Matrix-based Model Research Articles

Population Synthesis by Disaggregating OD Matrices with Time-Progressive Graphs for Agent-based Simulations

In the last decades, a shift from traditional travel demand modeling approaches to more fine-granular agent-based simulations occurred. This transition was supported by technological advances in computation capabilities and research regarding the capture of individual travel behaviors. While agent-based simulations have been well established, Origin-Destination (OD) matrices are still widely adopted, especially since much historical data is available in these formats. Furthermore, defining models with OD matrices requires less input than detailed microsimulation models. OD matrix-based modeling frameworks may be adequate for mostly car-and public transit-oriented traffic models; however, OD matrices fail to capture the interaction between different trips and do not regard the traveler as a central entity for travel decisions. These limits become especially apparent when regarding intermodal trips. Hence, we want to bridge the gap between traditional OD matrix-based travel demand analysis and modern agent-based simulations. We propose to compute realistic activity schedules from OD matrices that we refine with external statistics. The algorithm converts OD matrices into a graph, where each path represents a valid activity schedule. With a modified depth-first search, we extract activity schedules from the graph and assign them to agents. The practicability of the algorithm is demonstrated by a runtime analysis and a case study. The results show that the algorithm computes activity schedules while keeping the original flow from the OD matrices.

Color Image Recovery Using Low-Rank Quaternion Matrix Completion Algorithm.

As a new color image representation tool, quaternion has achieved excellent results in color image processing problems. In this paper, we propose a novel low-rank quaternion matrix completion algorithm to recover missing data of a color image. Motivated by two kinds of low-rank approximation approaches (low-rank decomposition and nuclear norm minimization) in traditional matrix-based methods, we combine the two approaches in our quaternion matrix-based model. Furthermore, the nuclear norm of the quaternion matrix is replaced by the sum of the Frobenius norm of its two low-rank factor quaternion matrices. Based on the relationship between the quaternion matrix and its equivalent complex matrix, the problem eventually is converted from the quaternion number domain to the complex number domain. An alternating minimization method is applied to solve the model. Simulation results on color image recovery show the superior performance and efficiency of the proposed algorithm over some tensor-based and quaternion-based ones.

Ferroptosis-related lncRNA pairs to predict the clinical outcome and molecular characteristics of pancreatic ductal adenocarcinoma.

Ferroptosis is a form of regulated cell death initiated by oxidative perturbations that can be blocked by iron chelators and lipophilic antioxidants, and ferroptosis may be the silver bullet treatment for multiple cancers, including immunotherapy- and chemotherapy-insensitive cancers such as pancreatic ductal adenocarcinoma (PDAC). Numerous studies have noted that long non-coding RNAs (lncRNAs) regulate the biological behaviour of cancer cells by binding to DNA, RNA and protein. However, few studies have reported the role of lncRNAs in ferroptosis processes and the function of ferroptosis-associated lncRNAs. The primary objective of the present study was to identify ferroptosis-related lncRNAs using bioinformatic approaches combined with experimental validation. The second objective was to construct a prognostic model to predict the overall survival of patients with PDAC. The present study identified ferroptosis-related lncRNAs using a bioinformatic approach and validated them in an independent pancreatic cancer cohort from Fudan University Shanghai Cancer Center. The lncRNA SLCO4A1-AS1 was identified as a novel molecule mediating ferroptosis resistance in vitro. A novel algorithm was used to construct a '0 or 1' matrix-based prognosis model, which showed promising diagnostic accuracy for potential clinical translation (area under the curve = 0.89 for the 2-year survival rate). Notably, molecular subtypes classified by the risk scores of the model did not belong to any previously reported subtypes of PDAC. The immune microenvironment, metabolic activities, mutation landscape and ferroptosis sensitivity were significantly distinct between patients with different risk scores. Sensitivity (IC50) to 30 common anticancer drugs was analysed between patients with different risks, and imatinib and axitinib were found to be potential drugs for the treatment of patients with lower risk scores. Overall, we developed an accurate prognostic model based on the expression patterns of ferroptosis lncRNAs, which may contribute greatly to the evaluation of patient prognosis, molecular characteristics and treatment modalities and could be further translated into clinical applications.

