Renormalization-group Method for Reduction of Evolution Equations; invariant manifolds and envelopes

The renormalization group (RG) method as a powerful tool for reduction of evolution equations is formulated in terms of the notion of invariant manifolds. We start with derivation of an exact RG equation which is analogous to the Wilsonian RG equations in statistical physics and quantum field theory. It is clarified that the perturbative RG method constructs invariant manifolds successively as the initial value of evolution equations, thereby the meaning to set $t_0=t$ is naturally understood where $t_0$ is the arbitrary initial time. We show that the integral constants in the unperturbative solution constitutes natural coordinates of the invariant manifold when the linear operator $A$ in the evolution equation has no Jordan cell; when $A$ has a Jordan cell, a slight modification is necessary because the dimension of the invariant manifold is increased by the perturbation. The RG equation determines the slow motion of the would-be integral constants in the unperturbative solution on the invariant manifold. We present the mechanical procedure to construct the perturbative solutions hence the initial values with which the RG equation gives meaningful results. The underlying structure of the reduction by the RG method as formulated in the present work turns out to completely fit to the universal one elucidated by Kuramoto some years ago. We indicate that the reduction procedure of evolution equations has a good correspondence with the renormalization procedure in quantum field theory; the counter part of the universal structure of reduction elucidated by Kuramoto may be the Polchinski's theorem for renormalizable field theories. We apply the method to interface dynamics such as kink-anti-kink and soliton-soliton interactions in the latter of which a linear operator having a Jordan-cell structure appears.Comment: 67 pages. No figures. v2: Additional discussions on the unstable motion in the the double-well potential are given in the text and the appendix added. Some references are also added. Introduction is somewhat reshape

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

Protective Role of HLA-DRB1*13:02 against Microscopic Polyangiitis and MPO-ANCA-Positive Vasculitides in a Japanese Population: A Case-Control Study

Among antineutrophil cytoplasmic antibody (ANCA)-associated vasculitides (AAV), granulomatosis with polyangiitis (GPA) and proteinase 3-ANCA-positive AAV (PR3-AAV) are prevalent in European populations, while microscopic polyangiitis (MPA) and myeloperoxidase-ANCA-positive AAV (MPO-AAV) are predominant in the Japanese. We previously demonstrated association of DRB1*09:01-DQB1*03:03 haplotype, a haplotype common in East Asians but rare in the European populations, with MPA/MPO-AAV, suggesting that a population difference in HLA-class II plays a role in the epidemiology of this disease. To gain further insights, we increased the sample size and performed an extended association study of DRB1 and DPB1 with AAV subsets in 468 Japanese patients with AAV classified according to the European Medicines Agency algorithm (MPA: 285, GPA: 92, eosinophilic GPA [EGPA]: 56, unclassifiable: 35) and 596 healthy controls. Among these patients, 377 were positive for MPO-ANCA and 62 for PR3-ANCA. The significance level was set at α = 3.3x10-4 by applying Bonferroni correction. The association of DRB1*09:01 with MPO-AAV was confirmed (allele model, P = 2.1x10-4, odds ratio [OR] = 1.57). Protective association of DRB1*13:02 was detected against MPO-AAV (allele model, P = 2.3x10-5, OR = 0.42) and MPA (dominant model, P = 2.7x10-4, OR = 0.43). A trend toward increased frequency of DPB1*04:01, the risk allele for GPA in European populations, was observed among Japanese patients with PR3-AAV when conditioned on DRB1*13:02 (Padjusted = 0.0021, ORadjusted = 3.48). In contrast, the frequency of DPB1*04:01 was decreased among Japanese patients with MPO-AAV, and this effect lost significance when conditioned on DRB1*13:02 (Padjusted = 0.16), suggesting that DRB1*13:02 or other allele(s) in linkage disequilibrium may be responsible for the protection. The differential association of DPB1*04:01 with PR3-AAV and MPO-AAV and difference in DPB1*04:01 allele frequencies between populations supported the hypothesis that the HLA-class II population difference may account in part for these epidemiologic characteristics. Furthermore, taken together with our previous observations, the haplotype carrying DRB1*13:02 was suggested to be a shared protective factor against multiple autoimmune diseases

Supernova remnants: the X-ray perspective

Supernova remnants are beautiful astronomical objects that are also of high scientific interest, because they provide insights into supernova explosion mechanisms, and because they are the likely sources of Galactic cosmic rays. X-ray observations are an important means to study these objects.And in particular the advances made in X-ray imaging spectroscopy over the last two decades has greatly increased our knowledge about supernova remnants. It has made it possible to map the products of fresh nucleosynthesis, and resulted in the identification of regions near shock fronts that emit X-ray synchrotron radiation. In this text all the relevant aspects of X-ray emission from supernova remnants are reviewed and put into the context of supernova explosion properties and the physics and evolution of supernova remnants. The first half of this review has a more tutorial style and discusses the basics of supernova remnant physics and thermal and non-thermal X-ray emission. The second half offers a review of the recent advances.The topics addressed there are core collapse and thermonuclear supernova remnants, SN 1987A, mature supernova remnants, mixed-morphology remnants, including a discussion of the recent finding of overionization in some of them, and finally X-ray synchrotron radiation and its consequences for particle acceleration and magnetic fields.Comment: Published in Astronomy and Astrophysics Reviews. This version has 2 column-layout. 78 pages, 42 figures. This replaced version has some minor language edits and several references have been correcte