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Yuki Ueda

Publications and source records attributed to Yuki Ueda.

33 records · Page 2Linked to original sources
arXiv2022

Rates of convergence for laws of the spectral maximum of free random variables

Let $\{X_n\}_n$ be a sequence of freely independent, identically distributed non-commutative random variables. Consider a sequence $\{W_n\}_n$ of the renormalized spectral maximum of random variables $X_1,\cdots, X_n$. It is known that the renormalized spectral maximum $W_n$ converges to the free extreme value distribution under certain conditions on the distribution function. In this paper, we provide a rate of convergence in the Kolmogorov distance between a distribution function of $W_n$ and the free extreme value distribution.

math.PR↗
arXiv2021

Stability of energy landscape for Ising models

In this paper, we explore the stability of the energy landscape of an Ising Hamiltonian when subjected to two kinds of perturbations: a perturbation on the coupling coefficients and external fields, and a perturbation on the underlying graph structure. We give sufficient conditions so that the ground states of a given Hamiltonian are stable under perturbations of the first kind in terms of order preservation. Here by order preservation we mean that the ordering of energy corresponding to two spin configurations in a perturbed Hamiltonian will be preserved in the original Hamiltonian up to a given error margin. We also estimate the probability that the energy gap between ground states for the original Hamiltonian and the perturbed Hamiltonian is bounded by a given error margin when the coupling coefficients and local external magnetic fields of the original Hamiltonian are i.i.d. Gaussian random variables. In the end we show a concrete example of a system which is stable under perturbations of the second kind.

math-ph↗
arXiv2021

Can We Benchmark Code Review Studies? A Systematic Mapping Study of Methodology, Dataset, and Metric

Code Review (CR) is the cornerstone for software quality assurance and a crucial practice for software development. As CR research matures, it can be difficult to keep track of the best practices and state-of-the-art in methodology, dataset, and metric. This paper investigates the potential of benchmarking by collecting methodology, dataset, and metric of CR studies. A systematic mapping study was conducted. A total of 112 studies from 19,847 papers published in high-impact venues between the years 2011 and 2019 were selected and analyzed. First, we find that empirical evaluation is the most common methodology (65% of papers), with solution and experience being the least common methodology. Second, we highlight 50% of papers that use the quantitative method or mixed-method have the potential for replicability. Third, we identify 457 metrics that are grouped into sixteen core metric sets, applied to nine Software Engineering topics, showing different research topics tend to use specific metric sets. We conclude that at this stage, we cannot benchmark CR studies. Nevertheless, a common benchmark will facilitate new researchers, including experts from other fields, to innovate new techniques and build on top of already established methodologies. A full replication is available at https://naist-se.github.io/code-review/.

cs.SE↗
arXiv2021

Analysis of fully discrete finite element methods for 2D Navier--Stokes equations with critical initial data

First-order convergence in time and space is proved for a fully discrete semi-implicit finite element method for the two-dimensional Navier--Stokes equations with $L^2$ initial data in convex polygonal domains, without extra regularity assumptions or grid-ratio conditions. The proof utilises the smoothing properties of the Navier--Stokes equations, an appropriate duality argument, and the smallness of the numerical solution in the discrete $L^2(0,t_m;H^1)$ norm when $t_m$ is smaller than some constant. Numerical examples are provided to support the theoretical analysis.

math.NA↗
arXiv2020

Limit theorems for classical, freely and Boolean max-infinitely divisible distributions

We investigate a Belinschi-Nica type semigroup for free and Boolean max-convolutions. We prove that this semigroup at time one connects limit theorems for freely and Boolean max-infinitely divisible distributions. Moreover, we also construct a max-analogue of Boolean-classical Bercovici-Pata bijection, establishing the equivalence of limit theorems for Boolean and classical max-infinitely divisible distributions.

math.PR↗
arXiv2020

Log-unimodality for free positive multiplicative Brownian motion

We prove that the marginal law $σ_{t}\boxtimesν$ of free positive multiplicative Brownian motion is log-unimodal for all $t>0$ if $ν$ is a multiplicatively symmetric log-unimodal distribution, and that $σ_{t}\boxtimesν$ is log-unimodal for sufficiently large $t$ if $ν$ is supported on a suitably chosen finite interval. Counterexamples are given when $ν$ is not assumed to be symmetric or having a bounded support.

