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This chapter covers analog and digital signals, number systems, binary addition and subtraction, floating point representation, ASCII and Unicode, parity bit application, and clock and signal transmission methods.

Standard IEEE floating point, which defines the representation and calculations of real numbers using a binary representation similar to scientific notation, does not define an exact floating-point result. In contrast, here we use a patented bounded floating-point (BFP) device and method for calculating and retaining the precision of the floating-point number represented, which provides an indication of exactness, with an “exact” floating-point result defined as a result that has error within + or – ½ units in the last place (ulps). Analysis and notification of exactness is important because subtraction of “similar,” but inexact, floating-point numbers can introduce an error (even catastrophic error) in the calculation. Here we also define “similar” and use bounded floating point to provide examples comparing subtraction of exact and inexact similar numbers by comparing the results from 64-bit and 128-bit standard and 80-bit bounded floating-point calculations.

In an automated manner, In an automated manner, holistic traffic management is essential to enhance management in metro cities and even in two-tier cities. Detection of Vehicle flow is deemed to be crucial in the management of Traffic. In fact, flow of the Traffic shows the state of the Traffic in a definite amount and helps to rectify situations leading to traffic jam. Particularly this project intends to elucidate a traffic TV for non-chaotic vehicular traffic management. The fundamental idea includes five steps: subtraction of background, detection of the blob, blob analysis, pursuit of blob and reckoning of vehicle. Ideally, a vehicle is considered as associate rectangular patch and classified via blob analysis. After analyzing the blob of vehicles, the pertinent choices unit of mensuration extracted. The pursuit of moving targets is achieved by examination the extracted choices and activity. The experimental results show that the projected system can give a huge amount of useful information for traffic investigation.

More than 90% of colorectal cancer is gradually transformed from colorectal polyps. In clinical practice, precise polyp segmentation provides important information in the early detection of colorectal cancer. Therefore, automatic polyp segmentation techniques are of great importance for both patients and doctors. Most existing methods are based on U-shape structure and use element-wise addition or concatenation to fuse different level features progressively in decoder. However, both the two operations easily generate plenty of redundant information, which will weaken the complementarity between different level features, resulting in inaccurate localization and blurred edges of polyps. To address this challenge, we propose a multi-scale subtraction network (MSNet) to segment polyp from colonoscopy image. Specifically, we first design a subtraction unit (SU) to produce the difference features between adjacent levels in encoder. Then, we pyramidally equip the SUs at different levels with varying receptive fields, thereby obtaining rich multi-scale difference information. In addition, we build a training-free network “LossNet” to comprehensively supervise the polyp-aware features from bottom layer to top layer, which drives the MSNet to capture the detailed and structural cues simultaneously. Extensive experiments on five benchmark datasets demonstrate that our MSNet performs favorably against most state-of-the-art methods under different evaluation metrics. Furthermore, MSNet runs at a real-time speed of \(\sim \)70fps when processing a \(352 \times 352\) image. The source code will be publicly available at https://github.com/Xiaoqi-Zhao-DLUT/MSNet.

This chapter focuses on the uses of MS Excel in handling engineering data. However, these uses are multidimensional and very versatile, which helps to extend the use of these functions in numerous fields. The chapter opens with the concepts of file management in Excel, which includes importing files to Excel and exporting files from Excel. Numerical methods of calculation can also be implemented in Excel, and demonstration has been provided to introduce the Gauss–Seidel method in Excel. The addition, subtraction, and multiplication of matrices have been included in this chapter. The methods of determining the transpose, inverse, and determinant of matrices are also explained. Plotting of equations and trendlines is also discussed in this chapter. Forecasting missing or future data is an essential task in Excel, which is given due space in this chapter. Three techniques of data manipulation, namely sorting, filtering, and flash fill, are covered here. Besides, some data cleaning techniques, such as removal of extra spaces within texts, blank cell handling, and duplicate data detection and removal are described in this chapter. The process of changing text into uppercase or lowercase letters is also contained here, along with the process of converting numbers that are stored as text into numbers. The functions used in data analysis are also included with examples. This chapter contains some very practical applications of MS Excel that eases handling large amounts of data. This chapter will be utterly useful for almost all Excel users.

