Structure Matrices Research Articles

MAGNETIC PROPERTIES OF MULTICOMPONENT HETEROGENEOUS MEDIA WITH A DOUBLY PERIODIC STRUCTURE

Heterogeneous media have a wide range of practical applications. Media with a doubly periodic structure (matrices of high-gradient magnetic separators, etc.) occupy an important place. Their study is usually based on experimental and approximate methods and is limited to simple two-phase systems. The development of universal and accurate methods of mathematical modelling of electrophysical processes in such environments is an urgent task. The aim of the paper is to develop a method for calculating local and effective parameters of a magnetostatic field with minimal restrictions on the number of phases, their geometry, concentration, and magnetic properties. Based on the theory of elliptic functions and secondary sources, an integral equation is formulated with respect to the magnetization vector of the elements of the main parallelogram of the periods. The calculated expressions for the complex potential, field strength, and components of the effective magnetic permeability tensor are obtained. The results of a series of computational experiments confirming the universality and effectiveness of the method are presented. As an example of a practical application, a detailed study of the field of the magnetic forces of the matrix is carried out: the lines of magnetic isodine and potential extraction areas for a complex version of the matrix are constructed. Within the framework of the developed method, the calculation of local and effective field characteristics is carried out by solving the field problem in the field of an arbitrary parallelogram of periods without specifying boundary conditions on its sides with a comprehensive consideration of significant interdependent factors. The practical value of the method is to create new opportunities for improving the technical characteristics of electrophysical devices for which the universality and accuracy of calculating local and effective field characteristics is decisive. An algorithm for optimizing the characteristics of the separator is proposed.

Chains of three-dimensional evolution algebras: A description

In this paper we describe locally all the chains of three-dimensional evolution algebras (3-dimensional CEAs). These are families of evolution algebras with the property that their structure matrices with respect to a certain natural basis satisfy the Chapman-Kolmogorov equation. We do it by describing all 3-dimensional CEAs whose structure matrices have a fixed rank equal to 3, 2 and 1, respectively. We show that arbitrary CEAs are locally CEAs of fixed rank. Since every evolution algebra can be regarded as a weighted digraph, this allows us to understand and visualize time-dependent weighted digraphs with 3 nodes.

On Linear Quadratic Regulation of Linear Port-Hamiltonian Systems

The linear quadratic regulator is a widely used and studied optimal control technique for the control of linear dynamical systems. It consists in minimizing a quadratic cost functional of the states and the control inputs by the means of solving a linear Riccati equation. The effectiveness of the linear quadratic regulator relies on the cost function parameters hence, an appropriate selection of these parameters is of mayor importance in the control design. Port-Hamiltonian system modelling arise from balance equations, interconnection laws and the conservation of energy. These systems encode the physical properties in their structure matrices, energy function and definition of input and output ports. This paper establishes a relation between two classical passivity based control tools for port-Hamiltonian systems, namely control by interconnection and damping injection, with the linear quadratic regulator. These relations allow then to select the weights of the quadratic cost functional on the base of physical considerations. A simple RLC circuit has been used to illustrate the approach.

Hm-toolbox: MATLAB Software for HODLR and HSS Matrices

Matrices with hierarchical low-rank structure, including HODLR and HSS matrices, constitute a versatile tool to develop fast algorithms for addressing large-scale problems. While existing software ...

Output Tracking of Boolean Control Networks With Impulsive Effects

In this article, the output tracking of Boolean control networks with impulsive effects (BCNs-IE) is discussed. Based on structure matrices of BCNs-IE and controllability matrices with respect to state subsets, stable complex attractors are studied. By constructing an auxiliary BCN-IE and using stable complex attractors, a necessary and sufficient condition for the output tracking problem is proposed. In addition, an algorithm to design state feedback controllers for the output tracking problem is provided. Moreover, an example is given to show the validity of the obtained results.

DSM-based variable ordering heuristic for reduced computational effort of symbolic supervisor synthesis

We consider the influence that the variable order of Binary Decision Diagrams (BDDs) has on the computational effort that is required for symbolic supervisor synthesis. In recent research it has been shown that improving the variable order can result in a substantial decrease of synthesis effort. We propose the combined use of the Dependency Structure Matrices (DSMs) and the matrix reordering heuristics Cuthill-McKee and Sloan to minimize the Weighted Event Span (WES) of the variable order. This is done by placing variables that often appear together in transition relations near each other. By performing benchmark experiments, we measure the reduction in synthesis effort by utilizing a variable order with minimized WES. The experiments show that our approach is competitive in reducing computational effort compared to FORCE, a state of practice variable ordering heuristic. Moreover, the best improvements in effort reduction are shown for the most computationally demanding models tested.

