On the interpolation constants over triangular elements

summary:We propose a simple method to obtain sharp upper bounds for the interpolation error constants over the given triangular elements. These constants are important for analysis of interpolation error and especially for the error analysis in the Finite Element Method. In our method, interpolation constants are bounded by the product of the solution of corresponding finite dimensional eigenvalue problems and constant which is slightly larger than one. Guaranteed upper bounds for these constants are obtained via the numerical verification method. Furthermore, we introduce remarkable formulas for the upper bounds of these constants

Lectures on error analysis of interpolation on simplicial triangulations without the shape-regularity assumption, Part 2: Lagrange interpolation on tetrahedrons

This is the second lecture note on the error analysis of interpolation on simplicial elements without the shape regularity assumption (the previous one is arXiv:1908.03894). In this manuscript, we explain the error analysis of Lagrange interpolation on (possibly anisotropic) tetrahedrons. The manuscript is not intended to be a research paper. We hope that, in the future, it will be merged into a textbook on the mathematical theory of the finite element methods.Comment: arXiv admin note: text overlap with arXiv:2102.0476

DNN-Based Source Enhancement to Increase Objective Sound Quality Assessment Score

We propose a training method for deep neural network (DNN)-based source enhancement to increase objective sound quality assessment (OSQA) scores such as the perceptual evaluation of speech quality (PESQ). In many conventional studies, DNNs have been used as a mapping function to estimate time-frequency masks and trained to minimize an analytically tractable objective function such as the mean squared error (MSE). Since OSQA scores have been used widely for soundquality evaluation, constructing DNNs to increase OSQA scores would be better than using the minimum-MSE to create highquality output signals. However, since most OSQA scores are not analytically tractable, i.e., they are black boxes, the gradient of the objective function cannot be calculated by simply applying back-propagation. To calculate the gradient of the OSQA-based objective function, we formulated a DNN optimization scheme on the basis of black-box optimization, which is used for training a computer that plays a game. For a black-box-optimization scheme, we adopt the policy gradient method for calculating the gradient on the basis of a sampling algorithm. To simulate output signals using the sampling algorithm, DNNs are used to estimate the probability-density function of the output signals that maximize OSQA scores. The OSQA scores are calculated from the simulated output signals, and the DNNs are trained to increase the probability of generating the simulated output signals that achieve high OSQA scores. Through several experiments, we found that OSQA scores significantly increased by applying the proposed method, even though the MSE was not minimized

Oligopeptides production by a method involving an enzymatic reaction and a subsequent chemical reaction

