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In this paper, we study the time-fractional Euler–Poisson–Darboux equation with the Bessel fractional derivative. The Laplacian operator of this equation is considered in the ordinary and fractional derivatives and also in different coordinates. For the multi-dimensional Euler–Poisson–Darboux equation in the infinite domain (the whole space), we use the joint modified Meijer–Fourier transforms and establish a complex inversion formula for deriving the fundamental solution. The fractional moment of this solution is also presented in different dimensions. For studying the time-fractional Euler–Poisson–Darboux equation by the numerical methods in finite domain, we sketch the semi- and fully-discrete methods along with the matrix transfer technique to analyze the equation with fractional Laplacian operators in the cartesian, polar and spherical coordinates. The associated error and convergence theorems are also discussed. The illustrative examples are finally presented to verify our results in different coordinates. [ABSTRACT FROM AUTHOR]

This paper presents a novel state-space model (SSM) realization approach for non-commensurate fractional-order (NCFO) systems. A new notion of the resolvent invariant backward shift space of Gleason's problem associated with the NCFO rational transfer function matrix is introduced firstly, based on which a necessary and sufficient condition for the existence of the NCFO-SSM realization is given. Then, a sufficient condition for the construction of the resolvent invariant backward shift space of NCFO Gleason's problem is presented, and the corresponding realization algorithms are developed. In order to obtain a lower-dimensional NCFO-SSM, further improvement based on a polynomial description is studied. Finally, symbolic and numerical examples are provided to illustrate the details as well as the effectiveness of the proposed NCFO-SSM realization approach. [ABSTRACT FROM AUTHOR]

In this paper, some techniques are proposed to determine the smallest perturbation that causes the loss of a structural property for a linear system with coefficients depending polynomially on a vector of parameters. In the case that the interest lies on a single structural property, the analysis is carried out using directly the state-space description of the system, whereas, in the case that the interest is to characterize either the pair (reachability and observability) or the pair (stabilizability and detectability), the analysis is carried out using the transfer matrix of the plant. Examples of application of the proposed methods are reported all throughout the paper to illustrate and validate the theoretical results. [ABSTRACT FROM AUTHOR]

Costa Rica has a housing deficit for its most vulnerable population. There is a lack of information and evaluation of possible construction systems for social interest housing that can improve indicators like scope, cost, quality and construction time in the early phases of a project. An evaluation was conducted with technical and impartial criterion on nine (9) construction systems for social housing, specifically for the activities of construction of foundations, walls and finishes, applying the Quality Function Deployment Matrix (QFD). The QFD Matrix transfers user requirements to production requirements using "What's" and "How's". The final ratings are based on a number of eight hundred and ten (810) results based on the variables for two study actors (the contractor and the user). For the contractor, the prefabricated concrete system consisting of columns and horizontal panels, that obtained the highest evaluation (236, 5), was the system with the best rating. For the user, concrete masonry system obtained the highest evaluation (196, 3). The results are not absolute; they vary on factors such as the market, regulations, social perception, among others. When a system obtains a better rating, it means that, for the variables considered, for its assigned importance and for the evaluated user, it is the most adequate. It cannot be concluded that, in absolute terms, that a system with a higher rating is better than the others. [ABSTRACT FROM AUTHOR]

Knowledge Graph Completion (KGC) is a fundamental problem for temporal knowledge graphs (TKGs), and TKGs embedding methods are one of the essential methods for KGC. However, existing TKG embedding methods encounter a scalability dilemma, i.e., the inconsistency in parameter scalability among different datasets, and the less use of global information, e.g., statistics and dependencies of facts. To mitigate these two issues, we propose a novel and effective TKG embedding method, named T emporal Knowledge Gr a ph Embedding via S parse T ransf e r Mat r ix (TASTER), which provides a framework to utilize both global and local information. Regarding a TKG as a static knowledge graph when ignoring the time dimension, TASTER first learns global embeddings based on this static knowledge graph to capture global information. To capture the local information in a specific timestamp, TASTER evolves local embeddings from global embeddings based on the corresponding subgraph. Besides, TASTER learns evolving entity embeddings through sparse transformation matrices, which could better adapt to TKGs with a varied number of subgraphs. We conduct experiments on three real-world datasets, and TASTER outperforms most existing models on the link prediction task of TKGs, which validates the its effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the fractional Sturm–Liouville operators and present the polar fractional Laplacian as a particular case of these operators. We also consider the distributed order space–time fractional diffusion equation involving the polar fractional Laplacian and propose three approaches for studying this problem on the circle and ring domains. First, we apply the integral transforms as the analytical methods to get the solution in terms of the Laplace-type integrals using the Titchmarsh theorem. Second, we use the finite difference method for discretization of the space variable and employ the matrix transfer technique to obtain a system of the distributed order fractional equations. For this system, we modify the Putzer's algorithm and get the solution in terms of the eigenvalues of discretization matrix. Third, we employ the backward Euler numerical method for discretization of the time variable and find the corresponding error bound. Moreover, we compare and verify the approximate solutions with the exact solutions in analytical form. [ABSTRACT FROM AUTHOR]

The paper develops the Green's function solution in matrix form for functionally graded and transversely isotropic material (FGTIM) due to the loading of a circular ring force vector. The force vector is concentrated along a horizontal circular ring and acts at any location in the interior of the FGTIM material occupying either a fullspace or a halfspace. Without loss of generality, the variations of the FGTIM's five elastic parameters are expressed as five arbitrary step functions with the depth as the independent variable. The two-dimensional Fourier integral transforms in the cylindrical coordinate system are used for the mathematical formulation and derivation in matrix form. The Green's function solution of the displacement and stress fields is explicitly expressed in the matrix form in terms of classical improper Hankel transform integrals of the orders of 0 to 3. The kernel functions of the Hankel transform integrals are explicitly expressed in the forms of backward transfer matrix. Their mathematical properties are analyzed analytically and numerically. The singular terms associated with the improper Hankel transform integrals are analytically isolated and expressed in the exact closed-form in terms of the complete elliptic integrals of the first, second and third kind. Such closed-form singular terms can be expressed as the matrix Green's function solution for the corresponding bi-material due to the same circular ring force vector. Numerical results show that the computation of the matrix Green's function solution can be achieved with high accuracy and efficiency and the heterogeneity and anisotropy can have significant effects on the elastic fields in the FGTIM induced by the circular ring force vector. [ABSTRACT FROM AUTHOR]

