Matrix-based Model Research Articles

Parasites and the ecology of fear: Nonconsumptive effects of ectoparasites on larvae reduce growth in simulated Drosophila populations.

Predators negatively affect prey outside of direct attack, and these nonconsumptive effects (NCEs) may cause over half the impacts of predators on prey populations. This "ecology of fear" framework has been extended to host-parasite interactions. The NCEs of parasites are thought to be small relative to those of predators. However, recent research shows ectoparasites exert NCEs on multiple life stages of Drosophila. In this study, we apply recent data to a matrix-based model of fly populations experiencing infection/consumption and NCEs from an ectoparasitic mite. We found the NCEs of parasites on larvae, which are not actively parasitized, decreased the size of simulated host populations. By contrast, the NCEs on adult flies increased population size through compensatory egg production. The negative NCEs on larvae outweighed the positive effects on adults to reduce population size. This study suggests that parasitic NCEs can suppress host populations independent of infection.

Photo-Cross-linked Gelatin Methacryloyl Hydrogels Enable the Growth of Primary Human Endometrial Stromal Cells and Epithelial Gland Organoids.

In vitro three-dimensional (3D) models are better able to replicate the complexity of real organs and tissues than 2D monolayer models. The human endometrium, the inner lining of the uterus, undergoes complex changes during the menstrual cycle and pregnancy. These changes occur in response to steroid hormone fluctuations and elicit crosstalk between the epithelial and stromal cell compartments, and dysregulations are associated with a variety of pregnancy disorders. Despite the importance of the endometrium in embryo implantation and pregnancy establishment, there is a lack of in vitro models that recapitulate tissue structure and function and as such a growing demand for extracellular matrix hydrogels that can support 3D cell culture. To be physiologically relevant, an in vitro model requires mechanical and biochemical cues that mimic those of the ECM found in the native tissue. We report a semisynthetic gelatin methacryloyl (GelMA) hydrogel that combines the bioactive properties of natural hydrogels with the tunability and reproducibility of synthetic materials. We then describe a simple protocol whereby cells can quickly be encapsulated in GelMA hydrogels. We investigate the suitability of GelMA hydrogel to support the development of an endometrial model by culturing the main endometrial cell types: stromal cells and epithelial cells. We also demonstrate how the mechanical and biochemical properties of GelMA hydrogels can be tailored to support the growth and maintenance of epithelial gland organoids that emerge upon 3D culturing of primary endometrial epithelial progenitor cells in a defined chemical medium. We furthermore demonstrate the ability of GelMA hydrogels to support the viability of stromal cells and their function measured by monitoring decidualization in response to steroid hormones. This study describes the first steps toward the development of a hydrogel matrix-based model that recapitulates the structure and function of the native endometrium and could support applications in understanding reproductive failure.

Rank Matrix Approach for Endometriosis: Integrating Data and Constructing Diagnostic Models

Background: Endometriosis is a debilitating gynecological disorder characterized by chronic pain, infertility, and the growth of endometrial tissue outside the uterus. Accurate and early detection of this condition is crucial for effective management and treatment. Methods: We developed a gene rank matrix-based model to integrate endometriosis cohorts across multiple platforms. After removing batch effects, we identified 83 genes associated with endometriosis and further refined a diagnostic model using 11 of these genes. The model was trained on two platforms and validated on two others using SVM, Random Forest, Logistic Regression, and gradient-boosting machine learning algorithms. Results: The integration via the gene rank matrix effectively mitigated batch effects. Utilizing a gradient boosting classifier with a subset of 11 genes, the model demonstrated commendable diagnostic efficacy, achieving an Area Under the Curve (AUC) of 0.77, an accuracy of 0.72, and an F1 score of 0.72 for the training dataset. When subjected to validation, the model maintained its performance, yielding an AUC of 0.769, an accuracy of 0.719, and an F1 score of 0.732. These 11 genes were found to be associated with immunosuppression. Conclusion: Our approach to integrating gene rank matrices effectively consolidates endometriosis data across diverse platforms. The diagnostic model, harnessing the predictive power of 11 specific genes, surpasses alternative models, thereby offering promising prospects for aiding clinical diagnosis of endometriosis. Further validation is imperative to elucidate the functional significance of these 11 genes. Our study underscores the potential of data integration coupled with machine learning techniques in advancing the diagnosis of intricate diseases, such as endometriosis.

