Block-diagonal Research Articles

Groundwater recharge estimation in Mediterranean mountain environments by isotope profiles – Partitioning of macropore and matrix flow

Developing and continuously improving effective and feasible methods to estimate groundwater recharge is essential to ensure sustainable resource assessment. Mountain environments represent key areas for the regional water balance. In this study, the isotope profile method was used to investigate water fluxes through the vadose zone and subsequent groundwater recharge in a Mediterranean mountain environment. Six high-resolution soil water isotope profiles were taken at two different locations in the Troodos Massif (Cyprus) in the eastern Mediterranean, focusing on estimating recharge in the soil of hillslopes. Analysis of the isotope profiles yielded recharge rates ranging from 30–70 mm/year, leading to a re-evaluation of previous studies on groundwater recharge. The comparison of results obtained by the peak-shift method and mathematical modeling was used to partition matrix and macropore flow, reaching up to 39 %. Potential methodological limits of the environmental isotope profile method in skeleton-rich soils were found.

Minimizing Computation and Communication Costs of Two-Sided Secure Distributed Matrix Multiplication under Arbitrary Collusion Pattern.

This paper studies the problem of minimizing the total cost, including computation cost and communication cost, in the system of two-sided secure distributed matrix multiplication (SDMM) under an arbitrary collusion pattern. In order to perform SDMM, the two input matrices are split into some blocks, blocks of random matrices are appended to protect the security of the two input matrices, and encoded copies of the blocks are distributed to all computing nodes for matrix multiplication calculation. Our aim is to minimize the total cost, overall matrix splitting factors, number of appended random matrices, and distribution vector, while satisfying the security constraint of the two input matrices, the decodability constraint of the desired result of the multiplication, the storage capacity of the computing nodes, and the delay constraint. First, a strategy of appending zeros to the input matrices is proposed to overcome the divisibility problem of matrix splitting. Next, the optimization problem is divided into two subproblems with the aid of alternating optimization (AO), where a feasible solution can be obtained. In addition, some necessary conditions for the problem to be feasible are provided. Simulation results demonstrate the superiority of our proposed scheme compared to the scheme without appending zeros and the scheme with no alternating optimization.

Secure Key Exchange in Tropical Cryptography: Leveraging Efficiency with Advanced Block Matrix Protocols

In the quest for robust and efficient digital communication, this paper introduces cutting-edge key exchange protocols leveraging the computational prowess of tropical semirings and the structural resilience of block matrices. Moving away from the conventional use of finite fields, these protocols deliver markedly faster processing speeds and heightened security. We present two implementations of our concept, each utilizing a different platform for the set of commuting matrices: one employing tropical polynomials of matrices and the other employing Linde–de la Puente matrices. The inherent simplicity of tropical semirings leads to a decrease in operational complexity, while using block matrices enhances our protocols’ security profile. The security of these protocols relies on the Matrix Decomposition Problem. In addition, we provide a comparative analysis of our protocols against existing matrix block-based protocols in finite fields. This research marks a significant shift in cryptographic protocol design, is specifically tailored for demanding engineering applications, and sets a new standard in secure and efficient digital communication.

Exact closed forms for the transmittance of electromagnetic waves in one-dimensional anisotropic periodic media

In this work, we obtain closed expressions for the transfer matrix and the transmittance of electromagnetic waves propagating in finite one-dimensional anisotropic periodic stratified media with an arbitrary number of cells. By invoking the Cayley–Hamilton theorem on the transfer matrix for the electromagnetic field in a periodic stratified media formed by N cells, we obtain a fourth-order recursive relation for the matrix coefficients that defines the so-called Tetranacci polynomials (TPs). In the symmetric case, corresponding to a unit-cell transfer matrix with a characteristic polynomial where the coefficients of the linear and cubic terms are equal, closed expressions for the solutions to the recursive relation, known as symmetric TPs, have recently been derived, allowing us to write the transfer matrix and transmittance in a closed form. We show as sufficient conditions that the 4×4 differential propagation matrix of each layer in the binary unit cell, Δ , a) has eigenvalues of the form ±p1 , ±p2 , with p1≠p2 , and b) its off-diagonal 2×2 block matrices possess the same symmetric structure in both layers. Otherwise, the recursive relations are still solvable for any 4×4 matrix and provide an algorithm to compute the Nth power of the transfer matrix without carrying out explicitly the matrix multiplication of N matrices. We obtain analytical expressions for the dispersion relation and transmittance, in closed form, for two finite periodic systems: the first one consists of two birefringent uniaxial media with their optical axis perpendicular to the z-axis, and the second consists of two isotropic media subject to an external magnetic field oriented along the z-axis and exhibiting the Faraday effect. Our formalism applies also to lossy media, magnetic anisotropy or optical activity.

