Inverse Operation Research Articles

An innovative fractional grey system model and its application

In order to expand the applicability of the conventional fractional grey model, an innovative fractional grey model is proposed by the introduction of the innovative fractional accumulation. Three efforts are made in this study. First, the innovative fractional accumulation and its inverse operation are designed. Based on the innovative form, the parameter estimation and discrete time response of the novel model are given. In addition, the moth flame optimization algorithm is used to determine optimal hyper parameters for the novel model, and the rolling mechanism is used to enhance the prediction performance. To comprehensively confirm the forecasting ability of the proposed model, it is applied in three kinds of data with inverted U-shaped, W-shaped and oscillating features. The experimental results show the novel model is superior to all competitors in terms of level accuracy. Therefore, the novel model is considered a promising method for enhancing the existing fractional grey model.

A Fourth-Order Tensorial Wiener Filter Using the Conjugate Gradient Method

The recently developed iterative Wiener filter using a fourth-order tensorial (FOT) decomposition owns appealing performance in the identification of long length impulse responses. It relies on the nearest Kronecker product representation (with particular intrinsic symmetry features), together with low-rank approximations. Nevertheless, this new iterative filter requires matrix inversion operations when solving the Wiener–Hopf equations associated with the component filters. In this communication, we propose a computationally efficient version that relies on the conjugate gradient (CG) method for solving these sets of equations. The proposed solution involves a specific initialization of the component filters and sequential connections between the CG cycles. Different FOT-based decomposition setups are also analyzed from the point of view of the resulting parameter space. Experimental results obtained in the context of echo cancellation confirm the good behavior of the proposed approach and its superiority in comparison to the conventional Wiener filter and other decomposition-based versions.

Parallel linearized ADMM with application to multichannel image restoration and reconstruction

Many large-scale regularized inverse problems in imaging such as image restoration and reconstruction can be modeled as a generic objective function involves sum of nonsmooth but proximable terms, which are usually linear-operator-coupled. For the solution of these problems, a parallel linearized alternating direction method of multipliers (PLADMM) is proposed in this paper. At each step of the proposed algorithm, the proximity operators of the nondifferential terms are called individually. This leads to a highly parallel algorithm structure, where most sub-steps can be simultaneously solved. Profiting from the linearization step, the linear inverse operation is excluded. The convergence property of the proposed method is analyzed. The image deblurring, inpainting, and pMRI reconstruction experiments show that the proposed method has vast applicable vistas. Compared with the state-of-the-art methods, such as PADMM [21], FTVD-v4 [22], PPDS [33], FUSL [8], LADM [36], and ALADMM [27], it gains competitive results both in terms of quantitative indicators, such as PSNR or SSIM, and in terms of visual impression.

Review of physics-informed machine-learning inversion of geophysical data

We review five types of physics-informed machine-learning (PIML) algorithms for inversion and modeling of geophysical data. Such algorithms use the combination of a data-driven machine-learning (ML) method and the equations of physics to model or invert geophysical data (or both). By incorporating the constraints of physics, PIML algorithms can effectively reduce the size of the solution space for ML models, enabling them to be trained on smaller data sets. This is especially advantageous in scenarios in which data availability may be limited or expensive to obtain. In this review, we restrict the physics to be that from the governing wave equation, either as a constraint that must be satisfied or by using numerical solutions of the wave equation for modeling and inversion. This approach ensures that the resulting models adhere to physical principles while leveraging the power of ML to analyze and interpret complex geophysical data. There are several potential benefits of PIML compared to standard numerical modeling or inversion of seismic data computed by, for example, finite-difference solutions to the wave equation. 1) Empirical tests suggest that PIML algorithms constrained by the physics of wave propagation can sometimes resist getting stuck in a local minima compared with standard full-waveform inversion (FWI). 2) After the weights of the neural network are found by training, then the forward and inverse operations by PIML can be more than several orders of magnitude more efficient than FWI. However, the computational cost for general training can be enormous. 3) If the ML inversion operator [Formula: see text] is locally trained on a small portion of the recorded data [Formula: see text], then there is sometimes no need for millions of training examples that aim for global generalization of [Formula: see text]. The benefit is that the locally trained [Formula: see text] can be used to economically invert the remaining test data [Formula: see text] for the true velocity [Formula: see text], where [Formula: see text] can comprise more than 90% of the recorded data.