Mueller matrix-based calculation model for extracting polarization parameters in full-wave simulation of all-dielectric Pancharatnam–Berry (PB)-phase metasurfaces

In this study, the Mueller matrix of all-dielectric Pancharatnam–Berry (PB)-phase metasurfaces was retrieved using finite-difference time-domain (FDTD) simulation, Stokes–Mueller calculus, and Lu–Chipman decomposition. The polarization properties are discussed for nanofin-shaped PB-phase metasurfaces made of GaN and Nb2O5 and L-shaped PB-phase metasurfaces made of GaN. The results show that both the nanofin-shaped and L-shaped PB-phase GaN metasurfaces are optically equivalent to a linear-diattenuating retarder, and the nanofin-shaped PB-phase Nb2O5 metasurface is optically equivalent to a linear phase retarder. The PB-phase GaN metasurface exhibits stronger diattenuation and lower transmittance than the Nb2O5 metasurface due to the inherent defect absorption in the visible range. With a similar refractive index but barely any absorption, Nb2O5 is a more suitable material for PB-phase metasurfaces in the visible range than GaN.

Compound Matrix-Based Project Database (CMPD)

The impact of projects is vital, from business operations to research to the national economy. Therefore, management science and operation research have extensively studied project scheduling and resource allocation for over six decades. Project databases were proposed to test algorithms, including simulated or real, single or multiprojects, and single-mode or multi-mode projects. However, the dozens of project databases are extremely heterogeneous regarding the file structure and the features of the modeled projects. Furthermore, the efficiency and performance of project scheduling and resource allocation algorithms are susceptible to the characteristics of projects. Therefore, the proposed Compound Matrix-Based Project Database (CMPD) collects and consolidates the most frequently used project databases. The proposed Unified Matrix-Based Project-Planning Model (UMP) sparse matrix-based model enables the addition of new features to existing project structures, such as completion priorities, structural flexibility, and quality parameters, to broaden the scope of considered projects and to take account of flexible approaches, such as agile, extreme, and hybrid projects.

Estimating the optimal duration of random loading as part of machine part durability research

Aim. Making an informed decision regarding the durability of machine parts requires information on the operational load that needs to be measured on a representative section of the track. It should not be too long as well. Thus, it is required to determine the optimal duration of implementation. The duration of implementation that is optimal in terms of the reliability of load registration is defined for a process that is stationary in a special sense. Stationarity in a special sense is defined specifically for the task of assessing the durability of a specific part. Methods. The use of spectral theory for the study of random processes is probably not the best way of examining non-stationary loading processes in the context of durability assessment. We believe it would be optimal to use a cycle counting procedure (rain flow method) with subsequent calculation of durability. A lemma and a theorem were formulated on the sufficient duration of implementation for a process that is stationary in a special sense. A sufficient duration of implementation is defined as a limit past which its increase will not lead to a noticeable change in the calculated durability. Results. The matters of stationarity of a process in a narrow sense and the required duration of implementation will help in planning operational tests to measure and record random processes of machine part loading. Both matters were examined in terms of fatigue damage accumulation using Miner linear damage rule, as well as the adjusted linear damage summation hypothesis taking into account the fatigue curve slope parameter m. Some practical engineering problems were examined, including the problem of the optimal duration of implementation of a mining machine whose loading process is characterized by a high degree of irregularity and the problem of finding the required duration of implementation of load recording in a rolling stock component. Conclusion. A theorem on the required and sufficient duration of implementation was formulated. In order to test the method, Markov transition matrix-based model processes were used. In addition, the method and theorem were tested using examples of some experimental processes obtained from operational tests of vehicles and production machines.

