| 1. |
Naoya Tanabe, Susumu Sato, Takafumi Shimada, Shizuo Kaji, Yusuke Shiraishi, Satoru Terada, Tomoki Maetani, Fumi Mochizuki, Kaoruko Shimizu, Masaru Suzuki, Shotaro Chubachi, Kunihiko Terada, Kazuya Tanimura, Ryo Sakamoto, Tsuyoshi Oguma, Atsuyasu Sato, Megumi Kanasaki, Shigeo Muro, Izuru Masuda, Hiroaki Iijima, Toyohiro Hirai, A reference equation for lung volume on computed tomography in Japanese middle-aged and elderly adults., Respiratory investigation, 10.1016/j.resinv.2023.12.004, 62, 1, 121-127, 2023.12, BACKGROUND: Effective use of lung volume data measured on computed tomography (CT) requires reference values for specific populations. This study examined whether an equation previously generated for multiple ethnic groups in the United States, including Asians predominantly composed of Chinese people, in the Multi-Ethnic Study of Atherosclerosis (MESA) could be used for Japanese people and, if necessary, to optimize this equation. Moreover, the equation was used to characterize patients with chronic obstructive pulmonary disease (COPD) and lung hyperexpansion. METHODS: This study included a lung cancer screening CT cohort of asymptomatic never smokers aged ≥40 years from two institutions (n = 364 and 419) to validate and optimize the MESA equation and a COPD cohort (n = 199) to test its applicability. RESULTS: In all asymptomatic never smokers, the variance explained by the predicted values (R2) based on the original MESA equation was 0.60. The original equation was optimized to minimize the root mean squared error (RMSE) by adjusting the scaling factor but not the age, sex, height, or body mass index terms of the equation. The RMSE changed from 714 ml in the original equation to 637 ml in the optimized equation. In the COPD cohort, lung hyperexpansion, defined based on the 95th percentile of the ratio of measured lung volume to predicted lung volume in never smokers (122 %), was observed in 60 (30 %) patients and was associated with centrilobular emphysema and air trapping on inspiratory/expiratory CT. CONCLUSIONS: The MESA equation was optimized for Japanese middle-aged and elderly adults.. |
| 2. |
Nariaki Tateiwa, Yuji Shinano, Masaya Yasuda, Shizuo Kaji, Keiichiro Yamamura, Katsuki Fujisawa, Development and analysis of massive parallelization of a lattice basis reduction algorithm, Japan Journal of Industrial and Applied Mathematics, 10.1007/s13160-023-00580-z, 2023.04. |
| 3. |
Tomoki Maetani, Naoya Tanabe, Yusuke Shiraishi, Takafumi Shimada, Satoru Terada, Hiroshi Shima, Fumi Mochizuki, Ryo Sakamoto, Shizuo Kaji, Tsuyoshi Oguma, Susumu Sato, Hiroaki Iijima, Izuru Masuda, Toyohiro Hirai, Centrilobular Emphysema Is Associated with Pectoralis Muscle Reduction in Current Smokers without Airflow Limitation., Respiration; international review of thoracic diseases, 10.1159/000529031, 1-9, 2023.01, BACKGROUND: Physiological and prognostic associations of centrilobular emphysema (CLE) and paraseptal emphysema (PSE) in smokers with and without chronic obstructive pulmonary disease (COPD) have been increasingly recognized, but the associations with extrapulmonary abnormalities, such as muscle wasting, osteoporosis, and cardiovascular diseases, remain unestablished. OBJECTIVES: The aim of the study was to investigate whether CLE was associated with extrapulmonary abnormalities independent of concomitant PSE in smokers without airflow limitation. METHODS: This retrospective study consecutively enrolled current smokers without airflow limitation who underwent lung cancer screening with computed tomography and spirometry. CLE and PSE were visually identified based on the Fleischner Society classification system. Cross-sectional areas of pectoralis muscles (PM) and adjacent subcutaneous adipose tissue (SAT), bone mineral density (BMD), and coronary artery calcification (CAC) were evaluated. RESULTS: Of 310 current smokers without airflow limitation, 83 (26.8%) had CLE. The PSE prevalence was higher (67.5% vs. 23.3%), and PM area, SAT area, and BMD were lower in smokers with CLE than in those without (PM area (mean), 34.5 versus 38.6 cm2; SAT area (mean), 29.3 versus 36.8 cm2; BMD (mean), 158.3 versus 178.4 Hounsfield unit), while CAC presence did not differ. In multivariable models, CLE was associated with lower PM area but not with SAT area or BMD, after adjusting for PSE presence, demographics, and forced expiratory volume in 1 s. CONCLUSIONS: The observed association between CLE and lower PM area suggests that susceptibility to skeletal muscle loss could be high in smokers with CLE even without COPD.. |
| 4. |
Sho Sugawara, Ryo Okada, Tze Mun Loo, Hisamichi Tanaka, Kenichi Miyata, Masatomo Chiba, Hiroko Kawasaki, Kaoru Katoh, Shizuo Kaji, Yoshiro Maezawa, Koutaro Yokote, Mizuho Nakayama, Masanobu Oshima, Koji Nagao, Chikashi Obuse, Satoshi Nagayama, Keiyo Takubo, Akira Nakanishi, Masato T. Kanemaki, Eiji Hara, Akiko Takahashi, RNaseH2A downregulation drives inflammatory gene expression via genomic DNA fragmentation in senescent and cancer cells, Communications Biology, 10.1038/s42003-022-04369-7, 5, 1, 2022.12, Abstract
Cellular senescence caused by oncogenic stimuli is associated with the development of various age-related pathologies through the senescence-associated secretory phenotype (SASP). SASP is mediated by the activation of cytoplasmic nucleic acid sensors. However, the molecular mechanism underlying the accumulation of nucleotide ligands in senescent cells is unclear. In this study, we revealed that the expression of RNaseH2A, which removes ribonucleoside monophosphates (rNMPs) from the genome, is regulated by E2F transcription factors, and it decreases during cellular senescence. Residual rNMPs cause genomic DNA fragmentation and aberrant activation of cytoplasmic nucleic acid sensors, thereby provoking subsequent SASP factor gene expression in senescent cells. In addition, RNaseH2A expression was significantly decreased in aged mouse tissues and cells from individuals with Werner syndrome. Furthermore, RNaseH2A degradation using the auxin-inducible degron system induced the accumulation of nucleotide ligands and induction of certain tumourigenic SASP-like factors, promoting the metastatic properties of colorectal cancer cells. Our results indicate that RNaseH2A downregulation provokes SASP through nucleotide ligand accumulation, which likely contributes to the pathological features of senescent, progeroid, and cancer cells.. |
| 5. |