Existence and Stability for Fractional Differential Equations with a ψ–Hilfer Fractional Derivative in the Caputo Sense

This article aims to explore the existence and stability of solutions to differential equations involving a ψ-Hilfer fractional derivative in the Caputo sense, which, compared to classical ψ-Hilfer fractional derivatives (in the Riemann–Liouville sense), provide a clear physical interpretation when dealing with initial conditions. We discovered that the ψ-Hilfer fractional derivative in the Caputo sense can be represented as the inverse operation of the ψ-Riemann–Liouville fractional integral, and used this property to prove the existence of solutions for linear differential equations with a ψ-Hilfer fractional derivative in the Caputo sense. Additionally, we applied Mönch’s fixed-point theorem and knowledge of non-compactness measures to demonstrate the existence of solutions for nonlinear differential equations with a ψ-Hilfer fractional derivative in the Caputo sense, and further discussed the Ulam–Hyers–Rassias stability and semi-Ulam–Hyers–Rassias stability of these solutions. Finally, we illustrated our results through case studies.

Time-lapse difference seismic inversion based on scattering theory

Time-lapse seismic monitoring technology is an effective tool for quantitatively estimating subsurface medium variations and plays a crucial role in resource and engineering explorations. Among existing time-lapse inversion methods, the difference inversion technique offers higher accuracy but requires linear inversion operators. During linearization, the background is often approximated as a homogeneous medium, resulting in the loss of effective information. Additionally, merely using reflection wave information is not conducive to improving inversion accuracy. However, the true structure of the subsurface is often complex and inhomogeneous, which can easily generate complex wavefields, such as scattering waves, thereby hindering the resolution of differences between time-lapse models. Therefore, incorporating more comprehensive wavefield information is essential for enhancing the accuracy of time-lapse seismic inversion. To address this issue, a wave-equation-based time-lapse difference inversion method is proposed to retrieve the production-induced property perturbation. In the proposed method, the forward operator is formulated through the scattering wave equation, the operator is linearized through the Born approximation, and the WKBJ method is used to approximate Green's function with high accuracy for the inhomogeneous background. In this study, time-lapse seismic parallel inversion and difference inversion are conducted using the proposed forward operator. Both numerical experiments and application of field seismic data indicate that the proposed time-lapse difference inversion method can realize a more accurate quantitative characterization of time-lapse variations.

A NOVEL CONCEPT: THE PRODUCT OF TWO NEGATIVELY DIRECTED NUMBERS IS A NEGATIVELY DIRECTED NUMBER THOUGH THE NEGATIVE OF A NEGATIVE NUMBER IS A POSITIVE NUMBER

In this paper, the author proved that the product of two negatively directed numbers is a negatively directed number. This article is the outcome of previously published (2021-2024) ten (10) articles of this author. It is true that the negative of a negative number is a positive number. It has been done by applying the inversion process to a negative number. The process of inversion does not satisfy the basic concept of multiplication. Multiplication is defined as the adding of a number concerning another number repeatedly. So, the process of inversion does not comply with the fundamental concept of multiplication. According to the Theory of Dynamics of Numbers there exist three types of numbers: (1) Neutral or discrete numbers (2) Positively directed numbers (3) Negatively directed numbers. In general, we use four types of operators: addition (+), subtraction (-), multiplication (x), and division (÷) in mathematical calculations. Besides these, we use the negative sign (-) as an inversion operator. The positive sign (+) and negative sign (-) also represent the direction of neutral or discrete numbers. In this paper, the author introduced Fermat's Last Theorem: xn + yn = zn for n = 2 in Bhattacharyya's Theorem to prove that the product of two negatively directed numbers is a negatively directed number using the concept of the Theory of Dynamics of Numbers. In this paper, the author framed new laws of multiplication and inversion. Also, the author has given a comparative study between the conventional method of multiplication and the present concept of multiplication citing some practical examples. The author has become successful in finding the root of a quadratic equation in real numbers even if the discriminant, b2 – 4ac < 0 without using the concept of the imaginary number and also in determining the radius of a circle even if g2 + f2 < c, in real number without using the concept of complex numbers. With one example the author proved that this theorem is applicable in ‘Calculus’ also.