Mechanistic analysis of acid gas storage and oil recovery in naturally fractured reservoirs using single matrix block approach

AbstractThe objective of this study is to assess the storage of acid gas, containing CO2 and H2S, in a depleted naturally fractured reservoir (NFR) using single matrix block (SMB) approach. The acid gas dissolution in oil is considered by Peng‐Robinson equation of state and compositional simulation. The PHREEQC package is used to determine acid gas solubility in formation brine. Three types of acid gases with different compositions are used for this study and their swelling behavior and miscibility in relation to the reservoir oil are analyzed. An SMB model, with a matrix block surrounded by fractures, is constructed, and validated for simulation of a real experiment. The simulation is conducted for synthetic and real reservoir fluids when the oil is in its residual saturation. A sensitivity analysis is performed to study the effects of key parameters, such as acid gas composition, reservoir pressure, permeability, porosity and matrix height on the storage capacity and oil recovery factor. The matrix has a volume of 27 m3 and about half of acid gas storage is achieved in the first 5 years while the simulations are run for 30 years. The results show that up to 90% of remained oil is recoverable, and more than 0.67 kmol of acid gas per cubic meter of matrix is stored whether matrix contains a real oil or a synthetic one. Higher storage is achieved for higher matrix porosities and heights and large H2S proportion in acid gas. In all cases about 10% of acid gas is trapped in water and the remaining 90% is dissolved in oil. The mineral trapping was more active in CO2‐rich acid gases. While about 10 kg of the matrix rock was dissolved in the acidic brine when the acid gas contained H2S, the amount of the dissolved minerals in acidic brine resulted from the injection of CO2‐rich acid gas was more than 16 kg. Finally, this study gives a comparative analysis of the storage performance of acid gas mixture and pure CO2. © 2024 Society of Chemical Industry and John Wiley & Sons, Ltd.

Two-dimensional counter-current capillary imbibition of a wetting phase into a partially submerged porous cylindrical matrix block

The purpose of this study is to address the two-dimensional counter-current capillary dominant imbibition of a wetting phase into a water-wet porous cylindrical matrix block partially submerged in the wetting phase. A two-dimensional unsteady-state diffusion equation is used to model the process. The governing equation is solved using a combination of the Laplace and the finite Fourier sine transforms to find and analyze the solutions for the normalized water saturation and the volume of the imbibed wetting phase. The results reveal that the volume of the imbibed wetting phase and the capillary diffusion shape factor for a partially submerged matrix block are significantly lower compared to those of a fully submerged matrix block, highlighting the overestimation of imbibed volume using available models based on full immersion in the wetting phase. It has been observed that the volume of the imbibed wetting phase increases over time until reaching a state of equilibrium. In the case of a partially submerged matrix block, the shape factor is inversely proportional to the square root of time (σ ∼ 1/t) during the early time and decreases sharply as the imbibed wetting phase reaches an equilibrium. In the case of a fully submerged matrix block, the shape factor is inversely proportional to the square root of time (σ ∼ 1/t) during the early time and later reaches a pseudo-steady-state value. The proposed model, along with the findings obtained, advances our understanding of capillary imbibition in porous media.

Modeling a neurological disorder as the result of an operator acting on the brain: A first sketch based on network channel modeling.

The brain is a complex network, and diseases can alter its structures and connections between regions. Therefore, we can try to formalize the action of diseases by using operators acting on the brain network. Here, we propose a conceptual model of the brain, seen as a multilayer network, whose intra-lobe interactions are formalized as the diagonal blocks of an adjacency matrix. We propose a general and abstract definition of disease as an operator altering the weights of the connections between neural agglomerates, that is, the elements of the brain matrix. As models, we consider examples from three neurological disorders: epilepsy, Alzheimer-Perusini's disease, and schizophrenia. The alteration of neural connections can be seen as alterations of communication pathways, and thus, they can be described with a new channel model.

A Note on the Laplacian Energy of the Power Graph of a Finite Cyclic Group

In this study, the Laplacian matrix concept for the power graph of a finite cyclic group is redefined by considering the block matrix structure. Then, with the help of the eigenvalues of the Laplacian matrix in question, the concept of Laplacian energy for the power graphs of finite cyclic groups was defined and introduced into the literature. In addition, boundary studies were carried out for the Laplacian energy in question using the concepts the trace of a matrix, the Cauchy-Schwarz inequality, the relationship between the arithmetic mean and geometric mean, and determinant. Later, various results were obtained for the Laplacian energy in question for cases where the order of a cyclic group is the positive integer power of a prime.