Tomoki Maetani, Naoya Tanabe, Satoru Terada, Yusuke Shiraishi, Hiroshi Shima, Shizuo Kaji, Ryo Sakamoto, Tsuyoshi Oguma, Susumu Sato, Izuru Masuda, Toyohiro Hirai, Physiological impacts of computed tomography airway dysanapsis, fractal dimension and branch count in asymptomatic never smokers., Journal of applied physiology (Bethesda, Md. : 1985), 10.1152/japplphysiol.00385.2022, 2022.10, Dysanapsis, a mismatch between airway tree caliber and lung size, contributes to a large variation in lung function on spirometry in healthy subjects. However, it remains unclear whether other morphological features of the airway tree could be associated with the variation in lung function independent of dysanapsis. This study used lung cancer screening chest computed tomography (CT) and spirometry data from asymptomatic never smokers. Dysanapsis and the complexity of airway tree geometry were quantified on CT by measuring airway to lung ratio (ALR) and airway fractal dimension (AFD). Moreover, total airway count (TAC), ratio of airway luminal surface area to volume (SA/V), longitudinal tapering and irregularity of the radius of the internal lumen from the central to peripheral airways (Tapering index and Irregularity index) were quantified. In 431 asymptomatic never smokers without a history of lung diseases, lower ALR was associated with lower forced expiratory volume in 1 sec (FEV1) and FEV1/forced vital capacity (FEV1/FVC). The associations of ALR with AFD and TAC (r = 0.41 and 0.13) were weaker than the association between TAC and AFD (r = 0.64). In multivariable models adjusted for age, sex, height, and mean lung density, lower AFD and TAC were associated with lower FEV1 and FEV1/FVC independent of ALR, whereas SA/V and Tapering index were not. These results suggest that the smaller airway tree relative to a given lung size and the lower complexity of airway tree shape, including lower branch count, are independently associated with lower lung function in healthy subjects.. |
| 6. |
Takenaga, Kodai, Kaji, Shizuo, Alexandrov Puzzle, Proceedings of Bridges 2022: Mathematics, Art, Music, Architecture, Culture, 371-374, 2022.08. |
| 7. |
Hideki Todo, Kunihiko Kobayashi, Jin Katsuragi, Haruna Shimotahira, Shizuo Kaji, Yonghao Yue, Stroke Transfer: Example-based Synthesis of Animatable Stroke Styles., SIGGRAPH (Conference Paper Track), 10.1145/3528233.3530703, 54-10, 2022.07. |
| 8. |
Hiroshi Shima, Naoya Tanabe, Akira Oguma, Kaoruko Shimizu, Shizuo Kaji, Kunihiko Terada, Tsuyoshi Oguma, Takeshi Kubo, Masaru Suzuki, Hironi Makita, Atsuyasu Sato, Masaharu Nishimura, Susumu Sato, Satoshi Konno, Toyohiro Hirai, Subtyping emphysematous COPD by respiratory volume change distributions on CT., Thorax, 10.1136/thoraxjnl-2021-218288, 2022.06, BACKGROUND: There is considerable heterogeneity among patients with emphysematous chronic obstructive pulmonary disease (COPD). We hypothesised that in addition to emphysema severity, ventilation distribution in emphysematous regions would be associated with clinical-physiological impairments in these patients. OBJECTIVE: To evaluate whether the discordance between respiratory volume change distributions (from expiration to inspiration) in emphysematous and non-emphysematous regions affects COPD outcomes using two cohorts. METHODS: Emphysema was quantified using a low attenuation volume percentage on inspiratory CT (iLAV%). Local respiratory volume changes were calculated using non-rigidly registered expiratory/inspiratory CT. The Ventilation Discordance Index (VDI) represented the log-transformed Wasserstein distance quantifying discordance between respiratory volume change distributions in emphysematous and non-emphysematous regions. RESULTS: Patients with COPD in the first cohort (n=221) were classified into minimal emphysema (iLAV% |
| 9. |
Bando Hiroaki, Kaji Shizuo, Yaguchi Takaharu, Causal inference for empirical dynamical systems based on persistent homology, JSIAM Letters, 10.14495/jsiaml.14.69, 14, 69-72, 2022.05, Given two correlated systems, detecting causality between them from observed data is an important but challenging task. Combining two mathematical techniques, delay coordinate embedding and persistent homology, we propose a novel causal inference method for data comprising a pair of scalar time series that are observed from two possibly coupled deterministic dynamical systems. The idea is to encode the topology of the dynamics in the form of the persistent homology of the reconstructed attractors and compare the involved systems by a metric defined on the persistent homology.. |
| 10. |
Sho Ozaki, Shizuo Kaji, Kanabu Nawa, Toshikazu Imae, Atsushi Aoki, Takahiro Nakamoto, Takeshi Ohta, Yuki Nozawa, Hideomi Yamashita, Akihiro Haga, Keiichi Nakagawa, Training of deep cross-modality conversion models with a small data set, and their application in megavoltage CT to kilovoltage CT conversion, MEDICAL PHYSICS, 10.1002/mp.15626, 49, 6, 3769-3782, 2022.04, Purpose In recent years, deep learning-based image processing has emerged as a valuable tool for medical imaging owing to its high performance. However, the quality of deep learning-based methods heavily relies on the amount of training data; the high cost of acquiring a large data set is a limitation to their utilization in medical fields. Herein, based on deep learning, we developed a computed tomography (CT) modality conversion method requiring only a few unsupervised images. Methods The proposed method is based on cycle-consistency generative adversarial network (CycleGAN) with several extensions tailored for CT images, which aims at preserving the structure in the processed images and reducing the amount of training data. This method was applied to realize the conversion of megavoltage computed tomography (MVCT) to kilovoltage computed tomography (kVCT) images. Training was conducted using several data sets acquired from patients with head and neck cancer. The size of the data sets ranged from 16 slices (two patients) to 2745 slices (137 patients) for MVCT and 2824 slices (98 patients) for kVCT. Results The required size of the training data was found to be as small as a few hundred slices. By statistical and visual evaluations, the quality improvement and structure preservation of the MVCT images converted by the proposed model were investigated. As a clinical benefit, it was observed by medical doctors that the converted images enhanced the precision of contouring. Conclusions We developed an MVCT to kVCT conversion model based on deep learning, which can be trained using only a few hundred unpaired images. The stability of the model against changes in data size was demonstrated. This study promotes the reliable use of deep learning in clinical medicine by partially answering commonly asked questions, such as "Is our data sufficient?" and "How much data should we acquire?". |
| 11. |