Low-complexity recursive constrained maximum Versoria criterion adaptive filtering algorithm

Linearly-constrained adaptive filtering algorithms have emerged as promising candidates for system estimation. The existing methods such as the constrained least mean square algorithm rely on mean square error based learning, which delivers suboptimal performance under non-Gaussian noise environments. Therefore, the recursive constrained maximum Versoria criterion (RCMVC) algorithm has been derived and is robust against impulsive distortions. Nonetheless, RCMVC suffers from a notable computational overhead stemming from matrix inversion operations. To circumvent this issue, utilizing the weighting method and the dichotomous coordinate descent (DCD) iteration method, this paper derives a low-complexity version of the RCMVC algorithm called DCD-RCMVC, which alleviates the requirement of matrix inversion and enhances the estimation accuracy and robustness against non-Gaussian interference. Furthermore, we also present a comprehensive theoretical analysis of the DCD-RCMVC algorithm, encompassing discussions on its equivalence, convergence properties, and computational complexity. Simulations performed for system identification problems indicate that the DCD-RCMVC algorithm outperforms the existing state-of-art approaches.

Graph pooling in graph neural networks: methods and their applications in omics studies

Graph neural networks (GNNs) process the graph-structured data using neural networks and have proven successful in various graph processing tasks. Currently, graph pooling operators have emerged as crucial components that bridge the gap between node representation learning and diverse graph-level tasks by transforming node representations into graph representations. Given the rapid growth and widespread adoption of graph pooling, this review aims to summarize the existing graph pooling operators for GNNs and their representative applications in omics. Specifically, we first present a comprehensive taxonomy of existing graph pooling algorithms, expanding the categorization for both global and hierarchical pooling operators, and for the first time reviewing the inverse operation of graph pooling, named unpooling. Next, we describe the general evaluation framework for graph pooling operators, encompassing three fundamental aspects: experimental setup, ablation analysis, and model interpretation. We also discuss open issues that significantly influence the design of graph pooling operators, including complexity, connectivity, adaptability, additional loss, and attention mechanisms. Finally, we summarize bioinformatics applications of graph pooling operators in omics, including graphs of gene interaction, medical images, and protein structures for drug discovery and disease diagnosis. Furthermore, we showcase the impact of graph pooling operators on research in specific real-world domains, with a focus on prediction performance and model interpretability. This review provides methodological insights in machine learning based graph modeling and related omics research, as well as an ongoing resource by gathering related papers and code in a dedicated GitHub repository (https://github.com/Hou-WJ/Graph-Pooling-Operators-and-Bioinformatics-Applications).

THE PERFORMANCE ANALYSIS OF PRECODED SPACE-TIME FREQUENCY MIMO-GFDM OVER RAYLEIGH FADING CHANNELS

The physical layer is implemented in the present communication era with new multicarrier modulation schemes such as Generalized Frequency Division Multiplexing with Multi-Input and Multi-Output (MIMO-GFDM) antenna systems to achieve good spectral efficiency and diversity order. This paper presents precoded Space-Time-Frequency MIMO-GFDM performance analysis to improve the bit error rate performance without increasing transmission power and bandwidth compared to conventional techniques. The proposed system also enhances the diversity order over frequency selective fading channels. In general, we need to perform channel matrix inversion operations at the receiver or channel precoding matrix operations at the transmitter to detect the symbols of MIMO-GFDM systems. This paper's proposed scheme completes the same task without performing channel matrix inversion. Orthogonal transform techniques such as Haar, Harley, Walsh-Hadamard, and Slant transforms are used as precoders at the transmitter for the proposed scheme. The simulation results are validated on the MATLAB working platform. We have compared the bit error rate of the PSTF-MIMO-GFDM system with Space-Time (ST) and Space Frequency (SF) as baseline schemes and different orthogonal transform precoding techniques.