Matrix-based predictive model of residual drift and analytical resilience design approach for self-centering columns

Residual displacement serves as a crucial indicator in evaluating the safety and reparability of structures following seismic events. As a novel self-centering structure, the unbonded prestressed reinforced concrete (UBPRC) column has demonstrated its effectiveness in reducing residual displacement. However, there remains a lack of quantitative research concerning the influence of various structural and material parameters on residual displacement. For the quick and convenient evaluation of the seismic performance and resilience of UBPRC columns, in this paper, the influence of various parameters on the residual drift ratio of UBPRC columns was investigated by establishing a logarithmic linear relationship between the parameters and the residual drift ratio. These parameters include the longitudinal reinforcement and concrete strength (fy and fc), reinforcement ratio of longitudinal and transverse (ρl and ρs), prestressed strand ratio (ρp), aspect ratio (Ar), axial load ratio (αc), and prestressing force ratio (αps). Among the two parameters related to prestressed strands, increasing the prestressing force ratio significantly reduces RDr, while the influence of the prestressed strand ratio on RDr is relatively small. On this basis, a matrix-based probabilistic predictive model for the residual drift ratio was established. According to various physical parameters, the proposed mathematical model accurately predicts the residual drift ratio and describes the influence of each parameter on it. Furthermore, an analytical resilience design approach was proposed, and an analytical expression in matrix form for a multi-parameter resilience design was derived. Lastly, the impact of parameters on the damage state was investigated, and the range of parameter values under investigation was established, according to the analytical resilience design approach.

Tensor-Based Forward–Backward Algorithms in the Physics-Informed Coupled Hidden Markov Model

Imposing data-driven with physical laws for user activity prediction could effectively solve various physical problems such as smart care, surveillance and human-robot. In the growing field of artificial intelligence, the application of activity prediction based on physical Coupled Hidden Markov Model (CHMM) and tensor theory with physical properties has attracted increasing attentions. However, existing CHMMs usually only consider the time-series characteristic of data, while ignoring physical characteristics of user activity such as periodicity, timing and correlation. Moreover, they are all matrix-based models, which could not holistically analyze the dependencies among physical states. The above disadvantages lead to lower prediction accuracy of CHMM. To remove these disadvantages, three physics-informed tensor-based CHMMs are first constructed by incorporating prior physical knowledge. Then the corresponding forward-backward algorithms are designed for resolving the evaluation problem of CHMM. These algorithms could overall model multiple physical features by imposing physics and prior knowledge into CHMM during training to improve the precision of probabilistic computing. The algorithms reduce the dependence of the model on training data by adding physical features. Finally, the comparative experiments show that our algorithms have better performances than existing prediction methods in precision and efficiency. In addition, further selfcomparison experiments verify that our algorithms are effective and practical.

Development of a maturity model to assess the FAIRness of architectural data in Switzerland

This research carries out an in-depth assessment of the application of the FAIR (Findable, Accessible, Interoperable and Reusable) principles by the Swiss scientific community specialized in architecture, and consequently its positioning in the context of open science. The FAIR maturity assessment of research data is based on the use of maturity models. They provide a structured framework for implementing and improving data management practices. Our methodology involved a careful comparison of six existing maturity models and their alignment with the FAIR principles. This ensured a relevant and appropriate selection of evaluation criteria for own model. Developing straightforward criteria that can be applied in real-world scenarios is a key aspect of our approach. Inspired by the FAIR principles, we formulated our matrix-based maturity model, the Architectural Maturity Model (AMM). The goal of the AMM is to improve the understanding of metrics using a question-answer approach. We then applied the AMM to evaluate selected datasets stored in the Zenodo and ETH Research Collection repositories to assess the FAIRness of architectural research data.
 The results show that architectural data are findable and accessible, but that they not very interoperable and can be reused only with limitations. To improve the FAIRness of architectural research data we recommend data producers to prioritize licences without restriction (e.g. CC0) and open formats. We also encourage researchers to discuss with their data stewards how to use controlled vocabularies to improve the visibility of their data on digital platforms.

A Method to Compute Frequency Domain Models Based on Direction-Dependent Derivative of the Variation of Voltage and Current Phasors

Harmonic pollution and other potential problems are increasing due to the rising demand for Power Electronic devices in low-voltage distribution systems. The adequate modeling of the harmonic characteristics of these devices is essential for assessing their impact. Frequency Domain Models (FDMs) are based on either matrix or tensor definitions, and different methods have been proposed to compute those models' parameters. This paper proposes a method to compute matrix or tensor-based FDMs by exploiting the nonholomorphic properties of complex functions. Thus, the direction-dependent derivative of the variation of voltage-current phasors is optimized over measurements set. By proving that tensor and matrix-based models are equivalent, it is guaranteed that the method can be applied to compute both models. The Proposed and Tensorial Parametrization methods are compared using the power of the error signal as a percentage of the power of the current signal achieving a one-digit reduction in a proportion of 4:1.