Ho Kyoung Ko, Suyoung Choi, Shizuo Kaji, Who has given up on mathematics? A data analysis, ASIA PACIFIC EDUCATION REVIEW, 10.1007/s12564-021-09709-6, 22, 4, 699-714, 2021.12, The newly coined term supoza (giving up mathematics) describes a critical social issue that needs to be addressed in South Korea's educational policy. Although the term has not received precise definition, it refers to students who have given up on learning mathematics. A precise definition would require detailing the current supoza situation and identifying its characteristics. This study therefore conducted a statistical investigation of commonalities among students who have given up on learning mathematics; the study results revealed that these students can be characterized by their affective domain for mathematics learning. We found that a statistical model could determine the likelihood that a particular student would report having given up mathematics based on responses to questions related to the affective domain of mathematics learning. This aspect suggests the possibility of understanding supoza with the exclusive use of affective factors and emphasizes the significance of the affective domain of mathematics learning. Additionally, this study provides a working example to show how exploratory analysis using big data can be used in relation to mathematical education.. |
| 12. |
Shizuo Kaji, Akira Horiguchi, Takuro Abe, Yohsuke Watanabe, A Hyper-surface Arrangement Model of Ranking Distributions, KDD '21: PROCEEDINGS OF THE 27TH ACM SIGKDD CONFERENCE ON KNOWLEDGE DISCOVERY & DATA MINING, 10.1145/3447548.3467253, 796-804, 2021.12, A distribution on the permutations over a fixed finite set is called a ranking distribution. Modelling ranking distributions is one of the major topics in preference learning as such distributions appear as the ranking data produced by many judges. In this paper, we propose a geometric model for ranking distributions. Our idea is to use hyper-surface arrangements in a metric space as the representation space, where each component cut out by hyper-surfaces corresponds to a total ordering, and its volume is proportional to the probability. In this setting, the union of components corresponds to a partial ordering and its probability is also estimated by the volume. Similarly, the probability of a partial ordering conditioned by another partial ordering is estimated by the ratio of volumes. We provide a simple iterative algorithm to fit our model to a given dataset. We show our model can represent the distribution of a real-world dataset faithfully and can be used for prediction and visualisation purposes.. |
| 13. |
Nariaki Tateiwa, Yuji Shinano, Keiichiro Yamamura, Akihiro Yoshida, Shizuo Kaji, Masaya Yasuda, Katsuki Fujisawa, CMAP-LAP: Configurable Massively Parallel Solver for Lattice Problems, 2021 IEEE 28TH INTERNATIONAL CONFERENCE ON HIGH PERFORMANCE COMPUTING, DATA, AND ANALYTICS (HIPC 2021), 10.1109/HiPC53243.2021.00018, 42-52, 2021.12, Lattice problems are a class of optimization problems that are notably hard. There are no classical or quantum algorithms known to solve these problems efficiently. Their hardness has made lattices a major cryptographic primitive for post-quantum cryptography. Several different approaches have been used for lattice problems with different computational profiles; some suffer from super-exponential time, and others require exponential space. This motivated us 10 develop a novel lattice problem solver, CMAP-LAP, based on the clever coordination of different algorithms that run massively in parallel. With our flexible framework, heterogeneous modules run asynchronously in parallel on a large-scale distributed system while exchanging information, which drastically boosts the overall performance. We also implement full checkpoint-and-restart functionality, which is vital to high-dimensional lattice problems. CMAP-LAP facilitates the implementation of large-scale parallel strategies for lattice problems since all the functions are designed to he customizable and abstract. Through numerical experiments with up to 103,680 cores, we evaluated the performance and stability of our system and demonstrated its high capability for future massive-scale experiments.. |
| 14. |
Naoya Tanabe, Shizuo Kaji, Hiroshi Shima, Yusuke Shiraishi, Tomoki Maetani, Tsuyoshi Oguma, Susumu Sato, Toyohiro Hirai, Kernel Conversion for Robust Quantitative Measurements of Archived Chest Computed Tomography Using Deep Learning-Based Image-to-Image Translation, Frontiers in artificial intelligence, 10.3389/frai.2021.769557, 4, 769557-769557, 2021.12, Chest computed tomography (CT) is used to screen for lung cancer and evaluate pulmonary and extra-pulmonary abnormalities such as emphysema and coronary artery calcification, particularly in smokers. In real-world practice, lung abnormalities are visually assessed using high-contrast thin-slice images which are generated from raw scan data using sharp reconstruction kernels with the sacrifice of increased image noise. In contrast, accurate CT quantification requires low-contrast thin-slice images with low noise, which are generated using soft reconstruction kernels. However, only sharp-kernel thin-slice images are archived in many medical facilities due to limited data storage space. This study aimed to establish deep neural network (DNN) models to convert sharp-kernel images to soft-kernel-like images with a final goal to reuse historical chest CT images for robust quantitative measurements, particularly in completed previous longitudinal studies. By using pairs of sharp-kernel (input) and soft-kernel (ground-truth) images from 30 patients with chronic obstructive pulmonary disease (COPD), DNN models were trained. Then, the accuracy of kernel conversion based on the established DNN models was evaluated using CT from independent 30 smokers with and without COPD. Consequently, differences in CT values between new images converted from sharp-kernel images using the established DNN models and ground-truth soft-kernel images were comparable with the inter-scans variability derived from repeated phantom scans (6 times), showing that the conversion error was the same level as the measurement error of the CT device. Moreover, the Dice coefficients to quantify the similarity between low attenuation voxels on given images and the ground-truth soft-kernel images were significantly higher on the DNN-converted images than the Gaussian-filtered, median-filtered, and sharp-kernel images (p |
| 15. |
