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This study presents an advanced approach to lumbar spine segmentation using deep learning techniques, focusing on addressing key challenges such as class imbalance and data preprocessing. Magnetic resonance imaging (MRI) scans of patients with low back pain are meticulously preprocessed to accurately represent three critical classes: vertebrae, spinal canal, and intervertebral discs (IVDs). By rectifying class inconsistencies in the data preprocessing stage, the fidelity of the training data is ensured. The modified U-Net model incorporates innovative architectural enhancements, including an upsample block with leaky Rectified Linear Units (ReLU) and Glorot uniform initializer, to mitigate common issues such as the dying ReLU problem and improve stability during training. Introducing a custom combined loss function effectively tackles class imbalance, significantly improving segmentation accuracy. Evaluation using a comprehensive suite of metrics showcases the superior performance of this approach, outperforming existing methods and advancing the current techniques in lumbar spine segmentation. These findings hold significant advancements for enhanced lumbar spine MRI and segmentation diagnostic accuracy.

Deep learning has revolutionized medical imaging by providing innovative solutions to complex healthcare challenges. Traditional models often struggle to dynamically adjust feature importance, resulting in suboptimal representation, particularly in tasks like semantic segmentation crucial for accurate structure delineation. Moreover, their static nature incurs high computational costs. To tackle these issues, we introduce Mamba-Ahnet, a novel integration of State Space Model (SSM) and Advanced Hierarchical Network (AHNet) within the MAMBA framework, specifically tailored for semantic segmentation in medical imaging.Mamba-Ahnet combines SSM's feature extraction and comprehension with AHNet's attention mechanisms and image reconstruction, aiming to enhance segmentation accuracy and robustness. By dissecting images into patches and refining feature comprehension through self-attention mechanisms, the approach significantly improves feature resolution. Integration of AHNet into the MAMBA framework further enhances segmentation performance by selectively amplifying informative regions and facilitating the learning of rich hierarchical representations. Evaluation on the Universal Lesion Segmentation dataset demonstrates superior performance compared to state-of-the-art techniques, with notable metrics such as a Dice similarity coefficient of approximately 98% and an Intersection over Union of about 83%. These results underscore the potential of our methodology to enhance diagnostic accuracy, treatment planning, and ultimately, patient outcomes in clinical practice. By addressing the limitations of traditional models and leveraging the power of deep learning, our approach represents a significant step forward in advancing medical imaging technology.

Dynamic Mode Decomposition (DMD) is a data-driven modeling tool that generates a model from spatio-temporal data. The data needs to be as clean as possible for DMD to come up with a faithful model. We review a few data-filtering methods to be integrated with DMD and test them on datasets of varying complexity. The impact of SNR on these methods and the error variation in the DMD model due to each method are observed and discussed., Comment: 13 pages

Respiratory ailments such as asthma, chronic obstructive pulmonary disease (COPD), pneumonia, and lung cancer are life-threatening. Respiration rate (RR) is a vital indicator of the wellness of a patient. Continuous monitoring of RR can provide early indication and thereby save lives. However, a real-time continuous RR monitoring facility is only available at the intensive care unit (ICU) due to the size and cost of the equipment. Recent researches have proposed Photoplethysmogram (PPG) and/ Electrocardiogram (ECG) signals for RR estimation however, the usage of ECG is limited due to the unavailability of it in wearable devices. Due to the advent of wearable smartwatches with built-in PPG sensors, it is now being considered for continuous monitoring of RR. This paper describes a novel approach to RR estimation using machine learning (ML) models with the PPG signal features. Feature selection algorithms were used to reduce computational complexity and the chance of overfitting. The best ML model and the best feature selection algorithm combination was fine-tuned to optimize its performance using hyperparameter optimization. Gaussian Process Regression (GPR) with fitrgp feature selection algorithm outperformed all other combinations and exhibits a root mean squared error (RMSE), mean absolute error (MAE), and two-standard deviation (2SD) of 2.57, 1.91, and 5.13 breaths per minute, respectively. This ML model based RR estimation can be embedded in wearable devices for real-time continuous monitoring of the patient., Comment: Under review in CMPB

We mainly consider the frequency limited $\mathcal{H}_2$ optimal model order reduction of large-scale sparse generalized systems. For this purpose we need to solve two Sylvester equations. This paper proposes efficient algorithm to solve them efficiently. The ideas are also generalized to index-1 descriptor systems. Numerical experiments are carried out using Python Programming Language and the results are presented to demonstrate the approximation accuracy and computational efficiency of the proposed techniques.

