Reflection Equation Research Articles

Unified Framework for Coupling Matrix Reconfiguration Through Sequential Householder Transformation

Unified Framework for Coupling Matrix Reconfiguration Through Sequential Householder Transformation

Quantitative analysis of the effect of illumination variations on image processing in machine vision inspection

Abstract When unavoidable light, age, expression, and gesture changes occur, the machine vision detection accuracy will be greatly reduced, especially the light change impact on image processing. Combining the reflection equation and frequency domain analysis to construct a light change model based on spherical harmonic function and process the image from four directions, namely, digital image conversion, median filtering, sharpening processing, and image global segmentation. Aiming at the shortcomings of traditional image processing algorithms, the light compensation based on the improved pulse-coupled neural network model is proposed, and the model is used to analyze the impact of light changes on image processing. Despite the changes in light conditions, this algorithm maintains above 0.95 in each subset and has the best overall performance, as shown by the results. When the light intensity is less than 41.88kLux, using the optimal threshold for background segmentation of adult green peppers with respect to a fixed threshold T=0.3 results in a significant reduction of the background segmentation error. When the light intensity is greater than 41.88kLux, the superiority of the optimal threshold is not obvious. The results of this research not only have a significant role in promoting the development of the field of computer vision but also can provide people with convenient and efficient services in all aspects of social life.

Bragg reflection of linear shallow-water waves by an array of widely spaced trapezoidal bars on a fringing reef flat

A closed-form solution to the linear shallow-water wave equation for wave reflection by a finite periodic array of widely spaced trapezoidal bars on a fringing reef flat is presented. It is shown that, when the total number, height, or top width of the trapezoidal bars increases, the strength of the Bragg resonance increases but the downward shift of the resonance phase becomes more pronounced. When the width of the reef face increases or when the reef face changes from a concave profile to a convex profile, the strength of the Bragg resonance decreases and the downward shift of the resonance phase also becomes more pronounced. Especially, it is found that the location of trapezoidal bars plays an important role in the strength and occurrence condition of the Bragg resonant reflection. Finally, the optimal collocation of the location and width of trapezoidal bars is investigated. Considering both construction cost and reflecting capacity, the relative width is recommended to be within 0.4≤wb/d≤0.6 and the distance from the reef edge to trapezoidal bars is suggested to be equal to the spacing of trapezoidal bars.

Quality-driven Gaussian mixture variational probabilistic network for soft sensor application in PET/PA6 polymerization process

Variational autoencoder has been widely used to build soft sensor models as a deep unsupervised feature extractor in recent years. However, the vanilla VAE employs a single diagonal Gaussian distribution as the approximate posterior in its latent feature space, which may lead to inferior performance when solving complex non-Gaussian multimode modeling problem. To address the issue, this paper proposes a quality-driven Gaussian mixture variational probabilistic network-based (QGMVPN) soft sensor model. First, Gaussian mixture density with diagonal covariance matrices and Householder transformations are implemented to characterize the distributions of non-Gaussian multimode feature. Then, a quality-driven strategy is designed to extract quality-related features and a novel gating mechanism is employed to enhance the nonlinear representation ability. Last, the trained decoder, coupled with the sampling space, is directly applied to soft sensor modeling owing to the special extra input of the decoder. The effectiveness of QGMVPN-based model is demonstrated on two polymerization datasets.

Domestic service and Chilean literature: fictional experiments in narrating the household

This article shines light on the interconnectedness of reproductive labour and Latin American literature through two Chilean novels that explore the relationship between peripheral capitalism and domestic servitude: José Donoso's The Obscene Bird of Night and Diamela Eltit's Mano de Obra. The study of these texts allows for a periodisation of the reproductive sphere under different phases of capitalist accumulation, and exposes an association between the literary treatment of domestic service and the achievement of highly experimental narratives in Latin America. My reading of Obscene goes beyond viewing this novel as postmodernist fiction, by showing how its nightmarish poetics are a consequence of the transformation of the oligarchic household vis-a-vis the collapse of systems of bonded labour in the 1960s. Whereas the prose of Obscene provides a harrowing descent into the intimate connections between master and servant at the moment of their decline, Mano de Obra unveils a surgical prose capable of expressing the new impersonality of social reproduction in the subsequent neoliberal period. Of special interest to this analysis is how Eltit suggests that even the proletariat household can recreate exploitative patterns of domestic servitude to guard against complete immiseration. Three main conclusions result from this reading. First, Latin American fiction is an important literary archive from which capitalism's exploitation of the reproductive sphere can be excavated. Second, Latin American literature shows formal uniqueness when representing domestic service in the periphery. Lastly, fictional representations of domestic service help us understand the institution not as remnant of previous modes of production, but as capitalist strategy for the reproduction of social forces that underpay the cost of life-making processes.

