Form Of Matrices Research Articles

Petrov-Galerkin method for small deflections in fourth-order beam equations in civil engineering

Abstract This study explores the Petrov–Galerkin method’s application in solving a linear fourth-order ordinary beam equation of the form u ″ ″ + q u = f u^{\prime\prime} ^{\prime\prime} +qu=f . The equation entails two distinct boundary conditions: pinned–pinned conditions on u u and u ′ u^{\prime} , and clamped–clamped conditions on u u and u ″ {u}^{^{\prime\prime} } . To satisfy these boundary conditions, we have built two sets of basis functions. The explicit forms of all spectral matrices were reported. The nonhomogeneous boundary conditions were easily handled using perfect transformations, ensuring the numerical solution’s accuracy. Detailed analysis of the method’s convergence was studied. Some numerical examples were presented, accompanied by comparisons with other existing methods in the literature.

Evaluation of optical, thermal and hydrophobic properties of sustainable stilbene-based benzoxazines for high-performance utilization

Currently there is a growing interest in the field of photosensitive benzoxazines synthesized from sustainable raw materials. An attempt has been made to synthesize nine structurally different benzoxazines through Mannich condensation reaction. The formation of the expected structure of the synthesized benzoxazine monomers were ascertained using spectroscopic methods. The ring-opening polymerization of benzoxazines was studied using DSC and found that THS-imp benzoxazine monomer exhibits the lowest value of curing temperature (Tp) of 179oC than the rest of the benzoxazine monomers. Thermal stability of polybenzoxazines were analyzed using thermogravimetric analyzer. Among the different polybenzoxazines studied, poly(THS-a) possesses the higher thermal stability with char yield of 53% than that of other benzoxazines. The band gap values of benzoxazines calculated from optical studies are ranged between 3.92-4.71 eV. The hydrophobic behavior of the polybenzoxazines assessed using the water contact angle obtained from goniometer for both neat polymer matrix and benzoxazine coated cotton fabric. Results from the water contact angle infer that the benzoxazines coated cotton fabric exhibited 152o, which shows the superhydrophobic behavior. The corrosion resistant properties of all the polybenzoxazines coated over MS specimen has been tested. Among them poly(THS-pfsa) and poly(THS-imp) have higher Icorr value and corrosion inhibition efficiency of 99%. Data obtained from different studies indicate that the benzoxazines developed from sustainable stilbene can be utilized in the form of coatings, adhesives, sealants, and matrices for composites for wide range of industrial and engineering applications, where high thermal stability and are required.

In-Memory modelling and simulations

A mechanism for modeling faults as addresses on smart data structures is proposed, which excludes the algorithm for modeling input test sets to obtain a test map of logical functionality. Smart data structures are represented by a logical vector and its derivatives in the form of truth tables and matrices. The test map is a matrix whose coordinates are defined by the combinations of all logical faults that are tested on the binary sets of the exhaustive test. The construction of the test map is focused on the architecture of in- memory computing based on read-write transactions, which makes the simulation mechanism economical in terms of simulation time and energy consumption due to the absence of a central processor. A logical vector as a single component of input data does not require synthesis into a technologically permitted structure of elements. Synthesis of smart data structures based on four matrix operations creates a fault test map like addresses for any logic. The proposed mechanism is focused on the service of SoC IP-cores under the control of the IEEE 1500 standard. The proposed mechanism has no analogues in the design and test industry in terms of simplicity and predictability of data structure sizes and the absence of a test set modeling algorithm.

A CFD‐PBM‐ANN framework to simulate the liquid–liquid two‐phase flow in a pulsed column

AbstractCFD‐PBM numerical simulation is a powerful tool in the research of droplet swarm behavior. In this work, an artificial neural network (ANN) based droplet breakage frequency function is established based on the directly measured data from our previous studies. Then, the weights and biases of ANN are embedded into the CFD‐PBM code in the form of matrices and vectors. For the first time, a CFD‐PBM‐ANN simulation framework is established. Simulation results are in good agreement with the experimental data under different operation conditions. The cumulative droplet size distribution decreases with the increase of interfacial tension and pulse intensity. It is also found by the simulation that the droplet breakage frequency is relatively high at the edge of disc and doughnut plate, which is accordant with the distribution of turbulent energy dissipation and velocity gradient.

Estimating the astigmatic power of the crystalline lens and eye from ocular biometry.