Leveraging pleat folds and soft compliant elements in inflatable fabric beams.

Inflatable fabric beams (IFBs) integrating pleat folds can generate complex motion by modifying the pleat characteristics (e.g., dimensions, orientations). However, the capability of the IFB to return to the folded configuration relies upon the elasticity of the fabrics, requiring additional pressure inputs or complementary mechanisms. Using soft compliant elements (SCEs) assembled onto pleat folds is an appealing approach to improving the IFB elasticity and providing a range of spatial configurations when pressurized. This study introduces an actuator comprising an IFB with pleat folds and SCEs. By methodologically assembling the SCEs onto the pleat folds, we constrain the IFB unfolding to achieve out-of-plane motion at 5 kPa. Besides, the proposed actuator can generate angular displacement by regulating the input pressure ( 5 kPa). A matrix-based representation and model are proposed to analyze the actuator motion. We experimentally study the actuator's angular displacement by modifying SCE shapes, fold dimensions, and assembly distances of SCEs. Moreover, we analyze the effects of incorporating two SCEs onto a pleat fold. Our results show that the actuator motion can be tuned by integrating SCEs with different stiffness and varying the pleat fold dimensions. In addition, we demonstrate that the integration of two SCEs onto the pleat fold permits the actuator to return to its folded configuration when depressurized. In order to demonstrate the versatility of the proposed actuator, we devise and conduct experiments showcasing the implementation of a planar serial manipulator and a soft gripper with two grasping modalities.

A green electrical matrix-based model for the energy transition: Maine, USA case example

Nowadays, climate change is a major global societal challenge that significantly increases environmental stress. Most international organizations and policies have promoted initiatives to minimize emissions, reduce fossil fuel dependence and increase renewable energy resource integration into different sectors. An energy transformation towards more renewable systems is thus a priority. Under this scenario, the present paper describes and evaluates an alternative energy conversion matrix-based model to combine sector electrification, power generation units from renewables, and new clean technologies. The proposed green matrix-based model allows analyzing future scenarios, including electricity participation in end-use consumption and electric power generated by renewables – potentially integrated into different sectors –. The proposed model is evaluated in the state of Maine (United States). This case study is focused on decarbonizing both residential heating and transport sector through the integration of large offshore wind power plant. Results and discussion is also included in the paper, providing expected energy demand reductions and decreasing emissions through the integration of renewables. This energy transition integration case study is proposed in three road-maps with different penetration rates and time scales. The proposed green matrix-based model can be also applied to other areas and energy resources, as an alternative way to analyze and estimate renewable integration into different sectors.

Heterogeneous Regularization-Based Tensor Subspace Clustering for Hyperspectral Band Selection.

Band selection (BS) reduces effectively the spectral dimension of a hyperspectral image (HSI) by selecting relatively few representative bands, which allows efficient processing in subsequent tasks. Existing unsupervised BS methods based on subspace clustering are built on matrix-based models, where each band is reshaped as a vector. They encode the correlation of data only in the spectral mode (dimension) and neglect strong correlations between different modes, i.e., spatial modes and spectral mode. Another issue is that the subspace representation of bands is performed in the raw data space, where the dimension is often excessively high, resulting in a less efficient and less robust performance. To address these issues, in this article, we propose a tensor-based subspace clustering model for hyperspectral BS. Our model is developed on the well-known Tucker decomposition. The three factor matrices and a core tensor in our model encode jointly the multimode correlations of HSI, avoiding effectively to destroy the tensor structure and information loss. In addition, we propose well-motivated heterogeneous regularizations (HRs) on the factor matrices by taking into account the important local and global properties of HSI along three dimensions, which facilitates the learning of the intrinsic cluster structure of bands in the low-dimensional subspaces. Instead of learning the correlations of bands in the original domain, a common way for the matrix-based models, our model learns naturally the band correlations in a low-dimensional latent feature space, which is derived by the projections of two factor matrices associated with spatial dimensions, leading to a computationally efficient model. More importantly, the latent feature space is learned in a unified framework. We also develop an efficient algorithm to solve the resulting model. Experimental results on benchmark datasets demonstrate that our model yields improved performance compared to the state-of-the-art.

Development and characterisation of suitably bioengineered microfibrillar matrix-based 3D prostate cancer model for in vitro drug testing

Bioengineered 3D models that can mimic patient-specific pathologies in vitro are valuable tools for developing and validating anticancer therapeutics. In this study, microfibrillar matrices with unique structural and functional properties were fabricated as 3D spherical and disc-shaped scaffolds with highly interconnected pores and the potential of the newly developed scaffolds for developing prostate cancer model has been investigated. The newly developed scaffolds showed improved cell retention upon seeding with cancer cells compared to conventional electrospun scaffolds. They facilitated rapid growth and deposition of cancer-specific extracellular matrix through-the-thickness of the scaffold. Compared to the prostate cancer cells grown in 2D culture, the newly developed prostate cancer model showed increased resistance to the chemodrug Docetaxel regardless of the drug concentration or the treatment frequency. A significant reduction in the cell number was observed within one week after the drug treatment in the 2D culture for both PC3 and patient-derived cells. Interestingly, almost 20%–30% of the cancer cells in the newly developed 3D model survived the drug treatment, and the patient-derived cells were more resistant than the tested cell line PC3. The results from this study indicate the potential of the newly developed prostate cancer model for in vitro drug testing.

Geometrically nonlinear analysis of compliant mechanisms using a dynamic beam constraint model (DBCM)

Compliant mechanisms with intermediate-deformation ranges are increasingly applied in large-stroke precision manipulators and other actuators. The nonlinearities of axially-loaded stiffening and kinematics-arching effects (P-Δ effects) have a pronounced influence on the kinetostatic and dynamic behaviors of such a class of compliant mechanisms. A dynamic beam constraint model (DBCM) with the pseudo-static characteristic is reported for the nonlinear kinetostatics and large-amplitude vibration analyses of intermediate-deformation compliant mechanisms. Firstly, the DBCM of flexure beams is derived in a closed-form equation on the frequency domain, including the P-Δ effects. A matrix-based modeling methodology with a step-by-step iteration procedure is then introduced to calculate the nonlinear performance of general planar compliant mechanisms with serial-parallel configurations avoiding inner force analysis and kinematics calculation. Except for the static constraint behaviors in the BCM, the amplitude-dependent resonance frequency is captured with the DBCM. Theoretical, numerical and experimental comparisons for a double parallel guiding flexure pivot and Scott-Russell compliant amplifying mechanism verify the feasibility of the DBCM. In summary, the DBCM enables both the nonlinear kinetostatics and large-amplitude vibration analyses of moderately large-stroke compliant mechanisms in a straightforward way.

Graph Database and Matrix-Based Intelligent Generation of the Assembly Sequence of Prefabricated Building Components

The assembly of prefabricated components is a critical process in prefabricated building construction, influencing both progress and accuracy. However, the assembly sequence planning and optimization (ASPO) of prefabricated components have yet to receive sufficient attention from researchers, and current research has displayed limited automation and poor generalization capabilities. Therefore, this paper proposes a framework for intelligently generating assembly sequences for prefabricated components based on graph databases and matrices. The framework utilizes an adjacency matrix and interference matrix-based modeling method to comprehensively describe the connections and constraint relationships between components, enabling better evaluation of assembly difficulty during optimization. The graph database serves as the central hub for data exchange, facilitating component information storage, automatic querying, and summarization. The obtained assembly sequence and progress plan are fed back into the graph database. To accomplish assembly sequence optimization, a genetic algorithm based on the double-elite strategy is employed. Furthermore, the effectiveness of the proposed framework is validated through an actual engineering case. The results demonstrate that the framework can effectively find an optimal assembly sequence to mitigate the assembly challenge of a prefabricated building.

Jacobian linear regression and Tate Bryant Euler angle enabled autonomous vehicle LiFi communication sustained IOT

Artificial Intelligence (AI) and the constant paradigm shift in road traffic have led to a need for significant improvement in road safety to minimize traffic accidents. LiFi helps minimize accidents by transmitting data between multiple vehicles (i.e. Vehicle-to-Vehicle (V2V)) and between vehicles and infrastructure (i.e. Vehicle-to-Infrastructure (V2I)) without interference. LiFi uses light to transmit data between devices or vehicles, which ensures efficient data transmission speed and is therefore considered a safe technology. A method called Deep Jacobian Regression and Tate Bryant Euler Recommendation (DJR-TBER) is proposed in this paper based on V2V and V2I autonomous vehicle communication. The proposed method DJR-TBER consists of an input layer, four hidden layers and finally an output layer. Sensors are first used to obtain the information. A linear regression-based speed evaluation model is developed and followed by a Jacobi matrix-based distance evaluation model in the hidden layer. The third hidden layer by developing a distance evaluation model. The use of Laplacian function ensures secure V2I communication for the autonomous vehicle. Finally, a Tate-Bryant-Euler angle-based model for emergency handling is proposed in the hidden layer to optimally consider the aspect of braking in emergency situations and thus increase driving safety.