Amylose content and molecular-order stability synergistically affect the digestion rate of indica rice starches

This work concerns the multi-scale structures and digestion behaviors of indica rice starches with apparent amylose contents (AACs) of ca. 14%–24%. A higher AAC not always allowed a lower digestion rate (k), different from previous findings that starches containing more amylose normally show slowed digestion. Here, the proportion of stable molecular orders (melting temperature above ca. 73 °C) and AAC synergistically governed starch digestion rate. With a similar AAC, a higher amount of stable orders (Rh/l, ratio of enthalpy of stable orders to that of the rest) led to a lower k. Also, with a similar Rh/l, a larger AAC caused a lower k. Consistently, JPZ starch had almost the highest AAC and Rh/l, showing the lowest k. Regarding this, amylose and stable orders played roles in increasing the bulk density of starch structure matrices, and eventually slow the diffusion, absorption and catalysis events of digestion enzymes within the matrices.

Quality characteristic decoupling planning of different meta-action units for computer numerical control machine tool

Since computer numerical control machine tool is composed of multiple meta-action units to achieve one specific function, including the meta-action units' own quality, it still needs to control the coupling relationships among different meta-action units' quality characteristics to guarantee the whole machine's quality. In this article, a method of quality characteristic decoupling planning based on meta-action unit for computer numerical control machine tool was proposed. Firstly, the coupling constraint models based on meta-action unit were established. Secondly, the comprehensive coupling strengths of meta-action units were calculated and introduced into the design structure matrices. Thirdly, multidisciplinary design optimization method was adopted to obtain the optimized control sequence of different meta-action units' quality characteristics. What is more, automatic pallet changer rotary motion of computer numerical control machine tool was taken as an example to illustrate the rightness and effectiveness of this method.

Modeling and structuring design rationale to enable knowledge reuse

AbstractWe aim to lend insights into “what” constitutes design rationale and “how” to capture these. We restrict the scope of design rationale to the cases of failures observed while testing real engineered systems. We propose a model as an integration of a system hierarchy, a causal chain, and a causality model to cast multiple views of design rationale. The model is structured into databases using a newly introduced version of design structure matrices and supported using a web interface called CRIS4P, which is deployed at a space agency. We report a case example from the spacecraft domain and benchmark the proposed model against IBIS‐FAD model.

A Methodology for Operationalizing Enterprise IT Architecture and Evaluating its Modifiability

Recent contributions to information systems theory suggest that the primary role of a firm’s information technology (IT) architecture is to facilitate, and therefore ensure the continued alignment of a firm’s IT investments with a constantly changing business environment. Despite the advances we lack robust methods with which to operationalize enterprise IT architecture, in a way that allows us to analyze performance, in terms of the ability to adapt and evolve over time. We develop a methodology for analyzing enterprise IT architecture based on “Design Structure Matrices” (DSMs), which capture the coupling between all components in the architecture. Our method addresses the limitations of prior work, in that it i) captures the architecture “in-use” as opposed to high level plans or conceptual models; ii) identifies discrete layers in the architecture associated with different technologies; iii) reveals the “flow of control” within the architecture; and iv) generates measures that can be used to analyze performance. We apply our methodology to a dataset from a large pharmaceutical firm. We show that measures of coupling derived from an IT architecture DSM predict IT modifiability – defined as the cost to change software applications. Specifically, applications that are tightly coupled cost significantly more to change.

Deeply fusing multimodal features in hypergraph

Utilizing multimodal features to describe multimedia data is a natural way to improve recognition accuracy. However, how to optimally cluster the raw features into different modalities in order to alleviate curse of dimension and how to exploit relationships between and within the feature modalities are still two tough issues. In this paper, we propose a new deep feature fusion framework: hypergraph feature fusion (HFF), to handle these two issues. First, we extract a collection of deep features from multiple images, then HFF constructs a features’ relationships hypergraph (FRH) to reveal relationships among raw features. Then HFF conducts generalized community learning by graph approximation (GCLGA) in FRH to cluster the raw features into k modalities and obtain the inter and intra modalities’ structure matrices. These matrices reveal relationships of inter and intra modalities and can help to build graph kernels in order to optimize kernel based classification. Finally, HFF applies a two level classifier to classify the fused feature vectors. Dimension of each level classifier’s input feature vector is much lower than raw feature vector. We conduct the kernel based classification on two experiments: (1) Using kernel SVM to classify ETH-80 image dataset by fusing 2 kinds of raw image features. (2) Using features extracted from kernel LDA on speech emotion recognition by fusing 6 kinds of raw speech features. The experimental result shows HFF can effectively solve these two issues and improve class-prediction accuracy over state-of-art feature fusion techniques.

