Extracting Koopman Operators for Prediction and Control of Non-linear Dynamics Using Two-stage Learning and Oblique Projections

The Koopman operator framework provides a perspective that non-linear dynamics can be described through the lens of linear operators acting on function spaces. As the framework naturally yields linear embedding models, there have been extensive efforts to utilize it for control, where linear controller designs in the embedded space can be applied to control possibly nonlinear dynamics. However, it is challenging to successfully deploy this modeling procedure in a wide range of applications. In this work, some of the fundamental limitations of linear embedding models are addressed. We show a necessary condition for a linear embedding model to achieve zero modeling error, highlighting a trade-off relation between the model expressivity and a restriction on the model structure to allow the use of linear systems theories for nonlinear dynamics. To address these limitations, neural network-based modeling is proposed based on linear embedding with oblique projection, which is derived from a weak formulation of projection-based linear operator learning. We train the proposed model using a two-stage learning procedure, wherein the features and operators are initialized with orthogonal projection, followed by the main training process in which test functions characterizing the oblique projection are learned from data. The first stage achieves an optimality ensured by the orthogonal projection and the second stage improves the generalizability to various tasks by optimizing the model with the oblique projection. We demonstrate the effectiveness of the proposed method over other data-driven modeling methods by providing comprehensive numerical evaluations where four tasks are considered targeting three different systems

Control-Consistent Learning of Koopman Embedding Models

A learning method is proposed for Koopman operator-based models with the goal of improving closed-loop control behavior. A neural network-based approach is used to discover a space of observables in which nonlinear dynamics is linearly embedded. While accurate state predictions can be expected with the use of such complex, high-dimensional state-to-observable maps, undesirable side-effects may be introduced when the model is deployed in a closed-loop environment. This is because of modeling or residual error in the linear embedding process, which can manifest itself in a different manner compared to the state prediction. To this end, a technique is proposed to refine the originally trained model with the goal of improving the closed-loop behavior of the model while retaining the state-prediction accuracy obtained in the initial learning. Finally, a simple data sampling strategy is proposed to use input signals deterministically sampled from continuous functions, leading to additional improvements in the controller performance for nonlinear dynamical systems. Several numerical examples are provided to show the efficacy of the proposed method

ケモカイン システム ニヨル コウクウ ガン ノ リンパセツ テンイ キコウ

Recently, it has been suggested that chemokine and its receptor interactions determine the destination of the penetrating tumor cells in several types of cancer. However, little information is available on the lymph node metastasis in oral squamous cell carcinoma (SCC). In this review, I would like to summarize the regulation of lymph node metastasis by the chemokine system in oral SCC using lymph node metastatic (HNt and B88) and non-metastatic (IH and BHY) oral SCC cells. Of 13 kinds of chemokine receptors examined by multiplex reverse transcriptase-polymerase chain reaction (RT-PCR), only CXCR4 expression was up-regulated in HNt and B88 cells. CXCR4 ligand, stromal cell-derived factor-1 (SDF-1 ; also called CXCL12), induced characteristic calcium fluxes and cell migration only in the CXCR4-expressing cells. Stable transfectant of CXCR4, IH-CXCR4, acquired the lymph node metastatic potentials in the orthotopic inoculation of nude mice. SDF-1 rapidly activated extracellular signal-regulated kinase (ERK)1/2 and Akt/protein kinase B (PKB) in B88 and IH-CXCR4 cells, and their synthetic inhibitors attenuated the migration by SDF-1. SDF-1 was detected in all the lymph node extracts and conditioned media from lymphatic fibroblast by the enzyme-linked immunosorbent assay. Moreover, the localization of SDF-1 in the submandibular lymph nodes was mainly in the stromal cells. The conditioned media from lymphatic fibroblasts promoted the migration of B88 cells, which was blocked by the CXCR4 neutralization. By using immunohistochemistry, the expression of CXCR4 was observed in 57.3% of the subjects and was significantly associated with lymph node metastasis (P=0.0417), the mode of invasion (P=0.0002) and recurrence of the tumors (P=0.0185). Moreover, the CXCR4-positive group showed a significantly poorer survival than the CXCR4-negative group (P=0.0401). Next, experimental chemotherapy was performed in the IH-CXCR4 tumor by the treatment of a mitogen-activated protein kinase/ERK kinase inhibitor, U0126, or a phosphatidylinositol 3 kinase inhibitor, Wortmannin. These kinase inhibitors markedly inhibited the lymph node metastasis of IH-CXCR4 cells. Moreover, vesnarinone, a novel anti-cancer drug, significantly down-regulated CXCR4 protein and mRNA. These results suggested that SDF-1/CXCR4 system regulates the establishment of lymph node metastasis in patients with oral SCC. It can be considered that blocking of SDF-1/CXCR4 system by the kinase inhibitors or vesnarinone might be a way to protect the patients with oral SCC from lymph node metastasis

Impact on permeability due to axial stress disturbances for cretaceous sandy shale

Seismic waves generated from earthquakes and artificial surface vibration might alter the water level in the wells and oil or gas production. These transient stress disturbances prospectively caused the permeability change due to new pathway occurring or existing pathway being cleared. The permeability change might encourage enhancing gas recovery, inducing small earthquakes preventing future large earthquakes, and de-routing underground water flow for various purposes. The prospective permeability increase by axial stress disturbances of Cretaceous sandy shale may effectively expand the capacity of methane gas recovery of Kushiro Coal Mine. The paper observes the permeability change of intact or triaxially fractured Kushiro Cretaceous sandy shale by axial stress disturbances. It will be shown that increasing and decreasing factors might work together on permeability.MMIJ Fall Meeting 2017, Sept. 26-28 2017, Sapporo, Japan （資源・素材2017（札幌）: 平成29年度資源・素材関係学協会合同秋季大会, 2017年9月26日～28日, 北海道大学, 札幌市

Making Compelling Movie Posters Using Statistical Science And An Eye Mark Recorder

This study focuses on advertising posters for movies, investigating methods of designing compelling posters to encourage viewing. The results of questionnaire surveys were analyzed using statistical science to produce new movie poster designs. The effects of the new posters were then validated using an eye mark recorder. As a result, the authors have succeeded in creating a decision-making method to assist in designing compelling movie posters

Experiments on Long-term Geodetic Monitoring by Low-cost GNSS Receivers and GoGPS Positioning Engine

This paper describes experiments of GNSS-based monitoring by means of different models and brands of low-cost receivers. Single-frequency observations were processed by Open Source goGPS Positioning Engine, in relative positioning mode with respect to a virtual reference station and three physical permanent stations. The experiments were carried out in Osaka, Japan and the results here described cover a timespan of eight months. The daily solutions show standard deviations ranging from about 1mm to 1cm, mainly depending on the base station observations quality

Improvement of zone control induction heating equipment for high-speed processing of semiconductor

In this paper, the effect of dividing into several small coil groups having different current and frequency on heating characteristics is investigated using FEM (finite element method). The heating characteristics of graphite of each coil is examined, and a useful information for controlling current and frequency, which realize the nearly uniform heating, is obtained.</p