We previously reported that an amide bond is unexpectedly formed1) by an acyl-CoA synthetase, AcsA, which plays an essential role in acid utilization in the nitrile-degrative pathway2). Although AcsA essentially catalyzes the formation of a carbon-sulfur bond (the ligation of an acid with CoA), it surprisingly synthesized N-acyl-l-cysteine when a suitable acid and l-cysteine are used as substrates. Furthermore, this unexpected enzyme activity was also observed for acetyl-CoA synthetase and firefly luciferase, both of which belong to the same superfamily of adenylate-forming enzymes. However, the mechanism underlying the carbon-nitrogen bond synthesis remained unknown. Next, we succeeded in producing N-(D-alanyl)-l-cysteine (a dipeptide) from D-alanine and l-cysteine by using DltA, which is homologous to the adenylation domain of nonribosomal peptide synthetase (NRPS) and belongs to the superfamily of adenylate-forming enzymes. To elucidate the mechanism of these surprising reaction, DltA was used. When cysteine derivatives with a protected amino group N-Boc-l-Cys was used instead of l-cysteine, we confirmed the formation of an thioester intermediate. Thereby, we proposed the following unprecedented reaction mechanism underlying these carbon-nitrogen bond synthetic reactions by the thioester-bond-synthesizing enzymes: (i) the formation of S-acyl-l-cysteine as an intermediate via its “enzymatic activity” and (ii) subsequent “chemical“ S→N acyl transfer in the intermediate, resulting in peptide formation3). Step (ii) of this reaction mechanism is identical to the corresponding reaction in native chemical ligation, a method of chemical peptide synthesis, whereas step (i) is not. We predicted that enzymes belonging to the superfamily of adenylate-forming enzymes can synthesize peptide/amide compounds by the same mechanism. Accordingly, we tried to express and purify DhbE, a stand-alone adebylation domain of NRPS, for production of valuable peptide/amide compounds. The purified DhbE synthesized N-aromatic acyl-l-cysteine4). Here, we reported the first demonstration of the N-acylation by “internal” adenylation domains in the multidomain enzyme DhbF. The adenylation domain of NRPS originally is responsible for its selective substrate recognition and activation of the substrate. DhbF is an NRPS involved in bacillibactin synthesis and consists of multiple domains (adenylation domain, condensation domain, peptidyl carrier protein domain, and thioesterase domain). DhbFA1 and DhbFA2 (here named) are “internal” adenylation domains in DhbF. Here, we firstly succeeded in expressing and purifying “internal” adenylation domain DhbFA1 or DhbFA2 separately. When glycine and l-cysteine were used as substrates of DhbFA1, the formation of N-glycyl-l-cysteine (Gly-Cys) was observed. When l-threonine and l-cysteine were used as substrates of DhbFA2, N-l-threonyl-l-cysteine (Thr-Cys) was formed. Furthermore, DhbFA1 or DhbFA2 synthesizes not only dipeptides but also various oligopeptides. Because many adenylation domains that could activate the respective substrates are present in the natural world, we can synthesize various peptides or amides by using adenylation domains or enzymes belonging to the superfamily of adenylate-forming enzymes. References: 1. Abe, T. et al., J. Biol. Chem. 283, 11312-11321 (2008). 2. Hashimoto, Y. et al., J. Biol. Chem. 280, 8660-8667 (2005). 3. Abe, T. et al., J. Biol. Chem. 291, 1735-1750 (2016). 4. Abe, T. et al., J. Antibiot. 70, 435-442 (2017)

Experiments on Classification of Electroencephalography (EEG) Signals in Imagination of Direction using Stacked Autoencoder

This paper presents classification methods for electroencephalography (EEG) signals in imagination of direction measured by a portable EEG headset. In the authors’ previous studies, principal component analysis extracted significant features from EEG signals to construct neural network classifiers. To improve the performance, the authors have implemented a Stacked Autoencoder (SAE) for the classification. The SAE carries out feature extraction and classification in a form of multi-layered neural network. Experimental results showed that the SAE outperformed the previous classifiers.The 2017 International Conference on Artificial Life and Robotics(ICAROB 2017) , January 19 to 22, 2017, Seagaia Convention Center, Miyazaki, Japan

Preliminary Test of Affective Virtual Reality Scenes with Head Mount Display for Emotion Elicitation Experiment

Emotion elicitation experiments are conducted to collect biological signals from a subject who is in a state　of emotion. The recorded signals are used as training/test dataset for constructing an emotion recognition system by　means of machine learning. In conventional emotion elicitation experiments, affective images or videos were provided　for a subject to draw out an emotion from them. However, the authors have concerns about the effectiveness. To surely　evoke a specific emotion from subjects, we have produced several Virtual Reality (VR) scenes and provided the　subjects with the scenes through a Head Mount Display (HMD) in emotion elicitation experiments. Usability and　effectiveness of the VR scenes with the HMD for emotion elicitation were experimentally verified. It was confirmed　that experience of the VR scenes with the HMD was effective in evoking emotions, but we have to improve how　subjects learn a way of playing VR scenes and provide measures against VR sickness at any cost. Moreover, Support　Vector Machine classifiers as an emotion recognition system were constructed using the biological signals measured　from the subjects in the emotion elicitation experiments.2017 17th International Conference on Control, Automation and Systems (ICCAS 2017), Oct. 18-21, 2017, Ramada Plaza, Jeju, Kore