Anisotropic interpolation error estimates using a new geometric parameter

We present precise anisotropic interpolation error estimates for smooth functions using a new geometric parameter and derive inverse inequalities on anisotropic meshes. In our theory, the interpolation error is bounded in terms of the diameter of a simplex and the geometric parameter. Imposing additional assumptions makes it possible to obtain anisotropic error estimates. This paper also includes corrections to an error in Theorem 2 of our previous paper, "General theory of interpolation error estimates on anisotropic meshes" (Japan Journal of Industrial and Applied Mathematics, 38 (2021) 163-191).Comment: 36 pages, 12 figure

Artificial Intelligence-based Detection of Epileptic Discharges from Pediatric Scalp Electroencephalograms: A Pilot Study

We developed an artificial intelligence (AI) technique to identify epileptic discharges (spikes) in pediatric scalp electroencephalograms (EEGs). We built a convolutional neural network (CNN) model to automatically classify steep potential images into spikes and background activity. For the CNN model’ training and validation, we examined 100 children with spikes in EEGs and another 100 without spikes. A different group of 20 children with spikes and 20 without spikes were the actual test subjects. All subjects were ≥ 3 to 0.97 when referential and combination EEG montages were used, and 0.99, indicating high performance of the classification method. EEG patterns that interfered with correct classification included vertex sharp transients, sleep spindles, alpha rhythm, and low-amplitude ill-formed spikes in a run. Our results demonstrate that AI is a promising tool for automatically interpreting pediatric EEGs. Some avenues for improving the technique were also indicated by our findings

Exclusion of the Possibility of "False Ripples" From Ripple Band High-Frequency Oscillations Recorded From Scalp Electroencephalogram in Children With Epilepsy

Aim Ripple-band epileptic high-frequency oscillations (HFOs) can be recorded by scalp electroencephalography (EEG), and tend to be associated with epileptic spikes. However, there is a concern that the filtration of steep waveforms such as spikes may cause spurious oscillations or "false ripples." We excluded such possibility from at least some ripples by EEG differentiation, which, in theory, enhances high-frequency signals and does not generate spurious oscillations or ringing. Methods The subjects were 50 pediatric patients, and ten consecutive spikes during sleep were selected for each patient. Five hundred spike data segments were initially reviewed by two experienced electroencephalographers using consensus to identify the presence or absence of ripples in the ordinary filtered EEG and an associated spectral blob in time-frequency analysis (Session A). These EEG data were subjected to numerical differentiation (the second derivative was denoted as EEG ''). The EEG '' trace of each spike data segment was shown to two other electroencephalographers who judged independently whether there were clear ripple oscillations or uncertain ripple oscillations or an absence of oscillations (Session B). Results In Session A, ripples were identified in 57 spike data segments (Group A-R), but not in the other 443 data segments (Group A-N). In Session B, both reviewers identified clear ripples (strict criterion) in 11 spike data segments, all of which were in Group A-R (p < 0.0001 by Fisher's exact test). When the extended criterion that included clear and/or uncertain ripples was used in Session B, both reviewers identified 25 spike data segments that fulfilled the criterion: 24 of these were in Group A-R (p < 0.0001). Discussion We have demonstrated that real ripples over scalp spikes exist in a certain proportion of patients. Ripples that were visualized consistently using both ordinary filters and the EEG '' method should be true, but failure to clarify ripples using the EEG '' method does not mean that true ripples are absent. Conclusion The numerical differentiation of EEG data provides convincing evidence that HFOs were detected in terms of the presence of such unusually fast oscillations over the scalp and the importance of this electrophysiological phenomenon

Physical Reservoir Computing Using Nonlinear MEMS Resonator Having High Memory Capacity at "Edge of Chaos"

2023 IEEE 36th International Conference on Micro Electro Mechanical Systems (MEMS), 15-19 Jan. 2023.This paper reports physical reservoir computing (PRC) using a single nonlinear electrostatic resonator and demonstrates its high memory capacity at "edge of chaos." The resonator is a simple doubly supported resonator fabricated from a silicon-on-insulator wafer. We proposed a PRC system without feedback loop, in which its memory capacity relies on the decay time of the high-Q resonator. The benchmark task results indicate that the system shows good linear and nonlinear memory capacities at the resonance and the maximum capacity was obtained at the vicinity of the instability edge of the frequency response

空間統計分析による民間賃貸住宅の地域格差の考察-地理的加重回帰法を用いた地域格差の要因分析-

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