Understanding the drying mechanism of straw substrate culture block: Physicochemical properties, pore structure, and drying optimization

As a new type of agricultural waste block substrate utilization, the initial wet base state of the substrate culture block needs to be dried. Therefore, studying the drying mechanism of substrate culture block is critical. In this study, the substrate culture block in a dry state was taken as the research object. Based on physical and chemical properties, the internal section of the substrate culture block was characterized by scanning electron microscopy and the pore condition of the particles was quantified. The results showed that the internal pore structure was uniform and favorable for plant root growth. Based on the pore structure, pore channel modeling was constructed to investigate the distribution of the internal multiphase medium and to distinguish between channels and pore-blind channels. The applicability of the modeling was verified and discussed. By measuring the drying rate of the substrate culture block and classifying its drying stages as fast speed, constant speed, and slow speed, it is clarified that the forms of moisture existence are bound-state water and free-state water, and the moisture migration is prioritized as surface adsorption water, interparticle water, particle attached water, and capillary water. Innovate a method to quantify the change of pore space in the drying process by pore coefficient ratio to evaluate the drying quality. The results show that when the pore coefficient ratio is about 40 %, its moisture content is 20 %∼30 %, and the drying effect is best at this time. The physical drying test further confirmed the correctness of the conclusion of the drying stage division and water loss law. This study can provide a theoretical reference for the modeling study of the pore structure of the block matrix and the exploration of its drying mechanism.

Robust elastic full-waveform inversion using an alternating direction method of multipliers with reconstructed wavefields

Elastic full-waveform inversion (EFWI) is a process used to estimate subsurface properties by fitting seismic data while satisfying wave propagation physics. The problem is formulated as a least-squares data fitting minimization problem with two sets of constraints: partial-differential equation (PDE) constraints governing elastic wave propagation and physical model constraints implementing prior information. The alternating direction method of multipliers is used to solve the problem, resulting in an iterative algorithm with well-conditioned subproblems. Although wavefield reconstruction is the most challenging part of the iteration, sparse linear algebra techniques can be used for moderate-sized problems and frequency domain formulations. The Hessian matrix is blocky with diagonal blocks, making model updates fast. Gradient ascent is used to update Lagrange multipliers by summing PDE violations. Various numerical examples are used to investigate algorithmic components, including model parameterizations, physical model constraints, the role of the Hessian matrix in suppressing interparameter cross-talk, computational efficiency with the source sketching method, and the effect of noise and near-surface effects.

A GenEO Domain Decomposition method for Saddle Point problems

We introduce an adaptive element-based domain decomposition (DD) method for solving saddle point problems defined as a block two by two matrix. The algorithm does not require any knowledge of the constrained space. We assume that all sub matrices are sparse and that the diagonal blocks are spectrally equivalent to a sum of positive semi definite matrices. The latter assumption enables the design of adaptive coarse space for DD methods that extends the GenEO theory (Spillane et al., 2014) to saddle point problems. Numerical results on three dimensional elasticity problems for steel-rubber structures discretized by a finite element with continuous pressure are shown for up to one billion degrees of freedom.

Remote restoring of (0,1)-excitation states and concurrence scaling

We study the long distance [Formula: see text]-excitation state restoring in the linear open chain governed by the XX-Hamiltonian. We show that restoring the 1-order coherence matrix results in restoring the 1-excitation block of the 0-order coherence matrix, so that only one 0-excitation element of the density matrix remains unrestored. Such restoring also scales the concurrence between any two qubits of the transferred state, the scaling factor is defined by the Hamiltonian and doesn’t depend on the initial sender’s state. Sender–Receiver entanglement is also studied via the PPT criterion.

Analytic representative element rate decline models for naturally fractured reservoir depletion

Representative single anisotropic matrix block 2D Green’s function models for depletion through fully-penetrating, vertical fractures through different numbers of fracture faces are constructed that analytically capture both fracture and block depletion with fracture-matrix mass transfer. The 1D Green’s function for a fracture system is likewise solved in terms of the time evolution of average fracture pressure. While transient average pressure values are not inherently measurable, they are transformed into cumulative production or instantaneous flowrate values, thus producing new rate decline model functional forms. Primary variables in assembling the interacting systems model are the volume ratio, Vf /Vm, permeability ratio, kf /kx, and geometry, (a/b)(ky/kx), with the last term accounting for both block shape and permeability anisotropy. We construct interacting systems models in terms of various ratios of Vf /Vm, and kf /kx for three fracture architecture prototypes: representative matrix blocks depleted by 4, 2, or 1 contacting fractures. The single matrix block models can be migrated to ones for heterogeneous systems using superposition and matrix block distributions, as demonstrated with a binary distribution of block sizes with variable fractions. Analytic solutions for rate decline problems can be used to understand the production signatures of naturally fractured reservoirs and interpretation of fracture volume fraction, permeability ratio, average matrix block size, and measures of heterogeneity.