Early tuberculosis (TB) screening through chest X-rays (CXRs) is essential for timely detection and treatment of the disease. Previous studies have shown that texture abnormalities in CXRs can be enhanced by bone suppression techniques, which may potentially improve TB diagnosis performance. However, existing TB datasets with CXRs usually lack bone-suppressed images, making it difficult to take advantage of bone suppression for TB recognition. Also, existing bone suppression models are usually trained on a relatively small dual-energy subtraction (DES) dataset with CXRs, without considering the image specificity of TB patients. To this end, we propose a bone-suppressed CXR-based tuberculosis recognition (BCTR) framework, where diagnosis-specific deep features are extracted and used to guide a bone suppression (BS) model to generate bone-suppressed CXRs for TB diagnosis. Specifically, the BCTR consists of a classification model for TB diagnosis and an image synthesis model for bone suppression of CXRs. The classification model is first trained on original CXRs from multiple TB datasets such as the large-scale TBX11K. The image synthesis model is trained on a DES dataset to produce bone-suppressed CXRs. Considering the heterogeneity of CXR images from the TB datasets and the DES dataset, we proposed to extract multi-scale task-specific features from the trained classification model and transfer them (via channel-wise addition) to the corresponding layers in the image synthesis model to explicitly guide the bone suppression process. With the bone-suppressed CXRs as input, the classification model is further trained for multi-class TB diagnosis. Experimental results on five TB databases and a DES dataset suggest that our BCTR outperforms previous state-of-the-arts in automated tuberculosis diagnosis.

Teenagers are mainly sedentary with the use of technological devices. However, technological devices may be part of recreational activities to challenge people to achieve better results. This paper described the acquisition of accelerometer data from mobile devices and BioPlux devices, measuring the correct jump flight time with the help of a pressure sensor in a jump platform. Also, this paper tested different methods for adjusting the calculation of the jump flight time, including the least-squares method, the subtraction of average error, and the multilayer perceptron. Currently, a mobile application is available with the Least Squares methods, but it will use the best method soon. Also, the method presented can be also incorporated in a game to stimulate the physical activity practice.

After the presentation of the basics of number systems and the introduction of the first basic arithmetic circuits, this chapter explores in detail addition and the circuits implementing the addition operation in their different variations. Addition is the basic arithmetic operation, so the circuits presented in this chapter are the foundation for the implementation of the remaining arithmetic operations, as it will be discussed in the following chapters. On the other hand, subtraction is just a variation of addition, only replacing the carry concept with that of borrow.

This paper presents how the PerFECt framework is employed to enable innovative teaching and learning mathematics in schools using drama-based approaches. The topic addressed lies in the cross-section between mathematics and computer science: teaching and learning the binary system of arithmetic that constitutes the basis of modern computing. The work builds on previous research efforts targeting gamification of mathematics and is seen under new light offered by the Theatre in Mathematics (TIM) Methodology. The result is an engaging game to teach the binary system to children using their bodies and simple rules for interacting with each other. Following these simple rules the participants enact the operation of a calculator that is able to transform integers into their binary representations and compute the result of the four arithmetic operations (addition, subtraction, multiplication and division). The game can be combined with online activities using a simulator of the game, so that learners can explore it for themselves and discover how the arithmetic operations are done, even when they are not in the same physical space with their peers. This way, an effective blended learning approach is ultimately offered combining face-to-face and online activities.

