Real K3 surfaces with non-symplectic involution and applications. II

We consider real forms of relatively minimal rational surfaces F_m. Connected components of moduli of real non-singular curves in |-2K_{F_m}| had been classified recently for m=0, 1, 4 in math.AG/0312396. Applying similar methods, here we fill the gap for m=2 and m=3 to complete similar classification for any 0\le m\le 4 when |-2K_{F_m}| is reduced. The case of F_2 is especially remarkable and classical (quadratic cone in P^3). As an application, we finished classification of connected components of moduli of real hyper-elliptically polarized K3 surfaces and their deformations to real polarized K3 surfaces started in math.AG/0312396, math.AG/0507197. This could be important in some questions because real hyper-elliptically polarized K3 surfaces can be constructed explicitly.Comment: 22 pages, 6 figure

Prospects for determination of thermal history after inflation with future gravitational wave detectors

Thermal history of the Universe between inflation and big-bang nucleosynthesis has not yet been revealed observationally. It will be probed by the detection of primordial gravitational waves generated during inflation, which contain information on the reheating temperature as well as the equation of state of the Universe after inflation. Based on Fisher information formalism, we examine how accurately the tensor-to-scalar ratio and reheating temperature after inflation can be simultaneously determined with space-based gravitational wave detectors such as the DECI-hertz Interferometer Gravitational-wave Observatory (DECIGO) and the Big-Bang Observer (BBO). We show that the reheating temperature is best determined if it is around 10^7 GeV for tensor-to-scalar ratio of around 0.1, and explore the detectable parameter space. We also find that equation of state of the early Universe can be also determined accurately enough to distinguish different equation-of-state parameters if the inflationary gravitational waves are successfully detected. Thus future gravitational wave detectors provide a unique and promising opportunity to reveal the thermal history of the Universe around 10^7 GeV.Comment: 21 pages, 8 figure

A note on Newton non-degeneracy of mixed weighted homogeneous polynomials

A mixed polynomial $f(\boldsymbol{z}, \bar{\boldsymbol{z}})$ is called a mixed weighted homogeneous polynomial (Definition 5) if it is both radially and polar weighted homogeneous. Let $f$ be a mixed weighted homogeneous polynomial with respect to a strictly positive radial weight vector $P$ and a polar weight vector $Q$. Suppose that $f$ is Newton non-degenerate over a compact face $\Delta(P)$ and polar weighted homogeneous of non-zero polar degree with respect to $Q$. Then $f : {{\mathbb{C}}^*}^n \to \mathbb{C}$ has no mixed critical points. Moreover, under the assumption $f^{-1}(0) \cap {{\mathbb{C}}^*}^n \neq \emptyset$, $f : {{\mathbb{C}}^*}^n \to \mathbb{C}$ is surjective. In other words, in this situation, Newton non-degeneracy over a compact face $\Delta(P)$ implies strong Newton non-degeneracy over $\Delta(P)$ (Proposition 10). With this fact as a starting point, we investigate the sets $f^{-1}(0) \cap {{\mathbb{C}}^*}^n$, and show the existence of a collection of mixed weighted homogeneous polynomials $f = f_{\Delta (P)}$ of non-zero polar degree which satisfy $\dim \Delta (P) \geq 1$ and $f^{-1}(0) \cap {{\mathbb{C}}^*}^n = \emptyset$ (Theorem 11). We also give an example of convenient mixed function germs of mixed weighted homogeneous face type which are not true non-degenerate (Definition 14).Comment: 11 page

KUS121 attenuates the progression of monosodium iodoacetate-induced osteoarthritis in rats

Currently there is no effective treatment available for osteoarthritis (OA). We have recently developed Kyoto University Substances (KUSs), ATPase inhibitors specific for valosin-containing protein (VCP), as a novel class of medicine for cellular protection. KUSs suppressed intracellular ATP depletion, endoplasmic reticulum (ER) stress, and cell death. In this study, we investigated the effects of KUS121 on chondrocyte cell death. In cultured chondrocytes differentiated from ATDC5 cells, KUS121 suppressed the decline in ATP levels and apoptotic cell death under stress conditions induced by TNFα. KUS121 ameliorated TNFα-induced reduction of gene expression in chondrocytes, such as Sox9 and Col2α. KUS121 also suppressed ER stress and cell death in chondrocytes under tunicamycin load. Furthermore, intraperitoneal administration of KUS121 in vivo suppressed chondrocyte loss and proteoglycan reduction in knee joints of a monosodium iodoacetate-induced OA rat model. Moreover, intra-articular administration of KUS121 more prominently reduced the apoptosis of the affected chondrocytes. These results demonstrate that KUS121 protects chondrocytes from stress-induced cell death in vitro and in vivo, and indicate that KUS121 is a promising novel therapeutic agent to prevent the progression of OA

Unexpected Instability of Family of Repeats (FR), the Critical cis-Acting Sequence Required for EBV Latent Infection, in EBV-BAC Systems

A group of repetitive sequences, known as the Family of Repeats (FR), is a critical cis-acting sequence required for EBV latent infection. The FR sequences are heterogeneous among EBV strains, and they are sometimes subject to partial deletion when subcloned in E. coli-based cloning vectors. However, the FR stability in EBV-BAC (bacterial artificial chromosome) system has never been investigated. We found that the full length FR of the Akata strain EBV was not stably maintained in a BAC vector. By contrast, newly obtained BAC clones of the B95-8 strain of EBV stably maintained the full length FR during recombinant virus production and B-cell transformation. Investigation of primary DNA sequences of Akata–derived EBV-BAC clones indicates that the FR instability is most likely due to a putative secondary structure of the FR region. We conclude that the FR instability in EBV-BAC clones can be a pitfall in E. coli-mediated EBV genetics