An efficient fictitious pile method based on elasticity theory is presented for the analysis of interaction factor of two laterally loaded piles embedded in non-homogeneous soils. The problem is decomposed into two systems, namely the two fictitious piles acted upon by (partial) external loading, and an extended multilayered soil continuum acted upon by a system of pile-soil interaction forces at imaginary positions of the piles. The behavior/responses of the multilayered isotropic soils are analyzed through a computationally effective transfer matrix solution procedure. A Fredholm integral equation of the second kind is then deduced for the load-deformation relationship of a two-pile group system, by considering the equilibrium of the pile-soil interaction forces and the displacement compatibility between the fictitious pile and the extended soil. Comparison of the results calculated by the present fictitious pile method for displacement interaction factor between two piles embedded in multilayered isotropic soils has shown good agreement with the previous ones obtained by using the more rigorous finite element approach. The parametric numerical study demonstrates that the soft-over-stiff-over-soft soil layers have a profound effect on the pile-to-pile displacement interaction factor for the case of moment loading, which should be carefully considered in the practical design. [ABSTRACT FROM AUTHOR]

In this paper, we define and study a class of linear hybrid dynamical systems characterized by differential–difference equations. We introduce two operators that facilitate the analysis of these systems and derive explicit formulas for their solutions. We examine the transfer function matrix and characteristic polynomial to assess stability. Our theoretical findings are supported by numerical examples, demonstrating their application in power systems stability analysis. Specifically, we substantiate our theory within the context of power systems stability analysis, incorporating elements of discrete behavior. • We study linear hybrid dynamical systems of differential–difference equations. • We define two operators to study solutions of the proposed hybrid systems. • We analyze the transfer function matrix, characteristic polynomial, and system stability. • We apply our theory to power systems stability with discrete behavior elements. [ABSTRACT FROM AUTHOR]

A recent study conducted by researchers at China Agricultural University explores the issue of regional disparities in healthcare services in China. The study focuses on cross-provincial inpatient mobility patterns and their determinants. Using data from over 5 million cross-provincial inpatients in 2019, the researchers identified the primary demand and supply provinces for healthcare services. They found that Beijing, Shanghai, Zhejiang, and Jiangsu provinces were the preferred medical destinations, while Anhui, Henan, Hebei, and Jiangsu provinces were the main sources for cross-provincial inpatients. The study also analyzed the impact of various factors, such as medical resources, quality, and expenses, on the spatial patterns of inpatient mobility. The findings provide insights into the inequality characteristics of healthcare access and offer evidence for optimizing healthcare services. [Extracted from the article]

A simple, necessary, and sufficient condition ensuring that a real matrix of dimension three is similar to a Metzler matrix is exhibited. When this condition is satisfied, a construction of the transfer matrix is given. This construction is used to design an interval observer for a family of continuous-time systems. An example is provided with interval observer design for the so-called love dynamics in the case of limit cycles [ABSTRACT FROM AUTHOR]

In this article, we deal with the continuous-time singular linear quadratic regulator (LQR) problems, which give rise to nonautonomous Hamiltonian systems. This case arises when the system’s transfer function matrix is not left-invertible. A special case of this problem can be solved using the constrained generalized continuous algebraic Riccati equation (CGCARE), when a certain condition on the input-cardinality of the Hamiltonian is satisfied. However, this condition is only a special case among many other possible cases. On the other hand, singular LQR problems with autonomous Hamiltonian systems have been well studied in the literature. In this article, we apply behavioral theoretic techniques to show that the general case of the singular LQR problem with nonautonomous Hamiltonian can be solved by a direct sum decomposition of the plant behavior, where one of the direct summands can be solved via CGCARE, while the other gives rise to an autonomous Hamiltonian system. [ABSTRACT FROM AUTHOR]

In this paper, springing responses of a container ship with forward speed in regular waves are studied by a time-domain TEBEM which is generalized to elastic modes. TEBEM is used principally to solve the steady and unsteady flow and the infinity radiation condition is achieved by the Damping Zone Method. In the structure part, the Transfer Matrix Method is used to get the generalized structural mass, damping, stiffness and principal mode of displacement and rotation of vertical oscillation modes which will participate in the subsequent hydrodynamic calculation. In the hydrodynamic part, the fourth-order Runge–Kutta method is used to solve the hydroelasticity equations. The effects of forward speed and 2nd order wave forces generated by 1st order velocity potential in head sea are analyzed. Meanwhile, the variation of different load components against wave direction for corresponding different stations and contribution of different part of ship for different load components in head sea are studied. Compared with the experimental results, the motions and loads of a 6750-TEU container ship with different forward speeds predicted by TEBEM show an acceptable agreement. φ I incident potential φ d disturbed potential ζ d disturbance wave elevations ζ I incident wave elevations μ 0 damping strength [ABSTRACT FROM AUTHOR]