As one of the basic arithmetic gates of DNA circuits, the DNA subtraction gate plays an important role in the design and optimization of circuits. A nonlinear system with stochastic perturbations and delays is constructed to accurately describe the reaction process of DNA subtraction gates and comprehensively analyze the system dynamics. At the same time, enzyme recognition sites are added to the original basis of the DNA subtraction gate to increase the reaction rate. According to the law of conservation of quality, the dimensionality reduction of the system model with stochastic perturbation and time delay is performed, which greatly reduces the computational complexity. The properties of the solution of a DNA subtraction gate system are discussed, and the Lyapunov analysis proves that the model solution is global and unique. The properties of the solutions indicate that the constructed DNA subtraction gate system with stochastic perturbations and time delays is of practical significance. Through systematic ergodic analysis, it is found that the DNA subtraction gate system is distributed smoothly, which provides a theoretical basis for the realization of the DNA subtraction function. The results of numerical simulation show that the DNA subtraction gate can be implemented successfully under the influence of stochastic disturbance and time delay.

Electronic cleansing (EC) is an image-processing technique for subtraction of tagged fecal regions in the colon for visualization of the entire colonic surface in CT colonography (CTC). This paper introduced a deep-learning based EC method in dual-energy CTC (DE-CTC), named “Deep-Cleansing”. First, we calculated the “effective” atomic number (EAN) by fractions of atomic mass number using the low- and high-energy images in DE-CT. Second, multiple types of combinations of input channels (images), and multiple backbone networks were investigated in U-Net architecture for the optimal performance of EC. Finally, we trained and evaluated our Deep-Cleansing by a total of 139 DE-CTC cases (approximately 80K DE-CTC images), which were randomly divided into training, validation and testing set at an approximate ratio of 55%:20%:25%. Our Deep-Cleansing method achieved DICE coefficients of 0.953 in validation and 0.956 in testing datasets, respectively. Overall, the average cleansing ratio was 96.14%, and the soft-tissue preservation ratio was 97.74%, both were significantly higher than EC without EAN maps. Our results indicated that the use of Deep-Cleansing substantially improved the accuracy of EC in the subtraction of tagged fecal regions in CTC.

The process of subtraction requires two images. Therefore, in CEM, paired mammograms are acquired in rapid succession after the administration of the iodinated contrast agent. They are then subtracted in order to cancel the appearance of normal breast tissue and permit the visualization of lesions with neoangiogenesis. Combining images acquired with different X-ray energy spectra would result in artefacts.

In this chapter, number sense is examined from a developmental perspective, based on results derived from a research conducted with Brazilian children attending Elementary School. Initially, definitions of number sense are presented, emphasizing its holistic and polysemic nature. Next, the various components that constitute it are discussed, mainly those which are investigated in studies involving children. The research presented here consists of three studies referring to three fields of mathematics knowledge: numbers (their meanings, number sequence, and the relative magnitude of digits in a number); operations (the effects of addition and subtraction on numbers, the inverse relationship between these operations, estimating results of additions and subtractions); and measurement (the use of instruments, units of measurement, the inverse relationship between the size of the unit and the quantity of units needed to measure a magnitude). Comparisons among the studies, between the tasks in each study, and between the school grades allowed identifying which components are understood before others, and how the development of number sense is characterized in this period of schooling.

3D recognition is one of the most progressive methods. The problem of face recognition is considered. In this model, special points, which form a feature vector, are identified. The method offers the following advantages: continuous and secret identification of the object; it is impossible to use a fake object; twins can be distinguished; weak dependence on head turning (the range of head deflection is substantially increased); weak dependence on external illumination, hair, and face turgidity in the case of a correct choice of the light range. Three-dimensional identification can be used in darkness, and it remains effective even in the case with head turning up to 90°. For this purpose, a method based on scalar perturbation functions and set-theoretic operation of subtraction is proposed. It is shown that all surface points and the mask volume are used in the process of sample testing for more accurate identification. Using the calibrated stereo pair for the face, the depth map is calculated by the correlation algorithm. As a result, a 3D mask of the face is obtained. Using three anthropomorphic points, a coordinate system that ensures a possibility of superposition of the tested masks is constructed; finally, certain parts are cut off by a clipping plane for equalization of the volumes. Applying the set-theoretic operation of subtraction the set of 3D points (voxels) belonging to the object is determined. This method differs from available 3D methods by the fact that it involves not only all points of the surface in the recognition procedure, but also the volume of the tested mask.

