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Quantitative spectroscopy of molecular hydrogen has generated substantial demand, leading to the accumulation of diverse elementary-process data encompassing radiative transitions, electron-impact transitions, predissociations, and quenching. However, their rates currently available are still sparse and there are inconsistencies among those proposed by different authors. In this study, we demonstrate an experimental validation of such molecular dataset by composing a collisional-radiative model (CRM) for molecular hydrogen and comparing experimentally-obtained vibronic populations across multiple levels. From the population kinetics of molecular hydrogen, the importance of each elementary process in various parameter space is studied. In low-density plasmas (electron density $n_\mathrm{e} \lesssim 10^{17}\;\mathrm{m^{-3}}$) the excitation rates from the ground states and radiative decay rates, both of which have been reported previously, determines the excited state population. The inconsistency in the excitation rates affects the population distribution the most significantly in this parameter space. On the other hand, in higher density plasmas ($n_\mathrm{e} \gtrsim 10^{18}\;\mathrm{m^{-3}}$), the excitation rates \textit{from} excited states become important, which have never been reported in the literature, and may need to be approximated in some way. In order to validate these molecular datasets and approximated rates, we carried out experimental observations for two different hydrogen plasmas; a low-density radio-frequency (RF) heated plasma ($n_\mathrm{e}\approx 10^{16}\;\mathrm{m^{-3}}$) and the Large Helical Device (LHD) divertor plasma ($n_\mathrm{e}\gtrsim 10^{18}\;\mathrm{m^{-3}}$)... [continued]

This paper focuses on the Bregman divergence defined by the reciprocal function, called the inverse divergence. For the loss function defined by the monotonically increasing function $f$ and inverse divergence, the conditions for the statistical model and function $f$ under which the estimating equation is unbiased are clarified. Specifically, we characterize two types of statistical models, an inverse Gaussian type and a mixture of generalized inverse Gaussian type distributions, to show that the conditions for the function $f$ are different for each model. We also define Bregman divergence as a linear sum over the dimensions of the inverse divergence and extend the results to the multi-dimensional case., Comment: Accepted to the 2024 IEEE International Symposium on Information Theory (ISIT 2024)

We analyzed a thousand visible spectra of Fulcher-$\alpha$ band measured for divertor plasmas in Large Helical Device. With a coronal model and Baysian inference, the population distribution of hydrogen molecule in the electronical ground state were estimated. The non-thermal population distribution was recovered with a two-temperature model, which has two sets of rotational and vibrational temperatures, as well as their mixture coefficient. The lower rotational temperature significantly changes according to the plasma parameters. Its nearly linear dependence on the electron density was found, which is consistent with previous works. The lower vibrational temperature also shows a small density dependence, as reported by a previous work. On the other hand, the higher rotational and vibrational temperatures as well as the mixture coefficient only show slight changes over the broad range of plasma parameters. These population parameters show a significant correlation; with higher electron density, all the temperatures and the fraction of the higher-temperature component increase simultaneously. This suggests that the electron-impact plays an important role to determine the population distribution.

The ultimate goal in machine learning is to construct a model function that has a generalization capability for unseen dataset, based on given training dataset. If the model function has too much expressibility power, then it may overfit to the training data and as a result lose the generalization capability. To avoid such overfitting issue, several techniques have been developed in the classical machine learning regime, and the dropout is one such effective method. This paper proposes a straightforward analogue of this technique in the quantum machine learning regime, the entangling dropout, meaning that some entangling gates in a given parametrized quantum circuit are randomly removed during the training process to reduce the expressibility of the circuit. Some simple case studies are given to show that this technique actually suppresses the overfitting., Comment: 7 pages, 8 figures

We discuss unbiased estimation equations in a class of objective function using a monotonically increasing function $f$ and Bregman divergence. The choice of the function $f$ gives desirable properties such as robustness against outliers. In order to obtain unbiased estimation equations, analytically intractable integrals are generally required as bias correction terms. In this study, we clarify the combination of Bregman divergence, statistical model, and function $f$ in which the bias correction term vanishes. Focusing on Mahalanobis and Itakura-Saito distances, we provide a generalization of fundamental existing results and characterize a class of distributions of positive reals with a scale parameter, which includes the gamma distribution as a special case. We discuss the possibility of latent bias minimization when the proportion of outliers is large, which is induced by the extinction of the bias correction term.