Analytical Approach to Two‐Dimensional Full Reflections of Fast Magnetosonic Waves Due To Mesoscale Density Boundaries

AbstractPropagation of fast magnetosonic (MS) waves in the equatorial plane has attracted a growing attention in recent studies. Although computer simulations including ray tracing, PIC, and full wave simulations have been utilized to study the propagation of MS waves, analytical approach is needed to investigate the physics insight. In this letter, we first derive the wave equations describing the two‐dimensional propagation of MS waves under the assumption that the mesoscale density inhomogeneity is only along one dimensional. After investigating the essential role of the potential function in the wave equation for the full reflection of MS waves, we find that full reflection can occur when the minimum potential is significantly negative. Finally, we have discussed the effects of incidence angles and wave frequencies on the full reflection. Our results show that MS waves with an incidence angle or wave frequency greater than the critical value would be fully reflected.

Accurate P-wave reflection and transmission coefficients for non-welded interface incorporating elasto-plastic deformation

P-wave reflection and transmission coefficients for non-welded interface play crucial roles in broad practical engineering productions, involving fracture properties prediction and seismic inversion. However, the existing reflection coefficient equations for non-welded interface in elasto-plastic media are seldom studied, although the elasto-plastic deformation is frequently encountered in the Earth’s subsurface due to artificial and tectonic activities. In this study, we proposed the accurate reflection and transmission coefficients equation for a non-welded interface embedded in an elasto-plastic deformed medium based on the elasto-plastic acoustoelastic and linear-slip theory. In detail, this paper uses elasto-plastic acoustoelastic theory to derive the reflection and transmission coefficients equation. The reflection and transmission coefficients matrix are solved using the linear-slip theory as the boundary condition. Moreover, we use the hardening parameter and plastic deformation to represent the plastic properties of the rock, which is a function of stress and plastic deformation. Through Numerical analysis, the deformation caused by static stress has significantly changed the amplitude and the slope of the reflection and transmission coefficients amplitude. As the stress increases, the rock’s velocity becomes higher, and all reflection and transmission coefficients (i.e., RPP, RPS, TPP, TPS) abruptly change at the critical angle. Furthermore, with the increase in plastic deformation, the critical angle of the incident P-wave and the hardening parameter becomes larger than the unstressed state. The non-welded interface exhibits a low-pass frequency filter for reflected SV-waves and a high-pass frequency filter for reflected P-waves and transmitted P and SV waves. In addition, we can observe that static vertical stress can weaken the anomalous reflections caused by non-welded formations, but the effect is insignificant. On the other hand, the effect of fracture normal compliance to reflection and transmission is detailly investigated. When N<2.5*10-10(MPa-1), The non-welded interface is close to the welded interface, while N>2.5*10-5(MPa-1), the non-welded interface is close to the solid-air interface.

Dipper Donkin Quantized Matrix Algebra and Reflection Equation Algebra at Root of Unity

Dipper Donkin Quantized Matrix Algebra and Reflection Equation Algebra at Root of Unity

Balancing Rotation Minimizing Frames with Additional Objectives

AbstractWhen moving along 3D curves, one may require local coordinate frames for visited points, such as for animating virtual cameras, controlling robotic motion, or constructing sweep surfaces. Often, consecutive coordinate frames should be similar, avoiding sharp twists. Previous work achieved this goal by using various methods to approximate rotation minimizing frames (RMFs) with respect to a curve's tangent. In this work, we use Householder transformations to construct preliminary tangent‐aligned coordinate frames and then optimize these initial frames under the constraint that they remain tangent‐aligned. This optimization minimizes the weighted sum of squared distances between selected vectors within the new frames and fixed vectors outside them (such as the axes of previous frames). By selecting different vectors for this objective function, we reproduce existing RMF approximation methods and modify them to consider additional objectives beyond rotation minimization. We also provide some example computer graphics use cases for this new frame tracking.