Single-input single-output (SISO), systems with zeros interlacing poles (ZIP) have been extensively studied in the literature and have received interest widely. However, the ZIP property for multiple-input and multiple-output (MIMO), systems has not been pursued sufficiently. In this article, we pursue the ZIP property for MIMO systems and link this to strict passivity. For the class of systems that admit a symmetric state-space realization, which for the SISO case is equivalent to ZIP, we obtain sufficient conditions under which MIMO systems too have ZIP. We also present new results in the context of “spectral-zero” of a system, a notion that plays a key role in many optimal control and estimation problems. We formulate conditions under which the spectral-zeros of a MIMO system are real, and further conditions that guarantee that the system-zeros, spectral-zeros, and the system-poles are all interlaced for MIMO systems. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach that can generate a state-space model with low inner dimension for an MIMO non-commensurate fractional order (NCFO) system. Specifically, the notion of an admissible digraph is firstly introduced associated with a fractional order transfer (function column) vector. Then, new state-space model realization conditions and corresponding procedures based on this admissible digraph are proposed for the state-space model realization of an NCFO polynomial transfer matrix. Finally, a new necessary and sufficient state-space model realization condition is proposed for the rational transfer matrix of an MIMO NCFO system, and it is shown, based on a matrix fractional description (MFD) of the given rational transfer matrix, a state-space model realization can be obtained by firstly converting it to the polynomial case and then utilizing the digraph approach for polynomial case. Symbolic and numerical examples are provided to demonstrate the main ideas and effectiveness of the proposed digraph approach. [ABSTRACT FROM AUTHOR]

Researchers at Madan Mohan Malaviya University of Technology in Gorakhpur, India, have proposed a highly sensitive hybrid biosensor for the detection of blood cancer. The biosensor utilizes a CaF2 Prism, Ag metal, an oxide layer Al2O3, and a 2D nanomaterial graphene. By optimizing the thickness of the layers and the number of graphene layers, the biosensor can achieve a sensitivity of up to 427.43 deg/RIU, with a detection accuracy and figure-of-merit (FOM) of 0.7027 deg-1 and 217 RIU-1, respectively. This research has the potential to lead to the development of a useful tool for the early detection of blood cancer. [Extracted from the article]

A recent study conducted at the Islamic University of Gaza has developed a new surface plasmon resonance sensor (SPRS) for the early detection of cervical cancer. The SPRS is constructed using layers of silver, BaTiO3, and graphene, along with a coupling prism. The researchers found that the optimal thicknesses of the materials used in the SPRS resulted in a sensitivity of 300 degrees RIU-1, which is higher than previously published SPRS structures. The study concludes that this SPRS shows promise for use in various biosensing applications. [Extracted from the article]

A new report discusses research conducted at El Manar University in Tunis, Tunisia, on the use of a 1D symmetrical photonic crystal as a blood cancer sensor. The researchers used simulation to study the performance of the sensor and obtained results that showed improved sensitivity and quality factor based on the thickness of the sample layer and the angle of incidence. The study was conducted using the Transfer Matrix method and included different blood cell samples, including normal blood cells and various cancerous blood cells. The research has been peer-reviewed and published in Physics of the Solid State. [Extracted from the article]

The Transfer Matrix Method (TMM) has become a prominent tool for the optical simulation of thin−film solar cells, particularly among researchers specializing in organic semiconductors and perovskite materials. As the commercial viability of these solar cells continues to advance, driven by rapid developments in materials and production processes, the importance of optical simulation has grown significantly. By leveraging optical simulation, researchers can gain profound insights into photovoltaic phenomena, empowering the implementation of device optimization strategies to achieve enhanced performance. However, existing TMM−based packages exhibit limitations, such as requiring programming expertise, licensing fees, or lack of support for bilayer device simulation. In response to these gaps and challenges, we present the TMM Simulator (TMM−Sim), an intuitive and user−friendly tool to calculate essential photovoltaic parameters, including the optical electric field profile, exciton generation profile, fraction of light absorbed per layer, photocurrent, external quantum efficiency, internal quantum efficiency, and parasitic losses. An additional advantage of TMM−Sim lies in its capacity to generate outcomes suitable as input parameters for electro−optical device simulations. In this work, we offer a comprehensive guide, outlining a step−by−step process to use TMM−Sim, and provide a thorough analysis of the results. TMM−Sim is freely available, accessible through our web server (nanocalc.org), or downloadable from the TMM−Sim repository (for Unix , Windows , and macOS) on GitHub. With its user−friendly interface and powerful capabilities, TMM−Sim aims to facilitate and accelerate research in thin−film solar cells, fostering advancements in renewable energy technologies. • Intuitive and user-friendly tool for optical simulation of essential photovoltaic parameters. • Ability to simulate two device architectures: bilayer and bulk heterojunction. • Possibility of calculating the photocurrent as a function of the active layer thickness for device optimization. • The software is freely available for use either through a dedicated web server or by downloading the binary files. [ABSTRACT FROM AUTHOR]

This paper deals with wave propagation in locally (i.e., bounded) periodic continuous systems where the wavefield cannot entirely be described in terms of Bloch waves. To gain better insights into this problem, use is made of the analogy, from wave propagations perspective, between homogeneous systems and their locally periodic counterparts, by viewing the former as equally locally periodic but with arbitrary small periods (Saeed and Vestroni (1998)). The effect of truncation of periodicity is illustrated by the response of locally periodic rod and beam models. It is found that, the wave solution is made of both Bloch waves, carrying the contribution of the repeated discontinuities, and conventional wave modes defining the transformation from the physical domain to the wave domain. This transformation matrix is dependent on whether the number of interior degrees of freedom is equal to or greater than that of the coupling coordinates between cells. In the former case (the monomode rod) it simply corresponds to the conventional wave basis describing the properties of the medium at the (left) edge of the unit cell regardless of its specific form, while in the latter case (the beam model) it changes with change of the unit cell configuration because information carried by Bloch modes about the scattering process is incomplete. • The response in physical coordinates of locally periodic rod and beam models is analogous in form to the homogeneous mono-mode case where the Bloch transmission and generation modes replace the corresponding conventional wave modes provided that the outer ends have simple conditions. • Wave solution, obtained by converting the overall mechanical transfer matrix into its wave version via an appropriate conventional wave transformation matrix for each model, is expressed in terms of single cell scattering properties, Bloch wavenumber of the infinite problem and the number of cells. [ABSTRACT FROM AUTHOR]

