arXiv subjects

Atsushi Inoue

Publications and source records attributed to Atsushi Inoue.

17 recordsLinked to original sources

arXiv2025

Uniform Validity of the Subset Anderson-Rubin Test under Heteroskedasticity and Nonlinearity

We consider the Anderson-Rubin (AR) statistic for a general set of nonlinear moment restrictions. The statistic is based on the criterion function of the continuous updating estimator (CUE) for a subset of parameters not constrained under the Null. We treat the data distribution nonparametrically with parametric moment restrictions imposed under the Null. We show that subset tests and confidence intervals based on the AR statistic are uniformly valid over a wide range of distributions that include moment restrictions with general forms of heteroskedasticity. We show that the AR based tests have correct asymptotic size when parameters are unidentified, partially identified, weakly or strongly identified. We obtain these results by constructing an upper bound that is using a novel perturbation and regularization approach applied to the first order conditions of the CUE. Our theory applies to both cross-sections and time series data and does not assume stationarity in time series settings or homogeneity in cross-sectional settings.

econ.EM↗

arXiv2024

Essential self-adjointness of the Laplacian on weighted graphs: harmonic functions, stability, characterizations and capacity

We give two characterizations for the essential self-adjointness of the weighted Laplacian on birth-death chains. The first involves the edge weights and vertex measure and is classically known; however, we give another proof using stability results, limit point-limit circle theory and the connection between essential self-adjointness and harmonic functions. The second characterization involves a new notion of capacity. Furthermore, we also analyze the essential self-adjointness of Schrödinger operators, use the characterizations for birth-death chains and stability results to characterize essential self-adjointness for star-like graphs, and give some connections to the $\ell^2$-Liouville property.

math.FA↗

arXiv2024

Does there exist the applicability limit of PDE to describe physical phenomena? -- A personal survey of Quantization, QED, Turbulence

What does it mean to study PDE(=Partial Differential Equation)? How and what to do "to claim proudly that I'm studying a certain PDE"? Newton mechanic uses mainly ODE(=Ordinary Differential Equation) and describes nicely movements of Sun, Moon and Earth etc. Now, so-called quantum phenomenum is described by, say Schr\"odinger equation, PDE which explains both wave and particle characters after quantization of ODE. The coupled Maxwell-Dirac equation is also "quantized" and QED(=Quantum Electro-Dynamics) theory is invented by physicists. Though it is said this QED gives very good coincidence between theoretical and experimental observed quantities, but what is the equation corresponding to QED? Or, is it possible to describe QED by "equation" in naive sense?

physics.gen-ph↗

arXiv2023

Towards a Universal Understanding of Color Harmony: Fuzzy Approach

Harmony level prediction is receiving increasing attention nowadays. Color plays a crucial role in affecting human aesthetic responses. In this paper, we explore color harmony using a fuzzy-based color model and address the question of its universality. For our experiments, we utilize a dataset containing attractive images from five different domains: fashion, art, nature, interior design, and brand logos. We aim to identify harmony patterns and dominant color palettes within these images using a fuzzy approach. It is well-suited for this task because it can handle the inherent subjectivity and contextual variability associated with aesthetics and color harmony evaluation. Our experimental results suggest that color harmony is largely universal. Additionally, our findings reveal that color harmony is not solely influenced by hue relationships on the color wheel but also by the saturation and intensity of colors. In palettes with high harmony levels, we observed a prevalent adherence to color wheel principles while maintaining moderate levels of saturation and intensity. These findings contribute to ongoing research on color harmony and its underlying principles, offering valuable insights for designers, artists, and researchers in the field of aesthetics.

cs.CV↗

arXiv2023

Color Aesthetics: Fuzzy based User-driven Method for Harmony and Preference Prediction

Color is the most important intrinsic sensory feature that has a powerful impact on product sales. Color is even responsible for raising the aesthetic senses in our brains. Account for individual differences is crucial in color aesthetics. It requires user-driven mechanisms for various e-commerce applications. We propose a method for quantitative evaluation of all types of perceptual responses to color(s): distinct color preference, color harmony, and color combination preference. Preference for color schemes can be predicted by combining preferences for the basic colors and ratings of color harmony. Harmonious pallets are extracted from big data set using comparison algorithms based on fuzzy similarity and grouping. The proposed model results in useful predictions of harmony and preference of multicolored images. For example, in the context of apparel coordination, it allows predicting a preference for a look based on clothing colors. Our approach differs from standard aesthetic models, since in accounts for a personal variation. In addition, it can process not only lower-order color pairs, but also groups of several colors.