Analysis and comparison of flexible mechanisms for parasitic motion principle piezoelectric actuator

This paper compares three flexible mechanisms in parasitic motion principle piezoelectric actuator through analytic calculation and experiment investigation. The flexible mechanism used in piezoelectric actuator can be classified into functional shape type and asymmetrical stiffness type. For comparing the benefits of these two types of flexible mechanisms and their hybrid structure, the relation between the force and displacement of three flexible mechanisms are deduced using matrix-based compliance modeling method. Also, the dynamic model of parasitic motion principle piezoelectric actuator is used to explore the influence of dimension of flexible mechanism. After that, a prototype and above-mentioned three flexible mechanisms are manufactured and tested, and the motion characteristics of prototype with different flexible mechanisms are investigated, including the step length, velocity and load capacity under different driving voltage and driving frequency. Based on experiment results, the advantages of three flexible mechanisms are analyzed, the hybrid flexible mechanism can achieve fast velocity at medium driving frequency, but asymmetrical stiffness flexible mechanism shows greater motion efficiency and better performance under high driving frequency.

Matrix-Based Formulation of Heterogeneous Individual-Based Models of Infectious Diseases: Using SARS Epidemic as a Case Study.

Heterogeneities of individual attributes and behaviors play an important role in the complex process of epidemic spreading. Compared to differential equation-based system dynamical models of infectious disease transmission, individual-based epidemic models exhibit the advantage of providing a more detailed description of realities to capture heterogeneities across a population. However, the higher granularity and resolution of individual-based epidemic models comes with the cost of increased computational complexities, which result in difficulty in formulating individual-based epidemic models with mathematics. Furthermore, it requires great effort to understand and reproduce existing individual-based epidemic models presented by previous researchers. We proposed a mathematical formulation of heterogeneous individual-based epidemic models using matrices. Matrices and vectors were applied to represent individual attributes and behaviors. We derived analytical results from the matrix-based formulations of individual epidemic models, and then designed algorithms to force the computation of matrix-based individual epidemic models. Finally, we used a SARS epidemic control as a case study to verify the matrix-based formulation of heterogeneous individual-based epidemic models.

Milieu matters: An in vitro wound milieu to recapitulate key features of, and probe new insights into, mixed-species bacterial biofilms

Bacterial biofilms are a major cause of delayed wound healing. Consequently, the study of wound biofilms, particularly in host-relevant conditions, has gained importance. Most in vitro studies employ refined laboratory media to study biofilms, representing conditions that are not relevant to the infection state. To mimic the wound milieu, in vitro biofilm studies often incorporate serum or plasma in growth conditions, or employ clot or matrix-based biofilm models. While incorporating serum or plasma alone is a minimalistic approach, the more complex in vitro wound models are technically demanding, and poorly compatible with standard biofilm assays. Based on previous reports of clinical wound fluid composition, we have developed an in vitro wound milieu (IVWM) that includes, in addition to serum (to recapitulate wound fluid), matrix elements and biochemical factors. With Luria-Bertani broth and Fetal Bovine Serum (FBS) for comparison, the IVWM was used to study planktonic growth, biofilm features, and interspecies interactions, of common wound pathogens, Staphylococcus aureus and Pseudomonas aeruginosa. We demonstrate that the IVWM recapitulates widely reported in vivo biofilm features such as biomass formation, metabolic activity, increased antibiotic tolerance, 3D structure, and interspecies interactions for monospecies and mixed-species biofilms. Further, the IVWM is simple to formulate, uses laboratory-grade components, and is compatible with standard biofilm assays. Given this, it holds potential as a tractable approach to study wound biofilms under host-relevant conditions.

Optimal production and maintenance scheduling for a degrading multi-failure modes single-machine production environment