Modeling of Multivariable Fuzzy Systems by Semitensor Product

A new fuzzy formulation technique based on semitensor product of matrices is proposed in this paper to construct multivariable fuzzy logic systems. A fuzzy relation matrix (FRM) model is suggested for direct modeling and indirect identification of the fuzzy matrix expression using the observed input–output data of fuzzy dynamical process. The center points of fuzzy sets for every output variable are optimized by using least squares estimation. The effectiveness of the proposed fuzzy formulation technology is verified by simulations. Test results show that the proposed formulation technique is an effective design method to construct and optimize fuzzy relation structure matrices for multivariable fuzzy systems. It can be used to design FRM models for multi-input multi-output systems.

A Bayesian Networks Approach to Estimate Engineering Change Propagation Risk and Duration

An engineering change (EC) is an alteration made to a system that has been released following a system design process. EC propagation is a series of ECs occurring due to dependencies among components of a product. ECs can consume up to 50% of the overall engineering efforts during the development of a complex system. Therefore, EC propagation prediction received considerable attention in past decades as the product development industries started to suffer from the negative impacts of change propagation. This paper evaluates the current approaches to EC propagation prediction and presents a dynamic Bayesian networks (DBNs) approach to estimate change propagation risk (CPR) as well as a novel approach to estimate EC durations. Literature research shows that although some studies have used design structure matrices to estimate CPR and the total redesign duration (TRD) due to change propagation, an approach that allows iteration while accounting for the conjunction of all impacts has not been explored. This paper aims to fill the gaps for calculating CPR using DBN and evaluating change propagation paths from a Split- and task outcome logic, which accounts for the conjunction of all component relationships. This paper compares the proposed method results with the existing CPR and engineering change duration estimation methods using a real-world dataset from a U.S. Navy shipbuilding program. The results indicate that the CPR can be calculated using the proposed method without the shortcomings of the existing method and the accuracy for estimating engineering change durations is increased.

Self-supporting, eutectic-like, nanoporous biphase bismuth-tin film for high-performance magnesium storage

Magnesium ion batteries are emerging as promising alternatives to lithium ion batteries because of their advantages including high energy density, dendrite-free features and low cost. Nevertheless, one of the major challenges for magnesium ion batteries is the kinetically sluggish magnesium insertion/extraction and diffusion in electrode materials. Aiming at this issue, biphase eutectic-like bismuth-tin film is designed herein to construct a self-supporting anode with interdigitated phase distribution and hierarchically porous structure, and further fabricated by a facile one-step magnetron cosputtering route. As benchmarked with single-phase bismuth or tin film, the biphase bismuth-tin film delivers high specific capacity (538 mAh/g at 50 mA/g), excellent rate performance (417 mAh/g at 1,000 mA/g) and good cycling stability (233 mAh/g at the 200th cycle). The superior magnesium storage performance of the sputtered bismuth-tin film could be attributed to the synergetic effect of the interdigitated bismuth/tin phase distribution, hierarchically porous structure and biphase buffering matrices, which could increase ionic transport channels, shorten diffusion lengths and reduce total volume changes.

The emergent structures in digital engineering work: what can we learn from dynamic DSMs of near-identical systems design projects?

Design structure matrices (DSMs) are widely known for their ability to support engineers in the management of dependencies across product and organisational architectures. Recent work in the field has exploited product lifecycle management systems to generate DSMs via the co-occurrence of edits to engineering files. These are referred to as dynamic DSMs and results have demonstrated both the efficacy and accuracy of dynamic DSMs in representing engineering work and emergent product architectures. The wide-ranging applicability of the theoretical model and associated analytical process to generate dynamic DSMs enables investigations into the evolving structures within digital engineering work. This paper uses this new capability and presents the results of the world’s first comparison of dynamic DSMs from a set of near-identical systems design projects. Through comparison of the dynamic DSMs’ end-of-project state, change propagation characteristics and evolutionary behaviour, 10 emergent structures are elicited. These emergent structures are considered in the context of team performance and design intent in order to explain and code the identified structures. The significance of these structures for the management of future systems design projects in terms of productivity and efficacy is also described.

