Search results for: variational auto-encoder

Authors: Sandeep Kumar, Naveen Gupta

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Terahertz (THz) generation has been investigated by beating two cosh-Gaussian laser beams of the same amplitude but different wavenumbers and frequencies through rippled collisionless plasma. The ponderomotive force is operative which is induced due to the intensity gradient of the laser beam over the cross-section area of the wavefront. The electrons evacuate towards a low-intensity regime, which modifies the dielectric function of the medium and results in cross focusing of cosh-Gaussian laser beams. The evolution of spot size of laser beams has been studied by solving nonlinear Schrodinger wave equation (NLSE) with variational technique. The laser beams impart oscillations to electrons which are enhanced with ripple density. The nonlinear oscillatory motion of electrons gives rise to a nonlinear current density driving THz radiation. It has been observed that the periodicity of the ripple density helps to enhance the THz radiation.

Keywords: rippled collisionless plasma, cosh-gaussian laser beam, ponderomotive force, variational technique, nonlinear current density

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Authors: Mohammad Farid

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In this paper, we introduce and study an explicit iterative method based on hybrid extragradient method to approximate a common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converge strongly to the common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, extension and generalization of the previously known results in this area.

Keywords: generalized mixed equilibrium problem, fixed-point problem, nonexpansive semigroup, variational inequality problem, iterative algorithms, hybrid extragradient method

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Authors: Arya Prakash Padhi, Anupam Chakrabarti, Rajib Chowdhury

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Topology or layout optimization often gives better performing economic structures and is very helpful in the conceptual design phase. But traditionally it is being done in finite element-based optimization schemes which, although gives a good result, is very time-consuming especially in 3D structures. Among other alternatives machine learning, especially deep learning-based methods, have a very good potential in resolving this computational issue. Here convolutional neural network (3D-CNN) based variational auto encoder (VAE) is trained using a dataset generated from commercially available topology optimization code ABAQUS Tosca using solid isotropic material with penalization (SIMP) method for compliance minimization. The encoded data in latent space is then fed to a 3D generative adversarial network (3D-GAN) to generate the outcome in 64x64x64 size. Here the network consists of 3D volumetric CNN with rectified linear unit (ReLU) activation in between and sigmoid activation in the end. The proposed network is seen to provide almost optimal results with significantly reduced computational time, as there is no iteration involved.

Keywords: 3D generative adversarial network, deep learning, structural topology optimization, variational auto encoder

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Authors: O. Punjarat, S. Chucheepsakul, T. Phanyasahachart

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This paper focuses on a variational formulation of large amplitude free vibration behavior of a very sag marine cable. In the static equilibrium state, the marine cable has a very large sag configuration. In the motion state, the marine cable is assumed to vibrate in in-plane motion with large amplitude from the static equilibrium position. The total virtual work-energy of the marine cable at the dynamic state is formulated which involves the virtual strain energy due to axial deformation, the virtual work done by effective weight, and the inertia forces. The equations of motion for the large amplitude free vibration of marine cable are obtained by taking into account the difference between the Euler’s equation in the static state and the displaced state. Based on the Galerkin finite element procedure, the linear and nonlinear stiffness matrices, and mass matrices of the marine cable are obtained and the eigenvalue problem is solved. The natural frequency spectrum and the large amplitude free vibration behavior of marine cable are presented.

Keywords: axial deformation, free vibration, Galerkin finite element method, large amplitude, variational method

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Authors: Omer Cahana, Maya Herman, Ofer Levi

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Magnetic resonance imaging (MRI) is a long medical scan that stems from a long acquisition time. This length is mainly due to the traditional sampling theorem, which defines a lower boundary for sampling. However, it is still possible to accelerate the scan by using a different approach, such as compress sensing (CS) or parallel imaging (PI). These two complementary methods can be combined to achieve a faster scan with high-fidelity imaging. In order to achieve that, two properties have to exist: i) the signal must be sparse under a known transform domain, ii) the sampling method must be incoherent. In addition, a nonlinear reconstruction algorithm needs to be applied to recover the signal. While the rapid advance in the deep learning (DL) field, which has demonstrated tremendous successes in various computer vision task’s, the field of MRI reconstruction is still in an early stage. In this paper, we present an extension of the state-of-the-art model in MRI reconstruction -VarNet. We utilize VarNet by using dilated convolution in different scales, which extends the receptive field to capture more contextual information. Moreover, we simplified the sensitivity map estimation (SME), for it holds many unnecessary layers for this task. Those improvements have shown significant decreases in computation costs as well as higher accuracy.