Two important aspects of manufacturing systems are production scheduling and maintenance planning. These aspects are interdependent, but in most research work, this dependency is ignored. This paper proposed an integrated mathematical model for joint production scheduling and maintenance planning for a degrading multi-failure single-machine manufacturing system, in which the machine has discrete deterioration states. The machine is subject to different failure modes. The first failure mode is the machine’s full deterioration, which is detected at the end of a job’s processing, and the other failure mode is random breakdowns, which are detected at the time of failure. Two machine deterioration state-based thresholds are considered, and five different maintenance actions may carry out a replacement, preventive, and corrective perfect or imperfect maintenance. Since the machine’s states’ transitions follow an exponential distribution, a closed-form matrix-based mathematical model with probabilistic input parameters is presented. This paper aims to optimize the total system’s cost, including the maintenance cost, machine energy consumption cost as well as the makespan penalty for exceeding a pre-determined threshold. The proposed model determines the optimal jobs’ sequence as well as the machine’s deterioration state-based thresholds. Due to the complexity of the developed model, a genetic algorithm (GA), simulated annealing (SA) algorithm, and a teaching–learning-based optimization (TLBO) algorithm have been used to solve the presented model. The algorithms are validated using a full enumeration technique, and the model is validated by applying different maintenance strategies. Our results demonstrate the superiority of the GA compared to the other algorithms.

Developing a framework for carbon accounting disclosure strategies: a strategic reference points (SRP) matrix-based analysis

Purpose During the current century, environmental sustainability and waste reduction processes have always been subject to scrutiny in developed societies. Developed communities have gained considerable momentum by investing in environmental infrastructure and integrating corporate performance disclosure and less developed communities are involved with it. Carbon disclosure is one of the aspects of green accounting in “corporate strategies,” especially those operating across the capital market. Adherence to the disclosure of facts can facilitate sustainable development in societies. This study aims to present strategic reference points matrix-based model to develop a framework for carbon disclosure strategies through institutional and stakeholder pressures throughout the capital market. Design/methodology/approach As a case study, by reviewing similar research on carbon disclosure, this study seeks to illustrate various carbon disclosure aspects and strategies in a matrix based on institutional (vertical axis) and stakeholder (horizontal axis) pressures Findings The study attempts to states that carbon disclosure is affected solely by the company because of the presence of agency gaps between external stakeholders and corporate executives. Originality/value However, the firm’s decision to adopt a carbon disclosure strategy depends on the performance of stakeholder pressure (stakeholder salience level) and managers’ perceptions of institutional pressure (institutional pressure centrality level).

Modeling first order additive × additive epistasis improves accuracy of genomic prediction for sclerotinia stem rot resistance in canola.

The fungus Sclerotinia sclerotiorum infects hundreds of plant species including many crops. Resistance to this pathogen in canola (Brassica napus L. subsp. napus) is controlled by numerous quantitative trait loci (QTL). For such polygenic traits, genomic prediction may be useful for breeding as it can capture many QTL at once while also considering nonadditive genetic effects. Here, we test application of common regression models to genomic prediction of S. sclerotiorum resistance in canola in a diverse panel of 218 plants genotyped at 24,634 loci. Disease resistance was scored by infection with an aggressive isolate and monitoring over 3 wk. We found that including first-order additive × additive epistasis in linear mixed models (LMMs) improved accuracy of breeding value estimation between 3 and 40%, depending on method of assessment, and correlation between phenotypes and predicted total genetic values by 14%. Bayesian models performed similarly to or worse than genomic relationship matrix-based models for estimating breeding values or overall phenotypes from genetic values. Bayesian ridge regression, which is most similar to the genomic relationship matrix-based approach in the amount of shrinkage it applies to marker effects, was the most accurate of this family of models. This confirms several studies indicating the highly polygenic nature of sclerotinia stem rot resistance. Overall, our results highlight the use of simple epistasis terms for prediction of breeding values and total genetic values for a complex disease resistance phenotype in canola.

Modeling and analysis of material anisotropy-topology effects of 3D cellular structures fabricated by powder bed fusion additive manufacturing

For lightweight cellular structures fabricated via powder bed fusion additive manufacturing (PBF-AM), both the material anisotropy and the cellular topology design are both important design factors. In this work, a direct stiffness matrix-based analytical modeling approach was employed for the evaluation of material anisotropy-topology effects on three representative 3D cellular structures (auxetic, BCC and octahedral). The established models were verified via experimentation with samples fabricated by EB-PBF using Ti6Al4V as material, using the material anisotropy information established experimentally using single struts with different build orientations (0°, 15°, 30°, 45°, 60°, 75° and 90°). The predicted mechanical properties of the Ti6Al4V cellular structures showed good agreement with experimental results. It was shown that both the strength and elastic modulus anisotropy of the materials affect the strength of the cellular structures, which must be determined based on the topology design. In addition, the material anisotropy-topology effects on cellular structures of varying cellular pattern sizes were also investigated in order to quantify the pattern size effects. It was found that the pattern size effects and the material anisotropy effects can be decoupled during the design of the mechanical properties of these cellular structures.