Set Stabilization of Probabilistic Boolean Networks Using Pinning Control.

Probabilistic Boolean network (PBN) is a kind of stochastic logical system in which update functions are randomly selected from a set of candidate Boolean functions according to a prescribed probability distribution at each time step. In this brief, a pinning controller design algorithm is proposed to set stabilize any PBN with probability one. First, an algorithm is given to change the columns of its transition matrix. Then, according to the newly obtained transition matrix, a fraction of nodes can be selected as pinning nodes to inject control inputs to achieve set stabilization. The problem is challenging since the Boolean functions in a PBN are not deterministic but are randomly chosen among several Boolean functions. Furthermore, the structure matrices of the pinning controllers are given by solving some logical matrices equations based on which a pinning controller design algorithm is provided to set stabilize the PBN with probability one. Finally, the theoretical results are validated using several examples.

On the solutions to the Witten–Dijkgraaf–Verlinde–Verlinde associativity equations and their algebraic properties

In this Letter I devise an algebraically feasible approach to investigating solutions to the oriented associativity equations, related with commutative and isoassociative algebras, interesting for applications in the quantum deformation theory and in some other fields of mathematics. The construction is based on a version of the Adler–Kostant–Symes scheme, applied to the Lie algebra of the loop diffeomorphism group of a torus and modified for the case of the Gauss–Manin displacement equations, depending on a spectral parameter. Their interpretation as characteristic equations for some system of the Lax–Sato type vector field equations made it possible to derive the determining separated Hamiltonian evolution equations for the related structure matrices, generating commutative and isoassociative algebras under regard.

One Layer Nonlinear Economic Closed-Loop Generalized Predictive Control for a Wastewater Treatment Plant

The main scope of this paper is the proposal of a new single layer Nonlinear Economic Closed-Loop Generalized Predictive Control (NECLGPC) as an efficient advanced control technique for improving economics in the operation of nonlinear plants. Instead of the classic dual-mode MPC (model predictive controller) schemes, where the terminal control law defined in the terminal region is obtained offline solving a linear quadratic regulator problem, here the terminal control law in the NECLGPC is determined online by an unconstrained Nonlinear Generalized Predictive Control (NGPC). In order to make the optimization problem more tractable two considerations have been made in the present work. Firstly, the prediction model consisting of a nonlinear phenomenological model of the plant is expressed with linear structure and state dependent matrices. Secondly, instead of including the nonlinear economic cost in the objective function, an approximation of the reduced gradient of the economic function is used. These assumptions allow us to design an economic unconstrained nonlinear GPC analytically and to state the NECLGPC allow for the design of an economic problem as a QP (Quadratic Programing) problem each sampling time. Four controllers based on GPC that differ in designs and structures are compared with the proposed control technique in terms of process performance and energy costs. Particularly, the methodology is implemented in the N-Removal process of a Wastewater Treatment Plant (WWTP) and the results prove the efficiency of the method and that it can be used profitably in practical cases.

Porous Aluminum Oxide and Magnesium Oxide Films Using Organic Hydrogels as Structure Matrices.

We describe the synthesis of mesoporous Al2O3 and MgO layers on silicon wafer substrates by using poly(dimethylacrylamide) hydrogels as porogenic matrices. Hydrogel films are prepared by spreading the polymer through spin-coating, followed by photo-cross-linking and anchoring to the substrate surface. The metal oxides are obtained by swelling the hydrogels in the respective metal nitrate solutions and subsequent thermal conversion. Combustion of the hydrogel results in mesoporous metal oxide layers with thicknesses in the μm range and high specific surface areas up to 558 m2∙g−1. Materials are characterized by SEM, FIB ablation, EDX, and Kr physisorption porosimetry.

Organic Polymers as Porogenic Structure Matrices for Mesoporous Alumina and Magnesia

Mesoporous alumina and magnesia were prepared using various polymers, poly(ethylene glycol) (PEG), poly(vinyl alcohol) (PVA), poly(N-(2-hydroxypropyl) methacrylamide) (PHPMA), and poly(dimethylacrylamide) (PDMAAm), as porogenic structure matrices. Mesoporous alumina exhibits large Brunauer–Emmett–Teller (BET) surface areas up to 365 m2 g−1, while mesoporous magnesium oxide possesses BET surface areas around 111 m2 g−1. Variation of the polymers has little impact on the structural properties of the products. The calcination of the polymer/metal oxide composite materials benefits from the fact that the polymer decomposition is catalyzed by the freshly formed metal oxide.