseon Lee,1 So Young Kim,1 Yong Beom Cho,3 Jhingook Kim1,41Samsung Biomedical Research Institute, Samsung Medical Center Sungkyunkwan University, School of Medicine, 2Department of Biomedical Science, Graduate School of Biomedical & Engineering, Hanyang University, 3Department of Surgery, 4Department of Thoracic Surgery, Samsung Medical Center, Sungkyunkwan University, School of Medicine, Seoul, Republic of Korea*These authors contributed equally to this workAbstract: Although lung cancers with activating mutations in the epidermal growth factor receptor (EGFR) are highly sensitive to selective EGFR tyrosine kinase inhibitors (TKIs), these tumors invariably develop acquired drug resistance. Host stromal cells have been found to have a considerable effect on the sensitivity of cancer cells to EGFR TKIs. Little is known, however, about the signaling mechanisms through which stromal cells contribute to the response to EGFR TKI in non-small cell lung cancer. This work examined the role of hedgehog signaling in cancer-associated fibroblast (CAF)-mediated resistance of lung cancer cells to the EGFR TKI erlotinib. PC9 cells, non-small cell lung cancer cells with EGFR-activating mutations, became resistant to the EGFR TKI erlotinib when cocultured in vitro with CAFs. Polymerase chain reaction and immunocytochemical assays showed that CAFs induced epithelial to mesenchymal transition phenotype in PC9 cells, with an associated change in the expression of epithelial to mesenchymal transition marker proteins including vimentin. Importantly, CAFs induce upregulation of the 7-transmembrane protein smoothened, the central signal transducer of hedgehog, suggesting that the hedgehog signaling pathway is active in CAF-mediated drug resistance. Indeed, downregulation of smoothened activity with the smoothened antagonist cyclopamine induces remodeling of the actin cytoskeleton independently of Gli-mediated transcriptional activity in PC9 cells. These findings indicate that crosstalk with CAFs plays a critical role in resistance of lung cancer to EGFR TKIs through induction of the epithelial to mesenchymal transition and may be an ideal therapeutic target in lung cancer.Keywords: CAFs, lung cancer, NSCLC, direct coculture, hedgehog signaling, EMT, actin, EGFR TKI

Validation of the measured q0 > 1.0 in MHD quiescent period after the sawtooth crash in KSTAR

Validation of the central safety factor (q0) during the sawtooth oscillation in the core of the Korean Superconducting Tokamak Advanced Research (KSTAR) is achieved by combination of the measured q-profile by Motional Stark Effect (MSE) and comparative study of the tearing modes experimentally excited with the current blip with the M3Dc1 (reduced MHD equations with finite resistivity) code. The measured central safety factor (q0) was ~1.0 and uncertainty in off-set may hinder whether it is below or above ~1.0 in sawtoothing L-mode discharge. The comparative study further validates that the central safety factor (q0) has to be above ~1.0, in the MHD quiescent regime after the sawtooth crash. The fact that transformation of the excited 3/3 mode into the 1/1 kink mode through 2/2 mode before the crash in one sawtooth period (~12ms) suggests that q0 goes below ~1.0 before the crash. Experimental observation of long lived (~400 ms) tearing modes (m=3 and m=5) in non-sawtoothing H-mode discharge (presumably  ??? 1.0) further supports the fact that q0 has to be above ~1.0 in the MHD quiescent period of the sawtoothing discharge