Block Diagonal Dominance-Based Model Reduction Method Applied to MMC Asymmetric Stability Analysis

Frequency-domain model reduction is a crucial concern in applying the prevailing impedance method for the stability analysis of complex systems, e.g., the modular multilevel converter (MMC). Recently, it has been shown that under symmetric conditions, a 2 × 2 matrix-based impedance model characterizing the two coupled frequencies of MMC are sufficient for its stability analysis. However, when the asymmetry occurs, principally, a much higher number of frequency couplings will appear in the MMC and thereby leads to a significant rise in the model dimension. Enlighted by this issue, there is an urgent need of finding a suitable frequency-domain method that can serve as a general criterion for model reduction. To this end, this article proposes a block diagonal dominance (BDD)-based model reduction method and applied it to the asymmetric MMC. Basically, the BDD can decompose an N-dimensional task to N one-dimensional tasks, via which a significant reduction in model dimension can be realized. It is shown that by properly shifting the impedance model from one domain to another (e.g., α-β domain to d-q domain), the BDD property can be achieved for most asymmetric scenarios. Finally, various case studies considering different asymmetry degrees are conducted to validate the effectiveness of the proposed method.

The Importance of Environmental Variability and Transient Population Dynamics for a Northern Ungulate

The pathways through which environmental variability affects population dynamics remain poorly understood, limiting ecological inference and management actions. Here, we use matrix-based population models to examine the vital rate responses to environmental variability and individual traits, and subsequent transient dynamics of the population in response to the environment. Using Sitka black-tailed deer (Odocoileus hemionus sitkensis) in Southeast Alaska as a study system, we modeled effects of inter-annual process variance of covariates on female survival, pregnancy rate, and fetal rate, and summer and winter fawn survival. To examine the influence of environmental variance on population dynamics, we compared asymptotic and transient perturbation analysis (elasticity analysis, a life-table response experiment, and transience simulation). We found that summer fawn survival was primarily determined by black bear (Ursus americanus) predation and was positively influenced by mass at birth and female sex. Winter fawn survival was determined by malnutrition in deep-snow winters and was influenced by an interaction between date of birth and snow depth, with late-born fawns at greater risk in deep-snow winters. Adult female survival was the most influential vital rate based on classic elasticity analysis, however, elasticity analysis based on process variation indicated that winter and summer fawn survival were most variable and thus most influential to variability in population growth. Transient dynamics produced by non-stable stage distributions produced realized annual growth rates different from predicted asymptotic growth rates in all years, emphasizing the importance of winter perturbations to population dynamics of this species.

Comparative Analysis of Cell-Cell Contact Abundance in Ovarian Carcinoma Cells Cultured in Two- and Three-Dimensional In Vitro Models.

Simple SummaryTumor resistance to therapy is a crucial problem of today’s oncology. The emerging data indicate that tumor microenvironment is the key participant in the resistance development. One of the most basic aspect of tumor microenvironment is intercellular adhesion. Our data obtained using monolayer culture, matrix-free and matrix-based three-dimensional in vitro models indicate that the abundance of cell-cell contact proteins is varying depending on the microenvironment. These differences coincided with the degree of the resistance to therapeutics. The importance of adhesion proteins in tumor resistance may provide the fundamental basis for improving cancer treatment approaches and must be taken into account when screening candidate drugs. Tumor resistance to therapy is associated with the 3D organization and peculiarities of the tumor microenvironment, of which intercellular adhesion is a key participant. In this work, the abundance of contact proteins was compared in SKOV-3 and SKOV-3.ip human ovarian adenocarcinoma cell lines, cultivated in monolayers, tumor spheroids and collagen hydrogels. Three-dimensional models were characterized by extremely low expression of basic molecules of adherens junctions E-cadherin and demonstrated a simultaneous decrease in desmosomal protein desmoglein-2, gap junction protein connexin-43 and tight junction proteins occludin and ZO-1. The reduction in the level of contact proteins was most pronounced in collagen hydrogel, accompanied by significantly increased resistance to treatment with doxorubicin and targeted anticancer toxin DARPin-LoPE. Thus, we suggest that 3D models of ovarian cancer, especially matrix-based models, tend to recapitulate tumor microenvironment and treatment responsiveness to a greater extent than monolayer culture, so they can be used as a highly relevant platform for drug efficiency evaluation.