Naoya Tanabe, Shizuo Kaji, Susumu Sato, Tomoo Yokoyama, Tsuyoshi Oguma, Kiminobu Tanizawa, Tomohiro Handa, Takashi Sakajo, Toyohiro Hirai, A homological approach to a mathematical definition of pulmonary fibrosis and emphysema on computed tomography., Journal of applied physiology (Bethesda, Md. : 1985), 10.1152/japplphysiol.00150.2021, 131, 2, 601-612, 2021.06, Three-dimensional imaging is essential to evaluate local abnormalities and understand structure-function relationships in an organ. However, quantifiable and interpretable methods to localize abnormalities remain unestablished. Visual assessments are prone to bias, machine learning methods depend on training images, and the underlying decision principle is usually difficult to interpret. Here, we developed a homological approach to mathematically define emphysema and fibrosis in the lungs on computed tomography (CT). Using persistent homology, the density of homological features, including connected components, tunnels, and voids, was extracted from the volumetric CT scans of lung diseases. A pair of CT values at which each homological feature appeared (birth) and disappeared (death) was computed by sweeping the threshold levels from higher to lower CT values. Consequently, fibrosis and emphysema were defined as voxels with dense voids having a longer lifetime (birth-death difference) and voxels with dense connected components having a lower birth, respectively. In an independent dataset including subjects with idiopathic pulmonary fibrosis (IPF), chronic obstructive pulmonary disease (COPD), and combined pulmonary fibrosis and emphysema (CPFE), the proposed definition enabled accurate segmentation with comparable quality to deep learning in terms of Dice coefficients. Persistent homology-defined fibrosis was closely associated with physiological abnormalities such as impaired diffusion capacity and long-term mortality in subjects with IPF and CPFE, and persistent homology-defined emphysema was associated with impaired diffusion capacity in subjects with COPD. The present persistent homology-based evaluation of structural abnormalities could help explore the clinical and physiological impacts of structural changes and morphological mechanisms of disease progression.. |
| 16. |
Tomohiro Hayakawa, Tomoya Kamimura, Shizuo Kaji, Fumitoshi Matsuno, Autonomous Distributed System for Gait Generation for Single-Legged Modular Robots Connected in Various Configurations, IEEE TRANSACTIONS ON ROBOTICS, 10.1109/TRO.2020.2992983, 36, 5, 1491-1510, 2020.10, To date, many gait generation strategies have been designed for robots with leg configurations that model those of natural creatures. However, their leg configurations are limited to the $2 imes N$ type, such as hexapod or myriapod; hence, simultaneously, the potential ability of legged robots is implicitly limited. We consider single-legged modular robots that can be arranged to form a cluster with arbitrary 2-D leg configurations. By choosing configurations appropriately, these robots have the potential to perform several types of tasks, as is the case for reconfigurable modular robots. However, to use appropriate configurations for a given task, a unified gait generation system for various configurations of a cluster is required. In this article, we propose an autonomous distributed control system for each single-legged modular robot to collectively achieve static walking of the cluster with various leg configurations on planar ground. Moreover, our system is an autonomous distributed system with scalability and fault tolerance, in which each module determines the moving pattern of its foot through local communication without global information, such as the entire leg configuration of the cluster. We verified that several types of clusters achieved static walking using our system not only in dynamic simulations, but also in real robot experiments.. |
| 17. |
Jinichi Mori, Shizuo Kaji, Hiroki Kawai, Satoshi Kida, Masaharu Tsubokura, Masahiko Fukatsu, Kayo Harada, Hideyoshi Noji, Takayuki Ikezoe, Tomoya Maeda, Akira Matsuda, Assessment of dysplasia in bone marrow smear with convolutional neural network., Scientific reports, 10.1038/s41598-020-71752-x, 10, 1, 14734-14734, 2020.09, In this study, we developed the world's first artificial intelligence (AI) system that assesses the dysplasia of blood cells on bone marrow smears and presents the result of AI prediction for one of the most representative dysplasia-decreased granules (DG). We photographed field images from the bone marrow smears from patients with myelodysplastic syndrome (MDS) or non-MDS diseases and cropped each cell using an originally developed cell detector. Two morphologists labelled each cell. The degree of dysplasia was evaluated on a four-point scale: 0-3 (e.g., neutrophil with severely decreased granules were labelled DG3). We then constructed the classifier from the dataset of labelled images. The detector and classifier were based on a deep neural network pre-trained with natural images. We obtained 1797 labelled images, and the morphologists determined 134 DGs (DG1: 46, DG2: 77, DG3: 11). Subsequently, we performed a five-fold cross-validation to evaluate the performance of the classifier. For DG1-3 labelled by morphologists, the sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), and accuracy were 91.0%, 97.7%, 76.3%, 99.3%, and 97.2%, respectively. When DG1 was excluded in the process, the sensitivity, specificity, PPV, NPV, and accuracy were 85.2%, 98.9%, 80.6%, and 99.2% and 98.2%, respectively.. |
| 18. |
Satoshi Kida, Shizuo Kaji, Kanabu Nawa, Toshikazu Imae, Takahiro Nakamoto, Sho Ozaki, Takeshi Ohta, Yuki Nozawa, Keiichi Nakagawa, Visual enhancement of Cone-beam CT by use of CycleGAN., Medical physics, 10.1002/mp.13963, 47, 3, 998-1010, 2020.03, PURPOSE: Cone-beam computed tomography (CBCT) offers advantages over conventional fan-beam CT in that it requires a shorter time and less exposure to obtain images. However, CBCT images suffer from low soft-tissue contrast, noise, and artifacts compared to conventional fan-beam CT images. Therefore, it is essential to improve the image quality of CBCT. METHODS: In this paper, we propose a synthetic approach to translate CBCT images with deep neural networks. Our method requires only unpaired and unaligned CBCT images and planning fan-beam CT (PlanCT) images for training. The CBCT images and PlanCT images may be obtained from other patients as long as they are acquired with the same scanner settings. Once trained, three-dimensionally reconstructed CBCT images can be directly translated into high-quality PlanCT-like images. RESULTS: We demonstrate the effectiveness of our method with images obtained from 20 prostate patients, and provide a statistical and visual comparison. The image quality of the translated images shows substantial improvement in voxel values, spatial uniformity, and artifact suppression compared to those of the original CBCT. The anatomical structures of the original CBCT images were also well preserved in the translated images. CONCLUSIONS: Our method produces visually PlanCT-like images from CBCT images while preserving anatomical structures.. |
| 19. |
Shizuo Kaji, Shintaro Kuroki, Eunjeong Lee, Dong Youp Suh, Flag bott manifolds of general lie type and their equivariant cohomology rings, Homology, Homotopy and Applications, 10.4310/HHA.2020.v22.n1.a21, 22, 1, 375-390, 2020.01, In this article we introduce flag Bott manifolds of general Lie type as the total spaces of iterated flag bundles. They generalize the notion of flag Bott manifolds and generalized Bott manifolds, and admit nice torus actions. We calculate the torus equivariant cohomology rings of flag Bott manifolds of general Lie type.. |
| 20. |
