Accelerated-gradient-based generalized Levenberg--Marquardt method with oracle complexity bound and local quadratic convergence

Minimizing the sum of a convex function and a composite function appears in various fields. The generalized Levenberg--Marquardt (LM) method, also known as the prox-linear method, has been developed for such optimization problems. The method iteratively solves strongly convex subproblems with a damping term. This study proposes a new generalized LM method for solving the problem with a smooth composite function. The method enjoys three theoretical guarantees: iteration complexity bound, oracle complexity bound, and local convergence under a H\"olderian growth condition. The local convergence results include local quadratic convergence under the quadratic growth condition; this is the first to extend the classical result for least-squares problems to a general smooth composite function. In addition, this is the first LM method with both an oracle complexity bound and local quadratic convergence under standard assumptions. These results are achieved by carefully controlling the damping parameter and solving the subproblems by the accelerated proximal gradient method equipped with a particular termination condition. Experimental results show that the proposed method performs well in practice for several instances, including classification with a neural network and nonnegative matrix factorization

Proposal for the Awakening Behavior Detection System Using Images and Adaptation for Fluctuation of Brightness Quantity in the Captured Image

Recently, accidents such that seniors fall down from the bed in care facilities or hospitals are increased. To prevent these accidents, we have developed the awakening behavior detection system using Neural Network. In this paper, it is a problem that the detection success rate of the current system using captured image in the clinical site is not enough. So, we analyze the captured image in the clinical site. From the result of the histogram analysis, it proves that the fluctuation of brightness quantity makes decrease the detection capability. Therefore, to decrease the influence of the brightness quantity, the histogram of the captured image should be equalized. Finally, we show that the histogram equalization reduces fluctuation of brightness quantity, numerically

An Attempt to Estimate the Charge Distribution in Sigma-Bond Systems

A classical inductive-effect model has been utilized in an attempt to estimate the change distribution in relatively complicated σ-bond systems. It is assumed that the formal charge on an atom is given as a vectorial sum of the polarities of the bonds attached to that atom and, further, that each bond induces a constant fraction of its own polarity in all of its neighboring bonds. Significance of the model has been tested for several model compounds which permit the closed-form solutions for the distributions of the internally self-consistent bond polarities. The model has been applied to the calculations of the charge distributions in alkanes, ｫ-alkyl halides and hydrated metallic ions ; the results are found to be compatible with observations

Periphyton contribution to nitrogen dynamics in the discharge from a wastewater treatment plant

To evaluate the importance of periphyton to nitrogen dynamics in the discharge from wastewater treatment plants (WWTPs), we examined changes in total and inorganic nitrogen content downstream from a WWTP on the Kurose River in Hiroshima Prefecture, Japan. At 0.7 km downstream of the WWTP (point A), NH4+-N was the dominant form of inorganic nitrogen, but concentrations decreased rapidly to 5 km downstream (point B). In contrast, no significant change in the [NO2– + NO3–]-N concentration was observed between the two points. Total nitrogen (TN) load decreased significantly between the two points, suggesting that sorption and/or denitrification occurred in the river channel. Potential rates of nitrogen sorption and transformation by periphyton were determined in a laboratory experiment in which changes in the nitrogen content of river water were examined in an acrylic chamber with periphyton. Nitrification and nitrogen removal occurred mainly in the periphyton. The contributions of periphyton activity to TN and NH4+-N decrease in the field, as estimated from the results of the laboratory experiments, were 6%–18% and 23%–72%, respectively. These results suggest that periphyton plays an important role in decreasing NH4+-N concentration in the discharge from wastewater treatment plants

Behavior of Latent Vector of Trivariate Wishart Matrix

This paper is concerned with the probability density function of the latent vector corresponding to the largest latent root of Wishart matrix. The latent vector may be expressed by the polar coordinates. Sugiyama (1966) give the exact expression of the probability density function of the polar coordinates. The function contained the alternating series, thus the function may not be converged on the domain of definition, numerically. In this paper we derived an improved expression of the function to be the positive series, for which we provide graphs of a population latent vector and latent roots.【査読有

Seek durability for CoCrTa perpendicular flexible disks

金沢大学理工研究域数物科学系The seek durability of CoCrTa perpendicular flexible disks was studied using a conventional 3.5-in double-sided flexible disk drive. The seek durability strongly depends on the CoCrTa film preparation conditions. The durability is increased by adding a Si underlayer for a CoCrTa film. Disk-media yield pressures were evaluated with a scratch test using a sapphire needle. It is shown that high media yield pressure leads to a high seek durability. Ta addition to CoCr film increases the media yield pressure. The number of seek operations achieved was 200 × 104, using the following disk construction: protective layer/CoCrTa film/Si underlayer/base film