To estimate the astigmatic power of the crystalline lens and the whole eye without phakometry using a set of linear equations and to provide estimates for the astigmatic powers of the crystalline lens surfaces. Linear optics expresses astigmatic powers in the form of matrices and uses paraxial optics and a 4 × 4 ray transfer matrix to generalise Bennett's method comprehensively to include astigmatic elements. Once this is established, the method is expanded to estimate the contributions of the front and back lens surfaces. The method is illustrated using two examples. The first example is of an astigmatic model eye and compares the calculated results to the original powers. In the second example, the method is applied to the biometry of a real eye with large lenticular astigmatism. When the calculated powers for the astigmatic model eye were compared to the actual powers, the difference in the power of the eye was (where T represents the matrix transpose) and for the crystalline lens, the difference was (power vector format). A second example applies the method to a real eye, obtaining lenticular astigmatism of -5.84 × 175. The method provides an easy-to-code way of estimating the astigmatic powers of the crystalline lens and the eye.

IMPLICATIONS OF COMPUTE AND INTERPRETABILITY FOR THE DIFFERENT SDN SECURITY MODELS

The main focus of this project is to design and implement an IDS for SDNs that are currently causing great interest in the networking society. Making the control plane and the data plane modularity, SDNs provide a higher level of flexibility and programming capabilities to manage the network but concurrently budding novel security risks. Several machine learning algorithms are in use such as the Logistic Regression, Decision Tree, Random Forest, etc. , which are used to identify malice within the network. As for the dataset sdn_intrusion. csv, preprocessing steps included were cleaning where missing values were managed, categorical data was encoded as well as handling for outliers existed. This paper applied feature selection by analysing correlation between the input features and the target variable with the aim of enhancing the model accuracy. The models were assessed with cross validation and several metrics like accuracy, Precision, Recall, F1 score, AUC and the results are quantitatively and qualitatively presented in the form of confusion matrices, ROC and Precision Recall curves. As the findings indicate, Extended Trees (Extra Trees Classifier) and Histograms Gradient Boosting models are efficient in identifying intrusions within SDN architectures. In conclusion, the study highlights the necessity of the proper choice of the machine learning algorithm and preliminary data processing for the effective IDS construction in SDNs, which enhances the readiness level of the networks against cyber threats. KEYWORDS: Software Defined Networks, Intrusion Detection System, Machine Learning, Network Security, Logistic Regression, Extra Trees Classifier, Random Forest, LightGBM, Precision-Recall Curve, ROC Curve.

Application of Improved Class of Weighted Averaging Operators in Intuitionistic Fuzzy Ann Guided MAGDM E-Commerce Problems

Objectives: To propose a novel and improvised Artificial Neural Network (ANN) technique to solve Multiple Attribute Group Decision Making (MAGDM) problems and an improved class of Aggregation operators for combining Intuitionistic Fuzzy Set (IFS) matrices for the ANN algorithm. Methods: A novel class of improved aggregation operators namely the Improved Intuitionistic Fuzzy Weighted Arithmetic Averaging (IM-IFWAA) operator and the Improved Intuitionistic Fuzzy Ordered Weighted Averaging (IM-IFOWA) operator are proposed in this work. The proposed improved class of aggregation operators will aggregate the IFS matrix data sets appearing in the form of matrices and then the revised input vectors which is then fed into the ANN algorithm following Delta, Perceptron, and Hebb Learning Rule for the next phase. Findings: Aggregating the Intuitionistic Fuzzy set information or data in today’s digital world is a tedious task in the field of MAGDM problem-solving. In this work, two new classes of operators for aggregating the data sets are proposed namely the IM-IFWAA operator and the IM-IFOWA operator which will improve the performance of the ANN. Necessary theorems for the proposed operators are proved to provide consistency of the same. The input created using the aforementioned operators is then fed into the novel ANN algorithm for further computations. Varieties of learning rules are then engaged for ranking of the best alternative for the decision problem. The developed theory is supported by a numerical example which is computed using all the proposed techniques. Novelty: Most of the research done on Intuitionistic Fuzzy Artificial Neural Network models are based on learning rules or using some other calculations. The proposed methods of using novel and improvised aggregation operators for ANN are used to find the inputs for ANN where varieties of learning rules for ANN are employed for effective decision analysis. Keywords: ANN, Learning Rules, MAGDM, Intuitionistic Fuzzy Sets, Weighted Aggregation Operator

Dynamic Model Reduction for Viscously Damped Structures with Statically Determinate Interfaces