This paper considers continuous transfer function representation for a cascade composed of N mutually interconnected square multiple-input multiple-output (MIMO) linear time-invariant (LTI) subsystems with general multidirectional input–output configurations. Such cascaded structure can arise, e.g., from the spatial discretization of one-dimensional distributed parameter systems (DPSs) described by partial differential equations (PDEs) with boundary conditions representing different configurations of boundary input signals. As shown in the paper, the transfer function matrix of the resulting cascade can be calculated using the Redheffer star product of the subsystems' transfer function matrices, which simplifies into the usual matrix product for the unidirectional cascade. For the particular case of 2 × 2 cascade composed of rational transfer function subsystems, the recursive formulas for its boundary and distributed transfer functions have been derived for both uni- and multidirectional configurations. The well-posedness and the stability criteria are also analyzed, proving to be more restrictive for the multidirectional cascade than for the unidirectional one due to the internal positive feedback in the first case. As shown in the attached example, the presented results can be used to approximate one-dimensional distributed parameter systems using rational transfer function subsystems representing the spatial sections of the original DPS. [ABSTRACT FROM AUTHOR]

• Zero assignment to make the transfer function matrix (TFM) from the disturbance to the residual rank-deficient at the disturbance frequencies. • Complex coefficient gain in residual evaluation is proposed to exploit the unique feature of rank-deficiency of the disturbance TFM. • A new optimization objective function based on the difference of the maximum singular value of the transfer function matrix is proposed. [Display omitted] Aiming at early detection of faults in dynamic systems subject to external periodic disturbances, this paper proposes a new generalized proportional-integral observer (GPIO) fault detection scheme with zero-pole joint optimization and novel complex coefficient gain (CCG) of residual evaluation. The focus of the proposed scheme is to reduce the adverse impacts caused by the semi-stationary periodic disturbance whose spectrum is uneven, with most energy being at some dominant frequencies. The proposed GPIO with a complex coefficient gain is designed in a two-stage procedure. In the first stage of zero assignment and pole optimization, the additional zeros introduced by the GPIO's integration action are allocated to near the disturbance frequency. The gain of the transfer function matrix relating from the disturbances to the fault indicator signals is minimized by pole optimization. In the second stage of designing complex coefficient gain in residual evaluation, the unique feature of rank-deficient caused by the additional zeros assigned in stage one is further exploited to cancel the disturbances in the fault indicator signals (which is also referred to as the fault detection residual in this article). It is proved that, for an arbitrary periodic disturbance with a specific spectrum, the remnant components of the disturbance in the indicator signals generated by the GPIO can cancel each other by a complex gain vector, which can be determined by the zero eigenvalue's left eigenvector of the rank-deficient of the disturbance transfer function matrix. The sufficient conditions for the convergence of the proposed fault detection filter are also given. Numerical examples illustrate the proposed method's better performance in detecting minor faults. [ABSTRACT FROM AUTHOR]

This article addresses the exponential almost sure (EAS) stability and stabilization problems of continuous-time Markovian jump systems with additional stochastic switches. Sufficient conditions for EAS stability are established by applying a method to its stochastic transfer matrix. Particularly, both sojourn time and distribution of such random switchings are considered in the design of a state-feedback controller. Compared with some existing references, the proposed controller could bear unmatched or asynchronous signals. Moreover, it can be seen that our results are more general but less conservative, when the information on sojourn time and distribution is used. Some of them include previous work as special cases. Two examples are used to demonstrate the effectiveness and superiority of the methods proposed in our study. [ABSTRACT FROM AUTHOR]

In this article, we generalize previously reported results for linear, time-invariant, stabilizable multivariable systems described by a strictly proper transfer function matrix $P(s)$ with number of outputs greater than or equal to the number of inputs. By making use of a special kind of a left generalized inverse $P(s)_{\alpha }^{\oplus }$ of $P(s)$ , we define and examine the equivalent relation $\mathcal {R}$ relating $P(s)$ with the members of the equivalence class $[P(s)]_{R}$ of the closed loop-transfer function matrices $P_{C}(s)$ obtainable from $P(s)$ by the use of a proper compensator $C(s)$ in the feedback path. For $\mathcal {R}$ , we establish a set of complete invariants and a canonical form. These results give rise to a simple algorithmic procedure for the computation of proper internally stabilizing and denominator assigning compensators $C(s)$ for the class of plants with $p=m$ and having no zeros in the closed right half complex plane: $\mathbb {C}^{+}$ and in the case when $p>m$ plants characterized by right polynomial matrix fraction descriptions with a polynomial matrix numerator having at least one subset of $m$ rows that give rise to a nonsingular polynomial matrix with no zeros in $\mathbb {C}^{+}$. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of identifying the interaction geometry of a set of agents, whose collective goal are to achieve consensus under an agreement protocol. By classifying agents into different subsets based on their behavior, as well as introducing the so-called input and output agents, a relationship between the transfer function matrix and the identifiability of system parameters is established. Specifically, two cases are considered. If the set of input agents coincides with the set of output agents, the number of edges in the input agent set, in the complement of input agent set, and between these two sets can be uniquely identified. Thus, the search space of feasible graphs becomes much smaller. The problem can be solved in polynomial time, and an algorithm is provided. Moreover, if all the agents in the system are output agents, parameters of the system can be uniquely identified, and an algebraic method is given to exactly recover the graph topology. A numerical example illustrates the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This work presents a novel approach based on vector decomposition for realizing the Fornasini–Marchesini (F–M) model in multidimensional (n -D) systems. The primary focus is on resolving coefficient dependencies within the n -D rational transfer function matrix (TFM) of a multiple-input multiple-output (MIMO) system, aiming to generate a lower-order F–M model. The proposed method is further extended to robust observational state feedback control. To achieve this, we introduce innovative sufficient conditions for designing a low-dimensional resolvent invariant space (RIS) and outline the corresponding low-order F–M model realization process. By incorporating the polynomial vector dependency technique, we comprehensively address coefficient dependencies, leading to the construction of an even lower-order F–M model and contributing to the simplification of analytical complexity. To accommodate generic rational TFMs, we propose a matrix fractional description (MFD)-based process. Finally, we apply the developed F–M model implementation method to derive descriptor multiple affine representations (DMARs). This application proves instrumental in the robust observed-state feedback control design for rationally uncertain systems, enhancing the overall effectiveness of the robust observed-state feedback control design. [ABSTRACT FROM AUTHOR]