Rock physics and seismic reflectivity parameterization for amplitude-variation-with-angle inversion of low-maturity source rocks

Rock-physics inversion has been widely used in reservoir prediction. However, the prediction and evaluation of source rocks still predominantly rely on data-driven inversion methods. To directly incorporate the rock-physics relationship into the seismic inversion of source rocks, we first introduce a linearization approximation of the rock-physics model through the first-order approximation of the Taylor series. Model examples and well-logging tests substantiate the reliability of this linear approximation in establishing the connection between the elastic moduli and essential physical parameters (EPPs) of source rocks. Subsequently, we develop a novel equation for the P-wave reflection coefficient by combining the linear rock-physics relationship and Gray approximation. The newly developed reflectivity equation is a linear expression of differences in EPPs of source rocks. Model-simulating results demonstrate a favorable agreement between the novel P-wave reflectivity equation and the exact Zoeppritz equation until the incident angle reaches 60°. Furthermore, we explore the amplitude-variation-with-angle (AVA) effects of EPPs to validate their contributions meet the requirement of seismic inversion. Under the Bayesian scheme, we further develop an AVA inversion method, based on the novel P-wave reflectivity equation, to predict the EPPs of source rocks. Our AVA inversion method obtains satisfactory results under noise testing and demonstrates promising application potential in field examples. The predicted EPPs indicate a strong agreement with the actual well loggings. Comparative analysis against data-driven inversion results reveals that the EPPs predicted by our AVA inversion method possess enhanced rock-physics support and significance. Specifically, this study focuses on isotropic clay-rich source rocks with low maturity.

Enhanced sensing performance of tapered profile in the apodized fiber Bragg grating for detection of cancerous cells utilizing their refractive index.

Tapered profiles are introduced in Bessel and Blackman apodized fiber Bragg grating, and their sensing performance is theoretically estimated. Reflectivity equation of proposed apodized tapered profiles is obtained using transfer matrix method and coupled mode theory. Since the effective refractive index (RI) of proposed waveguides varies with core radius therefore amplitude distribution and penetration depth of light in surroundings are modified. It is found that the exponential tapered profile with Bessel apodization shows a higher sensitivity of 682.5 nm/RIU, detection accuracy of 3858.45, and quality parameter 1718.02/RIU with minimum full width at half maxima (FWHM) 0.3972 nm of the reflection spectra. The spectral response of the tapered fiber Bragg grating is also analyzed through a group delay study. Again, exponential profile was found to be particularly effective, producing less group delay ripples 2.98 ps and is maximum slope of 42.43°. Hence, exponential tapered profile is demonstrated for detection of cancer cells lies between the refractive index of 1.3333-1.4412.

A Method for Improving the Caching Strategy for Computing Systems with Shared Memory

This paper considers the problem of increasing the software efficiency in terms of reducing the costs of their development and operation in the process of solving production and research tasks. We have analysed the existing approaches to solving this problem by example of parameterized algorithms for implementing mVm (matrix—vector multiplication) and MMM (matrix—matrix multiplication)) BLAS (Basic Linear Algebra Subroutines) operations. To achieve the goal of increasing the software efficiency, we proposed a new design method, designed to improve data caching algorithms in the software development for computing systems with a hierarchical memory structure. Using the proposed design procedure, we developed an analytical approach to evaluating the software effectiveness from the point of view of using a memory subsystem with a hierarchical structure is implemented. We applied the proposed method to the two-sided Householder transformation for the task of reducing the general form matrix to the Hessenberg form. Then we presented new algorithms for solving the problem, which are optimized variants of the Householder classical transformation: Row-Oriented Householder and Single-Pass Householder. The use of these algorithms can significantly reduce the software execution time. Computational experiments were carried out on a parallel computing system with shared memory, which is one of the nodes of the computing cluster of the Volgograd State Technical University. We made a comparison of the software execution time that reduce general-form matrices to Hessenberg form, written using the proposed algorithms and using the LAPACKE_dgehrd() function of the Intel MKL library. The conclusions made in the work are confirmed by the results of the conducted computational experiments.