A new high-precision numerical method for solving the HIV infection model of CD4(+) cells

This paper proposes a new method called the “Special Neural Network” to solve the HIV infection model of CD4(+) cells using a novel approximation approach. Unlike traditional methods that involve constructing loss functions and performing inverse matrix operations, our method discretizes the differential equations at configuration points, combines them, and transforms the system into a set of nonlinear equations. Parameters in the neural network are then iteratively solved using optimization to obtain an approximate solution. Additionally, when using the neural network as an approximate solution to the differential equations, we provide a form that satisfies the initial conditions through construction, eliminating the need to handle initial conditions during the solving process and thus streamlining the method. Finally, by comparing with other numerical methods using two sets of models and parameters, the Special Neural Network achieves high precision results and further demonstrates the advantages of our approach.

γ‐Valerolactone Enabling Spontaneously Inhibited Iodide Oxidation for High‐Quality Perovskite Single Crystal Fabrication

AbstractThe iodide precursor oxidation has persistently plagued solution grown iodine‐based perovskite single crystals (IPSCs) that inevitably introduce undesirable triiodide ion (I3−) defects and severely hindering crystal quality, despite IPSCs having garnered remarkable progress in multifarious photoelectronic applications. In this work, the spontaneously inhibited iodide oxidation is discovered in an eco‐friendly solvent, γ‐Valerolactone (GVL), and demonstrates a universal solution approach for fabricating high‐quality IPSCs. Compared to the routine γ‐Butyrolactone (GBL) system, GVL provides a lowered growth temperature and a significantly broadened inverse temperature operation window, thereby improving the theoretical utilization rate of perovskite precursors up to 88.6%. More importantly, due to its higher open‐ring hydrolysis energy, GVL can spontaneously inhibit the iodide precursors oxidation without any additional reductant and therefore effectively prevent the forming I3− defects. Typically, the as‐fabricated MAPbI3 single crystal possesses an extremely low trap density of 3.57 × 108 cm−3 and a high carrier mobility‐lifetime (µτ) product of 2.74 × 10−3 cm2 V−1, which enables its photodetection capabilities to be on a par with the state‐of‐art MAPbI3 single crystal photodetectors. This work paves an efficacious and green pathway for high‐quality IPSC fabrication toward advanced optoelectronic utilizations.

Comparative Assessment of U-Net-Based Deep Learning Models for Segmenting Microfractures and Pore Spaces in Digital Rocks

Summary Segmentation of high-resolution X-ray microcomputed tomography (µCT) images is crucial in digital rock physics (DRP), affecting the characterization and analysis of microscale phenomena in the porous media. The complexity of geological structures and nonideal scanning conditions pose significant challenges to conventional image segmentation approaches. Motivated by the recent increasing popularity of deep learning (DL) techniques in image processing, this work undertakes a comparative study of DL models, specifically U-Net and its variants, for segmenting multiple targets with distinguished features in digital rocks, including discrete fracture networks (DFNs), pore spaces, and solid rock. Particularly, DFNs have a smaller volumetric fraction over others, bringing in a substantial challenge of imbalanced segmentation. The primary focus is to evaluate the architecture and feature enhancement strategies of various DL models, including U-Net, attention U-Net, residual U-Net, U-Net++, and residual U-Net++. The models were designed as 2.5D, utilizing a central 2D image and its two adjacent upper and lower 2D images as input to provide a pseudo-3D context. In addition, because the ground truth of segmentation was unknown for real-world digital rocks, we created a benchmark data set following the inverse operations of segmentation. The data synthesis started from the label images (i.e., solid rock, pore spaces, and DFNs), followed by simulating partial volume blurring, adding random background noise, and introducing ring artifacts to mimic real raw X-ray µCT images. The data set, which included various rock types (i.e., sandstone and artificial data), scanning resolution, and magnitudes of noise and artifacts, was divided into training and testing data sets with a 90% and 10% ratio, respectively. Moreover, in addition to the conventional pixel-wise evaluation metrics, the physics-based metric of the lattice-Boltzmann method (LBM) simulated permeability provided more comprehensive assessments. The results demonstrated that the residual connections, nested architectures, and redesigned skip connections contribute to the model performance and give the residual U-Net++ the highest accuracy. The improvements were mainly on the boundaries and small targets, especially the DFNs, which dominate the interconnectivity and therefore affect the permeability greatly. This study also rigorously evaluated the efficiency and generalization of each model, demonstrating that the sophisticated architectures achieved excellent practicability and maintained robust performance on completely unseen data, ensuring their suitability for diverse and challenging DRP applications.

