Learning Deep Input-Output Stable Dynamics

Learning stable dynamics from observed time-series data is an essential problem in robotics, physical modeling, and systems biology. Many of these dynamics are represented as an inputs-output system to communicate with the external environment. In this study, we focus on input-output stable systems, exhibiting robustness against unexpected stimuli and noise. We propose a method to learn nonlinear systems guaranteeing the input-output stability. Our proposed method utilizes the differentiable projection onto the space satisfying the Hamilton-Jacobi inequality to realize the input-output stability. The problem of finding this projection can be formulated as a quadratic constraint quadratic programming problem, and we derive the particular solution analytically. Also, we apply our method to a toy bistable model and the task of training a benchmark generated from a glucose-insulin simulator. The results show that the nonlinear system with neural networks by our method achieves the input-output stability, unlike naive neural networks. Our code is available at https://github.com/clinfo/DeepIOStability.Comment: Accepted in NeurIPS 202

An Efficient Algorithm to Determine Equivalence of Pipelined Dependency Graphs for Their Simplification

　依存性グラフに基づいた非同期式パイプライン制御回路の設計方法が提案されている．この設計法の最終段階においては，依存性グラフと縮小した依存性グラフの等価性を何度も繰返し判定することにより，簡単化した依存性グラフが得られる．しかし，この判定には多数の状態をもつオートマトンを扱うため，その計算量は極めて大きい．本論文では，この等価性判定のための新たな効率的なアルゴリズムを提案する．まず，基本操作の実行順序の半順序をコンパクトに表現するために，基本操作直結因果関係グラフ O˙ を定義する．次に，分 岐系列ごとに O˙ の高々二つの部分グラフが一致するとき，かつそのときに限り，二つの依存性グラフが等価であることを証明する．更に，等価性の判定に必要な分岐系列のサイズと数が有限であることを証明する．最後に，上述の原理を用いたアルゴリズムの計算量が従来法に比べて大幅に小さいことを示す

Multidimensional replica-exchange method for free-energy calculations

We have developed a new simulation algorithm for free-energy calculations. The method is a multidimensional extension of the replica-exchange method. While pairs of replicas with different temperatures are exchanged during the simulation in the original replica-exchange method, pairs of replicas with different temperatures and/or different parameters of the potential energy are exchanged in the new algorithm. This greatly enhances the sampling of the conformational space and allows accurate calculations of free energy in a wide temperature range from a single simulation run, using the weighted histogram analysis method.Comment: 13 pages, (ReVTeX), 9 figures. J. Chem. Phys. 113 (2000), in pres

Minimum test sets for locally exhaustive testing of combinational circuits with five outputs

In this paper, features of dependence matrices of combinational circuits with five outputs are discussed, and it is shown that a minimum test set for locally exhaustive testing of such circuits always has 2 w test patterns, where w is the maximum number of inputs on which any output depends</p

Single-Image Super-Resolution Improvement of X-ray Single-Particle Diffraction Images Using a Convolutional Neural Network

Femtosecond X-ray pulse lasers are promising probes for the elucidation of the multiconformational states of biomolecules because they enable snapshots of single biomolecules to be observed as coherent diffraction images. Multi-image processing using an X-ray free-electron laser has proven to be a successful structural analysis method for viruses. However, the performance of single-particle analysis (SPA) for flexible biomolecules with sizes ≤100 nm remains difficult. Owing to the multiconformational states of biomolecules and noisy character of diffraction images, diffraction image improvement by multi-image processing is often ineffective for such molecules. Herein, a single-image super-resolution (SR) model was constructed using an SR convolutional neural network (SRCNN). Data preparation was performed in silico to consider the actual observation situation with unknown molecular orientations and the fluctuation of molecular structure and incident X-ray intensity. It was demonstrated that the trained SRCNN model improved the single-particle diffraction image quality, corresponding to an observed image with an incident X-ray intensity (approximately three to seven times higher than the original X-ray intensity), while retaining the individuality of the diffraction images. The feasibility of SPA for flexible biomolecules with sizes ≤100 nm was dramatically increased by introducing the SRCNN improvement at the beginning of the various structural analysis schemes