Affine Transformation Research Articles

Patient-specific Cardio-respiratory Motion Prediction in X-ray Angiography using LSTM Networks

Objective. To develop a novel patient-specific cardio-respiratory motion prediction approach for X-ray angiography time series based on a simple long short-term memory (LSTM) model. Approach. The cardio-respiratory motion behavior in an X-ray image sequence was represented as a sequence of 2D affine transformation matrices, which provide the displacement information of contrasted moving objects (arteries and medical devices) in a sequence. The displacement information includes translation, rotation, shearing, and scaling in 2D. A many-to-many LSTM model was developed to predict 2D transformation parameters in matrix form for future frames based on previously generated images. The method was developed with 64 simulated phantom datasets (pediatric and adult patients) using a realistic cardio-respiratory motion simulator (XCAT) and was validated using 10 different patient X-ray angiography sequences. Main results. Using this method we achieved less than 1 mm prediction error for complex cardio-respiratory motion prediction. The following mean prediction error values were recorded over all the simulated sequences: 0.39 mm (for both motions), 0.33 mm (for only cardiac motion), and 0.47 mm (for only respiratory motion). The mean prediction error for the patient dataset was 0.58 mm. Significance. This study paves the road for a patient-specific cardio-respiratory motion prediction model, which might improve navigation guidance during cardiac interventions.

Finite groups with an affine map of large order

AbstractLet 𝐺 be a group. A functionG→GG\to Gof the formx↦xα⁢gx\mapsto x^{\alpha}gfor a fixed automorphism 𝛼 of 𝐺 and a fixedg∈Gg\in Gis called anaffine map of 𝐺. The affine maps of 𝐺 form a group, called the holomorph of 𝐺. In this paper, we study finite groups 𝐺 with an affine map of large order. More precisely, we show that if 𝐺 admits an affine map of order larger than12⁢|G|\frac{1}{2}\lvert G\rvert, then 𝐺 is solvable of derived length at most 3. We also show that, more generally, for eachρ∈(0,1]\rho\in(0,1], if 𝐺 admits an affine map of order at leastρ⁢|G|\rho\lvert G\rvert, then the largest solvable normal subgroup of 𝐺 has derived length at most4⁢⌊log2⁡(ρ−1)⌋+34\lfloor\log_{2}(\rho^{-1})\rfloor+3.

Phylogenetic and functional constraints of plant facilitation rewiring.

Facilitative interactions bind community species in intricate ecological networks, preserving species that would otherwise be lost. The traditional understanding of ecological networks as static components of biological communities overlooks the fact that species interactions in a network can fluctuate. Analyzing the patterns that cause those shifts can reveal the principles that govern the identity of pairwise interactions and whether they are predictable based on the traits of the interacting species and the local environmental contexts in which they occur. Here we explore how abiotic stress and phylogenetic and functional affinities constrain those shifts. Specifically, we hypothesize that rewiring the facilitative interactions is more limited in stressful than in mild environments. We present evidence of a distinct pattern in the rewiring of facilitation-driven communities at different stress levels. In highly stressful environments with a firm reliance on facilitation, rewiring is limited to growing beneath nurse species with traits to overcome harsh stressful conditions. However, when environments are milder, rewiring is more flexible, although it is still constrained to nurses that are close relatives. Understanding the ability of species to rewire their interactions is crucial for predicting how communities may respond to the unprecedented rate of perturbations on Earth.

A novel algorithm for solving sum of several affine fractional functions

<abstract><p>By using the outer space branch-and-reduction scheme, we present a novel algorithm for globally optimizing the sum of several affine fractional functions problem (SAFFP) over a nonempty compact set. For providing the reliable lower bounds in the searching process of iterations, we devise a novel linearizing method to establish the affine relaxation problem (ARP) for the SAFFP. Thus, the main computational work involves solving a series of ARP. For improving the convergence speed of the algorithm, an outer space region reduction technique is proposed by utilizing the objective function characteristics. Through computational complexity analysis, we estimate the algorithmic maximum iteration times. Finally, numerical comparison results are given to reveal the algorithmic computational advantages.</p></abstract>