Finemap-MiXeR: A variational Bayesian approach for genetic finemapping.

Genome-wide association studies (GWAS) implicate broad genomic loci containing clusters of highly correlated genetic variants. Finemapping techniques can select and prioritize variants within each GWAS locus which are more likely to have a functional influence on the trait. Here, we present a novel method, Finemap-MiXeR, for finemapping causal variants from GWAS summary statistics, controlling for correlation among variants due to linkage disequilibrium. Our method is based on a variational Bayesian approach and direct optimization of the Evidence Lower Bound (ELBO) of the likelihood function derived from the MiXeR model. After obtaining the analytical expression for ELBO's gradient, we apply Adaptive Moment Estimation (ADAM) algorithm for optimization, allowing us to obtain the posterior causal probability of each variant. Using these posterior causal probabilities, we validated Finemap-MiXeR across a wide range of scenarios using both synthetic data, and real data on height from the UK Biobank. Comparison of Finemap-MiXeR with two existing methods, FINEMAP and SuSiE RSS, demonstrated similar or improved accuracy. Furthermore, our method is computationally efficient in several aspects. For example, unlike many other methods in the literature, its computational complexity does not increase with the number of true causal variants in a locus and it does not require any matrix inversion operation. The mathematical framework of Finemap-MiXeR is flexible and may also be applied to other problems including cross-trait and cross-ancestry finemapping.

An efficient illumination compensation method for reverse time migration

AbstractBy directly solving the full two‐way wave equation, reverse time migration has superiority over other imaging algorithms in handling steeply dipping structures and other complicated geological models. Moreover, by incorporating the asymptotic inversion operator into reverse time migration imaging condition, the imaging algorithm is able to give a quantitative estimation of parameter perturbation in high‐frequency approximation sense. However, because conventional asymptotic inversion only accounts for geometrical spreading, uneven illumination due to irregular acquisition geometry and inhomogeneous subsurface at each image point is neglected. The omit of illumination compensation significantly affects the imaging quality. Wave‐equation‐based illumination compensation methods have been extensively studied in the past. However, the traditional wave‐equation‐based illumination compensation methods usually require high computational cost and huge storage. In this paper, we propose an efficient wave‐equation‐based illumination compensation method. Under high‐frequency approximation, we first define a Jacobian determinant to measure the regularity of subsurface illumination, and then illumination compensation operators are proposed based on the Jacobian. Through boundary integration, we further express the illumination compensation operators through extrapolated wavefields; the explicit computation of asymptotic Green's functions is thus avoided, and an efficient illumination compensation implementation for reverse time migration is achieved. Numerical results with both synthetic and field data validate the effectiveness and efficiency of the presented method.

Unification of Mind and Matter through Hierarchical Extension of Cognition: A New Framework for Adaptation of Living Systems.

Living systems (LSs) must solve the problem of adapting to their environment by identifying external states and acting appropriately to maintain external relationships and internal order for survival and reproduction. This challenge is akin to the philosophical enigma of how the self can escape solipsism. In this study, a comprehensive model is developed to address the adaptation problem. LSs are composed of material entities capable of detecting their external states. This detection is conceptualized as "cognition", a state change in relation to its external states. This study extends the concept of cognition to include three hierarchical levels of the world: physical, chemical, and semiotic cognitions, with semiotic cognition being closest to the conventional meaning of cognition. This radical extension of the cognition concept to all levels of the world provides a monistic model named the cognizers system model, in which mind and matter are unified as a single entity, the "cognizer". During evolution, LSs invented semiotic cognition based on physical and chemical cognitions to manage the probability distribution of events that occur to them. This study proposes a theoretical model in which semiotic cognition is an adaptive process wherein the inverse causality operation produces particular internal states as symbols that signify hidden external states. This operation makes LSs aware of the external world.

Integrated photonic fractional convolution accelerator

An integrated photonic circuit architecture to perform a modified-convolution operation based on the discrete fractional Fourier transform (DFrFT) is introduced. This is accomplished by utilizing two nonuniformly coupled waveguide lattices with equally spaced eigenmode spectra, the lengths of which are chosen so that the DFrFT and its inverse operations are achieved. A programmable modulator array is interlaced so that the required fractional convolution operation is performed. Numerical simulations demonstrate that the proposed architecture can effectively perform smoothing and edge detection tasks even for noisy input signals, which is further verified by electromagnetic wave simulations. Notably, mild lattice defects do not jeopardize the architecture performance, showing its resilience to manufacturing errors.

