We propose two types of novel morphological metrics for quantifying the geometry of tubular structures on computed tomography (CT) images. We apply our metrics to identify irregularities in the airway of patients with chronic obstructive pulmonary disease (COPD) and demonstrate that they provide complementary information to the conventional metrics used to assess COPD, such as the tissue density distribution in lung parenchyma and the wall area ratio of the segmented airway. The three-dimensional shape of the airway and its abstraction as a rooted tree with the root at the trachea carina are automatically extracted from a lung CT volume, and the two metrics are computed based on a mathematical tool called persistent homology; treeH0 quantifies the distribution of branch lengths to assess the complexity of the tree-like structure and radialH0 quantifies the irregularities in the luminal radius along the airway. We show our metrics are associated with clinical outcomes.

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 to 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 be 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.

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.

Studies of acquiring appropriate continuous representations of a discrete objects such as graph and knowledge based data have been conducted by many researches in the field of machine learning. In this paper, we introduce Nested SubSpace arrangement (NSS arrangement), a comprehensive framework for representation learning. We show that existing embedding techniques can be regarded as a member of NSS arrangement. Based on the concept of the NSS arrangement, we implemented Disk-ANChor ARrangement (DANCAR), a representation learning method specializing to reproduce general graphs. Numerical experiments have shown that DANCAR has successfully embedded WordNet in ${\mathbb R}^{20}$ with the F1 score of 0.993 in the reconstruction task. DANCAR is also suitable for visualization to understand the characteristics of graph.

Lattice-based cryptography has received attention as a next-generation encryption technique, because it is believed to be secure against attacks by classical and quantum computers. Its essential security depends on the hardness of solving the shortest vector problem (SVP). In the cryptography, to determine security levels, it is becoming significantly more important to estimate the hardness of the SVP by high-performance computing. In this study, we develop the world’s first distributed and asynchronous parallel SVP solver, the MAssively Parallel solver for SVP (MAP-SVP). It can parallelize algorithms for solving the SVP by applying the Ubiquity Generator framework, which is a generic framework for branch-and-bound algorithms. The MAP-SVP is suitable for massive-scale parallelization, owing to its small memory footprint, low communication overhead, and rapid checkpoint and restart mechanisms. We demonstrate its performance and scalability of the MAP-SVP by using up to 100,032 cores to solve instances of the Darmstadt SVP Challenge.

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 × 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.

Good parametrizations of affine transformations are essential to interpolation, deformation, and analysis of shape, motion, and animation. It has been one of the central research topics in computer graphics. However, there is no single perfect method and each one has both advantages and disadvantages. In this paper, we propose a novel parametrization of affine transformations, which is a generalization to or an improvement of existing methods. Our method adds yet another choice to the existing toolbox and shows better performance in some applications. A C++ implementation is available to make our framework ready to use in various applications.