Shizuo Kaji, Kenji Kajiwara, Hyeongki Park, Linkage Mechanisms Governed by Integrable Deformations of Discrete Space Curves, Nonlinear Systems and Their Remarkable Mathematical Structures. Volume 2, CRC Press, https://doi.org/10.1201/9780429263743, 2019.12. |
| 21. |
Shizuo Kaji, Kenji Kajiwara, Hyeongki Park, Linkage Mechanisms Governed by Integrable Deformations of Discrete Space Curves, Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 2 (CRC Press,2019), 356-381, 2019.12, A linkage mechanism consists of rigid bodies assembled by joints which can be used to translate and transfer motion from one form in one place to another. In this paper, we are particularly interested in a family of spacial linkage mechanisms which consist of n-copies of a rigid body joined together by hinges to form a ring. Each hinge joint has its own axis of revolution and rigid bodies joined to it can be freely rotated around the axis. The family includes the famous threefold symmetric Bricard6R linkage also known as the Kaleidocycle, which exhibits a characteristic "turning over" motion. We can model such a linkage as a discrete closed curve in ℝ3 with a constant torsion up to sign. Then, its motion is described as the deformation of the curve preserving torsion and arc length. We describe certain motions of this object that are governed by the semi-discrete mKdV equations, where infinitesimally the motion of each vertex is confined in the osculating plane.. |
| 22. |
Keigo Matsumoto, Nami Ogawa, Hiroyuki Inou, Shizuo Kaji, Yutaka Ishii, Michitaka Hirose, Polyvision
4D space manipulation through multiple projections, SIGGRAPH Asia 2019 Emerging Technologies - International Conference on Computer Graphics and Interactive Techniques, SA 2019
SIGGRAPH Asia 2019 Emerging Technologies, SA 2019, 10.1145/3355049.3360518, 36-37, 2019.11, Seeing is believing. Our novel virtual reality system, Polyvision, applies this old saying to the fourth dimension. Various shadows of an object in a four-dimensional (4D) space are simultaneously projected onto multiple three-dimensional (3D) screens created in a virtual environment to reveal its intricate shape. The understanding of high-dimensional shapes and data can essentially be enhanced when good visualization is complemented by interactive functionality. However, a method to implement an interface for handling complex 4D transformations in a user-friendly manner must be developed. Using our Polyvision system, the user can manipulate each shadow as if it were a 3D object in their hand. The user’s action on each projection is reflected to the original 4D object, and in turn its projections, in real time. While controlling the object’s orientation minutely on one shadow, the user can grasp its global structure from multiple changing projections. Our system has a wide variety of applications in visualization, education, mathematical research, and entertainment, as we demonstrate with a variety of 4D objects that appear in mathematics and data sciences.. |
| 23. |
Alexandre Derouet-Jourdan, Shizuo Kaji, Yoshihiro Mizoguchi, A linear algorithm for Brick Wang tiling, Japan Journal of Industrial and Applied Mathematics, 10.1007/s13160-019-00369-z, 36, 3, 749-761, 2019.09, The Wang tiling is a classical problem in combinatorics. A major theoretical question is to find a (small) set of tiles which tiles the plane only aperiodically. In this case, resulting tilings are rather restrictive. On the other hand, Wang tiles are used as a tool to generate textures and patterns in computer graphics. In these applications, a set of tiles is normally chosen so that it tiles the plane or its sub-regions easily in many different ways. With computer graphics applications in mind, we introduce a class of such tileset, which we call sequentially permissive tilesets, and consider tiling problems with constrained boundary. We apply our methodology to a special set of Wang tiles, called Brick Wang tiles, introduced by Derouet-Jourdan et al. in 2016 to model wall patterns. We generalise their result by providing a linear algorithm to decide and solve the tiling problem for arbitrary planar regions with holes.. |
| 24. |
Shizuo Kaji, Satoshi Kida, Overview of image-to-image translation by use of deep neural networks
denoising, super-resolution, modality conversion, and reconstruction in medical imaging, Radiological physics and technology, 10.1007/s12194-019-00520-y, 12, 3, 235-248, 2019.09, Since the advent of deep convolutional neural networks (DNNs), computer vision has seen an extremely rapid progress that has led to huge advances in medical imaging. Every year, many new methods are reported at conferences such as the International Conference on Medical Image Computing and Computer-Assisted Intervention and Machine Learning for Medical Image Reconstruction, or published online at the preprint server arXiv. There is a plethora of surveys on applications of neural networks in medical imaging (see [1] for a relatively recent comprehensive survey). This article does not aim to cover all aspects of the field, but focuses on a particular topic, image-to-image translation. Although the topic may not sound familiar, it turns out that many seemingly irrelevant applications can be understood as instances of image-to-image translation. Such applications include (1) noise reduction, (2) super-resolution, (3) image synthesis, and (4) reconstruction. The same underlying principles and algorithms work for various tasks. Our aim is to introduce some of the key ideas on this topic from a uniform viewpoint. We introduce core ideas and jargon that are specific to image processing by use of DNNs. Having an intuitive grasp of the core ideas of applications of neural networks in medical imaging and a knowledge of technical terms would be of great help to the reader for understanding the existing and future applications. Most of the recent applications which build on image-to-image translation are based on one of two fundamental architectures, called pix2pix and CycleGAN, depending on whether the available training data are paired or unpaired (see Sect. 1.3). We provide codes ([2, 3]) which implement these two architectures with various enhancements. Our codes are available online with use of the very permissive MIT license. We provide a hands-on tutorial for training a model for denoising based on our codes (see Sect. 6). We hope that this article, together with the codes, will provide both an overview and the details of the key algorithms and that it will serve as a basis for the development of new applications.. |
| 25. |