Bayesian linearized rock-physics amplitude-variation-with-offset inversion for petrophysical and pore-geometry parameters in carbonate reservoirs

Rock-physics amplitude-variation-with-offset (AVO) inversion aims at directly predicting reservoir properties from prestack seismic data. However, carbonate reservoir rocks often develop complex pore structures, which limits the application of conventional inversion methods with fixed pore-geometry parameters. We derive a PP-wave reflectivity equation in terms of porosity, water saturation, and pore-aspect ratio and we develop a rock-physics AVO inversion method to jointly estimate the petrophysical and pore-geometry parameters in carbonates. The reflectivity equation is obtained by linearizing the rock-physics model based on the differential effective medium model and Gassmann’s equation using Taylor series approximation, and we combine the linearization with the Aki-Richards equation. Thanks to the linearized model, the analytical solution to the inverse problem is derived using Bayesian linear theory. Our solution combines simulated annealing to estimate the prior information of the pore geometry and the iterative Bayesian inversion to update the posterior model. The method is tested on a benchmark data set and compared with conventional methods with a fixed aspect ratio. The results show that our method improves the petrophysical results. The method is also compared with two-step and nonlinear inversion methods to demonstrate its advantages. The method is applied to a field seismic section from a carbonate reservoir with a complex pore structure to demonstrate its advantages in terms of prediction accuracy.

A family of gradient methods using Householder transformation with application to hypergraph partitioning

A family of gradient methods using Householder transformation with application to hypergraph partitioning

Noncommutative geometry on central extension of U(u(2))

In our previous publications, we have introduced analogs of partial derivatives on the reflection equation algebras, associated with Hecke symmetries. As a consequence, we get quantum partial derivatives on the enveloping algebras U(gl(N)). In the current paper, we consider the particular case N = 2 in detail and discuss the problem of a prolongation of these derivatives onto some central extension of the compact form U(u(2)) of the algebra U(gl(2)). Possible applications of this noncommutative geometry are discussed.

The Direction-encoded Neural Network: A machine learning approach to rapidly predict blast loading in obstructed environments

Machine learning (ML) methods are becoming more prominent in blast engineering applications, with their adaptability to new scenarios and rapid computation times providing key benefits when compared to empirical methods and physics-based approaches, respectively. However, ML approaches commonly used for blast analyses are regularly provided with inputs relating to domain-specific parameters, restricting their use beyond the initial problem set and reducing their generality. This article presents the ‘Direction-encoded Neural Network’ (DeNN); a novel way to structure an Artificial Neural Network (ANN) to predict blast loading in obstructed environments. Each point of interest (POI) is represented by the proximity to its surroundings and the shortest travel path of the blast wave in order to prime the network to learn the underlying physics of the problem. Furthermore, a bespoke wave reflection equation creates a zone of influence around each point so that obstacles are only captured in the network’s inputs if they would alter the path of the wave. It is shown that the DeNN can predict peak overpressures with mean absolute errors ∼5 kPa for unseen, complex domains of any shape or size, when compared to the results from physics-based numerical models with ∼30 times the solution time of the DeNN. The network is used to develop maps of likely human injury following detonation of a high explosive in an internal environment, with eardrum rupture levels being correctly predicted for over 93% of unseen test points. It is therefore highly suited for use in probabilistic, risk-based analyses which are currently impractical due to excessive computational cost.

