arXiv subjects

Shinya Sato

Publications and source records attributed to Shinya Sato.

13 recordsLinked to original sources

arXiv2024

Conditional Nested Pattern Matching in Interaction Net

Interaction nets are a form of restricted graph rewrite system that can serve as a graphical or textual programming language. As such, benefits include one-step confluence, ease of parallelism and explicit garbage collection. However, some of these restrictions burden the programmer, so they have been extended in several ways, notably to include data types and conditional rules. This paper introduces a further extension to allow nested pattern matching and to do so in a way that preserves these benefits and fundamental properties of interaction nets. We also show that by introducing a translation to non-nested matching, this extension is conservative in rewriting. In addition, we propose a new notation to express this pattern matching.

cs.PL↗

arXiv2024

Higher-order asymptotic profiles of solutions to the Cauchy problem for the convection-diffusion equation with variable diffusion

We consider the asymptotic behavior of solutions to the convection-diffusion equation: \[ \partial_t u - \mathrm{div}\left(a(x)\nabla u\right) = d\cdot\nabla \left(\left\lvert u\right\rvert ^{q-1}u\right),\ \ x\in\mathbb{R}^n, \ t>0 \] with an integrable initial data $u_{0}(x)$, where $n\ge1$, $q>1+\frac{1}{n}$ and $d\in \mathbb{R}^{n}$. Moreover, we take $a(x)=1+b(x)>0$, where $b(x)$ is smooth and decays fast enough at spatial infinity. It is known that the asymptotic profile of the solution to this problem can be given by the heat kernel. Moreover, some higher-order asymptotic expansions of the solution have already been studied. In particular, the structures of the second asymptotic profiles strongly depend on the nonlinear exponent $q$. More precisely, these profiles have different decay orders in each of the following three cases: $1+\frac{1}{n} 1+\frac{2}{n}$. In this paper, we focus on the critical case $q=1+\frac{2}{n}$. By analyzing the corresponding integral equation in details, we have succeeded to give the more higher-order asymptotic expansion of the solution, which generalizes the previous works.

math.AP↗

arXiv2021

Additivity violation of quantum channels via strong convergence to semi-circular and circular elements

Additivity violation of minimum output entropy, which shows non-classical properties in quantum communication, had been proved in most cases for random quantum channels defined by Haar-distributed unitary matrices. In this paper, we investigate random completely positive maps made of Gaussian Unitary Ensembles and Ginibre Ensembles regarding this matter. Using semi-circular systems and circular systems of free probability, we not only show the multiplicativity violation of maximum output norms in the asymptotic regimes but also prove the additivity violation via Haagerup inequality for a new class of random quantum channels constructed by rectifying the above completely positive maps based on strong convergence.

math-ph↗

arXiv2020

Variations in magnetotelluric response functions caused by Sq currents

The magnetotelluric (MT) responses of the Earth are biased by spatially heterogeneous source fields. Recently, such biases have been reported even in mid-latitude areas, where localized source currents rarely flow. This study focuses on shifts in the MT responses arising from variations in the focus latitude of the solar quiet (Sq) current. The MT responses at 60 s were calculated by changing the center of the Sq current. Slight variations in the focus latitude cause large shifts in the apparent resistivity and phase. During periods of quiet geomagnetic activity, the center varies within a wide range of 20-45 N, whereas this range narrows when there are disruptions. Even though this study considers only a limited case, the results demonstrate the instability of the impedances in periods of quiet geomagnetic activity and a correlation of the MT responses with the magnitude of the geomagnetic activity. As a consequence, even when a station is located at mid-latitudes, the impedances need to be treated carefully for time-lapse MT soundings, for example, by checking the ionospheric current conditions and their dependence on the geomagnetic activity.

physics.geo-ph↗

arXiv2020

Effects of localized source currents on magnetotelluric responses of a flat earth and spherical earth

Shifts in magnetotelluric (MT) responses owing to localized source currents should be considered when visualizing deep subsurface resistivity structures such as the earth mantle. The earth is not flat but spherical; nevertheless, non-uniform geomagnetic temporal variations arising from localized source currents are evaluated on the basis of components in a Cartesian coordinate system. To address this issue, this study assesses the difference in source bias within MT responses of a flat earth and spherical earth. Apparent resistivity and phases are calculated by setting the time period and conductivity of the earth interior to 200/2000 s and 0.001 S/m, respectively, and by changing the vertical and horizontal distances between the source current and an observation station. A deviation in the biased MT responses of the flat earth and spherical earth is not observed although both shift strongly from the true values. We can thus treat the source bias in a Cartesian coordinate system although it originally arises in a spherical coordinate system.

physics.geo-ph↗

arXiv2020

Altitude effects of localized source currents on magnetotelluric responses

The effects of localized source currents on Earth's magnetotelluric (MT) responses have been reported in the literature in terms of the changes in period and subsurface structure. The focus in this study is on the bias within the MT responses arising from variations in the vertical and horizontal distances of the source current. The MT responses at 20 and 200 s were calculated at various distances from the source current. A slight change in source distance causes a shift in the MT responses, and the bias is large, especially over the altitudes explored in the MT data analysis (i.e., 100-150 km), where the E layer exists. The vertical distance of the source field varies because the distribution of conductivity with altitude in the ionosphere and the region controlling the ionospheric electrical process change temporally. Thus, in assessing the temporal changes in MT responses, we should treat them carefully by checking the ionospheric environment.