Brain single-photon emission computed tomography (SPECT) is a functional nuclear imaging technique that can provide a regional map of cerebral blood flow (CBF) changes during the interictal or ictal period in patients with epilepsy and other neurological disorders. The radiotracer for brain SPECT is rapidly taken up by the brain within 30–60 s after its injection. The radiotracer injection during seizure activity (ictal SPECT) can show a snapshot of regional CBF (rCBF) changes during seizure. The sensitivity of ictal SPECT is high in temporal lobe epilepsy but relatively lower in extratemporal epilepsy. SISCOM is an imaging technique to subtract ictal and interictal SPECT images and to coregister them on brain MRI. SISCOM significantly improves the sensitivity of ictal SPECT and can further localize epileptic focus. But the successful localization of epileptic focus can be affected by the time of radiotracer injection, seizure duration, and propagation pattern of ictal EEG. Ictal hypoperfusion as well as ictal hyperperfusion is an important finding. Thus, ictal SPECT and SISCOM should be carefully interpreted by simultaneous review with seizure semiology, clinical information, features, injection time, duration of seizure, and ictal EEG pattern at the injection times. SISCOM is also useful for localizing brain structure generating specific feature of seizures and studying propagation pathways of epileptic seizures and pathomechanism of other neurological disorders and sleep disorders.

This paper deals with the analysis of fuzzy and evolutionary approaches for efficiently solving vehicle routing problems (VRP) with constraints on vehicle’s capacity (CVRP) and time-windows (VRPTW). Authors focused their research on CVRP for marine bunkering tankers, in particular, on the planning of tanker’s routes under uncertainty of fuel demands at nodes. Triangular fuzzy numbers (TFNs) are proposed for modeling uncertain demands. In this case, the maximum possible number of customers is calculated, which can be served based on the subtraction operation with TFNs. In the paper, the authors also analyzed the planning of transport routes with time-windows. Currently, there are several methods and algorithms for planning of transport routes with time-windows, in particular: saving and sweeping algorithms, ant colony optimization (ACO) algorithm, artificial bee colony (ABC) algorithm, etc. In this paper, the authors discussed the features of using the ACO algorithm and the ABC algorithm to solve the vehicle routing problems with time-windows and the influence of their application on the results. The modeling results confirm the efficiency of the proposed fuzzy and evolutionary algorithms.

The numbers of magic series of large orders are computed on Intel Xeon Phi processors with an improved and optimized Montgomery multiplication algorithm. The number of magic series can be efficiently computed by Kinnaes’ formula, of which the most time-consuming element is modular multiplication. We use Montgomery multiplication for faster modular multiplication, and the number of operations is reduced through procedural simplifications. Modular addition, subtraction, and multiplication operations are vectorized by using the following instructions: Intel Advanced Vector Extensions (AVX), Intel Advanced Vector Extensions 2 (AVX2), and Intel Advanced Vector Extensions 512 (AVX-512). The number of magic series of order 8000 is computed on multiple nodes of an Intel Xeon Phi processor with a total execution time of 1806 days. Results are compared with salient studies in the literature to confirm the efficacy of the approach.

Aiming at the problem of misprint or obscure of production date, batch number and the validity on the medicine package, a delay-based misplaced difference scheme for medical information detection is put forward. To be specific, medical images with delay in packaging are acquired by a vision detection system, based on which, character images are obtained through misplaced subtraction operation; and a convolution kernel is designed based on gray value distribution of the character images for multi-step convolution to remove speckle noise. Then a specific operation with corrosion and dilation is further utilized to remove speckle noise and enhance the target character area. In the end, the modified weighted median filter is adopted for noise inhibition to further improve the recognition accuracy. Experimental results show that when the double image overlap η is 80% and threshold λ (the percentage of non-zero gray values in each convolution block) is 60%, the scheme’s recognition can be as accurate as 97.8% and detection speed can reach up to 0.1373 s/image, the detection precision and efficiency can satisfy medical information recognition requirements in medical package.