A novel model reduction method for viscously damped structures with statically determinate interfaces, such as spacecraft flexible appendages, is proposed. The paper presents a derivation of the complete complex modal expansion of the interface dynamic stiffness of these structures. Based on the identity relation for all complex modes, which is obtained during the derivation, it is found that the interface acceleration impedance can be expressed as a rational fraction with high accuracy using only low-order complex modes. Using this rational fraction as an approximation model, numerical results of the frequency response can be fitted. The fitted interface acceleration impedance can be applied to real-time control as a reduced model in the form of a transfer function. Furthermore, it can be transformed into the form of system matrices by introducing auxiliary variables, which then participate in the dynamic analysis of the assembly. The reduction process circumvents complex modal analysis and necessitates only the results of frequency responses. Thanks to the powerful ability of conventional finite element software to perform frequency response analysis, this reduction method can be used for large-scale complex models in actual engineering applications.

A Review on Binary Alkaline‐Earth Trielides: an Overview of Compositions and Structures, of their Stabilities and Energetics and of Criteria for the Validity of the Zintl‐Concept

AbstractOmitting alloys with a compositional range we present a compilation of binary alkaline earth trielides AExTRy together with results of DFT calculations to estimate total energies and energies of formation in comparison and to analyse the distribution of charges at the atomic positions in a Bader analysis of the electron density. In a comparison of many structures, we furthermore analyse the effect of bonding on this charge distribution and reflect on the real bonding patterns in comparison with our expectations according to the Zintl concept, and we find mechanisms blocking an electron transfer as favoured by the electronegativity differences. We have subjected a variety of structural parameters together with the DFT results to a Principal Component Analysis to explore their relationship which we describe in the form of correlation matrices and biplots. The Zintl rules turn out to be a very slack guideline in rationalizing the structures of these compounds.

Diagnosing Thermalization Dynamics of Non-Hermitian Quantum Systems via GKSL Master Equations

Abstract The application of the eigenstate thermalization hypothesis to non-Hermitian quantum systems has become one of the most important topics in dissipative quantum chaos, recently giving rise to intense debates. The process of thermalization is intricate, involving many time-evolution trajectories in the reduced Hilbert space of the system. By considering two different expansion forms of the density matrices adopted in the biorthogonal and right-state time evolutions, we derive two versions of the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) master equations describing the non-Hermitian systems coupled to a bosonic heat bath in thermal equilibrium. By solving the equations, we identify a sufficient condition for thermalization under both time evolutions, resulting in Boltzmann biorthogonal and right-eigenstate statistics, respectively. This finding implies that the recently proposed biorthogonal random matrix theory needs an appropriate revision. Moreover, we exemplify the precise dynamics of thermalization and thermodynamic properties with test models.

LSTrAP-denovo: Automated Generation of Transcriptome Atlases for Eukaryotic Species Without Genomes.

Despite the abundance of species with transcriptomic data, a significant number of species still lack sequenced genomes, making it difficult to study gene function and expression in these organisms. While de novo transcriptome assembly can be used to assemble protein-coding transcripts from RNA-sequencing (RNA-seq) data, the datasets used often only feature samples of arbitrarily selected or similar experimental conditions, which might fail to capture condition-specific transcripts. We developed the Large-Scale Transcriptome Assembly Pipeline for de novo assembled transcripts (LSTrAP-denovo) to automatically generate transcriptome atlases of eukaryotic species. Specifically, given an NCBI TaxID, LSTrAP-denovo can (1) filter undesirable RNA-seq accessions based on read data, (2) select RNA-seq accessions via unsupervised machine learning to construct a sample-balanced dataset for download, (3) assemble transcripts via over-assembly, (4) functionally annotate coding sequences (CDS) from assembled transcripts and (5) generate transcriptome atlases in the form of expression matrices for downstream transcriptomic analyses. LSTrAP-denovo is easy to implement, written in Python, and is freely available at https://github.com/pengkenlim/LSTrAP-denovo/.

Intuitionistic Fuzzy Gram-Schmidt Orthogonalized Artificial Neural Network for Solving MAGDM Problems