physics.geo-ph↗

arXiv2016

In-place Graph Rewriting with Interaction Nets

An algorithm is in-place, or runs in-situ, when it does not need any additional memory to execute beyond a small constant amount. There are many algorithms that are efficient because of this feature, therefore it is an important aspect of an algorithm. In most programming languages, it is not obvious when an algorithm can run in-place, and moreover it is often not clear that the implementation respects that idea. In this paper we study interaction nets as a formalism where we can see directly, visually, that an algorithm is in-place, and moreover the implementation will respect that it is in-place. Not all algorithms can run in-place however. We can nevertheless still use the same language, but now we can annotate parts of the algorithm that can run in-place. We suggest an annotation for rules, and give an algorithm to find this automatically through analysis of the interaction rules.

cs.PL↗

arXiv2015

An Implementation Model for Interaction Nets

To study implementations and optimisations of interaction net systems we propose a calculus to allow us to reason about nets, a concrete data-structure that is in close correspondence with the calculus, and a low-level language to create and manipulate this data structure. These work together so that we can describe the compilation process for interaction nets, reason about the behaviours of the implementation, and study the efficiency and properties.

cs.LO↗

arXiv2012

Antiferromagnetic Order and Superconductivity in Sr4(Mg0.5-xTi0.5+x)2O6Fe2As2 with Electron Doping: 75As-NMR Study

We report an 75As-NMR study on iron (Fe)-based superconductors with thick perovskitetype blocking layers Sr4(Mg0.5-xTi0.5+x)2O6Fe2As2 with x=0 and 0.2. We have found that antiferromagnetic (AFM) order takes place when x=0, and superconductivity (SC) emerges below Tc=36 K when x=0.2. These results reveal that the Fe-pnictides with thick perovskitetype blocks also undergo an evolution from the AFM order to the SC by doping electron carriers into FeAs planes through the chemical substitution of Ti+4 ions for Mg+2 ions, analogous to the F-substitution in LaFeAsO compound. The reason why the Tc=36 K when x=0.2 being higher than the optimally electron-doped LaFeAsO with Tc=27 K relates to the fact that the local tetrahedron structure of FeAs4 is optimized for the onset of SC.

cond-mat.supr-con↗

arXiv2010

First Homologous Series of Iron Pnictide Oxide Superconductors (Fe2As2)(Can+1(Sc,Ti)nOy) [n = 3,4,5] with Extremely Thick Blocking Layers

We have discovered first homologous series of iron pnictide oxide superconductors (Fe2As2)(Can+1(Sc,Ti)nOy) [n = 3,4,5]. These compounds have extremely thick blocking layers up to quintuple perovskite oxide layers sandwiched by the Fe2As2 layers. These samples exhibited bulk superconductivity with relatively high Tc up to 42 K. The relationship between Tc and the iron-plane interlayer distance suggested that superconductivity due to the mono Fe2As2 layer is substantially 40 K-class.

cond-mat.supr-con↗

arXiv2010

An Implementation of Nested Pattern Matching in Interaction Nets

Reduction rules in interaction nets are constrained to pattern match exactly one argument at a time. Consequently, a programmer has to introduce auxiliary rules to perform more sophisticated matches. In this paper, we describe the design and implementation of a system for interaction nets which allows nested pattern matching on interaction rules. We achieve a system that provides convenient ways to express interaction net programs without defining auxiliary rules.

cs.LO↗

arXiv2009

Superconductivity at 39 K in New Iron Pnictide Oxide (Fe2As2)(Sr4(Mg,Ti)2O6)

We have discovered a new iron pnictide oxide superconductor (Fe2As2)(Sr4(Mg,Ti)2O6). This material is isostructual with (Fe2As2)(Sr4M2O6) (M = Sc, Cr), which was found in our previous study. The structure of this compound is tetragonal with a space group of P4/nmm and consists of the anti-fluorite type FeAs and perovskite-type blocking layers. The lattice constants are a = 3.935 A and c = 15.952 A for (Fe2As2)(Sr4MgTiO6). In both magnetization and resistivity measurements, this compound exhibits superconductivity below 10 K. Moreover, ratio of Mg and Ti in this compound can be changed toward Ti-rich composition. (Fe2As2)(Sr4Mg1-xTi1+xO6) phase is obtained at 0 < x as a main phase, and Tc and superconducting volume fraction increase with increasing x. The highest Tc(onset) was confirmed at 39 K for x = 0.6 in resistivity measurement.

cond-mat.supr-con↗

arXiv2008

Direct Observation of Local Magnetic Field Generated by Micromagnet

Using standard nuclear magnetic resonance (NMR) technique and a well-fabricated sample, we have succeeded in directly observing local magnetic field generated by a micro-magnet Ni45Fe55 (the thickness of 400-nm) which was sputtered on an Al layer of 20-nm thickness. Improved sensitivity of our NMR technique enabled us to clearly observe Al-NMR signals, which are confirmed to come from Al nuclei in the 20-nm layers. From the analysis of the Al-NMR spectra, the local magnetic field was found to be +0.17+-0.02 (-0.20+-0.01) Tesla, the sign of which is consistent with the geometry that the external magnetic field was applied perpendicular (parallel) to the Al layer. The present study gives a potential key element toward realizing higher resolution in magnetic resonance imaging (MRI).

cond-mat.mes-hall↗