Comparative Proton and Photon Irradiation Combined with Pharmacological Inhibitors in 3D Pancreatic Cancer Cultures.

Simple SummaryDue to higher precision and consequent sparing of normal tissue, pancreatic cancer patients might profit from proton beam radiotherapy, a treatment modality increasingly used. Since molecular data upon proton irradiation in comparison to standard photon radiotherapy are limited in pancreatic cancer, the aims of our study were to unravel differences in the effectiveness of photon versus proton irradiation and to exploit radiation type-specific molecular changes for radiosensitizing 3D PDAC cell cultures. Although protons showed a slightly higher effectiveness and a stronger induction of molecular alterations than photons, our results revealed a radiation-type independent sensitization of molecular-targeted agents selected according to the discovered molecular, radiation-induced alterations.Pancreatic ductal adenocarcinoma (PDAC) is a highly therapy-resistant tumor entity of unmet needs. Over the last decades, radiotherapy has been considered as an additional treatment modality to surgery and chemotherapy. Owing to radiosensitive abdominal organs, high-precision proton beam radiotherapy has been regarded as superior to photon radiotherapy. To further elucidate the potential of combination therapies, we employed a more physiological 3D, matrix-based cell culture model to assess tumoroid formation capacity after photon and proton irradiation. Additionally, we investigated proton- and photon-irradiation-induced phosphoproteomic changes for identifying clinically exploitable targets. Here, we show that proton irradiation elicits a higher efficacy to reduce 3D PDAC tumoroid formation and a greater extent of phosphoproteome alterations compared with photon irradiation. The targeting of proteins identified in the phosphoproteome that were uniquely altered by protons or photons failed to cause radiation-type-specific radiosensitization. Targeting DNA repair proteins associated with non-homologous endjoining, however, revealed a strong radiosensitizing potential independent of the radiation type. In conclusion, our findings suggest proton irradiation to be potentially more effective in PDAC than photons without additional efficacy when combined with DNA repair inhibitors.

Incremental fuzzy probability decision-theoretic approaches to dynamic three-way approximations

As a special model of three-way decision, three-way approximations in the fuzzy probability space can be interpreted, represented, and implemented as dividing the universe into three pair-wise disjoint regions, i.e., the positive, negative and boundary regions, which are transformed from the fuzzy membership grades with respect to the fuzzy concept. To consider the temporality and uncertainty of data simultaneously, this paper focuses on the integration of dynamics and fuzziness in the context of three-way approximations. We analyze and investigate three types of fuzzy conditional probability functions based on the fuzzy T-norm operators. Besides, we introduce the matrix-based fuzzy probability decision-theoretic models to dynamic three-way approximations based on the principle of least cost. Subsequently, to solve the time-consuming computational problem, we design the incremental algorithms by the updating strategies of matrices when the attributes evolve over time. Finally, a series of comparative experiments is reported to demonstrate and verify the performance of proposed models.

Design, analysis, and testing of a novel 2-DOF vibration-assisted polishing device driven by the piezoelectric actuators

In order to increase surface quality and material removal efficiency, a 2-DOF vibration-assisted polishing device driven by piezoelectric actuators (PZTs) was developed. The matrix-based compliance modeling (MCM) method was used to calculate stiffness, and Lagrange’s method was used to analyze the natural frequency of the device. To make the 2-DOF vibration-assisted polishing device achieve better performance, the dimensions of the device were optimized by the Whale optimization algorithm (WOA). Meanwhile, FEA was used in simulation and analysis of the device. The open-loop testing results show that the 2-DOF vibration-assisted polishing device has the characteristics of large stroke and high resolution. The polishing experimental results show that vibration-assisted polishing can improve the surface quality and material removal rate.