From port-based teleportation to Frobenius reciprocity theorem: partially reduced irreducible representations and their applications

In this paper, we present the connection of two concepts as induced representation and partially reduced irreducible representations (PRIR) appear in the context of port-based teleportation protocols. Namely, for a given finite group G with arbitrary subgroup H, we consider a particular case of matrix irreducible representations, whose restriction to the subgroup H, as a matrix representation of H, is completely reduced to diagonal block form with an irreducible representation of H in the blocks. The basic properties of such representations are given. Then as an application of this concept, we show that the spectrum of the port-based teleportation operator acting on n systems is connected in a very simple way with the spectrum of the corresponding Jucys–Murphy operator for the symmetric group S(n-1)⊂S(n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S(n-1)\\subset S(n)$$\\end{document}. This shows on the technical level relation between teleporation and one of the basic objects from the point of view of the representation theory of the symmetric group. This shows a deep connection between the central object describing properties of deterministic PBT schemes and objects appearing naturally in the abstract representation theory of the symmetric group. In particular, we present a new expression for the eigenvalues of the Jucys–Murphy operators based on the irreducible characters of the symmetric group. As an additional but not trivial result, we give also purely matrix proof of the Frobenius reciprocity theorem for characters with explicit construction of the unitary matrix that realizes the reduction in the natural basis of induced representation to the reduced one.

Numerical study of the impact of stress concentration on shale gas production

Predicting the production amounts has great significance for exploitation of oil and gas resources. The flow–geomechanical coupling effect plays an important role in predicting production. Shale rocks and the stress-dependent permeability model are critical for representing this coupling effect. The pore network of shale rock is not abundant like that of coal rock, and the matrix blocks of shale rock are not completely separated by the pore network. There is stress concentration around the pores when shale rock is deformed. Based on previous studies, the stress-dependent permeability model considering the impact of stress concentration is used in this study to build a numerical simulation model for flow–geomechanical coupling in a shale gas reservoir and validation using field data. Sensitivity studies are conducted to discuss the difference in production prediction between the new and common models. The main conclusions of this study are as follows: 1) The new model can fit both the field and experimental data well; the average error in daily production rate between the numerical solution and field data is 8%, which indicates that the new model can be used to predict shale gas production. 2) Under the geomechanical condition of a real reservoir, the difference in predicted production between models with and without stress concentration can be large and increase with the ratio of a to b. If this ratio is less than 50, the impact of stress concentration is not significant. Otherwise, the impact of stress concentration on production increases sharply and can exceed 20%. 3) The adsorption-induced strain enhances the impact of stress concentration on production. When the Langmuir pressure exceeds 1 MPa and Langmuir strain exceeds 0.01, the impact magnitude of stress concentration can exceed 10%.

An infrastructure for secure data sharing: a clinical data implementation.

To address database interoperability challenges to improve collaboration among disparate organizations. We developed a lightweight system to allow broad but well-controlled data sharing while preserving local data protection policies. We used 2 NIST-developed technologies-Next-generation Database Access Control (NDAC) and the Data Block Matrix (DBM)-to create a proof-of-concept system called the Secure Federated Data Sharing System (SFDS). NDAC controls access to database resources down to the field level based on attributes assigned to users. The DBM manages and shares authoritative user-attribute assignments across a federation of organizations, implemented using a modified open-source permissioned blockchain, to manage and share authoritative user-attribute assignments across a federation of organizations. We used synthetic data to demonstrate a clinical research data-sharing use case using the SFDS. We demonstrated, through consent, the onboarding of previously unknown users into NDAC via assignments to their DBM-validated attributes, allowing those users policy-preserving access to local database resources. The SFDS main system components-NDAC and DBM-also showed excellent performance metrics. The SFDS provides a generic data-sharing infrastructure that effectively and securely achieves data-sharing objectives. It is completely transparent to the otherwise normal business operations of participating organizations. It requires no changes to database management systems or existing methods of authenticating and authorizing local user access to local resources. This efficiency, flexibility of deployment, and granularity of control make this new infrastructure solution practical for meeting the data-sharing and protection objectives of the clinical research community.

