On a q-analogue of the multiple gamma functions

A $q$-analogue of the multiple gamma functions is introduced, and is shown to satisfy the generalized Bohr-Morellup theorem. Furthermore we give some expressions of these function.Comment: 8 pages, AMS-Late

Looking at a soliton through the prism of optical supercontinuum

A traditional view on solitons in optical fibers as robust particle-like structures suited for informa- tion transmission has been significantly altered and broadened over the past decade, when solitons have been found to play the major role in generation of octave broad supercontinuum spectra in photonic-crystal and other types of optical fibers. This remarkable spectral broadening is achieved through complex processes of dispersive radiation being scattered from, emitted and transformed by solitons. Thus solitons have emerged as the major players in nonlinear frequency conversion in optical fibers. Unexpected analogies of these processes have been found with dynamics of ultracold atoms and ocean waves. This colloquium focuses on recent understanding and new insights into physics of soliton-radiation interaction and supercontinuum generation.Comment: http://rmp.aps.org/abstract/RMP/v82/i2/p1287_1 (some figures have been deleted due to space limits imposed by archive

Cosmological test of gravity with polarizations of stochastic gravitational waves around 0.1-1 Hz

In general relativity, a gravitational wave has two polarization modes (tensor mode), but it could have additional polarizations (scalar and vector modes) in the early stage of the universe, where the general relativity may not strictly hold and/or the effect of higher-dimensional gravity may become significant. In this paper, we discuss how to detect extra-polarization modes of stochastic gravitational wave background (GWB), and study the separability of each polarization using future space-based detectors such as BBO and DECIGO. We specifically consider two plausible setups of the spacecraft constellations consisting of two and four clusters, and estimate the sensitivity to each polarization mode of GWBs. We find that a separate detection of each polarization mode is rather sensitive to the geometric configuration and distance between clusters and that the clusters should be, in general, separated by an appropriate distance. This seriously degrades the signal sensitivity, however, for suitable conditions, space-based detector can separately detect scalar, vector and tensor modes of GWBs with energy density as low as ~10^-15.Comment: 16 pages, 11 figure

Direct Measurement of the Positive Acceleration of the Universe and Testing Inhomogeneous Models under Gravitational Wave Cosmology

One possibility for explaining the apparent accelerating expansion of the universe is that we live in the center of a spherically inhomogeneous universe. Although current observations cannot fully distinguish $\Lambda$CDM and these inhomogeneous models, direct measurement of the acceleration of the universe can be a powerful tool in probing them. We have shown that, if $\Lambda$CDM is the correct model, DECIGO/BBO would be able to detect the positive redshift drift (which is the time evolution of the source redshift $z$) in 3--5 year gravitational wave (GW) observations from neutron-star binaries, which enables us to rule out any Lema\^itre-Tolman-Bondi (LTB) void model with monotonically increasing density profile. We may even be able to rule out any LTB model unless we allow unrealistically steep density profile at $z\sim 0$. This test can be performed with GW observations alone, without any reference to electromagnetic observations, and is more powerful than the redshift drift measurement using Lyman $\alpha$ forest.Comment: 5 pages, 2 figure

Nutrient-Regulated Antisense and Intragenic RNAs Modulate a Signal Transduction Pathway in Yeast

The budding yeast Saccharomyces cerevisiae alters its gene expression profile in response to a change in nutrient availability. The PHO system is a well-studied case in the transcriptional regulation responding to nutritional changes in which a set of genes (PHO genes) is expressed to activate inorganic phosphate (Pi) metabolism for adaptation to Pi starvation. Pi starvation triggers an inhibition of Pho85 kinase, leading to migration of unphosphorylated Pho4 transcriptional activator into the nucleus and enabling expression of PHO genes. When Pi is sufficient, the Pho85 kinase phosphorylates Pho4, thereby excluding it from the nucleus and resulting in repression (i.e., lack of transcription) of PHO genes. The Pho85 kinase has a role in various cellular functions other than regulation of the PHO system in that Pho85 monitors whether environmental conditions are adequate for cell growth and represses inadequate (untimely) responses in these cellular processes. In contrast, Pho4 appears to activate some genes involved in stress response and is required for G1 arrest caused by DNA damage. These facts suggest the antagonistic function of these two players on a more general scale when yeast cells must cope with stress conditions. To explore general involvement of Pho4 in stress response, we tried to identify Pho4-dependent genes by a genome-wide mapping of Pho4 and Rpo21 binding (Rpo21 being the largest subunit of RNA polymerase II) using a yeast tiling array. In the course of this study, we found Pi- and Pho4-regulated intragenic and antisense RNAs that could modulate the Pi signal transduction pathway. Low-Pi signal is transmitted via certain inositol polyphosphate (IP) species (IP7) that are synthesized by Vip1 IP6 kinase. We have shown that Pho4 activates the transcription of antisense and intragenic RNAs in the KCS1 locus to down-regulate the Kcs1 activity, another IP6 kinase, by producing truncated Kcs1 protein via hybrid formation with the KCS1 mRNA and translation of the intragenic RNA, thereby enabling Vip1 to utilize more IP6 to synthesize IP7 functioning in low-Pi signaling. Because Kcs1 also can phosphorylate these IP7 species to synthesize IP8, reduction in Kcs1 activity can ensure accumulation of the IP7 species, leading to further stimulation of low-Pi signaling (i.e., forming a positive feedback loop). We also report that genes apparently not involved in the PHO system are regulated by Pho4 either dependent upon or independent of the Pi conditions, and many of the latter genes are involved in stress response. In S. cerevisiae, a large-scale cDNA analysis and mapping of RNA polymerase II binding using a high-resolution tiling array have identified a large number of antisense RNA species whose functions are yet to be clarified. Here we have shown that nutrient-regulated antisense and intragenic RNAs as well as direct regulation of structural gene transcription function in the response to nutrient availability. Our findings also imply that Pho4 is present in the nucleus even under high-Pi conditions to activate or repress transcription, which challenges our current understanding of Pho4 regulation