This chapter is on arithmetic and related operations over the field GF(2m) with polynomial-basis representations. The first section is on addition, subtraction, multiplication, and squaring; although subtraction is just an instance of addition, optimal squaring is not just multiplication with the same operand. The second section is on reduction. And the third section is on exponentiation, inversion, and division.

We study the algorithmic complexity of solving subtraction games in a fixed dimension with a finite difference set. We prove that there exists a game in this class such that solving the game is \({\mathbf {EXP}}\)-complete and requires time \(2^{\varOmega (n)}\), where n is the input size. This bound is optimal up to a polynomial speed-up.

We study the applicability of quantum algorithms in computational game theory and generalize some results related to Subtraction games, which are sometimes referred to as one-heap Nim games.

This chapter consists of a brief review or introduction, depending on the reader’s background, of the basics of computer arithmetic. The first two sections are on algorithms and designs of hardware units for addition and multiplication. (Subtraction is another fundamental operation, but it is almost always realized as the addition of the negation of the subtrahend.) For each of the two operations, a few architectures for hardware implementation are sketched that are sufficiently exemplary of the variety of possibilities. The third section of the chapter is on division, an operation that in its direct form is (in this book) not as significant as addition and multiplication but which may nevertheless be useful in certain cases. The discussions on algorithms and architectures for division are therefore limited.

Images generated from Cycle-Consistent Adversarial Network (CycleGAN) become blurry especially in areas with complex edges because of loss of edge information in downsampling of encoders. To solve this problem, we design a new model called ED-CycleGAN based on original CycleGAN. The key idea is using a pre-trained encoder: training an Encoder-Decoder Block (ED-Block) at first in order to get a difference map, which we call an edge map and is produced by the subtraction of input and output of the block. Then, the encoder part of a generator in CycleGAN share the parameters with the trained encoder of ED-Block and they will be frozen during training. Finally, by adding the output from a generator to the edge map, higher quality images can be produced. This structure performs excellently on “Apple2Orange”, “Summer2Winter” and “blond-hair2brown-hair” datasets. We use SSIM and PSNR to evaluate resolution of results and our method achieved the highest evaluation scores among CycleGAN, Unit and DiscoGAN.

Chest X-ray (CXR) is the most common examination for fast detection of pulmonary abnormalities. Recently, automated algorithms have been developed to classify multiple diseases and abnormalities in CXR scans. However, because of the limited availability of scans containing nodules and the subtle properties of nodules in CXRs, state-of-the-art methods do not perform well on nodule classification. To create additional data for the training process, standard augmentation techniques are applied. However, the variance introduced by these methods are limited as the images are typically modified globally. In this paper, we propose a method for local feature augmentation by extracting local nodule features using a generative inpainting network. The network is applied to generate realistic, healthy tissue and structures in patches containing nodules. The nodules are entirely removed in the inpainted representation. The extraction of the nodule features is processed by subtraction of the inpainted patch from the nodule patch. With arbitrary displacement of the extracted nodules in the lung area across different CXR scans and further local modifications during training, we significantly increase the nodule classification performance and outperform state-of-the-art augmentation methods.

This chapter consists of two sections that cover algorithms and hardware architectures for modular addition and multiplication: (x + y) mod m and xy mod m. Subtraction and division are also included—as the addition of an inverse and as multiplication by an inverse. The underlying algorithms and hardware structures are those of Chap. 1, modified for modular arithmetic. For both operations we shall consider generic algorithms and hardware structures for arbitrary moduli and also those for special moduli.

Arithmetic operations are part of digital signal processing. The arithmetic operations, binary addition and subtraction, are illustrated with examples. The combinational logic circuits for performing addition and subtraction are presented. Binary multiplication and division are illustrated with examples.