Keywords: MRI, deep learning, variational network, computer vision, compress sensing

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Authors: Qingsong Xiong, Cheng Yuan, Qingzhao Kong, Haibei Xiong

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Deep-learning-driven approaches based on vibration responses have attracted larger attention in rapid structural condition assessment while obtaining sufficient measured training data with corresponding labels is relevantly costly and even inaccessible in practical engineering. This study proposes an integrated label propagation network for structural condition assessment, which is able to diffuse the labels from continuously-generating measurements by intact structure to those of missing labels of damage scenarios. The integrated network is embedded with damage-sensitive features extraction by deep autoencoder and pseudo-labels propagation by optimized fuzzy clustering, the architecture and mechanism which are elaborated. With a sophisticated network design and specified strategies for improving performance, the present network achieves to extends the superiority of self-supervised representation learning, unsupervised fuzzy clustering and supervised classification algorithms into an integration aiming at assessing damage conditions. Both numerical simulations and full-scale laboratory shaking table tests of a two-story building structure were conducted to validate its capability of detecting post-earthquake damage. The identifying accuracy of a present network was 0.95 in numerical validations and an average 0.86 in laboratory case studies, respectively. It should be noted that the whole training procedure of all involved models in the network stringently doesn’t rely upon any labeled data of damage scenarios but only several samples of intact structure, which indicates a significant superiority in model adaptability and feasible applicability in practice.

Keywords: autoencoder, condition assessment, fuzzy clustering, label propagation

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Authors: Lokes Parvatha Kumaran S., Sakthi Jay Mahenthar C., Sathyaprakash P., Jayakumar V., Shobanadevi A.

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With the evolution of technology, the need to solve complex computational problems like machine learning and deep learning has shot up. But even the most powerful classical supercomputers find it difficult to execute these tasks. With the recent development of quantum computing, researchers and tech-giants strive for new quantum circuits for machine learning tasks, as present works on Quantum Machine Learning (QML) ensure less memory consumption and reduced model parameters. But it is strenuous to simulate classical deep learning models on existing quantum computing platforms due to the inflexibility of deep quantum circuits. As a consequence, it is essential to design viable quantum algorithms for QML for noisy intermediate-scale quantum (NISQ) devices. The proposed work aims to explore Variational Quantum Circuits (VQC) for Deep Reinforcement Learning by remodeling the experience replay and target network into a representation of VQC. In addition, to reduce the number of model parameters, quantum information encoding schemes are used to achieve better results than the classical neural networks. VQCs are employed to approximate the deep Q-value function for decision-making and policy-selection reinforcement learning with experience replay and the target network.

Keywords: quantum computing, quantum machine learning, variational quantum circuit, deep reinforcement learning, quantum information encoding scheme

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Authors: Mohammad Saber Rohi, Saghar Heidari

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In this paper, we studied the pricing problem of American options under a regime-switching model with the possibility of a non-optimal exercise policy (early or late exercise time) which is called an irrational strategy. For this, we consider a Markovmodulated model for the dynamic of the underlying asset as an alternative model to the classical Balck-Scholes-Merton model (BSM) and an intensity-based model for the irrational strategy, to provide more realistic results for American option prices under the irrational behavior in real financial markets. Applying a partial differential equation (PDE) approach, the pricing problem of American options under regime-switching models can be formulated as coupled PDEs. To solve the resulting systems of PDEs in this model, we apply a finite element method as the numerical solving procedure to the resulting variational inequality. Under some appropriate assumptions, we establish the stability of the method and compare its accuracy to some recent works to illustrate the suitability of the proposed model and the accuracy of the applied numerical method for the pricing problem of American options under the regime-switching model with irrational behaviors.