Objectives: To propose a suitable decision-making model based on Intuitionistic Fuzzy sets (IFSs) and Gram-Schmidt orthogonalization process for Artificial Neural Network (ANN). Methods: The IFS data sets appearing in the form of matrices are aggregated using the available aggregation operators in the literature and then the collective aggregated information is processed through Gram-Schmidt orthogonalization for the revised input vectors which is then fed into the ANN algorithm following Delta Learning Rule for the next phase. The weight updation is performed through the ANN and the output is improvised. Findings: The proposed Gram-Scmidt Orthogonalization process is utilized in Intuitionistic Fuzzy Artificial Neural Network model. The Delta learning rule is utilized in the process of the Neural Network, where the Intuitionistic Fuzzy nature of the input data is transformed into a fuzzy data and then the ranking of the alternatives is done based on the weights updation through the learning phase of the ANN. Once the vector is trained out of the learning phase, it is then processed through the activation function for the final selection of the best alternative required of the Multiple Attribute Group Decision Making (MAGDM) problem posed in this work. To demonstrate the usefulness and applicability of this new method with the Gram-Schmidt process, the numerical example also adds more insight to the proposed methodology of ANN with the application of some Linear Space techniques. Novelty: Most of the research done on Intuitionistic Fuzzy Artificial Neural Network model are based on learning rules or using some other calculations. The proposed Gram-Schmidt Orthogonalization process is used to find the orthogonal basis that are used as input training vectors in the Delta learning rule for ANN. Keywords: MAGDM, ANN, Aggregation operators, Learning Rules, Intuitionistic Fuzzy sets, Gram-Scmidt Orthogonalization

HiCDiff: single-cell Hi-C data denoising with diffusion models.

The genome-wide single-cell chromosome conformation capture technique, i.e. single-cell Hi-C (ScHi-C), was recently developed to interrogate the conformation of the genome of individual cells. However, single-cell Hi-C data are much sparser than bulk Hi-C data of a population of cells, and noise in single-cell Hi-C makes it difficult to apply and analyze them in biological research. Here, we developed the first generative diffusion models (HiCDiff) to denoise single-cell Hi-C data in the form of chromosomal contact matrices. HiCDiff uses a deep residual network to remove the noise in the reverse process of diffusion and can be trained in both unsupervised and supervised learning modes. Benchmarked on several single-cell Hi-C test datasets, the diffusion models substantially remove the noise in single-cell Hi-C data. The unsupervised HiCDiff outperforms most supervised non-diffusion deep learning methods and achieves the performance comparable to the state-of-the-art supervised deep learning method in terms of multiple metrics, demonstrating that diffusion models are a useful approach to denoising single-cell Hi-C data. Moreover, its good performance holds on denoising bulk Hi-C data.

The qudit Pauli group: non-commuting pairs, non-commuting sets, and structure theorems

Qudits with local dimension d>2 can have unique structure and uses that qubits (d=2) cannot. Qudit Pauli operators provide a very useful basis of the space of qudit states and operators. We study the structure of the qudit Pauli group for any, including composite, d in several ways. To cover composite values of d, we work with modules over commutative rings, which generalize the notion of vector spaces over fields. For any specified set of commutation relations, we construct a set of qudit Paulis satisfying those relations. We also study the maximum size of sets of Paulis that mutually non-commute and sets that non-commute in pairs. Finally, we give methods to find near minimal generating sets of Pauli subgroups, calculate the sizes of Pauli subgroups, and find bases of logical operators for qudit stabilizer codes. Useful tools in this study are normal forms from linear algebra over commutative rings, including the Smith normal form, alternating Smith normal form, and Howell normal form of matrices. Possible applications of this work include the construction and analysis of qudit stabilizer codes, entanglement assisted codes, parafermion codes, and fermionic Hamiltonian simulation.

Influence of Dy3+ ions on spectroscopic studies of thermally stable telluro zinc phosphate glasses for white light emitting devices

A transparent series of telluro zinc phosphate glasses with varying Dy3+ ion concentrations (BTZPDy) were synthesized using a melt-quenching procedure. The non-crystalline/amorphous form of the BTZPDy glass matrices has been demonstrated via an X-ray diffraction (XRD) profile. As a way of recognizing the proficient usage of the obtained BTZPDy glass matrices in the white light emitting devices, the spectroscopic characteristics such as optical absorption, photoluminescence excitation (PLE) and emission, as well as temperature-dependent photoluminescence (TDPL) were conducted and investigated in detail. The absorption spectrum was determined in the n-UV to NIR range for the as-prepared BTZPDy1.0 glass sample and the optical energy band gap has been assessed via utilizing Tauc’s plot. In the visible range, photoluminescence spectra demonstrate three distinct emission peaks under different n-UV excitations, among which an intense emission peak around 575 nm is related to the 4F9/2 → 6H13/2 transition in the prepared BTZPDy glasses. The color coordinates (x, y) for the prepared BTZPDy1.0 glass were situated in the white light zone of the CIE graph and adjacent to the standard white light region (0.33, 0.33). Furthermore, TDPL spectral studies suggest the excellent thermal stability of BTZPDy glass samples alongside a high value of activation energy. In view of the above results, as-prepared BTZPDy glasses can be utilized for the fabrication of thermally stable white light emitting devices.