Clustering algorithms have wide applications and play an important role in data analysis fields including time series data analysis. However, in time series analysis, most of the algorithms used signal shape features or the initial value of hidden variable of a neural network. Little has been discussed on the methods based on the generative model of the time series. In this paper, we propose a new clustering algorithm focusing on the generative process of the signal with a recurrent neural network and the variational Bayes method. Our experiments show that the proposed algorithm not only has a robustness against for phase shift, amplitude and signal length variations but also provide a flexible clustering based on the property of the variational Bayes method., Comment: 8 pages, 11 figures, accepted for publication in IJCNN

Network functions virtualization (NFV) enables telecommunications service providers to realize various network services by flexibly combining multiple virtual network functions (VNFs). To provide such services, an NFV control method should optimally allocate such VNFs into physical networks and servers by taking account of the combination(s) of objective functions and constraints for each metric defined for each VNF type, e.g., VNF placements and routes between the VNFs. The NFV control method should also be extendable for adding new metrics or changing the combination of metrics. One approach for NFV control to optimize allocations is to construct an algorithm that simultaneously solves the combined optimization problem. However, this approach is not extendable because the problem needs to be reformulated every time a new metric is added or a combination of metrics is changed. Another approach involves using an extendable network-control architecture that coordinates multiple control algorithms specified for individual metrics. However, to the best of our knowledge, no method has been developed that can optimize allocations through this kind of coordination. In this paper, we propose an extendable NFV-integrated control method by coordinating multiple control algorithms. We also propose an efficient coordination algorithm based on reinforcement learning. Finally, we evaluate the effectiveness of the proposed method through simulations., Comment: 17 pages, 8 figures, 7 tables, accepted for publication in IEICE Transactions on Communications. copyright(c) 2019 IEICE, https://search.ieice.org/

DP-means clustering was obtained as an extension of $K$-means clustering. While it is implemented with a simple and efficient algorithm, it can estimate the number of clusters simultaneously. However, DP-means is specifically designed for the average distortion measure. Therefore, it is vulnerable to outliers in data, and can cause large maximum distortion in clusters. In this work, we extend the objective function of the DP-means to $f$-separable distortion measures and propose a unified learning algorithm to overcome the above problems by selecting the function $f$. Further, the influence function of the estimated cluster center is analyzed to evaluate the robustness against outliers. We demonstrate the performance of the generalized method by numerical experiments using real datasets.

A discrete-time two-dimensional quasi-birth-and-death process (2d-QBD process), $\{{\boldsymbol{Y}}_n\}=\{(X_{1,n},X_{2,n},J_n)\}$, is a two-dimensional skip-free random walk $\{(X_{1,n},X_{2,n})\}$ on $\mathbb{Z}_+^2$ with a supplemental process $\{J_n\}$ on a finite set $S_0$. The supplemental process $\{J_n\}$ is called a phase process. The 2d-QBD process $\{{\boldsymbol{Y}}_n\}$ is a Markov chain in which the transition probabilities of the two-dimensional process $\{(X_{1,n},X_{2,n})\}$ vary according to the state of the phase process $\{J_n\}$. This modulation is assumed to be space homogeneous except for the boundaries of $\mathbb{Z}_+^2$. Under certain conditions, the directional exact asymptotic formulae of the stationary distribution of the 2d-QBD process have been obtained in "T. Ozawa and M. Kobayashi, Exact asymptotic formulae of the stationary distribution of a discrete-time two-dimensional QBD process, Queueing Systems (2018) DOI:10.1007/s11134-018-9586-x." In this paper, we give an example of 2d-QBD process and proofs of some lemmas and propositions appeared in that paper., Comment: 30 pages, 2 figures. arXiv admin note: text overlap with arXiv:1707.05475

We consider a discrete-time two-dimensional process $\{(L_{1,n},L_{2,n})\}$ on $\mathbb{Z}_+^2$ with a supplemental process $\{J_n\}$ on a finite set, where individual processes $\{L_{1,n}\}$ and $\{L_{2,n}\}$ are both skip free. We assume that the joint process $\{Y_n\}=\{(L_{1,n},L_{2,n},J_n)\}$ is Markovian and that the transition probabilities of the two-dimensional process $\{(L_{1,n},L_{2,n})\}$ are modulated depending on the state of the background process $\{J_n\}$. This modulation is space homogeneous except for the boundaries of $\mathbb{Z}_+^2$. We call this process a discrete-time two-dimensional quasi-birth-and-death (2D-QBD) process and, under several conditions, obtain the exact asymptotic formulae of the stationary distribution in the coordinate directions., Comment: 54 pages

This paper considers the QBD approximation of a special class of two-dimensional reflecting random walks (2D-RRWs). A typical example of the 2D-RRWs is a two-node Jackson network with cooperative servers. The main contribution of this paper is to provide simple upper bounds for the relative absolute difference between the time-averaged functionals of the original 2D-RRW and its QBD approximation., Comment: This manuscript is the full version of the paper submitted to QTNA2016