Data Assimilation (DA) is a computational tool that uses value from the model and the real measurement to arrive to an optimally acceptable value. Rather, this technique relies on the idea of Kalman gain. We point out that DA has two different perspectives based on the type of problem. In this paper, we look into two problem types: one that does not rely on the initial condition, and the other that is initial condition dependent. Data Assimilation is demonstrated on two examples: runoff monitoring and forecasting in the city of Dhaka (initial condition independent) and convection in the atmosphere (initial condition dependent). We show that standard DA works well for problems with no initial condition dependence and piecewise DA is to be utilized when the problem has initial condition dependence. In the first example, we exploited standard Data Assimilation to arrive at values that are more realistic than the ones from the model and the observations. The second example is where we devised a method to find the dynamics of the system in a piecewise manner in Data Assimilation framework and noticed that the data assimilated dynamics (even due to noisy initial condition) is in good agreement with the true dynamics for a reasonable extent of time in future., Comment: 5 pages

Dynamic Mode Decomposition (DMD) is a data based modeling tool that identifies a matrix to map a quantity at some time instant to the same quantity in future. We design a new version which we call Adaptive Dynamic Mode Decomposition (ADMD) that utilizes time delay coordinates, projection methods and filters as per the nature of the data to create a model for the available problem. Filters are very effective in reducing the rank of high-dimensional dataset. We have incorporated 'discrete Fourier transform' and 'augmented lagrangian multiplier' as filters in our method. The proposed ADMD is tested on several datasets of varying complexities and its performance appears to be promising., Comment: 15 pages. arXiv admin note: substantial text overlap with arXiv:2001.03332

The work aims to stabilize the unstable index-1 descriptor systems by Riccati-based feedback stabilization via a modified form of Iterative Rational Krylov Algorithm (IRKA), which is a bi-tangential interpolation-based technique. In the basic IRKA, for the stable systems the Reduced Order Models (ROMs) can be found conveniently, but it is unsuitable for the unstable ones. In the proposed technique, the initial feedback is implemented within the construction of the projectors of the IRKA approach. The solution of the Riccati equation is estimated from the ROM achieved by IRKA and hence the low-rank feedback matrix is attained. Using the reverse projecting process, for the full model the optimal feedback matrix is retrieved from the low-rank feedback matrix. Finally, to validate the aptness and competency of the proposed technique it is applied to unstable index-1 descriptor systems. The comparison of the present work with two previous works is narrated. The simulation is done by numerical computation using MATLAB, and both the tabular method and graphical method are used as the supporting tools of comparative analysis., Comment: 12 pages, 7 figures

In this article, the focus is mainly on gaining the optimal control for the unstable power system models and stabilizing them through the Riccati-based feedback stabilization process with sparsity-preserving techniques. We are to find the solution of the Continuous-time Algebraic Riccati Equations (CAREs) governed from the unstable power system models derived from the Brazilian Inter-Connected Power System (BIPS) models, which are large-scale sparse index-1 descriptor systems. We propose the projection-based Rational Krylov Subspace Method (RKSM) for the iterative computation of the solution of the CAREs. The novelties of RKSM are sparsity-preserving computations and the implementation of time-convenient adaptive shift parameters. We modify the Low-Rank Cholesky-Factor integrated Alternating Direction Implicit (LRCF-ADI) technique based nested iterative Kleinman-Newton (KN) method to a sparse form and adjust this to solve the desired CAREs. We compare the results achieved by the Kleinman-Newton method with that of using the RKSM. The applicability and adaptability of the proposed techniques are justified numerically with MATLAB simulations. Transient behaviors of the target models are investigated for comparative analysis through the tabular and graphical approaches., Comment: 28 pages, 15 figures

This paper focuses on exploring efficient ways to find $\mathcal{H}_2$ optimal Structure-Preserving Model Order Reduction (SPMOR) of the second-order systems via interpolatory projection-based method Iterative Rational Krylov Algorithm (IRKA). To get the reduced models of the second-order systems, the classical IRKA deals with the equivalent first-order converted forms and estimates the first-order reduced models. The drawbacks of that of the technique are failure of structure preservation and abolishing the properties of the original models, which are the key factors for some of the physical applications. To surpass those issues, we introduce IRKA based techniques that enable us to approximate the second-order systems through the reduced models implicitly without forming the first-order forms. On the other hand, there are very challenging tasks to the Model Order Reduction (MOR) of the large-scale second-order systems with the optimal $\mathcal{H}_2$ error norm and attain the rapid rate of convergence. For the convenient computations, we discuss competent techniques to determine the optimal $\mathcal{H}_2$ error norms efficiently for the second-order systems. The applicability and efficiency of the proposed techniques are validated by applying them to some large-scale systems extracted form engineering applications. The computations are done numerically using MATLAB simulation and the achieved results are discussed in both tabular and graphical approaches., Comment: It was a duplicate version

