Heat flow method to Lichnerowicz type equation on closed manifolds

In this paper, we establish existence results for positive solutions to the Lichnerowicz equation of the following type in closed manifolds -\Delta u=A(x)u^{-p}-B(x)u^{q},\quad in\quad M, where $p>1, q>0$, and $A(x)>0$, $B(x)\geq0$ are given smooth functions. Our analysis is based on the global existence of positive solutions to the following heat equation {ll} u_t-\Delta u=A(x)u^{-p}-B(x)u^{q},\quad in\quad M\times\mathbb{R}^{+}, u(x,0)=u_0,\quad in\quad M with the positive smooth initial data $u_0$.Comment: 10 page

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Random matrix theory and symmetric spaces

In this review we discuss the relationship between random matrix theories and symmetric spaces. We show that the integration manifolds of random matrix theories, the eigenvalue distribution, and the Dyson and boundary indices characterizing the ensembles are in strict correspondence with symmetric spaces and the intrinsic characteristics of their restricted root lattices. Several important results can be obtained from this identification. In particular the Cartan classification of triplets of symmetric spaces with positive, zero and negative curvature gives rise to a new classification of random matrix ensembles. The review is organized into two main parts. In Part I the theory of symmetric spaces is reviewed with particular emphasis on the ideas relevant for appreciating the correspondence with random matrix theories. In Part II we discuss various applications of symmetric spaces to random matrix theories and in particular the new classification of disordered systems derived from the classification of symmetric spaces. We also review how the mapping from integrable Calogero--Sutherland models to symmetric spaces can be used in the theory of random matrices, with particular consequences for quantum transport problems. We conclude indicating some interesting new directions of research based on these identifications.Comment: 161 pages, LaTeX, no figures. Revised version with major additions in the second part of the review. Version accepted for publication on Physics Report

Differential regulation of CHOP translation by phosphorylated eIF4E under stress conditions

Cells respond to environmental stress by inducing translation of a subset of mRNAs important for survival or apoptosis. CHOP, a downstream transcriptional target of stress-induced ATF4, is also regulated translationally in a uORF-dependent manner under stress. Low concentration of anisomycin induces CHOP expression at both transcriptional and translational levels. To study specifically the translational aspect of CHOP expression, and further clarify the regulatory mechanisms underlying stress-induced translation initiation, we developed a CMV promoter-regulated, uORFchop-driven reporter platform. Here we show that anisomycin-induced CHOP expression depends on phosphorylated eIF4E/S209 and eIF2α/S51. Contrary to phospho-eIF2α/S51, phospho-eIF4E/S209 is not involved in thapsigargin-induced CHOP expression. Studies using various kinase inhibitors and mutants uncovered that both the p38MAPK-Mnk and mTOR signaling pathways contribute to stress-responsive reporter and CHOP expression. We also demonstrated that anisomycin-induced translation is tightly regulated by partner binding preference of eIF4E. Furthermore, mutating the uORF sequence abolished the anisomycin-induced association of chop mRNA with phospho-eIF4E and polysomes, thus demonstrating the significance of this cis-regulatory element in conferring on the transcript a stress-responsive translational inducibility. Strikingly, although insulin treatment activated ERK-Mnk and mTOR pathways, and consequently eIF4E/S209 phosphorylation, it failed to induce phospho-eIF2α/S51 and reporter translation, thus pinpointing a crucial determinant in stress-responsive translation

Activation of SK2 channels preserves ER Ca(2+) homeostasis and protects against ER stress-induced cell death

Alteration of endoplasmic reticulum (ER) Ca(2+) homeostasis leads to excessive cytosolic Ca(2+) accumulation and delayed neuronal cell death in acute and chronic neurodegenerative disorders. While our recent studies established a protective role for SK channels against excessive intracellular Ca(2+) accumulation, their functional role in the ER has not been elucidated yet. We show here that SK2 channels are present in ER membranes of neuronal HT-22 cells, and that positive pharmacological modulation of SK2 channels with CyPPA protects against cell death induced by the ER stressors brefeldin A and tunicamycin. Calcium imaging of HT-22 neurons revealed that elevated cytosolic Ca(2+) levels and decreased ER Ca(2+) load during sustained ER stress could be largely prevented by SK2 channel activation. Interestingly, SK2 channel activation reduced the amount of the unfolded protein response transcription factor ATF4, but further enhanced the induction of CHOP. Using siRNA approaches we confirmed a detrimental role for ATF4 in ER stress, whereas CHOP regulation was dispensable for both, brefeldin A toxicity and CyPPA-mediated protection. Cell death induced by blocking Ca(2+) influx into the ER with the SERCA inhibitor thapsigargin was not prevented by CyPPA. Blocking the K(+) efflux via K(+)/H(+) exchangers with quinine inhibited CyPPA-mediated neuroprotection, suggesting an essential role of proton uptake and K(+) release in the SK channel-mediated neuroprotection. Our data demonstrate that ER SK2 channel activation preserves ER Ca(2+) uptake and retention which determines cell survival in conditions where sustained ER stress contributes to progressive neuronal death.Cell Death and Differentiation advance online publication, 20 November 2015; doi:10.1038/cdd.2015.146.</p

