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.

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 of in conferences such as the International Conference on Medical Image Computing and Computer Assisted Intervention (MIC-CAI) and Machine Learning for Medical Image Reconstruction (MLMIR), 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 point of view. 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 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 imageto-image translation are based on one of two fundamental The two authors contributed equally to this work.

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.

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.

Abstract. 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. BackgroundBoolean models have proved very useful in the analysis of various networks in biology. However, it is often convenient to introduce multilevel variables to account for multiple threshold effects. We are often faced with choices between using Boolean variables or multilevel variables. This can be crucial since theoretical results are sometimes proved only for Boolean or multilevel networks. A particular example of this situation is in René Thomas' conjecture that a local negative circuit is necessary to produce sustained (asynchronous) oscillations. This paper stems from the simple idea that a Boolean counter-example to that conjecture could be found by transposing a multilevel counter-example found earlier by Richard and Comet. However, we believe the method developed in this paper, together with a handy script which implements it, is widely applicable to other theoretical studies which involves discrete networks. We also find the notion of asymptotic evolution function defined in this paper sheds light on the understanding of relation between the state transition graph and the interaction graph.1.1. Introduction. Introduced in the 1960s-70s to model biological regulatory networks, the logical (discrete) formalism has...

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 2015 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.

Abstract. We introduce a new presentation of the two dimensional rigid transformation which is more concise and efficient than the standard matrix presentation. By modifying the ordinary dual number construction for the complex numbers, we define the ring of the anti-commutative dual complex numbers, which parametrizes two dimensional rotation and translation all together. With this presentation, one can easily interpolate or blend two or more rigid transformations at a low computational cost. We developed a library for C++ with the MIT-licensed source code ([13]) and demonstrate its facility by an interactive deformation tool developed for iPad. Rigid TransformationThe n-dimensional rigid transformation (or Euclidean) group E(n) consists of transformations of R n which preserves the standard metric. This group serves as an essential mathematical backend for many applications (see [2,9]). It is well-known (see [6], for example) that any element of E(n) can be written as a composition of a rotation, a reflection, and a translation, and hence, it is represented by (n + 1) × (n + 1)-homogeneous matrix;Here, we adopt the convention that a matrix acts on a (column) vector by the multiplication from the left. E(n) has two connected components. The identity component SE(n) consists of those without reflection. More precisely,The group SE(n) is widely used in computer graphics such as for expressing motion and attitude, displacement ([10]), deformation ([1, 5, 11]), skinning ([8]), and camera control ([3]). In some cases, the matrix representation of the group SE(n) is not convenient. In particular, a linear combination of two matrices in SE(n) does not necessarily belong to SE(n) and

Good parametrisations 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 parametrisation of affine transformations, which is a generalisation 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.Throughout this paper all vectors should be considered as real column vectors, and hence, matrices act on them by the multiplication from the left.2010 Mathematics Subject Classification. 68U05,65D18,65F60,15A16.