A cancellable iris template protection scheme based on inverse merger and Bloom filter

Iris recognition has found extensive applications in real-world situations and financial contexts. However, Iris template protection schemes are highly vulnerable to well-planned attacks that can lead to the leakage of personal information. Once biological information is compromised, this loss is irreversible for the individual. Cancelable protection schemes for iris templates based on the Bloom filter have substantial attention in the field of iris biometrics. Nevertheless, Bloom filter-based template protection schemes face specific security challenges. Therefore, it is crucial to propose a method to protect iris templates that is both secure and efficient. To address irreversible limitations in security analysis, we propose a template protection scheme, a cancelable iris biometric protection scheme based on inverse merger and Bloom filter. The primary idea of the proposed scheme is to perform an inverse merger operation on the acquired codewords before mapping the iris templates to the Bloom filter specifically. Through a comparison of the sizes between the original templates and their inverted counterparts, the template with the smaller size is chosen as the definitive result, subsequently being mapped into the Bloom filter. Our proposed scheme exhibits significant advancements in accuracy across multiple datasets, as evidenced by empirical validations. In the optimal case, our model achieves an excellent performance of 98.04% in terms of GAR, while achieving a significant reduction of 0.51% in terms of EER. Furthermore, a comparative analysis with existing iris template protection methods is performed to evaluate its relative effectiveness in resisting the attack of averaging the columns of a block. The results demonstrate that the scheme exhibits robust resistance to such attacks. The experimental analysis demonstrated that the scheme provided a good balance between accuracy and safety.

Ring-shaped segmentation phase design method for the combined point spread function

The study presents a method for designing phase masks, specifically the ring-shaped segmentation method, which can be employed in creating the modulation phase for specialized point spread functions (PSFs), such as multi-focus PSFs and those with axial encoding functions. An algorithm for phase inversion optimization is introduced to enhance the optical transfer function efficiency of the designed phase mask, which is based on the Fresnel approximation imaging inverse operation and iterative Fourier transform algorithm. The ring-shaped segmentation phase design approach effectively combines individual phases, resulting in unified PSFs with unique properties. The promising outcomes demonstrated by the designed PSFs are truly remarkable. The refined phase masks and experimental verification further validate the effectiveness of this groundbreaking approach. This advancement in ring-shaped segmentation method development has significant potential for real-world applications, representing a noteworthy contribution to the field of optical imaging.

나눗셈 도입 단원의 곱셈과 나눗셈의 관계 지도 내용 분석

Multiplication and division can cancel each other's calculation results, and they are in the relationsheep of inverse operations. Division is mathematically defined based on multiplication. This means that division assumes a multiplication structure. It is also possible to explain the inverse operation relationship between multiplication and division in the way that division utilizes the multiplication structure. In particular, when expressed as a multiplicative expression, division corresponds to the problem of finding the number to be multiplied or multiplied with a given product. This is the opposite of the calculation direction of multiplication, and the number to be found can vary depending on the context of division. Based on the analysis of the inverse operation relationship between multiplication and division, the division introduction unit of 11 elementary school textbooks were analyzed. Korea's elementary school mathematics textbooks teach division and division calculation methods based on the context of the inverse operation relationship between multiplication, and the contexs of division. As a result of the textbook analysis, it was found that the textbooks taught the relationship between multiplication and division as the quotient of division could be obtained using the related multiplication formula, and the number to divide the related multiplication formula was fixed as the number to be multiplied. Accordingly, the position of the quotient is at the multiplier in the multiplication expression, and this means that the context of the division is measurement division. As a result of adhering to this division quotient calculation method, problems arise when Korean elementary school mathematics textbooks explain the division calculation process in the context of the equal division system using multiplication formulas, and there are cases where the division quotient calculation method is inappropriate for the multiplication structure. Based on the textbook analysis results, some ideas were proposed to improve the teaching of the relationship between multiplication and division, and division.