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.
This study proposes a homological approach to mathematically define a three-dimensional texture feature of emphysema and fibrosis on chest computed tomography using persistent homology. The proposed ...definition enabled accurate segmentation with comparable quality to deep learning while offering higher interpretability than deep learning-based methods.
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). With the use of 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.
NEW & NOTEWORTHY This study proposes a homological approach to mathematically define a three-dimensional texture feature of emphysema and fibrosis on chest computed tomography using persistent homology. The proposed definition enabled accurate segmentation with comparable quality to deep learning while offering higher interpretability than deep learning-based methods.
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.
We determine the mod \(2\) cohomology over the Steenrod algebra of the classifying spaces of the free loop groups \(LG\) for compact groups \(G=Spin(7)\), \(Spin(8)\), \(Spin(9)\), and \(F_4\). Then, ...we show that they are isomorphic as algebras over the Steenrod algebra to the mod \(2\) cohomology of the corresponding Chevalley groups of type \(G(q)\), where \(q\) is an odd prime power. In a similar manner, we compute the cohomology of the free loop space over \(BDI(4)\) and show that it is isomorphic to that of \(BSol(q)\) as algebras over the Steenrod algebra.
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.
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.
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.
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.
The MESA equation was optimized for Japanese middle-aged and elderly adults.
A closed linkage mechanism in three-dimensional space is an object comprising
rigid bodies connected with hinges in a circular form like a rosary. Such
linkages include Bricard6R and Bennett4R. To ...design such a closed linkage, it
is necessary to solve a high-degree algebraic equation, which is generally
difficult. In this lecture, the author proposes a new family of closed linkage
mechanisms with an arbitrary number of hinges as an extension of a certain
Bricard6R. They have singular properties, such as one-dimensional degree of
freedom (1-DOF), and certain energies taking a constant value regardless of the
state. These linkage mechanisms can be regarded as discrete M\"obius strips and
may be of interest in the context of pure mathematics as well. However, many of
the properties described here have been confirmed only numerically, with no
rigorous mathematical proof, and should be interpreted with caution.
PDF