CONSTRUCTION OF NEW AFFINE AND NON-AFFINE FRACTAL INTERPOLATION FUNCTIONS THROUGH THE WEYL–MARCHAUD DERIVATIVE

This paper investigates the Weyl–Marchaud fractional derivative of affine and non-affine fractal interpolation functions with function scaling factors. The dependence of fractal interpolation function on the scaling factor is mainly explored by choosing the scaling factor as a function instead of a constant. In addition, for some fixed order [Formula: see text], the Weyl–Marchaud fractional derivative of a linear fractal interpolation function is estimated by predefining the fractional derivative values at the end points. Similarly, the Weyl–Marchaud fractional derivative of a [Formula: see text]-fractal function is investigated for some fixed order [Formula: see text] with additional constraints on the derivative of prescribed continuous function and base function.

SwISS: A scalable Markov chain Monte Carlo divide‐and‐conquer strategy

Divide‐and‐conquer strategies for Monte Carlo algorithms are an increasingly popular approach to making Bayesian inference scalable to large data sets. In its simplest form, the data are partitioned across multiple computing cores and a separate Markov chain Monte Carlo algorithm on each core targets the associated partial posterior distribution, which we refer to as a sub‐posterior, that is, the posterior given only the data from the segment of the partition associated with that core. Divide‐and‐conquer techniques reduce computational, memory and disk bottle necks but make it difficult to recombine the sub‐posterior samples. We propose SwISS: Sub‐posteriors with Inflation, Scaling and Shifting; a new approach for recombining the sub‐posterior samples, which is simple to apply, scales to high‐dimensional parameter spaces and accurately approximates the original posterior distribution through affine transformations of the sub‐posterior samples. We prove that our transformation is asymptotically optimal across a natural set of affine transformations and illustrate the efficacy of SwISS against competing algorithms on synthetic and real‐world data sets.

Automatic detection of internal corrosion defect in a natural gas gathering pipeline using improved YOLOv5 model

The detection of internal corrosion of the very long gas pipeline is a fundamental task for the prevention of possible failures, also one of the major challenges facing gas companies. Pipeline endoscopy based on the corrosion inspection method provides direct visual observation of defects, but the post-video analysis is time-consuming and not practical. In this work, we propose an improved YOLOv5 model-based software approach to automatically detect inner corrosion defects in nature gas-gathering pipelines. Video streaming of pipe interiors is provided by an endoscope robot. Sample augmentation strategies such as affine transformation and defect segmentation with background fusion are used to generate defect images and expand the data set. The region-based recursive localization method can be effectively optimized to improve the localization of corrosion regions.

Global Phase Portraits of the Quadratic Systems Having a Singular and Irreducible Invariant Curve of Degree 3

Any singular irreducible cubic curve (or simply, cubic) after an affine transformation can be written as either [Formula: see text], or [Formula: see text], or [Formula: see text]. We classify the phase portraits of all quadratic polynomial differential systems having the invariant cubic [Formula: see text]. We prove that there are [Formula: see text] different topological phase portraits for such quadratic polynomial differential systems. We control all the bifurcations among these distinct topological phase portraits. These systems have no limit cycles. Only three phase portraits have a center, 19 of these phase portraits have one polycycle, three of these phase portraits have two polycycles. The maximum number of separartices that have these phase portraits is 26 and the minimum number is nine, the maximum number of canonical regions of these phase portraits is seven and the minimum is three.

The structure of disintegrating defect clusters in smectic C freely suspended films.

Disclinations or disclination clusters in smectic C freely suspended films with topological charges larger than one are unstable. They disintegrate, preferably in a spatially symmetric fashion, into single defects with individual charges of +1, which is the smallest positive topological charge allowed in polar vector fields. While the opposite process of defect annihilation is well-defined by the initial defect positions, disintegration starts from a singular state and the following scenario including the emerging regular defect patterns must be selected by specific mechanisms. We analyze experimental data and compare them with a simple model where the defect clusters adiabatically pass quasi-equilibrium solutions in one-constant approximation. It is found that the defects arrange in geometrical patterns that correspond very closely to superimposed singular defect solutions, without additional director distortions. The patterns expand by affine transformations where all distances between individual defects scale with the same time-dependent scaling factor proportional to the square-root of time.