• Formulation of a well-posed nonlocal model for nonuniform beams under bending. • The transfer matrix method is used for an efficient solution to the problem. • Explicit, closed-form solutions derived for various boundary conditions. • Results reveal intricate behavior of nonlocal nonuniform beams vs. local ones. A mathematically well-posed nonlocal model is formulated based on the variational approach and the transfer matrix method to investigate the size-dependent elastostatics of nonuniform miniaturized beams. The beams are composed of an arbitrary number of sub-beams with diverse material and geometrical properties, as well as small-scale size dependency. The model adopts a stress-driven nonlocal approach, a well-established framework in the Engineering Science community. The curvature of a sub-beam is defined through an integral convolution, considering the bending moments across all cross-sections of the sub-beam and a kernel function. The governing equations are solved and the deflections are derived in terms of some constants. The formulation uses local and interfacial transfer matrices, incorporating continuity conditions at cross-sections where sub-beams are joined, to define relations between constants in the solution of a generic sub-beam and those of the first sub-beam at the left end. The boundary conditions are then imposed to derive an explicit, closed-form solution for the deflection. The solution significantly simplifies the study of nonuniform beams with multiple sub-beams. The predictions of the model for two limiting cases, namely local nonuniform and nonlocal uniform beams, are in excellent agreement with the available literature data. The flexural behavior of nonuniform miniaturized beams, composed of two to five different sub-beams and subjected to different boundary conditions, is studied. The results are presented and discussed, emphasizing the effects of the material properties, nonlocalities, and lengths of the sub-beams on the deflection. It is demonstrated that the flexural response of nonlocal nonuniform beams is more complex than local counterparts. Unlike the local beams, dividing a nonlocal uniform beam into multiple sub-beams and then reconnecting them changes the overall stiffness of the beam. The study highlights the potential to design nonuniform miniaturized beams with specific configurations to control their flexural response effectively. [ABSTRACT FROM AUTHOR]

We release a set of GPU programs for the study of the Quantum (S = 1 / 2) Spin Glass on a square lattice, with binary couplings. The library contains two main codes: MCQSG (that carries out Monte Carlo simulations using both the Metropolis and the Parallel Tempering algorithms, for the problem formulated in the Trotter-Suzuki approximation), and EDQSG (that obtains the extremal eigenvalues of the Transfer Matrix using the Lanczos algorithm). EDQSG has allowed us to diagonalize transfer matrices with size up to 2 36 × 2 36. From its side, MCQSG running on four NVIDIA A100 cards delivers a sub-picosecond time per spin-update, a performance that is competitive with dedicated hardware. We include as well in our library GPU programs for the analysis of the spin configurations generated by MCQSG. Finally, we provide two auxiliary codes: the first generates the lookup tables employed by the random number generator of MCQSG; the second one simplifies the execution of multiple runs using different input data. Program Title: QISG Suite CPC Library link to program files: https://doi.org/10.17632/g97sn2t8z2.1 Licensing provisions: MIT Programming language: CUDA-C Nature of problem: The critical properties of quantum disordered systems are known only in a few, simple, cases whereas there is a growing interest in gaining a better understanding of their behaviour due to the potential application of quantum annealing techniques for solving optimization problems. In this context, we provide a suite of codes, that we have recently developed, to the purpose of studying the 2D Quantum Ising Spin Glass. Solution method: We provide a highly tuned multi-GPU code for the Montecarlo simulation of the 2D QISG based on a combination of Metropolis and Parallel Tempering algorithms. Moreover, we provide a code for the evaluation of the eigenvalues of the transfer matrix of the 2D QISG for size up to L=6. The eigenvalues are computed by using the classic Lanczos algorithm that, however, relies on a custom multi-GPU-CPU matrix-vector product that speeds-up dramatically the execution of the algorithm. [ABSTRACT FROM AUTHOR]

This article discusses the use of innovative solutions to analyze and harness the collective potential of multi-omic data in biomedical science. The authors have curated a collection of gene-level transcriptomic data focused on mammalian excitatory neurogenesis in the neocortex, which is available for exploration on nemoanalytics.org. By applying a structured joint decomposition approach to mouse, macaque, and human data, the authors identify transcriptome dynamics that are conserved across mammalian neurogenesis and map onto the genetics of human brain structure and disease. They also analyze transcriptomic data from adult human neocortex to define molecular signatures specific to excitatory neuronal cell types in different layers of the mature neocortex. The authors propose these analyses as specific applications of combining joint decomposition with curated collections of multi-omics data matrices. [Extracted from the article]

In this paper, we use input and output data to study the functional observer design problem for observable Boolean control networks (BCNs). By taking advantage of the algebraic forms of BCNs, a necessary and sufficient condition for the existence of reducible states is presented, and an algorithm is proposed to separate reducible states. Based on input and output data, we construct state-output transfer matrices for observable BCNs with unknown structures, and then propose a procedure to design functional observers estimating the states of BCNs. Examples are provided to demonstrate the efficiency of the obtained results. [ABSTRACT FROM AUTHOR]

Multi-stand combined rolling is the key process to determine the quality of strip. The rolled piece presents different states in each stand unit, and there is information transmission and interaction between stands. To reduce the impact of quality-related faults on subsequent production systems, it is particularly important to effectively identify the transmission path of quality-related information for locating the root cause of abnormalities. However, the causes of quality defects are misidentified due to the neglect of genetic characteristics of quality in the overall quality diagnosis. Focus on hot rolled strip thickness diagnosis, an abnormal transmission path identification method based on sub stand strategy and Kernel Principal Least Square-Maximal Information Coefficient-Transfer Entropy (KPLS-MIC-TE) was proposed to improve the accurate identification of defect roots, the sub-stand was diagnosed, and the abnormal variable diagnosis of a sub stand was conducted with the KPLS algorithm. Secondly, based on the asymmetric characteristics of the transfer entropy matrix, a directed transfer topology with the causality of variables was constructed. Finally, the production data of the 1580 hot rolling line is used for industrial validation. The results show that the method can accurately diagnose process abnormal variables and identify the path of abnormal variables. [ABSTRACT FROM AUTHOR]