Householder Transformation-Based Temporal Knowledge Graph Reasoning

Knowledge graphs’ reasoning is of great significance for the further development of artificial intelligence and information retrieval, especially for reasoning over temporal knowledge graphs. The rotation-based method has been shown to be effective at modeling entities and relations on a knowledge graph. However, due to the lack of temporal information representation capability, existing approaches can only model partial relational patterns and they cannot handle temporal combination reasoning. In this regard, we propose HTTR: Householder Transformation-based Temporal knowledge graph Reasoning, which focuses on the characteristics of relations that evolve over time. HTTR first fuses the relation and temporal information in the knowledge graph, then uses the Householder transformation to obtain an orthogonal matrix about the fused information, and finally defines the orthogonal matrix as the rotation of the head-entity to the tail-entity and calculates the similarity between the rotated vector and the vector representation of the tail entity. In addition, we compare three methods for fusing relational and temporal information. We allow other fusion methods to replace the current one as long as the dimensionality satisfies the requirements. We show that HTTR is able to outperform state-of-the-art methods in temporal knowledge graph reasoning tasks and has the ability to learn and infer all of the four relational patterns over time: symmetric reasoning, antisymmetric reasoning, inversion reasoning, and temporal combination reasoning.

Investigation of the electromagnetic properties of a transverse insert based on a planar layer of a chiral metamaterial in a rectangular waveguide

The paper considers the solution of the problem of diffraction of the fundamental wave of a rectangular waveguide H10 on a planar transverse insert based on a chiral metamaterial created on the thin-wire conducting helices. To describe the chiral layer, a particular mathematical model is constructed that takes into account the properties of heterogeneity and dispersion of the permittivity and the chirality parameter of the artificial media. The well-known in physics model of Maxwell Garnett was used to take into account the heterogeneity property. To take into account the permittivity dispersion the Drude–Lorentz formula was applied and for the chirality parameter was used the Condon formula. The problem of diffraction of the rectangular waveguide main wave on a planar layer of a chiral metamaterial was solved by the partial regions method and was reduced to a system of linear algebraic equations for unknown reflection and transmission coefficients. It is shown that in the presence of a transverse chiral layer in the waveguide structure, a wave of the H01 type cross-polarized with respect to the main one arises. An analysis of the frequency dependences of the moduli of the reflection and transmission coefficients of the fundamental H10 and cross-polarized H01 showed that in some narrow frequency intervals in the single-mode gap, situations arise when the fundamental wave type is replaced from H10 to H01 near resonant frequencies. The transmission line under consideration can find application in the creation of frequency selective filters and polarization converters in the microwave range.

Investigation of the microwave chiral metamaterial based on a uniform set of C-shaped conductive inclusions

The paper considers an artificial chiral metamaterial created on a homogeneous container basefrom foamed dielectric, in which flat conducting S-shaped microelements are evenly placed and arbitrarily oriented. To describe the metamaterial, a particular mathematical model was constructed that takes into account chirality, dispersion, and heterogeneity of the structure. The Maxwell Garnett model was used to account for heterogeneity. To take into account the dispersion of the chirality parameter, the Condon model known from the theory of optically active media was used. The partial domain method was used to solve the problem of the incidence of a plane electromagnetic wave of linear polarization on a planar layer created on the base of the investigated chiral metamaterial. The solution of the problem was reduced to an inhomogeneous system of linear algebraic equations for unknown reflection and transmission coefficients, taking into account the cross-polarization of the electromagnetic field. An analysis of the numerical results showed that the structure has pronounced frequency selective properties, in particular, as in the case of chiral metamaterial based on three-dimensional conductive elements, discrete frequencies were determined at which the structure is transparent to microwave radiation. Chiral metamaterial based on C-shaped microelements can be used to create narrow-band frequency-selective microwave energy concentrators of planar type.

A Machine Learning Study of High Robustness Quantum Walk Search Algorithm with Qudit Householder Coins

In this work, the quantum random walk search algorithm with a walk coin constructed by generalized Householder reflection and phase multiplier has been studied. The coin register is one qudit with an arbitrary dimension. Monte Carlo simulations, in combination with supervised machine learning, are used to find walk coins that make the quantum algorithm more robust to deviations in the coin’s parameters. This is achieved by introducing functional dependence between these parameters. The functions that give the best performance of the algorithm are studied in detail by numerical statistical methods. A thorough comparison between our modification and an algorithm, with coins made using only Householder reflection, shows significant advantages of the former. By applying a deep neural network, we make a prediction for the parameters of an optimal coin with an arbitrary size and estimate the algorithm’s stability for such a coin.