Design of Nonlinear Component of Block Cipher Using Gravesian Octonion Integers

Being the only nonlinear component in many cryptosystems, an S-box is an integral part of modern symmetric ciphering techniques that creates randomness and increases confidentiality at the substitution stage of the encryption. The ability to construct a cryptographically strong S-box solely depends on its construction scheme. The primary purpose of an S-box in encryption standards is to establish confusion between the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> -bit input into the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> -bit output (both <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m, n &gt;= 2$ </tex-math></inline-formula> ). This article proposed a robust way to construct S-boxes based on the Gravesian octonion integers. We chunk the paper into threefold: firstly, a comprehensive technique for constructing S-box using affine mapping is described. The presented work is developed in such a way that for every valid input, it generates two S-boxes. Secondly, the strength of the newly generated S-box is evaluated by passing through a rigorous security analysis. Finally, a thorough comparison of the newly developed method with some well-known existing schemes is conducted. We mainly targeted some elliptic curve-based S-boxes in comparison by taking the same parameters in our scheme. The computational results and performance analysis reveal that the propose algorithm can construct a large number of distinct S-boxes that are cryptographically secured and create high resistance against various cryptanalysis attacks.

On approximately convex and affine functions

On approximately convex and affine functions

Polynomial Sliding Surfaces to Control a Boost Converter With Constant Power Load

The unstable ON and OFF state trajectories of a boost converter supplying a constant power load (CPL) are appropriately combined using sliding-mode control (SMC) with a suitable surface to yield a stable trajectory that reaches a specified equilibrium point. Selecting the optimum surface involves a comparative analysis among potential candidates in terms of stability, disturbance rejection, conduction losses and inrush current. The performance as switching function of polynomials of degree zero (non-zero constant), degree one (affine function) and degree 2 (quadratic function) are analyzed in depth to conclude that the affine function leads to the best static and dynamic results. The theoretical predictions are verified by means of simulations and measurements in a prototype.

Dynamic Hyperspectral Pansharpening CNNs

Hyperspectral (HS) pansharpening seeks to integrate low spatial resolution HS (LRHS) images with connected panchromatic (PAN) images to produce high spatial resolution HS (HRHS) images. Traditional pansharpening convolutional neural networks (CNNs) directly map LRHS and PAN images into HRHS images under fixed network parameters, which imply static pansharpening rules. However, real-world HS data are often characterized by spatial variations and intuitively the pansharpening rules should be dynamic. To deal with the dilemma, in this paper we develop dynamic HS pansharpening CNNs. We first specify the concepts of dynamic pansharpening and static pansharpening. Then, we propose a learn-to-learn oriented pansharpening CNN paradigm, which aims to learn a how-to-learn rule to produce spatially adaptive pansharpening rules and comprises three stages of preliminary fusion, scene-sensitive modulation and spectral reconstruction. Finally, following the paradigm, we design two groups of dynamic pansharpening CNNs (DyPNNs), i.e., internal-connection-based and external-connection-based. They involve various spatial modulations, including spatial affine transform (AT), spatial dynamic convolution (DC) or improved spatial attention (SA), and thus consist of six specific DyPNNs: IC-AT-DyPNN, IC-DC-DyPNN, IC-SA-DyPNN, EC-AT-DyPNN, EC-DC-DyPNN and EC-SA-DyPNN. Experimental results on several HS datasets verify the effectiveness of the proposed DyPNNs in terms of both the spatial reconstruction and spectral fidelity.

Experimental evidence for large negative electron affinity from scandium-terminated diamond

Two Sc–diamond (100) and (111) surfaces have the highest negative electron affinity for a metal adsorbed onto bare diamond measured to date, as well as being thermally stable up to 900 °C.

Effects of quantum size on the thermoelectric properties of bismuth.

First principles and the Boltzmann transport equation have been combined to investigate the effects of quantum size L/λ, the ratio of quantum confinement length L to thermal de Broglie wavelength λ, on the thermoelectric properties of 2D β-bismuth. It is revealed that the thermoelectric properties of 2D β-bismuth are highly influenced by quantum size, especially when the L/λ is less than 0.1. Specifically, the Seebeck coefficients of both electrons and holes decrease as the L/λ ratio increases, while the electrical and thermal conductivity show the opposite trend. The results also show that 2D bismuth with three or more layers has semimetal properties, with the first observation of a semiconductor-semimetal transition in 2D bismuth. Moreover, the electron affinity, ionization energy, and work function of 2D β-bismuth do not exhibit a significant variation or trend with quantum size effects. The detailed electronic structures provide a fundamental understanding of the thermoelectric properties of bismuth, and the obtained results may provide a deep understanding of the relationship between the quantum size and the thermoelectric properties of 2D β-bismuth.