Shizuo Kaji, Satoshi Kida, Overview of image-to-image translation by use of deep neural networks: denoising, super-resolution, modality conversion, and reconstruction in medical imaging., Radiological physics and technology, 10.1007/s12194-019-00520-y, 12, 3, 235-248, 2019.09, Since the advent of deep convolutional neural networks (DNNs), computer vision has seen an extremely rapid progress that has led to huge advances in medical imaging. Every year, many new methods are reported at conferences such as the International Conference on Medical Image Computing and Computer-Assisted Intervention and Machine Learning for Medical Image Reconstruction, or published online at the preprint server arXiv. There is a plethora of surveys on applications of neural networks in medical imaging (see [1] for a relatively recent comprehensive survey). This article does not aim to cover all aspects of the field, but focuses on a particular topic, image-to-image translation. Although the topic may not sound familiar, it turns out that many seemingly irrelevant applications can be understood as instances of image-to-image translation. Such applications include (1) noise reduction, (2) super-resolution, (3) image synthesis, and (4) reconstruction. The same underlying principles and algorithms work for various tasks. Our aim is to introduce some of the key ideas on this topic from a uniform viewpoint. We introduce core ideas and jargon that are specific to image processing by use of DNNs. Having an intuitive grasp of the core ideas of applications of neural networks in medical imaging and a knowledge of technical terms would be of great help to the reader for understanding the existing and future applications. Most of the recent applications which build on image-to-image translation are based on one of two fundamental architectures, called pix2pix and CycleGAN, depending on whether the available training data are paired or unpaired (see Sect. 1.3). We provide codes ([2, 3]) which implement these two architectures with various enhancements. Our codes are available online with use of the very permissive MIT license. We provide a hands-on tutorial for training a model for denoising based on our codes (see Sect. 6). We hope that this article, together with the codes, will provide both an overview and the details of the key algorithms and that it will serve as a basis for the development of new applications.. |
| 26. |
Shizuo Kaji, Toshiaki Maeno, Koji Nuida, Yasuhide Numata, Polynomial expressions of p-ary auction functions, Journal of Mathematical Cryptology, 10.1515/jmc-2018-0016, 13, 2, 69-80, 2019.06, One of the common ways to design secure multi-party computation is twofold: To realize secure fundamental operations and to decompose a target function to be securely computed into them. In the setting of fully homomorphic encryption, as well as some kinds of secret sharing, the fundamental operations are additions and multiplications in the base field such as the field F2 with two elements. Then the second decomposition part, which we study in this paper, is (in theory) equivalent to expressing the target function as a polynomial. It is known that any function over the finite prime field Fp has a unique polynomial expression of degree at most p-1 with respect to each input variable; however, there has been little study done concerning such minimal-degree polynomial expressions for practical functions. This paper aims at triggering intensive studies on this subject, by focusing on polynomial expressions of some auction-related functions such as the maximum/minimum and the index of the maximum/minimum value among input values.. |
| 27. |
Shizuo Kaji, Toshiaki Maeno, Koji Nuida, Yasuhide Numata, Polynomial expressions of p-ary auction functions, JOURNAL OF MATHEMATICAL CRYPTOLOGY, 10.1515/jmc-2018-0016, 13, 2, 69-80, 2019.06, One of the common ways to design secure multi-party computation is twofold: to realize secure fundamental operations and to decompose a target function to be securely computed into them. In the setting of fully homomorphic encryption, as well as some kinds of secret sharing, the fundamental operations are additions and multiplications in the base field such as the field F-2 with two elements. Then the second decomposition part, which we study in this paper, is (in theory) equivalent to expressing the target function as a polynomial. It is known that any function over the finite prime field F-p has a unique polynomial expression of degree at most p - 1 with respect to each input variable; however, there has been little study done concerning such minimal-degree polynomial expressions for practical functions. This paper aims at triggering intensive studies on this subject, by focusing on polynomial expressions of some auction-related functions such as the maximum/minimum and the index of the maximum/minimum value among input values.. |
| 28. |
Shizuo Kaji, Stephen Theriault, Suspension Splittings and Self-maps of Flag Manifolds, Acta Mathematica Sinica, English Series, 10.1007/s10114-019-8051-z, 35, 4, 445-462, 2019.04, If G is a compact connected Lie group and T is a maximal torus, we give a wedge decomposition of ΣG/T by identifying families of idempotents in cohomology. This is used to give new information on the self-maps of G/T.. |
| 29. |
Shizuo Kaji, Stephen Theriault, Suspension Splittings and Self-maps of Flag Manifolds, ACTA MATHEMATICA SINICA-ENGLISH SERIES, 10.1007/s10114-019-8051-z, 35, 4, 445-462, 2019.04, If G is a compact connected Lie group and T is a maximal torus, we give a wedge decomposition of sigma G/T by identifying families of idempotents in cohomology. This is used to give new information on the self-maps of G/T.. |
| 30. |
S. Kaji, A. Derouet-Jourdan, H. Ochiai, Dappled tiling, Mathematical Insights into Advanced Computer Graphics Techniques, 10.1007/978-981-13-2850-3, 59-72, 2019.03. |
| 31. |
Soojin Cho, Suyoung Choi, Shizuo Kaji, Geometric representations of finite groups on real toric spaces, Journal of the Korean Mathematical Society, 10.4134/JKMS.j180646, 56, 5, 1265-1283, 2019.01, We develop a framework to construct geometric representations of finite groups G through the correspondence between real toric spaces XR and simplicial complexes with characteristic matrices. We give a combinatorial description of the G-module structure of the homology of XR. As applications, we make explicit computations of the Weyl group representations on the homology of real toric varieties associated to the Weyl chambers of type A and B, which show an interesting connection to the topology of posets. We also realize a certain kind of Foulkes representation geometrically as the homology of real toric varieties.. |
| 32. |
Shizuo Kaji, Representing a point and the diagonal as zero loci in flag manifolds, Algebraic and Geometric Topology, 10.2140/agt.2019.19.2061, 19, 4, 2061-2075, 2019.01, The zero locus of a generic section of a vector bundle over a manifold defines a submanifold. A classical problem in geometry asks to realise a specified submanifold in this way. We study two cases: a point in a generalised flag manifold and the diagonal in the direct product of two copies of a generalised flag manifold. These cases are particularly interesting since they are related to ordinary and equivariant Schubert polynomials, respectively.. |