MoRF_ESM: Prediction of MoRFs in disordered proteins based on a deep transformer protein language model.

Molecular recognition features (MoRFs) are particular functional segments of disordered proteins, which play crucial roles in regulating the phase transition of membrane-less organelles and frequently serve as central sites in cellular interaction networks. As the association between disordered proteins and severe diseases continues to be discovered, identifying MoRFs has gained growing significance. Due to the limited number of experimentally validated MoRFs, the performance of existing MoRF's prediction algorithms is not good enough and still needs to be improved. In this research, we present a model named MoRF_ESM, which utilizes deep-learning protein representations to predict MoRFs in disordered proteins. This approach employs a pretrained ESM-2 protein language model to generate embedding representations of residues in the form of attention map matrices. These representations are combined with a self-learned TextCNN model for feature extraction and prediction. In addition, an averaging step was incorporated at the end of the MoRF_ESM model to refine the output and generate final prediction results. In comparison to other impressive methods on benchmark datasets, the MoRF_ESM approach demonstrates state-of-the-art performance, achieving [Formula: see text] higher AUC than other methods when tested on TEST1 and achieving [Formula: see text] higher AUC than other methods when tested on TEST2. These results imply that the combination of ESM-2 and TextCNN can effectively extract deep evolutionary features related to protein structure and function, along with capturing shallow pattern features located in protein sequences, and is well qualified for the prediction task of MoRFs. Given that ESM-2 is a highly versatile protein language model, the methodology proposed in this study can be readily applied to other tasks involving the classification of protein sequences.

Jordan structures of nilpotent matrices in the centralizer of a nilpotent matrix with two Jordan blocks of the same size

In this paper we characterize all nilpotent orbits under the action by conjugation that intersect the nilpotent centralizer of a nilpotent matrix B consisting of two Jordan blocks of the same size. We list all the possible Jordan canonical forms of the nilpotent matrices that commute with B by characterizing the corresponding partitions.

Bivariate Polynomial Matrix and Smith Form

Matrix equivalence plays a pivotal role in multidimensional systems, which are typically represented by multivariate polynomial matrices. The Smith form of matrices is one of the important research topics in polynomial matrices. This article mainly investigates the Smith forms of several types of bivariate polynomial matrices and has successfully derived several necessary and sufficient conditions for matrix equivalence.

Lepton universality in a model with three generations of sterile Majorana neutrinos

The extension of the Standard Model lepton sector by three right-handed Majorana neutrinos [heavy neutral leptons (HNLs)] with masses up to GeV scale is considered. While the lightest heavy neutral lepton is the dark matter particle with mass of the order of 5 keV, the remaining two HNLs ensure standard (active) neutrino mass generation by means of the seesaw type I mechanism. Two heavy sterile neutrinos with quasidegenerate masses up to 5 GeV can induce the deviation of lepton universality violation parameter in the decays of π+ and K+ mesons from the Standard Model value. Contours are obtained for the permissible values of this parameter within the framework of two mixing scenarios, taking into account the lifetime boundary for heavy neutral lepton from big bang nucleosynthesis in the Universe. When calculating the HNL decay width in the framework of the model with six Majorana neutrinos, three active and three heavy, both two-particle and three-particle lepton decays, essential for masses below the mass of the pion, were taken into account. When calculating the decay widths, the limiting case known as the “Dirac limit” is not used. The results based on the explicit form of mixing matrices for three HNL generations and the diagram technique for Majorana neutrinos, which explicitly take into account the interference terms for diagrams with identical mass states, can lead to some differences in lifetime from the results using the Dirac limit and the displacement of the corresponding experimental exclusion contours of the “mass-mixing” type. For the second mixing scenario, a mass region of 460 MeV<M<485 MeV has been found that allows violation of lepton universality in charged kaon decays at the level observed in the experiment. Published by the American Physical Society 2024

A note on a generalized Jordan form of an infinite upper triangular matrix

In this paper, several equivalent conditions for the existence of a generalized Jordan form for matrices of locally nilpotent linear operators acting on an infinite countable dimensional vector space are presented, and an example is given showing that these conditions are not always fulfilled, which means the existence of infinite upper triangular matrices that are not similar to any generalized infinite Jordan matrix. Besides, it is shown that these conditions are not applicable in the case of an arbitrary dimensional of a vector space.