Implementation of asynchronous mode in a linear periodic system with the nontrivial lower left block of averaging of the coefficient matrix

A linear control system with a periodic matrix of coefficients and program control is considered. The matrix under control is constant, rectangular (the number of columns does not exceed the number of rows) and its rank is not maximum, i. e. less than the number of columns. It is assumed that the control is periodic, and the module of its frequencies, i. e. the smallest additive group of real numbers, including all Fourier exponents of this control, is contained in the frequency module of the coefficient matrix. The following task is posed: to construct such a control from an admissible set that switches the system to asynchronous mode, i. e. the system must have periodic solutions such that the intersection of the frequency moduli of the solution and the coefficient matrix is trivial. The problem posed is called the problem of synthesis of asynchronous mode. The solution to the formulated problem significantly depends on the structure of the average value of the coefficient matrix. In particular, its solution is known for systems with zero average. In addition, solvability conditions were obtained in the case when the matrix under control has zero rows, the averaging of the coefficient matrix is reduced to the form with upper left diagonal block and with zero remaining blocks. In this paper we consider a more general case with a nontrivial left lower block. Assuming an incomplete column rank of the matrix function composed from the rows of oscillation path of the coefficient matrix, we construct the control explicitly. This control switches the system to asynchronous mode.

Lévy noise-induced global bifurcation with the compatible cell mapping method

Stochastic bifurcation of dynamical system induced by Lévy noise is investigated in this paper from the global viewpoint, which is demonstrated based on the global attractor obtained with the compatible cell mapping (CCM) method. Compared with the traditional cell mapping method, the efficiency of CCM method is greatly improved by concentrating the computational domain on the covering set of the global attractor rather than the whole state space. The computation time can be further reduced by a simple parallel procedure with the block matrix strategy. With the proposed method, the evolutionary process of global properties has been presented. It shows that the shape and size of stochastic attractors and stochastic saddles vary along the direction of unstable manifold with the parameters of Lévy noise. Stochastic bifurcation occurs when stochastic attractor collides with stochastic saddle. It can be also found that the global bifurcation under Lévy noise is discontinuous because of the jump property. The results are significantly different from those of Gaussian noise, which reveals a distinct global evolutionary mechanism of stochastic bifurcation. Furthermore, it also indicates that the CCM method with block matrix is an effective tool for global analysis.

Enforced Block Diagonal Graph Learning for Multikernel Clustering

The existing multikernel graph clustering (MKGC) methods have emerged with notable success on nonlinear clustering tasks since the graph learning can effectively capture graph structure similarity between sample pair. Ideally, a high-quality graph should enjoy the good block diagonal property, i.e. the intercluster similarities correspond to zeros, while intracluster similarities represent nonzeros. Meanwhile, the number of diagonal blocks for a graph equals to the number of clusters on the dataset. However, most of the existing MKGC methods design a corpulent three-parts graph leaning process that poses challenges for hyperparameter tuning, time cost, and clustering performance. To overcome these challenging issues, we propose an enforced block diagonal graph learning for multikernel clustering (EBDGL-MKC) method, where we pursue a high-quality block diagonal graph via well-designed one-part graph leaning scheme rather than three parts. Inspired by symmetric matrix factorization (SMF), we first design a one-part block diagonal graph learning scheme to learn multiple block diagonal graphs, by exploring an explicit theoretical connection between the clustering partition of kernel <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula> -means and the excellent block diagonal graph. Then, these block diagonal graphs are stacked into a low-rank tensor for exploiting the high-order structure information hidden in the nonlinear data. After that, an effective alternate algorithm with convergence proof is performed on extensive experiments to demonstrate the superiority of EBDGL compared with the state-of-the-art multikernel clustering (MKC) methods.

The Binary Broadening Function

We propose an extended formalism for the spectral broadening function (BF) based on the multiplication rule of block matrices. The formalism, which we named the binary BF (BBF), can produce decomposed BFs for individual components of a binary star system by using two spectral templates. The decomposed BFs can be used to derive precise rotational profiles and radial velocities for individual components. We test the BBF on simulated spectra and actual observational spectra to show that the method is feasible on spectroscopic binaries, even when the spectral lines of two stellar components are heavily blended. To demonstrate the capability of the method, we conduct a simulation of “sketching” (imaging) a transiting circumbinary exoplanet using the BBF. We also discuss issues of implementation such as the variation of BBF with biased templates, the pros and cons of BBF, and cases when the method is not applicable.