| 33. |
Adrien Fauré, Shizuo Kaji, A circuit-preserving mapping from multilevel to Boolean dynamics, Journal of Theoretical Biology, 10.1016/j.jtbi.2017.12.013, 440, 71-79, 2018.03. |
| 34. |
Adrien Fauré, Shizuo Kaji, A circuit-preserving mapping from multilevel to Boolean dynamics., Journal of theoretical biology, 10.1016/j.jtbi.2017.12.013, 440, 71-79, 2018.03, Many discrete models of biological networks rely exclusively on Boolean variables and many tools and theorems are available for analysis of strictly Boolean models. However, multilevel variables are often required to account for threshold effects, in which knowledge of the Boolean case does not generalise straightforwardly. This motivated the development of conversion methods for multilevel to Boolean models. In particular, Van Ham's method has been shown to yield a one-to-one, neighbour and regulation preserving dynamics, making it the de facto standard approach to the problem. However, Van Ham's method has several drawbacks: most notably, it introduces vast regions of "non-admissible" states that have no counterpart in the multilevel, original model. This raises special difficulties for the analysis of interaction between variables and circuit functionality, which is believed to be central to the understanding of dynamic properties of logical models. Here, we propose a new multilevel to Boolean conversion method, with software implementation. Contrary to Van Ham's, our method doesn't yield a one-to-one transposition of multilevel trajectories; however, it maps each and every Boolean state to a specific multilevel state, thus getting rid of the non-admissible regions and, at the expense of (apparently) more complicated, "parallel" trajectories. One of the prominent features of our method is that it preserves dynamics and interaction of variables in a certain manner. As a demonstration of the usability of our method, we apply it to construct a new Boolean counter-example to the well-known conjecture that a local negative circuit is necessary to generate sustained oscillations. This result illustrates the general relevance of our method for the study of multilevel logical models.. |
| 35. |
Neşet Deniz Turgay, Shizuo Kaji, The mod 2 dual Steenrod algebra as a subalgebra of the mod 2 dual Leibniz-Hopf algebra, Journal of Homotopy and Related Structures, 10.1007/s40062-016-0163-x, 12, 3, 727-739, 2017.09. |
| 36. |
Neset Deniz Turgay, Shizuo Kaji, The mod 2 dual Steenrod algebra as a subalgebra of the mod 2 dual Leibniz-Hopf algebra, JOURNAL OF HOMOTOPY AND RELATED STRUCTURES, 10.1007/s40062-016-0163-x, 12, 3, 727-739, 2017.09, The mod 2 Steenrod algebra A(2) can be defined as the quotient of the mod 2 Leibniz-Hopf algebra F-2 by the Adem relations. Dually, the mod 2 dual Steenrod algebra A(2)(*)can be thought of as a sub-Hopf algebra of the mod 2 dual Leibniz-Hopf algebra F-2(*). We study A(2)(*)and F(2)(*)from this viewpoint and give generalisations of some classical results in the literature.. |
| 37. |
Suyoung Choi, Shizuo Kaji, Stephen Theriault, Homotopy decomposition of a suspended real toric space, Boletin de la Sociedad Matematica Mexicana, 10.1007/s40590-016-0090-1, 23, 1, 153-161, 2017.04. |
| 38. |
Ho Kyoung Ko, Hyung Won Kim, Shizuo Kaji, Suyoung Choi, Elementary school students who give up on learning mathematics: Correlations with non-cognitive learner characteristics, J. Korea Soc. Math. Ed. Ser. C, 20, 2, 143-151, 2017.04. |
| 39. |
S. Choi, S. Kaji, S. Theriault, Homotopy decomposition of a suspended real toric space, the Boletin de la Sociedad Matematica Mexicana, 10.1007/s40590-016-0090-1, 23, 1, 153-161, 2017.04. |
| 40. |
Shizuo Kaji, Michihiro Sakai, Stephen Theriault, Counting the number of homotopy associative multiplications on certain H-spaces, Topology and its Applications, 10.1016/j.topol.2016.10.008, 214, 137-149, 2016.12. |
| 41. |
Shizuo Kaji, Michihiro Sakai, Stephen Theriault, Counting the number of homotopy associative multiplications on certain H-spaces, TOPOLOGY AND ITS APPLICATIONS, 10.1016/j.topol.2016.10.008, 214, 137-149, 2016.12, We determine an upper bound for the number of homotopy associative multiplications on certain H-spaces. This is applied to SU(3) and Sp(2) at odd primes, and to give examples of p-local H-spaces with more than one multiplication but a unique homotopy associative multiplication. (C) 2016 Elsevier B.V. All rights reserved.. |
| 42. |
Shizuo Kaji, Hiroyuki Ochiai, A concise parametrization of affine transformation, SIAM Journal on Imaging Sciences, 10.1137/16M1056936, 9, 3, 1355-1373, 2016.09. |
| 43. |
S. Kaji, Tetrisation of triangular meshes and its application in shape blending, Mathematical Progress in Expressive Image Synthesis III, 10.1007/978-981-10-1076-7_2, 7-19, 2016.05. |
| 44. |
Shizuo Kaji, Akihiro Ohsita, Stephen Theriault, Mod p decompositions of the loop spaces of compact symmetric spaces, Algebraic and Geometric Topology, 10.2140/agt.2015.15.1771, 15, 3, 1771-1811, 2015.06. |
| 45. |
Shizuo KAJI, Akihiro Ohsita, Stephen Theriault, Mod p decompositions of the loop spaces of compact symmetric spaces,, Algebraic & Geometric topology, 10.2140/agt.2015.15.1771, 15, 3, 1771-1811, 2015.06. |
| 46. |
S. Kaji and G. Liu, Probe-type deformers, Mathematical Progress in Expressive Image Synthesis I, 10.1007/978-4-431-55483-7_6, 63-77, 2015.05. |
| 47. |
S. Kaji, Three presentations of torus equivariant cohomology of flag manifolds, Perspectives and Developments in Mathematics, Proceedings of the International Mathematics Conference in honour of the 70th Birthday of Professor S. A. Ilori, 37-54, 2015.05. |
| 48. |
Koji Nuida, Takuro Abe, Shizuo Kaji, Toshiaki Maeno, Yasuhide Numata, A mathematical problem for security analysis of hash functions and pseudorandom generators, International Journal of Foundations of Computer Science, 10.1142/S0129054115500100, 26, 2, 169-194, 2015.02. |
| 49. |
Koji Nuida, Takuro Abe, Shizuo Kaji, Toshiaki Maeno, Yasuhide Numata, A Mathematical Problem for Security Analysis of Hash Functions and Pseudorandom Generators, INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE, 10.1142/S0129054115500100, 26, 2, 169-194, 2015.02, In this paper, we specify a class of mathematical problems, which we refer to as "Function Density Problems" (FDPs, in short), and point out novel connections of FDPs to the following two cryptographic topics; theoretical security evaluations of keyless hash functions (such as SHA-1.), and constructions of provably secure pseudorandom generators (PRGs) with some enhanced security property introduced by Dubrov and Ishai (STOC 2006). Our argument aims at proposing new theoretical frameworks for these topics (especially for the former) based on FDPs, rather than providing some concrete and practical results on the topics. We also give some examples of mathematical discussions on FDFs, which would be of independent interest from mathematical viewpoints. Finally, we discuss possible directions of future research on other cryptographic applications of FDPs and on mathematical studies on FDPs themselves.. |