To achieve the efficient and accurate long-time integration, we propose a fast and stable high-order numerical method for solving fractional-in-space reaction–diffusion equations. The proposed method is explicit in nature and utilizes the fourth-order compact finite difference scheme and matrix transfer technique (MTT) in space with FFT-based implementation. Time integration is done through the modified fourth-order exponential time differencing Runge–Kutta scheme. The linear stability analysis and various numerical experiments including two-dimensional (2D) Fitzhugh–Nagumo, Allen–Cahn, Gierer–Meinhardt, Gray–Scott and three-dimensional (3D) Schnakenberg models are presented to demonstrate the accuracy, efficiency, and stability of the proposed method. [ABSTRACT FROM AUTHOR]

Click-through rate prediction is an important method for online advertising and marketing evaluations. However, for environmental reasons, there is a scarcity and imbalance in the advertising data available. We found that a feature transfer can be applied in a transfer learning method to obtain potential connections from less relevant advertisement data. Considering the complexity and diverse features of advertisement data, a feature transfer cannot allow researchers to discover the relationships among such features within the advertisement data. Therefore, we propose a click-through rate method based on a multi-view feature transfer (MFT). MFT divides the data into common and selected features during the data pretreatment process. It then combines the important feature vectors obtained using a Laplacian matrix with the common features obtained during the pretreatment process to form groups of views. Therefore, combining feature transfer matrix with mutli-view clustering is an innovation of the CTR data prediction process. In our experiments, the MFT model achieved good results. Experiments on a large number of datasets of different sizes and the application of three evaluation indicators show that the MFT method delivers excellent prediction results using the transfer relationships among the characteristics of an advertising dataset, and its performance is better than that of many other advertising click-through rate prediction methods. [ABSTRACT FROM AUTHOR]

In this article, we consider the controllability of a discrete-time linear dynamical system with sparse control inputs. Sparsity constraints on the input arises naturally in networked systems, where activating each input variable adds to the cost of control. We derive algebraic necessary and sufficient conditions for ensuring controllability of a system with an arbitrary transfer matrix. The derived conditions can be verified in polynomial time complexity, unlike the more traditional Kalman-type rank tests. Further, we characterize the minimum number of input vectors required to satisfy the derived conditions for controllability. Finally, we present a generalized Kalman decomposition-like procedure that separates the state-space into subspaces corresponding to sparse-controllable and sparse-uncontrollable parts. These results form a theoretical basis for designing networked linear control systems with sparse inputs. [ABSTRACT FROM AUTHOR]

The collocation-based impedance-to-scattering matrix method recently developed in conjunction with the boundary element method (BEM) for large silencer analysis is reformulated by using the reciprocal identity integral. The reciprocal identity integral also forms the foundation of the classical theory of acoustic reciprocity for silencers. Contrary to the conventional wisdom, when the inlet and the outlet of a large silencer are switched, the transmission loss (TL) may not remain the same at frequencies above the plane-wave cutoff of the inlet and outlet. Numerical results using the BEM as well as the finite element method (FEM) are provided to confirm the hypothesis. Some practical issues related to the application of the impedance-to-scattering matrix method are also investigated. One issue is on the combination of subsystems in series connection using the scattering matrices. It is found that the more stable Redheffer star product must be used instead of the simple matrix multiplication using the transfer scattering matrices. Another practical issue is on the modeling of large silencers with a ½ or a ¼ reflective symmetry. A more restrictive selection of modes must be used in place of the general complete modal expansion in cylindrical coordinates. [ABSTRACT FROM AUTHOR]

A model matching and passivating control architecture for multi-input/multi-output linear systems, comprising dynamic feedback and feedforward, is proposed. The approach—essentially without any restriction on the relative degree and the zeros of the underlying system and by relying only on input/output measurements—provides a closed-loop system, the transfer matrix of which matches any desired matrix of rational functions. An alternative implementation of the above design allows to achieve an arbitrary approximation accuracy of a desired transfer matrix while also preserving structural properties—in particular observability—of the overall interconnected system. Such a construction can be then specialized to provide input/output decoupling or a system that is passive from a novel control input to a modified output. The result is achieved by arbitrarily assigning the relative degree and location of the poles and zeros on the complex plane of the interconnected system in a systematic way. It is also shown that similar ideas can be employed to enforce a desired, arbitrarily small, L2-gain from an unknown disturbance input to a modified output, while preserving the corresponding gain from the control input to the same output. The article is concluded with applications and further discussions on the results. [ABSTRACT FROM AUTHOR]

This paper considers the exponential almost sure (EAS) stability and stabilization problems of continuous-time Markovian jump systems (MJSs) with alternative and continuous controller failures. By introducing a piecewise constant function, the dwell times of a controller useful or not are modeled to be time-variant, whose bounds are also included. Then, sufficient conditions for EAS stability are established by using a method on its stochastic transfer matrix. Moreover, the statistically transient properties of Markov process are considered, and the control gains is gotten by solving some Lyapunov equations. Two examples are used to demonstrate the effectiveness and superiority of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper proposes a novel realization approach to generate a low-order Fornasini–Marchesini (F-M) (second) model for multidimensional (n -D) systems. First, based on two developed matrix relation properties, the F-M model realization problem is converted to establishing a desired standard matrix by performing elementary operations on an associated matrix initialized from the given transfer matrix. Then, a general constructive procedure and two corresponding techniques to compute the F-M models are established for both the left and right matrix fractional descriptions (MFDs) of the given transfer matrix. It turns out that compared with the existing methods the proposed approach can produce an F-M model with lower order, and furthermore, this is the first method that can treat both the left and right MFDs for obtaining an F-M model realization in a unified manner. Non-trivial examples are given to illustrate the details and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