This paper proposes a diagonal symmetric pattern (DSP) to develop the illumination invariant measure for severe illumination variations. Firstly, the subtraction of two diagonal symmetric pixels is defined as the DSP unit in the face local region, which may be positive or negative. The DSP model is obtained by combining the positive and negative DSP units. Then, the DSP model can be used to generate several DSP images based on the 4 × 4 block region by controlling the proportions of positive and negative DSP units, which results in the DSP image. The single DSP image with the arctangent function can develop the DSP-face. Multi DSP images employ the extended sparse representation classification (ESRC) as the classifier that can form the DSP images based classification (DSPC). Further, the DSP model is integrated with the pre-trained deep learning (PDL) model to construct the DSP-PDL model. Finally, the experimental results on the Extended Yale B, CMU PIE and VGGFace2 test face databases indicate that the proposed methods are efficient to tackle severe illumination variations.

Reconstruction of the craniomaxillofacial (CMF) skeleton requires patient specific implants that restore cosmesis and protect the neural structures. Designing 3D patient specific geometries is challenging and labor intensive because of the lack of pre-injury information. We present an automated shape completion framework for the MICCAI AutoImplant Challenge 2020. The automated workflow selected standardized segmented skull volumes from the skull base to the apex. A U-Net style encoder/decoder framework was used to create the predictive model. The training data consisted of defective skulls with matched intact skulls. The challenge training set (100 cases) was augmented by randomly placed cubic and spherical defects on the same 100 cases for a total of 300 samples split 75/25% by case into a training and validation set. Probability volumes of the predicted skulls were generated by the U-Net and segmented to create an intact skull. Subtraction with defect skulls was used to isolate the implant geometry and were denoised with a connected region extraction of the single largest object, followed by a spherical topological filter. Dice Score (DSC) was 0.86 and Hausdorff distance (HD) was 14.2 mm for the validation set of 25 skulls (×3 defect types). Filtering improved the predicted implants with DSC of 0.87 and HD of 6.72. The automated pipeline for generating implants, produced geometries suitable for integration into a clinical pipeline that could dramatically decrease design time, cost, and increase reconstruction accuracy.

Ordinary arithmetic has the basic operations of addition, subtraction, multiplication, and division defined over the integers and the real numbers. Similar operations can be defined over other mathematical structures—certain subsets of integers, polynomials, matrices, and so forth. This chapter is a short discussion on such generalizations. The first section of the chapter is an introduction to two types of abstract mathematical structures that are especially important in cryptography: groups and fields. The second section consists of a review of ordinary polynomial arithmetic. The third section draws on the first two sections and covers polynomial arithmetic over certain types of fields. And the last section is on the construction of some fields that are especially important in cryptography.

Generating dual-energy subtraction (DES) soft-tissue images from chest radiographs (also called bone suppression) is an important task, as it improves the detection rates for lung nodules. Previous studies focus on generating DES-like soft-tissue images from CXRs through machine/deep learning techniques. However, they usually require tedious image processing steps for bone segmentation/delineation or ignore anatomical structure information (e.g., edges of ribs and clavicles) in CXRs. In this work, we propose a bone Edge-guided Generative Adversarial Network (EGAN) to generate DES-like soft-tissue images from conventional CXRs, which does not require human intervention and can explicitly use anatomical structure information of bones in CXRs. Specifically, the edges of ribs and clavicles in an input CXR were first detected by a trained fully convolutional network. Then, the edge probability map, as well as the original CXR image, are fed into a GAN model to generate the DES-like soft-tissue image, where the detected edge information is used as the prior knowledge to directly and specifically guide the image generation process. Experimental results on 504 subjects (each equipped with a CXR, a DES bone image, and a DES soft-tissue image) demonstrate that EGAN can produce DES-like soft-tissue images with high-quality and high-resolution, compared with classic deep learning methods. We further apply the trained EGAN to CXRs acquired by different types of X-ray machines in the public JSRT and NIH ChestXray 14 datasets, and our method can also produce visually appealing DES-like soft-tissue images.