Averaging of random affine transformations of functions domain

Averaging of random affine transformations of functions domain

Аппроксимация решений многомерного уравнения Колмогорова с помощью итераций Фейнмана-Чернова

In this paper we propose a new algorithm for the numerical approximation of solutions to the multidimensional Kolmogorov equation, based on the averaging of Feynman-Chernoff iterations for random operator-valued functions. In the case when the values of operator-valued functions belong to the representation of some finite-dimensional Lie group, the proposed algorithm has a lower computational complexity compared to the standard Monte Carlo algorithm that uses the Feynman-Kac formula. In particular, we study the case of a group of affine transformations of a Euclidean space. For the considered algorithms we also present the results of numerical calculations.

An Integrated Image Encryption Scheme Based on Elliptic Curve

Due to the extensive demand for digital images across all fields, the security of multimedia data over insecure networks is a challenging task. The majority of the existing modern encryption schemes are merely developed that ensure the confidentiality of the image data. This manuscript presents a new image encryption scheme that ensures confidentiality, user authentications, and secure key sharing among the communicating parties. Initially, the users share a secret parameter using Diffie-Hellman over the elliptic curve and pass it through SHA-256. Afterwards, the proposed scheme uses the first 128-bits for the confidentiality of the data, while the remaining 128-bits are for authentication. In the encryption algorithm, the confusion module is achieved by affine power affine transformation. At the same time, the diffusion module is attained through highly nonlinear sequences, which are generated through the elliptic curve. Experimental testing and the latest available security tools are used to verify the effectiveness of the proposed algorithm. The simulation findings and the comparison of the proposed scheme with the existing image encryption techniques reveal that the suggested scheme offers a sufficient degree of security. Furthermore, the outcome of the simulation results divulges several advantages of the proposed scheme, including a large key space, resistance to differential attacks, high efficiency, and strong statistical performance.

Proposal of fully augmented complex-valued neural networks

In this paper, we propose a complex-valued neural network based on the widely linear estimation taking advantage of its geometric structure, and show that it can learn geometric transformations that the conventional neural networks cannot. First we formulate a fully augmented complex-valued neuron model based on the widely linear estimation. It is a generalized complex-valued neuron model that includes a usual complex-valued neuron and a degenerated case called a degenerated fully augmented complex-valued neuron. A fully augmented complex-valued neural network consists of such fully augmented complex-valued neurons. Secondly, we derive the back-propagation learning algorithms for the multi-layered fully augmented complex-valued neural networks. Finally, we find out via experiments that the multi-layered fully augmented complex-valued neural network has the different ability to learn 2D affine transformation from that of the usual complex-valued neural network.

Illumination Guided Attentive Wavelet Network for Low-Light Image Enhancement

Deep convolutional neural networks have recently been applied to improve the quality of low-light images and have achieved promising results. However, most existing methods cannot suppress noise during the enhancement process effectively, resulting in unknown artifacts and color distortions. In addition, these methods do not fully utilize illumination information and perform poorly under extremely low-light condition. To alleviate these problems, we propose the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">illumination guided attentive wavelet network</i> (IGAWN) for low-light image enhancement (LLIE). Considering that the wavelet transform can separate high-frequency noise and desired low-frequency content effectively, we enhance low-light images in the frequency domain. By integrating attention mechanisms with wavelet transform, we develop the attentive wavelet transform to capture more important wavelet features, which enables the desired content to be enhanced and the redundant noise to be suppressed. To improve the image enhancement performance under extremely low-light environment, we extract illumination information from the input images and exploit it as the guidance for image enhancement through the frequency feature transform (FFT) layer. The proposed FFT layer generates frequency-aware affine transformation from the estimated illumination information, which can adaptively modulate the image features of different frequencies. Extensive experiments on synthetic and real-world datasets demonstrate that our IGAWN performs favorably against state-of-the-art LLIE methods.