For an arbitrary rational matrix (RM), a new descriptor realization of its all-pass factorization is presented. The coefficients of the factors are expressed explicitly in the solution of a linear matrix inequality, which is well known in control theory. Using the all-pass factorization, necessary and sufficient conditions for existence of a solution of an equation with RMs where the unknown RM has its poles in the left closed complex half plane and it can be improper are presented, as well as all solutions. As an application of the latter result, the notion of almost disturbance decoupling, i.e., when the infimum of the ${\mathscr {H}}_{\infty}$ norm of the transfer matrix from the disturbance input to the controlled output over the stabilizing controllers is zero, is generalized. The generalization is such that instead of the whole frequency axis, the frequency axis with excluded intervals of small lengths, is considered. The controller consists of output feedback plus disturbance feedforward designed independently. A necessary and sufficient solvability condition is presented, which is expressed in terms of the given data. The three main results are illustrated by an example. [ABSTRACT FROM AUTHOR]

We consider a class of dynamical systems described by linear delay differential algebraic equations (DDAEs) called strangeness free, which is broader than the class commonly studied within the control theory field. Two problems arise in the study of the $\mathcal {H}_2$ norm of DDAEs: the first one is that it may be infinite even if the system is stable or has no seemingly feedthrough term, and the second one is the computation. In this paper, both problems are addressed. We provide a necessary and sufficient condition for the finiteness of the $\mathcal {H}_2$ norm, which is based on controllability and observability properties of the delay-difference part of the system, and we present a formula for computing the $\mathcal {H}_2$ norm whenever it is finite, which is obtained by means of a neutral-type system whose transfer matrix is equivalent to the transfer matrix of DDAEs. [ABSTRACT FROM AUTHOR]

In this paper, we study robust stabilization for the networked control system (NCS) over the communication channels described by cascaded two-port networks. Such an NCS involves simultaneous uncertainties in the plant, controller, and two-port communication channels. The cascaded two-port connections arise when signals in the NCS are transmitted through bidirectional communication channels separated by a sequence of relays. Distortions and interferences occurring in communications are taken into account. We consider ${\mathcal H}_{\infty }$ -norm bounded uncertainties in the transmission matrices of the two-port channels, and the gap-type uncertainties in the plant and controller models. A necessary and sufficient condition for the robust stability of the NCS is presented in the form of an “arcsine” inequality, which states that the NCS is stable whenever the uncertainties quantified by the aforementioned metrics are well bounded and satisfy the “arcsine” inequality. A stability margin related to the Gang of Four transfer matrix is obtained, based on which the controller synthesis problem can be solved through a special ${\mathcal H}_{\infty }$ optimization with favorable properties. Furthermore, a generalized stability condition is studied in terms of frequency-wise bounded uncertainties, and the corresponding controller synthesis problem is proposed and solved. [ABSTRACT FROM AUTHOR]

This paper studies some useful properties of lossless negative imaginary transfer matrices for both continuous-time and discrete-time systems. Necessary and sufficient conditions are established for lossless negative imaginary systems both in frequency domain and state-space realization. Meanwhile, a minor decomposition method for lossless negative imaginary systems is proposed in terms of a partial-fraction expansion. This method is important for developing non-proper lossless negative imaginary theory in this paper by allowing poles at the origin and infinity. Two new relationships between lossless positive real and lossless negative imaginary systems are consequently established. According to these new established relationships, a generalized continuous-time lossless negative imaginary lemma and a different version of discrete-time lossless negative imaginary lemma are developed in terms of a minimal state-space realization. Several examples are provided to illustrate the main results. [ABSTRACT FROM AUTHOR]

With the growing attention on multimedia security, various MP3 steganographic and steganalytic algorithms have been proposed increasingly. However, the existing MP3 steganalysis is lack of good universality and detection performance. To address this problem, we devise an effective MP3 steganalytic algorithm based on joint point-wise and block-wise correlations of quantified modified discrete cosine transfer coefficients matrix. On the one hand, a universal rich high pass filtering module for MP3 steganalysis is deployed to boost the sensitiveness of the algorithm to the subtle signal brought by the data hiding. On the other hand, based on the principle of MP3 encoding and the characteristics of MP3 steganography, multi-scale correlations measure module is introduced, which is used to measure the changes of point-wise, 2 × 2 block-wise, and 4 × 4 block-wise correlations due to steganography separately. Additionally, customized feature optimization, including truncated threshold selection and high pass filters measure, is performed based on the properties of MP3 steganography. Experimental results illustrate that our proposed algorithm can be applied to various MP3 steganographic algorithms, bitrates, duration, and relative payloads. Detection accuracies are promoted by more than 20% averagely compared with state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In this paper, a novel constructive procedure is proposed for the realization of a low-order Fornasini–Marchesini state-space model for a given multidimensional system. In particular, essential properties for the constructions of a backward shift space and a resolvent invariant space associated with the Gleason's problem from a given transfer function matrix are investigated and some new sufficient conditions for such constructions are developed. Then, based on these conditions, a systematic constructive procedure is proposed for the multidimensional Fornasini–Marchesini model realization. It turns out that the new constructive procedure can generate Fornasini–Marchesini models with much lower orders and even the minimal realizations for a much larger class of multidimensional systems than the existing methods. Nontrivial examples are also provided to illustrate the basic idea as well as the effectiveness of the proposed procedure. [ABSTRACT FROM AUTHOR]

