arXiv subjects

Ryo Kato

Publications and source records attributed to Ryo Kato.

26 records · Page 2Linked to original sources

arXiv2020

Search for ultralight scalar dark matter with NANOGrav pulsar timing arrays

An ultralight scalar field is a candidate for the dark matter. The ultralight scalar dark matter with mass around $10^{-23}\,{\rm eV}$ induces oscillations of the pulse arrival time in the sensitive frequency range of the pulsar timing arrays. We search for the ultralight scalar dark matter using the North American Nanohertz Observatory for Gravitational Waves 11-year Data Set. We give the 95% confidence upper limit for the signal induced by the ultralight scalar dark matter. In comparison with the published Bayesian upper limits on the amplitude of the ultralight scalar dark matter obtained by Bayesian analysis using the Parkes Pulsar Timing Array 12-year data set (Porayko et al. 2018), we find three times stronger upper limit in the frequency range from $10^{-8.34}$ to $10^{-8.19}\,{ \rm Hz}$ which corresponds to the mass range from $9.45\times10^{-24}$ to $1.34\times10^{-23}\,{\rm eV}$. In terms of the energy density of the dark matter, we find that the energy density near the Earth is less than $7\,{\rm GeV/cm^3}$ in the range from $10^{-8.55}$ to $10^{-8.01}\,{ \rm Hz}$ (from $5.83\times10^{-24}$ to $2.02\times10^{-23}\,{\rm eV}$). The strongest upper limit on the the energy density is given by $2\,{\rm GeV/cm^3}$ at a frequency $10^{-8.28}\,{ \rm Hz}$ (corresponding to a mass $1.09\times10^{-23}\,{\rm eV}$). We find that the signal of the ultralight scalar dark matter can be explained by the solar system ephemeris effect. Also, we reveal that the model of the solar system ephemeris effect prefers parameters which are contrary to the expectation that noise will be reduced on all pulsars.

astro-ph.HE↗

arXiv2016

cvpaper.challenge in 2015 - A review of CVPR2015 and DeepSurvey

The "cvpaper.challenge" is a group composed of members from AIST, Tokyo Denki Univ. (TDU), and Univ. of Tsukuba that aims to systematically summarize papers on computer vision, pattern recognition, and related fields. For this particular review, we focused on reading the ALL 602 conference papers presented at the CVPR2015, the premier annual computer vision event held in June 2015, in order to grasp the trends in the field. Further, we are proposing "DeepSurvey" as a mechanism embodying the entire process from the reading through all the papers, the generation of ideas, and to the writing of paper.

cs.CV↗

arXiv2016

Rational orbits of the space of pairs of exceptional Jordan algebras

Let $k$ be a field of characteristic not equal to $2,3$, $\mathbb{O}$ an octonion over $k$ and $\mathcal{J}$ the exceptional Jordan algebra defined by $\mathbb{O}$. We consider the prehomogeneous vector space $(G,V)$ where $G=GE_6\times \mathrm{GL}(2)$ and $V=\mathcal{J}\oplus \mathcal{J}$. We prove that generic rational orbits of this prehomogeneous vector space are in bijective correspondence with $k$-isomorphism classes of pairs $(\mathcal{M},\mathfrak{n})$ where $\mathcal{M}$'s are isotopes of $\mathcal{J}$ and $\mathfrak{n}$'s are cubic étale subalgebras of $\mathcal{M}$. Also we prove that if $\mathbb{O}$ is split, then generic rational orbits are in bijective correspondence with isomorphism classes of separable extensions of $k$ of degrees up to $3$.

math.NT↗

arXiv2016

On equivariant maps related to the space of pairs of exceptional Jordan algebras

Let $\mathcal{J}$ be the exceptional Jordan algebra and $V=\mathcal{J}\oplus \mathcal{J}$. We construct an equivariant map from $V$ to $\mathrm{Hom}_k(\mathcal{J}\otimes \mathcal{J},\mathcal{J})$ defined by homogeneous polynomials of degree $8$ such that if $x\in V$ is a generic point, then the image of $x$ is the structure constant of the isotope of $\mathcal{J}$ corresponding to $x$. We also give an alternative way to define the isotope corresponding to a generic point of $\mathcal{J}$ by an equivariant map from $\mathcal{J}$ to the space of trilinear forms.

math.RT↗

arXiv2015

Probing circular polarization in stochastic gravitational wave background with pulsar timing arrays

We study the detectability of circular polarization in a stochastic gravitational wave background from various sources such as supermassive black hole binaries, cosmic strings, and inflation in the early universe with pulsar timing arrays. We calculate generalized overlap reduction functions for the circularly polarized stochastic gravitational wave background. We find that the circular polarization can not be detected for an isotropic background. However, there is a chance to observe the circular polarization for an anisotropic gravitational wave background. We also show how to separate polarized gravitational waves from unpolarized gravitational waves.

gr-qc↗

arXiv2014

A remark on the Wiener-Ikehara Tauberian theorem

In this paper we point out that the proof of Kable's extension of the Wiener-Ikehara Tauberian theorem can be applied to the case where the Dirichlet series has a pole of order "$l / m$" without much modification (Kable proved the case $l = 1$).

math.NT↗

arXiv2012

The first line of the Bockstein spectral sequence on a monochromatic spectrum at an odd prime

The chromatic spectral sequence is introduced in \cite{mrw} to compute the $E_2$-term of the \ANSS\ for computing the stable homotopy groups of spheres. The $E_1$-term $E_1^{s,t}(k)$ of the spectral sequence is an Ext group of $BP_*BP$-comodules. There are a sequence of Ext groups $E_1^{s,t}(n-s)$ for non-negative integers $n$ with $E_1^{s,t}(0)=E_1^{s,t}$, and Bockstein spectral sequences computing a module $E_1^{s,*}(n-s)$ from $E_1^{s-1,*}(n-s+1)$. So far, a small number of the $E_1$-terms are determined. Here, we determine the $E_1^{1,1}(n-1)=\e^1M^1_{n-1}$ for $p>2$ and $n>3$ by computing the Bockstein spectral sequence with $E_1$-term $E_1^{0,s}(n)$ for $s=1,2$. As an application, we study the non-triviality of the action of $α_1$ and $β_1$ in the homotopy groups of the second Smith-Toda spectrum V(2).

math.AT↗

arXiv2012

Products of Greek letter elements dug up from the third Morava stabilizer algebra

Oka and the second author considered the cohomology of the second Morava stabilizer algebra to study nontriviality of the products of beta elements of the stable homotopy groups of spheres. In this paper, we use the cohomology of the third Morava stabilizer algebra to find nontrivial products of Greek letters of the stable homotopy groups of spheres: $\al_1\ga_t$, $\be_2\ga_t$, $\lrk{\al_1,\al_1,\be_{p/p}^p}\ga_t\be_1$ and $\lrk{\be_1,p,\ga_t}$ for $t$ with $p\nmid t(t^2-1)$ for a prime number $p>5$.

math.AT↗