math.PR↗
arXiv2020

DevReplay: Automatic Repair with Editable Fix Pattern

Static analysis tools, or linters, detect violation of source code conventions to maintain project readability. Those tools automatically fix specific violations while developers edit the source code. However, existing tools are designed for the general conventions of programming languages. These tools do not check the project/API-specific conventions. We propose a novel static analysis tool DevReplay that generates code change patterns by mining the code change history, and we recommend changes using the matched patterns. Using DevReplay, developers can automatically detect and fix project/API-specific problems in the code editor and code review. Also, we evaluate the accuracy of DevReplay using automatic program repair tool benchmarks and real software. We found that DevReplay resolves more bugs than state-of-the-art APR tools. Finally, we submitted patches to the most popular open-source projects that are implemented by different languages, and project reviewers accepted 80% (8 of 10) patches. DevReplay is available on https://devreplay.github.io.

cs.SE↗
arXiv2019

Numerical computations of split Bregman method for fourth order total variation flow

The split Bregman framework for Osher-Solé-Vese (OSV) model and fourth order total variation flow are studied. We discretize the problem by piecewise constant function and compute $\nabla(-Δ_{\mathrm{av}})^{-1}$ approximately and exactly. Furthermore, we provide a new shrinkage operator for Spohn's fourth order model. Numerical experiments are demonstrated for fourth order problems under periodic boundary condition.

math.NA↗
arXiv2019

Unimodality for free multiplicative convolution with free normal distributions on the unit circle

We study unimodality for free multiplicative convolution with free normal distributions $\{λ_t\}_{t>0}$ on the unit circle. We give four results on unimodality for $μ\boxtimesλ_t$: (1) if $μ$ is a symmetric unimodal distribution on the unit circle then so is $μ\boxtimes λ_t$ at any time $t>0$; (2) if $μ$ is a symmetric distribution on $\mathbb{T}$ supported on $\{e^{iθ}: θ\in [-φ,φ]\}$ for some $φ\in (0,π/2)$, then $μ\boxtimes λ_t$ is unimodal for sufficiently large $t>0$; (3) ${\bf b} \boxtimes λ_t$ is not unimodal at any time $t>0$, where ${\bf b}$ is the equally weighted Bernoulli distribution on $\{1,-1\}$; (4) $λ_t$ is not freely strongly unimodal for sufficiently small $t>0$. Moreover, we study unimodality for classical multiplicative convolution (with Poisson kernels), which is useful in proving the above four results.

math.PR↗
arXiv2018

Free infinite divisibility for generalized power distributions with free Poisson term

We study free infinite divisibility (FID) for a class which is called generalized power distributions with free Poisson term by using a complex analytic technique and a calculation for the free cumulants and Hankel determinants. In particular, our main result implies that (i) if $X$ follows the free Generalized Inverse Gaussian distribution, then $X^r$ follows an FID distribution when $|r|\ge1$, (ii) if $S$ follows the standard semicircle law and $u\ge 2$, then $(S+u)^r$ follows an FID distribution when $r\le -1$, and (iii) if $B_p$ follows the beta distribution with parameters $p$ and $3/2$, then (a) $B_p^r$ follows an FID distribution when $|r|\ge 1$ and $0 1/2$.

math.PR↗
arXiv2018

Large time unimodality for classical and free Brownian motions with initial distributions

We prove that classical and free Brownian motions with initial distributions are unimodal for sufficiently large time, under some assumption on the initial distributions. The assumption is almost optimal in some sense. Similar results are shown for a symmetric stable process with index 1 and a positive stable process with index $1/2$. We also prove that free Brownian motion with initial symmetric unimodal distribution is unimodal, and discuss strong unimodality for free convolution.

math.PR↗
arXiv2018

The inf-sup condition and error estimates of the Nitsche method for evolutionary diffusion-advection-reaction equations

The Nitsche method is a method of "weak imposition" of the inhomogeneous Dirichlet boundary conditions for partial differential equations. This paper explains stability and convergence study of the Nitsche method applied to evolutionary diffusion-advection-reaction equations. We mainly discuss a general space semidiscrete scheme including not only the standard finite element method but also Isogeometric Analysis. Our method of analysis is a variational one that is a popular method for studying elliptic problems. The variational method enables us to obtain the best approximation property directly. Actually, results show that the scheme satisfies the inf-sup condition and Galerkin orthogonality. Consequently, the optimal order error estimates in some appropriate norms are proven under some regularity assumptions on the exact solution. We also consider a fully discretized scheme using the backward Euler method. Numerical example demonstrate the validity of those theoretical results.

math.NA↗