Intuitively, the main novelties of the proposed Tk-MaOEA can be presented as follows. • In the global space optimization level, a new transfer learning approach is developed to reduce a large number of objectives while the original property of the problem is kept well. The proposed approach uses a specific transfer matrix to compress the search space, which is simple yet effective to handle with the curse of dimensionality in MaOPs. • In the objective optimization level, the Kriging model is devised for each objective to further reduce its computational cost. This Bayesian based surrogate model is to measure not only the objective value itself but also stochastic error of the approximation, which is essentially conductive to improve the accuracy of the optimization. • The multi-scale normalization approach is employed so as to avoid the distortion caused by conventional normalization in the high-dimensional objective space. This is a significant operation for the MaOEA to keep unchanged spatial distribution when the original population are normalized. • The FCS approach is incorporated instead of the traditional crowding distance method in the environmental selection. This approach is more effective to select a set of representative non-dominated solutions in a single run. Due to the curse of dimensionality caused by the increasing number of objectives, it is very challenging to tackle many-objective optimization problems (MaOPs). Aiming at this issue, this paper proposes a novel many-objective evolutionary algorithm, called Tk-MaOEA, based on transfer matrix assisted by Kriging model. In this approach, for the global space optimization, a transfer matrix is used as a map tool to reduce the number of objectives, which can simplify the optimization process. For the objective optimization, the Kriging model is incorporated to further reduce the computation cost. In addition, the fast non-dominated sorting and farthest-candidate selection (FCS) methods are used to guarantee the diversity of solutions. Comprehensive experiments on a set of benchmark functions have been conducted. Experimental results show that Tk-MaOEA is effective for solving complex MaOPs. [ABSTRACT FROM AUTHOR]

Researchers from Nanjing University of Science and Technology in China have developed a new type of metamaterial-based polarization device for broadband applications. The device, which consists of stacked gold split-rings, can transmit circularly polarized light and block orthogonally polarized light. It has a wide operating bandwidth and can be used in fields such as optical communication and biomedicine. The research has been peer-reviewed and published in Physical Review Materials. [Extracted from the article]

In this work, the behavior of acoustic black holes (ABHs) serving as an anechoic termination of air-filled waveguides with a rectangular cross-section is numerically studied. These ABHs consist of a set of rigid ribs separated by narrow slits, whose height smoothly varies along the structure and whose aim is to slow-down the impinging acoustic wave and cause its absorption. For the purpose of this study, a 2D mathematical model based on linearized Navier–Stokes equations and employing the finite element method has been proposed, which allows for an accurate capturing the thermoviscous losses in the acoustic boundary layer adjacent to the solid–fluid interfaces, as well as the effects connected with geometrical details of the ABHs' inner structure. The numerical results show that in rectangular ABHs with a fine internal structure, the acoustic wave slow-down plays a significant role and that absorption properties are strongly dependent on their inner structure details. Simplified 1D mathematical models of rectangular ABHs based on the Riccati equation or transfer matrix method have also been proposed. These simplified models are computationally highly efficient, as it has been demonstrated, they provide accurate results, especially in the case of ABHs with a fine internal structure, which feature superior acoustic energy absorbing properties. [ABSTRACT FROM AUTHOR]

Abstract This papers investigates the scattering of oblique shear horizontal (SH) waves off finite periodic media made of elastic and viscoelastic layers. It further considers whether a Willis-type constitutive matrix (in temporal and spatial Fourier domain) may reproduce the scattering matrix (SM) of such a system. In answering this question the procedure to determine the relevant overall constitutive parameters for such a medium is presented. To do this, first the general form of the dispersion relation and impedances for oblique SH propagation in such coupled Willis-type media are developed. The band structure and scattering of layered media are calculated using the transfer matrix (TM) method. The dispersion relation may be derived based on the eigen-solutions of an infinite periodic domain. The wave impedances associated with the exterior surfaces of a finite thickness slab are extracted from the scattering of such a system. Based on reciprocity and available symmetries of the structure and each constituent layer, the general form of the dispersion and impedances may be simplified. The overall quantities may be extracted by equating the scattering data from TM with those expected from a Willis-type medium. It becomes evident that a Willis-type coupled constitutive tensor with components that are assumed independent of wave vector is unable to reproduce all oblique scattering data. Therefore, non-unique wave vector dependent formulations are introduced, whose SM matches that of the layered media exactly. It is further shown that the dependence of the overall constitutive tensors of such systems on the wave vector is not removable even at very small frequencies and incidence angles and that analytical considerations significantly limit the potential forms of the spatially dispersive constitutive tensors. Highlights • Overall parameters of Willis-type constitutive tensors in spatial Fourier representation are extracted from scattering data. • The method is successfully applied to oblique incidence of shear horizontal waves in layered slabs. • The periodic micro-structure leads to spatially dispersive results. • Symmetry related and analytical restrictions limit the possible representations of the constitutive tensors. [ABSTRACT FROM AUTHOR]

This paper studies the connection between discrete-time and continuous-time negative imaginary systems. First, we analyze differences between two statements that are claimed to provide equivalent conditions for systems to be discrete-time positive real. Our conclusion is that one is equivalent to the definition of discrete-time positive real transfer matrices, the other is not. Second, by means of the bilinear transformation, a connection between discrete-time and continuous-time negative imaginary transfer matrices is established. Third, the concept of discrete-time lossless negative imaginary systems is introduced, and a discrete-time lossless negative imaginary lemma is developed to characterize the lossless negative imaginary properties in terms of minimal state-space realization. Some properties of discrete-time lossless negative imaginary transfer matrices are also studied. Several numerical examples illustrate the developed theory. [ABSTRACT FROM AUTHOR]

Researchers from Beni-Suef University have conducted a study on the ultra-high sensitive cancer cell detection capabilities of a one-dimensional photonic crystal with a defect. The researchers used simulations with MATLAB programming and the transfer matrix method to study the performance of the proposed biosensor. The biosensor works by sensing minute changes in the refractive index of analytes containing different cancer cells, resulting in a maximum shifting in the position of the defect mode and an ultra-high sensitivity of 4270.525928 nm/RIU. This research provides valuable insights into the potential of photonic biosensors for cancer detection. [Extracted from the article]