| 50. |
Shizuo Kaji, Weyl group symmetry on the gkm graph of a gkm manifold with an extended lie group action, Osaka Journal of Mathematics, 52, 1, 31-41, 2015.01. |
| 51. |
Shizuo Kaji, WEYL GROUP SYMMETRY ON THE GKM GRAPH OF A GKM MANIFOLD WITH AN EXTENDED LIE GROUP ACTION, OSAKA JOURNAL OF MATHEMATICS, 52, 1, 31-41, 2015.01, We consider the class of manifolds with compact Lie group actions which restrict to GKM-actions on the maximal torus. First, we see their GKM-graphs admit symmetry of the Weyl groups. And then, we study its combinatorial abstraction; starting with abstract GKM-graphs with symmetry, we derive certain properties which reflect topology in a purely combinatorial way.. |
| 52. |
G. Matsuda, S. Kaji, H. Ochiai, Anti-commutative Dual Complex Numbers and 2D Rigid Transformation, Mathematical Progress in Expressive Image Synthesis I, 10.1007/978-4-431-55007-5_17, 131-138, 2014.05. |
| 53. |
Shizuo Kaji, S. Hirose, S. Sakata, Yoshihiro Mizoguchi, K. Anjyo, Mathematical analysis on affine maps for 2D shape interpolation, 11th ACM SIGGRAPH / Eurographics Symposium on Computer Animation, SCA 2012
Computer Animation 2012 - ACM SIGGRAPH / Eurographics Symposium Proceedings, SCA 2012, 71-76, 2012.07. |
| 54. |
Shizuo Kaji, Equivariant Schubert calculus of Coxeter groups, Proceedings of the Steklov Institute of Mathematics, 10.1134/S0081543811080177, 275, 1, 239-250, 2011.12, We consider an equivariant extension for Hiller's Schubert calculus on the coinvariant ring of a finite Coxeter group.. |
| 55. |
Shizuo Kaji, Equivariant Schubert Calculus of Coxeter Groups, PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 10.1134/S0081543811080177, 275, 1, 239-250, 2011.12, We consider an equivariant extension for Hiller's Schubert calculus on the coinvariant ring of a finite Coxeter group.. |
| 56. |
Koji Nuida, Takuro Abe, Shizuo Kaji, Toshiaki Maeno, Yasuhide Numata, A mathematical problem for security analysis of hash functions and pseudorandom generators, 6th International Workshop on Security, IWSEC 2011
Advances in Information and Computer Security - 6th International Workshop, IWSEC 2011, Proceedings, 10.1007/978-3-642-25141-2_10, 144-160, 2011.11, The aim of this paper is to emphasize the significance of a certain mathematical problem in research on information security. We point out that the mathematical problem, which we refer to as "Function Density Problem," has connections to the following two major cryptographic topics; security analysis of hash functions in the real world (like SHA-1), and construction of pseudorandom generators with some enhanced security property. We also provide a first example to show how a study of Function Density Problem can contribute to the progress of the above-mentioned two topics. Other potential applications of Function Density Problem to information security are also discussed.. |
| 57. |
S. Kaji, Schubert calculus, seen from torus equivariant topology, Trends in Mathematics - New Series, 12, 1, 71-89, 2010.05.  |
| 58. |
Shizuo Kaji, Daisuke Kishimoto, Homotopy nilpotency in p-regular loop spaces, Mathematische Zeitschrift, 10.1007/s00209-008-0459-6, 264, 1, 209-224, 2010.01, We consider the problem how far from being homotopy commutative is a loop space having the homotopy type of the p-completion of a product of finite numbers of spheres. We determine the homotopy nilpotency of those loop spaces as an answer to this problem.. |
| 59. |
Shizuo Kaji, Daisuke Kishimoto, Homotopy nilpotency in $p$-regular loop spaces（共著）, Mathematische Zeitschrift, 10.1007/s00209-008-0459-6, 264, 1, 209-224, 2010.01. |
| 60. |
Hiroaki Hamanaka, Shizuo Kaji, Akira Kono, Samelson products in Sp (2), Topology and its Applications, 10.1016/j.topol.2008.02.008, 155, 11, 1207-1212, 2008.06, We calculate certain Samelson products of Sp (2). Using the result, we classify the homotopy types of the gauge groups of principal Sp (2) bundles over S8 and we also derive the homotopy commutativity of Sp (2) localized at 3.. |
| 61. |
Hiroaki Hamanaka, Shizuo Kaji, Akira Kono, Samelson products in $Sp(2)$ （共著）, Topology and its Applications, 10.1016/j.topol.2008.02.008, 155, 11, 1207-1212, 2008.06. |
| 62. |
Shizuo Kaji, Mod 2 cohomology of 2-compact groups of low rank, Kyoto Journal of Mathematics, 10.1215/kjm/1250281055, 47, 2, 441-450, 2007.01, We determine the mod 2 cohomology algebra over the Steenrod algebra A 2 of the classifying space of loop groups LG where G = Spin(7), Spin(8), Spin(9), F4 and DI(4). Then we show they are isomorphic as algebras over A2 to the mod 2 cohomology of the 2-compact groups of type G.. |
| 63. |
Shizuo Kaji, Low rank cohomology of the classifying spaces of gauge groups over 3-manifolds, Publications of the Research Institute for Mathematical Sciences, 10.2977/prims/1166642116, 42, 2, 581-587, 2006.06, The purpose of this paper is to calculate the cohomology of the function space Map(M, BG) for degree less than or equal to 3, where G is a simply connected compact Lie group and M is a closed orientable 3-manifold. The calculation enables us to obtain a simple proof and an improvement of the result [4, Theorem 1.2].. |
| 64. |
Shizuo Kaji, Low rank cohomology of the classifying spaces of gauge groups over 3-manifolds, PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 10.2977/prims/1166642116, 42, 2, 581-587, 2006.06, The purpose of this paper is to calculate the cohomology of the function space Map(M, BG) for degree less than or equal to 3, where G is a simply connected compact Lie group and M is a closed orientable 3-manifold. The calculation enables us to obtain a simple proof and an improvement of the result [4, Theorem 1.2].. |
| 65. |
Shizuo Kaji, On the nilpotency of rational H-spaces, Journal of the Mathematical Society of Japan, 10.2969/jmsj/1150287307, 57, 4, 1153-1165, 2005.10, In [BG], it is proved that the Whitehead length of a space Z is less than or equal to the nilpotency of ΩZ. As for rational spaces, those two invariants are equal. We show this for a 1-connected rational space Z by giving a way to calculate those invariants from a minimal model for Z. This also gives a way to calculate the nilpotency of an homotopy associative rational H-space.. |
| 66. |
S Kaji, On the nilpotency of rational H-spaces, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 10.2969/jmsj/1150287307, 57, 4, 1153-1165, 2005.10, In [BG], it is proved that the Whitehead length of a space Z is less than or equal to the nilpotency of Omega Z. As for rational spaces, those two invariants are equal. We show this for a 1-connected rational space Z by giving a way to calculate those invariants from a minimal model for Z. This also gives a way to calculate the nilpotency of an homotopy associative rational H-space.. |