Convex regions of stationary spacetimes and Randers spaces. Applications to lensing and asymptotic flatness

By using Stationary-to-Randers correspondence (SRC), a characterization of light and time-convexity of the boundary of a region of a standard stationary (n+1)-spacetime is obtained, in terms of the convexity of the boundary of a domain in a Finsler n or (n+1)-space of Randers type. The latter convexity is analyzed in depth and, as a consequence, the causal simplicity and the existence of causal geodesics confined in the region and connecting a point to a stationary line are characterized. Applications to asymptotically flat spacetimes include the light-convexity of stationary hypersurfaces which project in a spacelike section of an end onto a sphere of large radius, as well as the characterization of their time-convexity with natural physical interpretations. The lens effect of both light rays and freely falling massive particles with a finite lifetime, (i.e. the multiplicity of such connecting curves) is characterized in terms of the focalization of the geodesics in the underlying Randers manifolds.Comment: AMSLaTex, 41 pages. v2 is a major revision: new discussions on physical applicability of the results, especially to asymptotically flat spacetimes; references adde

Methamphetamine Causes Differential Alterations in Gene Expression and Patterns of Histone Acetylation/Hypoacetylation in the Rat Nucleus Accumbens

Methamphetamine (METH) addiction is associated with several neuropsychiatric symptoms. Little is known about the effects of METH on gene expression and epigenetic modifications in the rat nucleus accumbens (NAC). Our study investigated the effects of a non-toxic METH injection (20 mg/kg) on gene expression, histone acetylation, and the expression of the histone acetyltransferase (HAT), ATF2, and of the histone deacetylases (HDACs), HDAC1 and HDAC2, in that structure. Microarray analyses done at 1, 8, 16 and 24 hrs after the METH injection identified METH-induced changes in the expression of genes previously implicated in the acute and longterm effects of psychostimulants, including immediate early genes and corticotropin-releasing factor (Crf). In contrast, the METH injection caused time-dependent decreases in the expression of other genes including Npas4 and cholecystokinin (Cck). Pathway analyses showed that genes with altered expression participated in behavioral performance, cell-to-cell signaling, and regulation of gene expression. PCR analyses confirmed the changes in the expression of c-fos, fosB, Crf, Cck, and Npas4 transcripts. To determine if the METH injection caused post-translational changes in histone markers, we used western blot analyses and identified METH-mediated decreases in histone H3 acetylated at lysine 9 (H3K9ac) and lysine 18 (H3K18ac) in nuclear sub-fractions. In contrast, the METH injection caused time-dependent increases in acetylated H4K5 and H4K8. The changes in histone acetylation were accompanied by decreased expression of HDAC1 but increased expression of HDAC2 protein levels. The histone acetyltransferase, ATF2, showed significant METH-induced increased in protein expression. These results suggest that METH-induced alterations in global gene expression seen in rat NAC might be related, in part, to METH-induced changes in histone acetylation secondary to changes in HAT and HDAC expression. The causal role that HATs and HDACs might play in METH-induced gene expression needs to be investigated further

Emerging roles of ATF2 and the dynamic AP1 network in cancer

Cooperation among transcription factors is central for their ability to execute specific transcriptional programmes. The AP1 complex exemplifies a network of transcription factors that function in unison under normal circumstances and during the course of tumour development and progression. This Perspective summarizes our current understanding of the changes in members of the AP1 complex and the role of ATF2 as part of this complex in tumorigenesis.Fil: Lopez Bergami, Pablo Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental (i); Argentina; ArgentinaFil: Lau, Eric . Burnham Institute for Medical Research; Estados UnidosFil: Ronai, Zeev . Burnham Institute for Medical Research; Estados Unido

Exploring new physics frontiers through numerical relativity

The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We review techniques for solving Einstein's equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology