Input Matrix Research Articles

ANN modeling and RSM optimization of ultrasound-assisted extraction of protodioscin-rich extracts from Tribulus terrestris L.

Tribulus terrestris L. is a herb renowned for its abundance of saponins, flavonoids, and alkaloids, which are utilized in treating various health conditions. Protodioscin functions by enhancing the conversion of testosterone into potent dihydrotestosterone, stimulating an increase in libido, red blood cell production from the bone marrow, and muscle development. Contemporary ultrasound-assisted-extraction (UAE) process employing green extraction solvents was selected to design the required separation system. The experimental plan was developed based on the independent operating variables – extraction time, operating temperature and solvent system composition in order to determine the influence of defined parameters and their interactions on the extraction yield and the presence of protodioscin. The 3D-RSM approach was introduced to determine the optimal values of studied independent variables in the area of maximal extraction yield. UAE process performed at optimal operating conditions generated maximal extraction yield (31 %, w/w) and protodioscin content of 5.9 mg/g dry plant matrix. Experimental data was used to develop an ANN for the defined extraction system using the operating variables values as the input matrix and observed yield as target matrix. Successfully designed and trained ANN generated high correlation (r = 0.9992) between observed data and predictive model’ outputs, and MSE value of 0.29107.

Temperature modeling of wave rotor refrigeration process based on variable time-delay compensation and SDAE-GRU

Abstract Aiming at the problem of noise and time-delay in temperature prediction modeling of large wave rotor refrigeration process, this paper proposes a novel modeling algorithm that combines the advantages of stacked denoising autoencoder (SDAE) network and Gate Recurrent Unit (GRU) algorithm and utilizes the Maximal Information Coefficient (MIC) algorithm to solve the targeting problem. The MIC algorithm is utilized to calculate the delay time of each input variable and output variable, and the input matrix is reconstructed to compensate for the time-delay, thus solving the problem afterwards. The SDAE network is utilized for denoising the input data and feature extraction to solve the problem of presence of noise in the data. The simulation results show that the proposed MIC-SDAE-GRU algorithm achieves a Root Mean Squared Error (RMSE) of 0.6432 and an R-squared (R²) value of 0.9638, outperforming traditional machine learning methods and other deep learning approaches. Specifically, compared to the standard GRU algorithm, it improves the accuracy of temperature prediction for the wave rotor refrigeration process by 24.7% and exhibits strong generalization ability across various operating conditions.

Adversarial nonnegative matrix factorization for temporal link prediction

Temporal link prediction has been extensively studied and widely applied in various applications, aiming to predict future network links based on the historical networks. However, most existing methods ignore the behavior of previous network updating information in temporal networks. To address these issues, we propose a novel link prediction model based on adversarial nonnegative matrix factorization, which fuses graph representation and adversarial learning to perform temporal link prediction. Specifically, we add a bounded adversary matrix to the input matrix to provide the robustness against real perturbations. Then, our model fully exploits the impact of snapshots by using communicability. Simultaneously, we utilize the cosine similarity to extract the node similarity and map it to low-dimensional latent representation to preserve the local structure. Additionally, we provide effective updating rules to learn the parameters of this model. Extensive experiments results on six real-world networks demonstrate that the proposed method outperforms several classical and the state-of-art matrix-based methods.

Research on Pattern Classification Based on Double Pseudo-Inverse Extreme Learning Machine

This research aims to address the limitations inherent in the traditional Extreme Learning Machine (ELM) algorithm, particularly the stochastic determination of input-layer weights and hidden-layer biases, which frequently leads to an excessive number of hidden-layer neurons and inconsistent performance. To augment the neural network’s efficacy in pattern classification, Principal Component Analysis (PCA) is employed to reduce the dimensionality of the input matrix and alleviate multicollinearity issues during the computation of the input weight matrix. This paper introduces an enhanced ELM methodology, designated the PCA-DP-ELM algorithm, which integrates PCA with Double Pseudo-Inverse Weight Determination (DP). The PCA-DP-ELM algorithm proposed in this study consistently achieves superior average classification accuracy across various datasets, irrespective of whether assessed through longitudinal or cross-sectional experiments. The results from both experimental paradigms indicate that the optimized algorithm not only enhances accuracy but also improves stability. These findings substantiate that the proposed methodology exerts a positive influence on pattern classification.

Controllability measure for disturbance rejection capabilities of control systems with undamped flexible structures

This paper introduces a controllability measure for quantitatively evaluating the disturbance rejection capabilities of control systems with undamped flexible structures. The measure is derived by obtaining the steady-state solution of the degree of disturbance rejection capability (DoDR), a Gramian-based measure used to assess controllability under external disturbances. To address the issue of Gramian matrices diverging over time in undamped systems, we have developed and proven several theorems related to Gramian matrices in undamped systems. The resulting solution, derived using these theorems is represented in a closed-form and expressed in terms of the modal matrix, input matrix, disturbance matrix, and disturbance covariance matrix. Since the derived solution does not require solving Lyapunov equations, which is typically required in most Gramian-based measures, it enables efficient computations, even for high-dimensional systems. Numerical examples confirm that the proposed measure serves as an exact DoDR solution for undamped systems, preserving the previously established physical meaning of DoDR. Control simulations further validate its accuracy in predicting disturbance rejection performance, highlighting its value in actuator allocation.

A self-supervised deep Riemannian representation to classify parkinsonian fixational patterns

Parkinson’s disease (PD) is the second most prevalent neurodegenerative disorder, and it remains incurable. Currently there is no definitive biomarker for detecting PD, measuring its severity, or monitoring of treatments. Recently, oculomotor fixation abnormalities have emerged as a sensitive biomarker to discriminate Parkinsonian patterns from a control population, even at early stages. For oculomotor analysis, current experimental setups use invasive and restrictive capture protocols that limit the transfer in clinical routine. Alternatively, computational approaches to support the PD diagnosis are strictly based on supervised strategies, depending of large labeled data, and introducing an inherent expert-bias. This work proposes a self-supervised architecture based on Riemannian deep representation to learn oculomotor fixation patterns from compact descriptors. Firstly, deep convolutional features are recovered from oculomotor fixation video slices, and then encoded in compact symmetric positive matrices (SPD) to summarize second-order relationships. Each SPD input matrix is projected onto a Riemannian encoder until obtain a SPD embedding. Then, a Riemannian decoder reconstructs SPD matrices while preserving the geometrical manifold structure. The proposed architecture successfully recovers geometric patterns in the embeddings without any label diagnosis supervision, and demonstrates the capability to be discriminative regarding PD patterns. In a retrospective study involving 13 healthy adults and 13 patients diagnosed with PD, the proposed Riemannian representation achieved an average accuracy of 95.6% and an AUC of 99% during a binary classification task using a Support Vector Machine.

Insight of low flammability limit on sustainable aviation fuel blend and prediction by ANN model

Sustainable aviation fuel (SAF) blend has been confirmed to benefit for greenhouse gases reduction, and thus the property of blend fuel should be understanded the detail to support the utilization in aircraft. Low flammability limit (LFL) is a key property of jet fuel which should be sufficiently flammable to burn in combustor of aeroengine and meanwhile should be non-flammable for safety storage in fuel tank of aircraft. LFL of fuel could be influenced by integrating effects including molecule structure, intramolecular chemical bond energy and binding energy of molecule to molecule. Three types of theoretical models, based on different individual view including LFL of every pure hydrocarbon, stoichiometric concentration, and combustion enthalpy, present unsatisfactory simulation results, which can be deduced without integrating all potential influence factors together. The artificial neural network (ANN) approaches have been involved to bridge the relationship of the complex compositions in jet fuels with LFL. For providing adequate and available composition input, the boundary of fuel compositions has been extracted based on constrains of boiling point, flash point and freeze point coupling with statistic petroleum-based jet fuels. By clustering analysis, 43 critical classes of compositions, extracted as surrogate hydrocarbons based on with similar LFL within 1 % deviation, have been deployed as input matrix. ANN-LFL model, trained by only drop-in fuel with feature of Sigmoid function as an activation function, can distinguish drop-in fuel with non-drop-in fuel. ANN LFL model can predict LFL of drop-in fuel with 0.988 accuracy. The predict output value of non-drop-in fuel could present obvious deviation with traditional jet fuel. The optimization methodologies of ANN-LFL model could be improved the understanding of LFL and extend ANN in SAF utilization.

Mentor: A Memory-Efficient Sparse-dense Matrix Multiplication Accelerator Based on Column-Wise Product

Sparse-dense matrix multiplication (SpMM) is the performance bottleneck of many high-performance and deep-learning applications, making it attractive to design specialized SpMM hardware accelerators. Unfortunately, existing hardware solutions do not take full advantage of data reuse opportunities of the input and output matrices or suffer from irregular memory access patterns. Their strategies increase the off-chip memory traffic and bandwidth pressure, leaving much room for improvement. We present Mentor , a new approach to designing SpMM accelerators. Our key insight is that column-wise dataflow, while rarely exploited in prior works, can address these issues in SpMM computations. Mentor is a software-hardware co-design approach for leveraging column-wise dataflow to improve data reuse and regular memory accesses of SpMM. On the software level, Mentor incorporates a novel streaming construction scheme to preprocess the input matrix for enabling a streaming access pattern. On the hardware level, it employs a fully pipelined design to unlock the potential of column-wise dataflow further. The design of Mentor is underpinned by a carefully designed analytical model to find the trade-off between performance and hardware resources. We have implemented an FPGA prototype of Mentor . Experimental results show that Mentor achieves speedup by geomean 2.05 × (up to 3.98 ×), reduces the memory traffic by geomean 2.92 × (up to 4.93 ×), and improves bandwidth utilization by geomean 1.38 × (up to 2.89 ×), compared to the state-of-art hardware solutions.

On the optimality of voronoi‐based column selection

AbstractWhile there exists a rich array of matrix column subset selection problem (CSSP) algorithms for use with interpolative and CUR‐type decompositions, their use can often become prohibitive as the size of the input matrix increases. In an effort to address these issues, in earlier work we developed a general framework that pairs a column‐partitioning routine with a column‐selection algorithm. Two of the four algorithms presented in that work paired the Centroidal Voronoi Orthogonal Decomposition (CVOD; Centroidal Voronoi Tessellation Based Proper Orthogonal Decomposition Analysis, 2003, 137–150) and an adaptive variant (adaptCVOD) with the Discrete Empirical Interpolation Method (DEIM; SIAM J. Sci. Computer. 38 (2016), no. 3, A1454–A1482). In this work, we extend this framework and pair the CVOD‐type algorithms with any CSSP algorithm that returns linearly independent columns. Our results include detailed error bounds for the solutions provided by these paired algorithms, as well as expressions that explicitly characterize how the quality of the selected column partition affects the resulting CSSP solution. In addition to examples involving matrix approximation, we test several of our partition‐based constructions on tasks commonly encountered in model order reduction (MOR).

Robust control of uncertain fully actuated systems with nonlinear uncertainties and perturbed input matrices

Robust control of uncertain fully actuated systems (FASs) with nonlinear uncertainties and perturbed input matrices is considered. Motivated by the recent work on this issue, two novel robust controllers are further developed for two cases under different assumptions. For both cases, the assumption on the perturbation input matrix in the previous work is relaxed to a significant extent, which allows many typical perturbation input matrices, such as constant ones, to be handled, while the previous method cannot. Moreover, for the first case, the assumption on the system uncertainty is further relaxed, and the states of the closed-loop system are globally bounded and converge into an arbitrarily small spherical domain centered at the origin. For the second case, with another requirement on the system nonlinearity imposed, the global exponential stability of the closed-loop system is achieved. The successful application in an electromechanical system verifies the effectiveness of the method.

The implicit inversion method for calculating the forward dynamics input Jacobian

AbstractThis paper presents the implicit inversion method (IIM), a recursive method to evaluate the Jacobian of the forward dynamics w.r.t. the system inputs, using intermediate results obtained from an O(n) forward dynamics algorithm. The resulting coefficient matrix, called the inertia-weighted input matrix (IWIM), can be used to significantly improve the performance of solving optimal control problems that take into account system dynamics for only the current time step. As the relationship between inputs and accelerations appears fixed within a time step, this matrix can be evaluated in the initialization step of the optimization. This means that the forward dynamics only needs to be solved once at the initialization of the optimization, rather than having to solve the equations in every iteration of the optimization. The method presented in this paper especially targets a case where the forward dynamics are calculated using an O(n) method and takes advantage of variables that are already known through the evaluation of that method. These quantities allow us to obtain the inertia-weighted input matrix without having to convert the system to its generalized coordinate form. Exploiting the shape of the resulting equation, it is even possible to avoid an explicit inversion of any matrices in the process. Finally, runtime comparisons between three different methods to calculate the IWIM are made for several examples.

Understanding Childhood Victimization Experiences and Mental Health Outcomes in a Sample of Prison Inmates in Northern Chile

In this paper, the weak points have been investigated, the proposal to solve them, the application of the solution and the comparison of the results in the mode of simulation and experimental testing have been discussed. For this purpose, a four-wheel mobile robot has been considered for simulation and implementation, and a linear quadratic regulator controller and a nonlinear model predictive controller have been used to control it. But the combination of these classic and modern controllers with machine learning can greatly help to make these controllers work more accurately; As a result, in order to increase the accuracy of the performance of these controllers, by training neural networks of multilayer perceptrons, the controllers have been made intelligent. Controllers with cost function have coefficients as weighting to the matrix of system state variables and control input, which are greatly affected by changing these two weighting matrices of problem solving and optimization. For this reason, it is necessary to extract these two matrices for each separate path in order to improve the performance of the controller by trial and error. But by applying the proposed network which is trained with a new algorithm, not only the performance accuracy has increased, but the network extracts these two matrices without the need to spend human energy. Also, in order to reduce the existing time delays, especially in the implementation of the nonlinear controller on the robot in the experimental mode, by training other neural networks to optimally extract the benefit of the forecast horizon, reducing the calculations and increasing the speed of the solution has been achieved. In the hardware part, by examining and using operators such as the pixy camera and the U2D2 interface, which are faster than the usual method, the solution time has been reduced.

Solving Sparse Linear Systems Faster than Matrix Multiplication

Can linear systems be solved faster than matrix multiplication? While there has been remarkable progress for the special cases of graph-structured linear systems, in the general setting, the bit complexity of solving an n × n linear system Ax = b is Õ ( n ω ), where ω is the matrix multiplication exponent. Improving on this has been an open problem even for sparse linear systems with poly( n ) condition number. In this paper, we present an algorithm that solves linear systems with sparse coefficient matrices asymptotically faster than matrix multiplication for any ω > 2. This speedup holds for any input matrix A with o ( n ω−1 / log (κ( A ))) non-zeros, where κ( A ) is the condition number of A . Our algorithm can be viewed as an efficient, randomized implementation of the block Krylov method via recursive low displacement rank factorization. It is inspired by an algorithm of Eberly et al. for inverting matrices over finite fields. In our analysis of numerical stability, we develop matrix anti-concentration techniques to bound the smallest eigenvalue and the smallest gap in the eigenvalues of semi-random matrices.

The Effect of Poverty, Unemployment and Zakat Rates on The Islamic-Human Development Index in Jambi Province Through Economic Growth as an Intervening Variable.

This study is entitled the effect of poverty, unemployment and zakat levels on the Islamic- Human Development Index in Jambi Province through economic growth as an intervening variable. The purpose of this study is 1) to analyze the effect of poverty, unemployment and zakat rates on economic growth in Jambi Province. 2) to analyze the effect of economic growth on the Islamic-Human Development Index in Jambi Province. 3) to analyze the effect of poverty, unemployment and zakat levels on the Islamic-Human Development Index through economic growth in Jambi Province. The research method used is a quantitative descriptive analysis method with secondary data. The analytical tools used by the SEM (Structural Equation Modeling) method , using AMOS 26, use the stages of modeling and structural equation analysis into 7 steps, namely: 1. Theoretical model development; 2. Drawing up a path diagram; 3. Convert path diagrams into structural equations; 4. Choose input matrix for data analysis; 5. Assess model identification; 6. Assess Goodness-of-Fit criteria; 7. Interpretation of model estimation The results showed that the factors that directly affect economic growth in Jambi Province are the poverty rate and national zakat index, while the open unemployment rate does not affect economic growth in Jambi Province. The national zakat index directly has a significant effect on I-HDI in Jambi Province, however, the poverty rate and open unemployment rate directly do not have a significant effect on I- HDI in Jambi Province. Economic growth directly affects I-HDI in Jambi Province. Factors that indirectly influence I-HDI in Jambi Province through economic growth as an intervening variable are the national zakat index, open unemployment rate, and poverty rate against I-HDI in Jambi Province

A Note on the Application of Identity Matrix

Objectives: The Identity Matrix is an important notion in linear algebra with various applications across computational and mathematical domains. The objective of the paper is to introduce a novel method for transposing matrices by utilizing the properties of Identity Matrix as agent. Method: In the proposed method, the input matrix performs Sum of Product (SOP) operations with the Identity Matrix gives the transpose. This involves describing specific mathematical operations that exploit the properties of the Identity Matrix to achieve matrix transpose. Findings: The results show that the Identity Matrix can be used to transpose binary, non- binary and complex matrices. The paper explores results obtained through empirical studies. The result shows that the algorithm runs in polynomial time. Novelty: The case study explores the application of the Identity Matrix for transposing the binary, non- binary and complex matrices with the support of examples and implementation. The uniqueness of the method is its competence to transpose matrix by operating the Sum of Product (SOP) structure. The method of matrix transpose by briefing Identity Matrix as the agent can be applied to develop a way of research to address artificial intelligence problems. Keywords: Agent­ Based Simulation, Binary Matrix, Complex Matrix, Identity Matrix, Matrix Transpose, Sum of Product

SpChar: Characterizing the sparse puzzle via decision trees

Sparse matrix computation is crucial in various modern applications, including large-scale graph analytics, deep learning, and recommender systems. The performance of sparse kernels varies greatly depending on the structure of the input matrix, making it difficult to gain a comprehensive understanding of sparse computation and its relationship to inputs, algorithms, and target machine architecture. Despite extensive research on certain sparse kernels, such as Sparse Matrix-Vector Multiplication (SpMV), the overall family of sparse algorithms has yet to be investigated as a whole. This paper introduces SpChar, a workload characterization methodology for general sparse computation. SpChar employs tree-based models to identify the most relevant hardware and input characteristics, starting from hardware and input-related metrics gathered from Performance Monitoring Counters (PMCs) and matrices. Our analysis enables the creation of a characterization loop that facilitates the optimization of sparse computation by mapping the impact of architectural features to inputs and algorithmic choices. We apply SpChar to more than 600 matrices from the SuiteSparse Matrix collection and three state-of-the-art Arm Central Processing Units (CPUs) to determine the critical hardware and software characteristics that affect sparse computation. In our analysis, we determine that the biggest limiting factors for high-performance sparse computation are (1) the latency of the memory system, (2) the pipeline flush overhead resulting from branch misprediction, and (3) the poor reuse of cached elements. Additionally, we propose software and hardware optimizations that designers can implement to create a platform suitable for sparse computation. We then investigate these optimizations using the gem5 simulator to achieve a significant speedup of up to 2.63× compared to a CPU where the optimizations are not applied.

Short-Term Load Forecasting of Electric Vehicle Charging Stations Accounting for Multifactor IDBO Hybrid Models

The charging behavior of electric vehicle users is highly stochastic, which makes the short-term prediction of charging load at electric vehicle charging stations difficult. In this paper, a data-driven hybrid model optimized by the improved dung beetle optimization algorithm (IDBO) is proposed to address the problem of the low accuracy of short-term prediction. Firstly, the charging station data are preprocessed to obtain clear and organized load data, and the input feature matrix is constructed using factors such as temperature, date type, and holidays. Secondly, the optimal CNN-BiLSTM model is constructed using convolutional neural network (CNN) and Bi-directional Long Short-Term Memory (BiLSTM), which realizes the feature extraction of the input matrix and better captures the hidden patterns and regularities in it. Then, methods such as Bernoulli mapping are used to improve the DBO algorithm and its hyperparameters; for example, hidden neurons of the hybrid model are tuned to further improve the model prediction accuracy. Finally, a simulation experiment platform is established based on MATLAB R2023a to validate the example calculations on the historical data of EV charging stations in the public dataset of ANN-DATA, and comparative analyses are carried out. The results show that compared with the traditional models such as CNN, BiLSTM and PSO-CNN-BiLSTM, the coefficient of determination of the model exceeds 0.8921 and the root mean square error is maintained at about 4.413 on both the training and test sets, which proves its effectiveness and stability.

Explainable graph clustering via expanders in the massively parallel computation model

Explainable clustering provides human-understandable reasons for decisions in black-box learning models. In a previous work, a decision tree built on the set of dimensions was used to define ranges of values for k-means clusters. For explainable graph clustering, we use expander graphs instead of dense subgraphs since powering an expander graph is guaranteed to result in a clique after at most a logarithmic number of steps.Consider a set of multi-dimensional points labeled with k labels. We introduce the heat map sorting problem as reordering the rows and columns of an input matrix (each point is a column and each row is a dimension) such that the labels of the entries of the matrix form connected components (clusters). A cluster is preserved if it remains connected, i.e., if it is not split into several clusters and no two clusters are merged. In the massively parallel computation model (MPC), each machine has a sublinear memory and the total memory of the machines is linear.We prove the problem is NP-hard. We give a fixed-parameter algorithm in MPC and an approximation algorithm based on expander decomposition. We empirically compare our algorithm with explainable k-means on several graphs of email and computer networks.

Reduction of lidar ranging error in turbulent water based on WT-ICA method

A new signal-processing method for the underwater lidar system based on wavelet transform (WT) and independent component analysis (ICA) is presented in this paper. Turbulence in water causes stronger scattering in underwater lidar returns, which can reduce the ranging accuracy and spatial resolution of the underwater lidar system. The method we proposed combines wavelet decomposition and independent component analysis (ICA), the data sets from wavelet decomposition are used to form the input matrix of ICA. The new method benefits from adaptive filtering of WT and blind source separation of ICA, therefore, the scattering clutters are further reduced. The WT-ICA signal processing algorithm is tested with experimental data. A mirror and a black Polyvinyl chloride (PVC) plate were used as the targets, respectively. Without using the WT-ICA, the ranging error with the mirror was 10.0 cm at 3 m distance when the attenuation coefficient of the water was 2.0 m-1. A pump was used to generate turbulence in the water tank. When the flow rate of the pump was 200 L/min, after using WT-ICA, the ranging error was reduced from 14.0 cm to 4.0 cm. For the PVC plate, the ranging errors were 4.5 cm and 19.0 cm at 6.0 attenuation length with and without the algorithm respectively. In both cases, applying this algorithm can significantly improve the ranging accuracy. When the algorithm is applied, the ranging error and detection probability of target echoes with and without turbulence were similar. These results indicated that the WT-ICA method had the ability to reduce the influence of turbulence.

Graph Kernel Neural Networks.

The convolution operator at the core of many modern neural architectures can effectively be seen as performing a dot product between an input matrix and a filter. While this is readily applicable to data such as images, which can be represented as regular grids in the Euclidean space, extending the convolution operator to work on graphs proves more challenging, due to their irregular structure. In this article, we propose to use graph kernels, i.e., kernel functions that compute an inner product on graphs, to extend the standard convolution operator to the graph domain. This allows us to define an entirely structural model that does not require computing the embedding of the input graph. Our architecture allows to plug-in any type of graph kernels and has the added benefit of providing some interpretability in terms of the structural masks that are learned during the training process, similar to what happens for convolutional masks in traditional convolutional neural networks (CNNs). We perform an extensive ablation study to investigate the model hyperparameters' impact and show that our model achieves competitive performance on standard graph classification and regression datasets.