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?”
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.
A linear algorithm for Brick Wang tiling Derouet-Jourdan, Alexandre; Kaji, Shizuo; Mizoguchi, Yoshihiro
Japan journal of industrial and applied mathematics,
09/2019, Letnik:
36, Številka:
3
Journal Article
Recenzirano
Odprti dostop
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.
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.
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 cm 2 ; SAT area (mean), 29.3 versus 36.8 cm 2 ; 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.
We develop a framework to construct geometric representations of finite groups G through the correspondence between real toric spaces $X^{\mathbb{R}}$ and simplicial complexes with characteristic ...matrices. We give a combinatorial description of the G-module structure of the homology of $X^{\mathbb{R}}$. 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.
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.
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