Eigensystem Realization Algorithm (ERA) is a tool that can produce a reduced order model (ROM) from just input-output data of a given system. ERA creates the ROM while keeping the number of internal states to a minimum level. This was first implemented by Juang and Pappa (1984) to analyze the vibration of aerospace structures from impulse response. We reviewed ERA and tested it on single input single output (SISO) system as well as on multiple input single output (MISO) system. ERA prediction agreed with the actual data. Unlike other model reduction techniques (Balanced truncation, balanced proper orthogonal decomposition), ERA works just as fine without the need of the adjoint system, that makes ERA a promising, completely data-driven, thrifty model reduction method. In this work, we propose a modified Eigensystem Realization Algorithm that relies upon an optimally chosen time resolution for the output used and also checks for good performance through frequency analysis. Four examples are discussed: the first two confirm the model generating ability and the last two illustrate its capability to produce a low-dimensional model (for a large scale system) that is much more accurate than the one produced by the traditional ERA., Comment: 15 pages

Numerical predictions of blood flow and hemodynamic properties through a stenotic and aneurysmal rigid artery are studied in the presence of blood clot at constricted area. Finite element method has been used to solve the steady partial differential equations of continuity, momentum, Oldroyd-B and bioheat transport in two dimensional cartesian coordinates system.The present investigation carries the potential to compute blood velocity, pressure and drag coefficient with major significance at the throat of stenosis and aneurysm. The models are also employed to study of simulation, influence of blood clot and hemodynamical characteristics for all modifications. The back flow and recirculation zones are found at stenotic and aneurysmal region for the model. The quantitative analysis is completed by numerical calculation having physiological significance of hemodynamical factors of blood flow depends on the dimensionless parameters which show the validity of present model.

This paper studies the model order reduction of second-order index-1 descriptor systems using a tangential interpolation projection method based on the Iterative Rational Krylov Algorithm (IRKA). Our primary focus is to reduce the system into a second-order form so that the structure of the original system can be preserved. For this purpose, the IRKA based tangential interpolatory method is modified to deal with the second-order structure of the underlying descriptor system efficiently in an implicit way. The paper also shows that by exploiting the symmetric properties of the system the implementing computational costs can be reduced significantly. Theoretical results are verified for the model reduction of the piezo actuator based adaptive spindle support which is second-order index-1 differential-algebraic form. The efficiency and accuracy of the method are demonstrated by analyzing the numerical results., Comment: 20 pages and 7 figures

Hypertension is a potentially unsafe health ailment, which can be indicated directly from the Blood pressure (BP). Hypertension always leads to other health complications. Continuous monitoring of BP is very important; however, cuff-based BP measurements are discrete and uncomfortable to the user. To address this need, a cuff-less, continuous and a non-invasive BP measurement system is proposed using Photoplethysmogram (PPG) signal and demographic features using machine learning (ML) algorithms. PPG signals were acquired from 219 subjects, which undergo pre-processing and feature extraction steps. Time, frequency and time-frequency domain features were extracted from the PPG and their derivative signals. Feature selection techniques were used to reduce the computational complexity and to decrease the chance of over-fitting the ML algorithms. The features were then used to train and evaluate ML algorithms. The best regression models were selected for Systolic BP (SBP) and Diastolic BP (DBP) estimation individually. Gaussian Process Regression (GPR) along with ReliefF feature selection algorithm outperforms other algorithms in estimating SBP and DBP with a root-mean-square error (RMSE) of 6.74 and 3.59 respectively. This ML model can be implemented in hardware systems to continuously monitor BP and avoid any critical health conditions due to sudden changes., Comment: Accepted for publication in Sensor, 14 Figures, 14 Tables

We have deluge of data in time series format for numerous phenomena. The number of snapshots, resolution and many other factors come into play as we look to identify the dynamics in a given problem. The pre-processing and post-processing steps while working with the data may be related to the resources in terms of the hardware used to collect data and computations that we perform on the data to create a model for the problem. Dynamic Mode Decomposition (DMD) is a data based modeling tool that identifies a matrix to map a quantity at some time instant to the same quantity in future. It is possible to generate a model by projecting the high dimensional spatiotemporal data to a lower dimensional subspace in a probabilistic framework. Sampling and gaussian projection have been used in the past to increase efficiency in the computation. Here, we design an optimized version of DMD that utilizes time delay coordinates and a projection matrix. In our proposal, we discussed about two projection matrices -- one is inspired by the Krylov subspace and the other promotes and leverages sparsity to bring computational benefits in producing a model. Satisfactory results are obtained as they are tested on data related to Double gyre (present in ocean mixing) and on a 2D compressible signal. The motivation behind this scheme of DMD comes from the fact that data from many phenomena are 'big' and 'highly oscillatory.', Comment: 18 pages