Estimating the number of usability problems affecting medical devices: modelling the discovery matrix

BackgroundUsability testing of medical devices are mandatory for market access. The testings’ goal is to identify usability problems that could cause harm to the user or limit the device’s effectiveness. In practice, human factor engineers study participants under actual conditions of use and list the problems encountered. This results in a binary discovery matrix in which each row corresponds to a participant, and each column corresponds to a usability problem. One of the main challenges in usability testing is estimating the total number of problems, in order to assess the completeness of the discovery process. Today’s margin-based methods fit the column sums to a binomial model of problem detection. However, the discovery matrix actually observed is truncated because of undiscovered problems, which corresponds to fitting the marginal sums without the zeros. Margin-based methods fail to overcome the bias related to truncation of the matrix. The objective of the present study was to develop and test a matrix-based method for estimating the total number of usability problems.MethodsThe matrix-based model was based on the full discovery matrix (including unobserved columns) and not solely on a summary of the data (e.g. the margins). This model also circumvents a drawback of margin-based methods by simultaneously estimating the model’s parameters and the total number of problems. Furthermore, the matrix-based method takes account of a heterogeneous probability of detection, which reflects a real-life setting. As suggested in the usability literature, we assumed that the probability of detection had a logit-normal distribution.ResultsWe assessed the matrix-based method’s performance in a range of settings reflecting real-life usability testing and with heterogeneous probabilities of problem detection. In our simulations, the matrix-based method improved the estimation of the number of problems (in terms of bias, consistency, and coverage probability) in a wide range of settings. We also applied our method to five real datasets from usability testing.ConclusionsEstimation models (and particularly matrix-based models) are of value in estimating and monitoring the detection process during usability testing. Matrix-based models have a solid mathematical grounding and, with a view to facilitating the decision-making process for both regulators and device manufacturers, should be incorporated into current standards.

The kinematics solving algorithm of single-axis polishing machine

The traditional single-axis polishing machine has simple structure and high processing efficiency, and can efficiently polish optical elements such as flat or spherical surfaces. By introducing an active polishing head to a single-axis machine and changing the manual linear translation axis to a servo motor automatically controlled one, and then a CNC single-axis polishing machine is formed to achieve automatic smoothing processing or annular error correction of the mirror surface. Based on the mechanical structure of the single-axis machine and the geometric relationship between the processing body and the moving body, this manuscript employs the matrix-based model method of the serial robot to build the relationship between the coordinates of the linear translation axis and the polishing ring radius of the mirror during the processing. The model is used to build a single-axis machine position calculation algorithm, which establishes the basis for precise position control of single-axis machine.

Matrix-based network heat transfer modeling approach and its application in thermal system analysis

Different from the mature network modeling and analysis method of power systems, the traditional modeling approach of thermal systems is still confined to stacking nonlinear constraints of components and linear temperature relations among components, which brings great inconvenience to the holistic analysis for the attractive integrated power and thermal systems. This paper proposes a matrix-based network heat transfer modeling approach for thermal system, which establishes general matrix description of topologic relations and heat transfer constraints of components to the holistic. These matrices derive the system governing equations based on the node-listing method in electrical network theory, and the conditions of determining solution are further discussed by applying the graph theory. Meanwhile, the governing equations of the proposed modeling approach coincide with those obtained by the heat current modeling approach, which originates from the same essence in forming the analysis of topology of heat flows by combining the analysis of topology of fluid flows and heat transfer between fluids based on a redefined thermal resistance. Due to both the strictly logical generating step and the linear matrix forms of governing equations, the proposed modeling approach benefits the standardized modeling of complex thermal system automatically to avoid human errors.

Probabilistic Analysis of Domino Effects by Using a Matrix-Based Simulation Approach.

Major industrial accidents occurring at so-called major hazard installations may cause domino accidents which are among the most destructive industrial accidents existing at present. As there may be many hazard installations in an area, a primary accident scenario may potentially propagate from one installation to another, and correlations exist in probability calculations of domino effects. In addition, during the propagation of a domino effect, accidents of diverse types may occur, some of them having a synergistic effect, while others do not. These characteristics make the analytical formulation of domino accidents very complex. In this work, a simple matrix-based modeling approach for domino effect analysis is proposed. Matrices can be used to represent the mutual influences of different escalation vectors between installations. On this basis, an analysis approach for accident propagation as well as a simulation-based algorithm for probability calculation of accidents and accident levels is provided. The applicability and flexibility of this approach is discussed while applying it to estimate domino probabilities in a case study.