cs.CV↗

arXiv2023

Inference for Local Projections

Inference for impulse responses estimated with local projections presents interesting challenges and opportunities. Analysts typically want to assess the precision of individual estimates, explore the dynamic evolution of the response over particular regions, and generally determine whether the impulse generates a response that is any different from the null of no effect. Each of these goals requires a different approach to inference. In this article, we provide an overview of results that have appeared in the literature in the past 20 years along with some new procedures that we introduce here.

econ.EM↗

arXiv2021

WIP: Medical Incident Prediction Through Analysis of Electronic Medical Records Using Machine Lerning: Fall Prediction

This paper reports our preliminary work on medical incident prediction in general, and fall risk prediction in specific, using machine learning. Data for the machine learning are generated only from the particular subset of the electronic medical records (EMR) at Osaka Medical and Pharmaceutical University Hospital. As a result of conducting three experiments such as (1) machine learning algorithm comparison, (2) handling imbalance, and (3) investigation of explanatory variable contribution to the fall incident prediction, we find the investigation of explanatory variables the most effective.

cs.LG↗

arXiv2021

Two Sample Unconditional Quantile Effect

This paper proposes a new framework to evaluate unconditional quantile effects (UQE) in a data combination model. The UQE measures the effect of a marginal counterfactual change in the unconditional distribution of a covariate on quantiles of the unconditional distribution of a target outcome. Under rank similarity and conditional independence assumptions, we provide a set of identification results for UQEs when the target covariate is continuously distributed and when it is discrete, respectively. Based on these identification results, we propose semiparametric estimators and establish their large sample properties under primitive conditions. Applying our method to a variant of Mincer's earnings function, we study the counterfactual quantile effect of actual work experience on income.

econ.EM↗

arXiv2015

Lectures on Super Analysis -- Why necessary and What's that?

Roughly speaking, RA(=real analysis) means to study properties of (smooth) functions defined on real space, and CA(=complex analysis) stands for studying properties of (holomorphic) functions defined on spaces with complex structure. But to treat boson and fermion on equal footing, we need to prepare as a "ground ring", Fréchet-Grassmann algebra having countably many Grassmann generators and we define so-called superspace over such algebra. On such superspaces, we introduce spaces of super-smooth functions and develop elementary differential and integral calculus. With a slight preparation of functional analysis, we explain the Efetov's method in RMT(=random matrix theory). The free Weyl equation is treated to answer the problem posed by Feynman in their famous book. Simple examples of SUSYQM(=supersymmetric quantum mechanics) are calculated from this point of view. In the final chapter, we give a precise proof of Berezin's formula for changing variables under integral sign, brief introduction of real analysis on superspace, another construction of fundamental solution of Qi's weakly hyperbolic equation, Bernardi's question for a system version of Egorov's theorem, etc. A little discussion of Funtional Derivative Equations which are candidates of new branch of mathematics, is given. And finally, we construct a Hamilton flow corresponding to the Weyl equation with external electro-magnetic potentials, where we need the countably infinite Grassmann generators and weak topology! I mention many open problems at least for me (alias ATLOM=a tiny little old mathematician).

math-ph↗

arXiv2014

Definition and characterization of supersmooth functions on superspace based on Fréchet-Grassmann algebra

Preparing the Fréchet-Grassmann (FG-)algebra ${\fR}$ composed with countably infinite Grassmann generators, we introduce the superspace ${\fR}^{m|n}$. After defining Grassmann continuation of smooth functions on ${\euc}^m$ to those on ${\fR}^{m|0}$, we introduce a class of functions on ${\fR}^{m|n}$ which are called supersmooth. In this paper, we characterize such supersmooth functions in Gâteaux (but not necessarily Fréchet) differentiable category on Fréchet but not on Banach space. This type of arguments for $G^{\infty}$-functions is mainly done on the Banach-Grassmann (BG-)algebra, but we find it rather natural to work within FG-algebra when we treat systems of PDE such as Dirac, Weyl or Pauli equations. In that application, we need to prove that the solution of the (super) Hamilton equation is supersmooth w.r.t. initial data. Though we took this point of view in our previous works, but is managed rather insufficiently. Therefore, we re-treat this subject here to answer affirmatively. We give also local or global inverse function theorems for supersmooth functions on ${\fR}^{m|n}$.

math-ph↗

arXiv2014

Remarks on elementary integral calculus for supersmooth functions on superspace ${\mathfrak{R}}^{m|n}$