A novel transfer matrix-based method for steady-state modeling and analysis of thermal systems

Performance analysis and optimization of thermal systems are unprecedentedly crucial in pursuing higher energy efficiency. However, the precise modeling and high-efficiency calculation of modern, complex thermal systems are still challenging. Here we present a transfer matrix-based system modeling method to tackle these challenges. The transfer matrix of heat exchangers is defined to describe the temperature mapping relation between inlet and outlet nodes. Heat-work conversion devices are described by the working fluid temperature variation. The system modeling follows a three-step procedure: (1) building system transfer matrix by aggregating component models; (2) separate given and unknown node temperatures by removing redundant rows and columns in the system transfer matrix; (3) rearrange the reduced system transfer matrix to calculate internal and outlet node temperatures. The constructed system model does not introduce unnecessary simplifications and describes the system’s nonlinearity accurately. The proposed modeling method is first presented and validated on a parallel-series and a multi-loop heat exchanger network. Numerical results with both constant and varying fluid properties confirm the method’s validity. Case studies on three thermodynamic systems further validate the method’s capability and efficiency. The proposed method is finally compared with conventional modeling methods and heat current method to highlight its features and advantages.

Design and analysis of a 2-DOF compliant serial micropositioner based on "S-shaped" flexure hinge

A serial 2D planar compliant mechanism has been proposed based on novel "S-shaped" flexure hinges for atomic force microscopy applications. The bridge-lever type mechanism driven by piezoelectric actuators serves as a displacement amplifier. The optimal geometrical parameters were found to maximize the workspace and natural frequency through the Monte-Carlo search algorithm. Also, the performance of the developed system was investigated by Matrix-based Compliance Modeling (MCM), Finite Element Analysis (FEA), and experiments. All models indicate that the mechanism has an approximately linear force-deflection relationship, high safety factor, and a reasonable amplification ratio of about 4.5 and 5.5 for the inner and outer stages in the analytical approach, 4.4 and 5.3 in FEA. Finally, experiments on a fabricated open-loop controlled prototype revealed 4.2 and 5.1 amplification ratio for stages that resulted in a 94 × 124 μm rectangular workspace and a natural frequency of 224.6 Hz, which is about 5% lower than the results predicted using FEA.

A novel hollow-type XY piezoelectric positioning platform

To enhance space efficiency and reduce the planar dimensions of the piezoelectric platform, propose an innovative three-stage flexible lever hollow XY piezoelectric platform powered by piezoelectric stack. This paper details the platform's design configuration and operational principles. Analyze and optimize the platform's static and dynamic characteristics using matrix-based compliance modeling and finite element methods. The platform measures 39 mm × 39 mm × 40 mm with a hollow diameter of 29 mm × 29 mm × 40 mm and weighs 60.12 g. An array of experiments was performed to evaluate the prototype platform's performance. Experimental results revealed that the platform's motion ranges are 30.76 μm and 29.79 μm, the cross-coupling ratios are 2.02% and 2.26%, the hysteresis ratios are approximately 5.48% and 5.56%, the displacement resolution are less than 29.3 nm and 31.4 nm, and the carrying load exceeds 1 kg, all measured in the X-axis and Y-axis respectively. Moreover, after installing a simulated laser generator load, achieved square and elliptical motion trajectories by exciting different signals. The study further highlights the successful application of the novel piezoelectric positioning platform for precise motion positioning and inspection of minute electronic components under an optical microscope, signifying its potential to enhance detection and sorting processes in the electronics industry. When compared with earlier piezoelectric positioning platforms, proposed platform not only provides a superior space utilization rate but also exhibits enhanced performance. In the future, the platform will be used for high performance scanning and optical system tracking for atomic force microscopes.