After introducing Berezin integral for polynomials of odd variables, we develop the elementary integral calculus based on supersmooth functions on the superspace ${\mathfrak{R}}^{m|n}$. Here, ${\mathfrak{R}}$ is the Fréchet-Grassmann algebra with countably infinite Grassmann generators, which plays the role of real number field ${\mathbb{R}}$. As is well-known that the formula of change of variables under integral sign is indispensable not only to treat PDE applying funtional analytic method but also to introduce analysis on supermanifolds. But, if we define naively the integral for supersmooth functions, there exists discrepancy which should be ameliorated. Here, we extend the contour integral modifying the parameter space introduced basically by de Witt, Rogers and Vladimirov and Volovich

math-ph↗

arXiv2013

Weak commutation relations of unbounded operators: nonlinear extensions

We continue our analysis of the consequences of the commutation relation $[S,T]=\Id$, where $S$ and $T$ are two closable unbounded operators. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space $\H$ where the operators act. {We also consider what we call, adopting a physical terminology}, a {\em nonlinear} extension of the above commutation relations.

math-ph↗

arXiv2012

Locally convex quasi $C^*$-normed algebras

If $\ca_0[|\cdot|_0]$ is a $\cs$-normed algebra and $τ$ a locally convex topology on $\ca_0$ making its multiplication separately continuous, then $\widetilde{\ca_0}[τ]$ (completion of $\ca_0[τ]$) is a locally convex quasi *-algebra over $\ca_0$, but it is not necessarily a locally convex quasi *-algebra over the $\cs$-algebra $\widetilde{\ca_0}[|\cdot|_0]$ (completion of $\ca_0[|\cdot|_0]$). In this article, stimulated by physical examples, we introduce the notion of a locally convex quasi $\cs$-normed algebra, aiming at the investigation of $\widetilde{\ca_0}[τ]$; in particular, we study its structure, *-representation theory and functional calculus.

math-ph↗

arXiv2012

Representable linear functionals on partial *-algebras

A GNS - like *-representation of a \pa\ $\A$ defined by certain representable linear functionals on $\A$ is constructed. The study of the interplay with the GNS construction associated with invariant positive sesquilinear forms (ips) leads to the notions of pre-core and of singular form. It is shown that a positive sesquilinear form with pre-core always decomposes into the sum of an ips form and a singular one.

math-ph↗

arXiv2012

Induced and reduced unbounded operator algebras

The induction and reduction precesses of an O*-vector space $\M$ obtained by means of a projection taken, respectively, in $\M$ itself or in its weak bounded commutant $\M'_\w$ are studied. In the case where $\M$ is a partial GW*-algebra, sufficient conditions are given for the induced and the reduced spaces to be partial GW*-algebras again.

math-ph↗

arXiv2011

Weak commutation relations of unbounded operators and applications

Four possible definitions of the commutation relation $[S,T]=\Id$ of two closable unbounded operators $S,T$ are compared. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space $\H$ where the operators act. Some consequences on the existence of eigenvectors of two number-like operators are derived and the partial O*-algebra generated by $S,T$ is studied. Some applications are also considered.

math-ph↗

arXiv2002

An extension of the method of characteristic to a system of Partial Differential Operators-- an application to the Weyl equation with external field by "Super Hamiltonian path-integral method"

By taking the Weyl equation with external electro-magnetic potentials as the simplest representative for a system of PDOs, we give a new method of treating non-commutativity of coefficients matrices. More precisely, we construct a Fourier Integral Operator with``matrix-like phase and amplitude'' which gives a parametrix for that Weyl equation. To do this, we first reduce the usual matrix valued Weyl equation on the Euclidian space to the one on the superspace, called the super Weyl equation. Using analysis on superspace, we may associate a function, called the super Hamiltonian function, corresponding to that super Weyl equation. Starting from this super Hamiltonian function, we define phase and amplitude functions which are solutions of the Hamilton-Jacobi equation and the continuity equation on the superspace, respectively. Then, we define a Fourier integral operator with these phase and amplitude functions which gives a good parametrix for the initial value problem of that super Weyl equation. After taking the Lie-Trotter-Kato limit with respect to the time slicing, we get the desired evolutional operator of the super Weyl equation. Bringing back this result to the matrix formulation, we have the final result. Therefore, we get a quantum mechanics with spin from a classical mechanics on the superspace which answers partly the problem of Feynman.

math-ph↗