Keywords: irrational exercise strategy, rationality parameter, regime-switching model, American option, finite element method, variational inequality

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Authors: Hozaifa Zaki, Ghada Soliman

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In this paper, we introduced an approach for Automated Dotted Arabic Expiration Date Extraction using Optimized Convolutional Autoencoder (ARABEX) with bidirectional LSTM. This approach is used for translating the Arabic dot-matrix expiration dates into their corresponding filled-in dates. A custom lightweight Convolutional Recurrent Neural Network (CRNN) model is then employed to extract the expiration dates. Due to the lack of available dataset images for the Arabic dot-matrix expiration date, we generated synthetic images by creating an Arabic dot-matrix True Type Font (TTF) matrix to address this limitation. Our model was trained on a realistic synthetic dataset of 3287 images, covering the period from 2019 to 2027, represented in the format of yyyy/mm/dd. We then trained our custom CRNN model using the generated synthetic images to assess the performance of our model (ARABEX) by extracting expiration dates from the translated images. Our proposed approach achieved an accuracy of 99.4% on the test dataset of 658 images, while also achieving a Structural Similarity Index (SSIM) of 0.46 for image translation on our dataset. The ARABEX approach demonstrates its ability to be applied to various downstream learning tasks, including image translation and reconstruction. Moreover, this pipeline (ARABEX+CRNN) can be seamlessly integrated into automated sorting systems to extract expiry dates and sort products accordingly during the manufacturing stage. By eliminating the need for manual entry of expiration dates, which can be time-consuming and inefficient for merchants, our approach offers significant results in terms of efficiency and accuracy for Arabic dot-matrix expiration date recognition.

Keywords: computer vision, deep learning, image processing, character recognition

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Authors: Jack R. McKenzie, Peter A. Appleby, Thomas House, Neil Walton

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Cold-start is a notoriously difficult problem which can occur in recommendation systems, and arises when there is insufficient information to draw inferences for users or items. To address this challenge, a contextual bandit algorithm – the Fast Approximate Bayesian Contextual Cold Start Learning algorithm (FAB-COST) – is proposed, which is designed to provide improved accuracy compared to the traditionally used Laplace approximation in the logistic contextual bandit, while controlling both algorithmic complexity and computational cost. To this end, FAB-COST uses a combination of two moment projection variational methods: Expectation Propagation (EP), which performs well at the cold start, but becomes slow as the amount of data increases; and Assumed Density Filtering (ADF), which has slower growth of computational cost with data size but requires more data to obtain an acceptable level of accuracy. By switching from EP to ADF when the dataset becomes large, it is able to exploit their complementary strengths. The empirical justification for FAB-COST is presented, and systematically compared to other approaches on simulated data. In a benchmark against the Laplace approximation on real data consisting of over 670, 000 impressions from autotrader.co.uk, FAB-COST demonstrates at one point increase of over 16% in user clicks. On the basis of these results, it is argued that FAB-COST is likely to be an attractive approach to cold-start recommendation systems in a variety of contexts.

Keywords: cold-start learning, expectation propagation, multi-armed bandits, Thompson Sampling, variational inference

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Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park

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In this paper, we propose a novel inference algorithm for the multi-class Gaussian process classification model that can be used in the field of human behavior recognition. This algorithm can drive simultaneously both a posterior distribution of a latent function and estimators of hyper-parameters in a Gaussian process classification model with multi-class. Our algorithm is based on the Laplace approximation (LA) technique and variational EM framework. This is performed in two steps: called expectation and maximization steps. First, in the expectation step, using the Bayesian formula and LA technique, we derive approximately the posterior distribution of the latent function indicating the possibility that each observation belongs to a certain class in the Gaussian process classification model. Second, in the maximization step, using a derived posterior distribution of latent function, we compute the maximum likelihood estimator for hyper-parameters of a covariance matrix necessary to define prior distribution for latent function. These two steps iteratively repeat until a convergence condition satisfies. Moreover, we apply the proposed algorithm with human action classification problem using a public database, namely, the KTH human action data set. Experimental results reveal that the proposed algorithm shows good performance on this data set.

Keywords: bayesian rule, gaussian process classification model with multiclass, gaussian process prior, human action classification, laplace approximation, variational EM algorithm

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Authors: Hassan Samadi, Mustapha El Jarroudi

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In this work, we consider the homogenization of a non-linear problem in periodic medium with two periodic connected media exchanging a heat flux throughout their common interface. The interfacial exchange coefficient λ is assumed to tend to zero or to infinity following a rate λ=λ(ε) when the size ε of the basic cell tends to zero. Three homogenized problems are determined according to some critical value depending of λ and ε. Our method is based on Γ-Convergence techniques.

Keywords: variational methods, epiconvergence, homogenization, convergence technique

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Authors: Thomas Bryan, Veton Kepuska, Ivica Kostanic

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Speaker recognition is performed in high Additive White Gaussian Noise (AWGN) environments using principals of Computational Auditory Scene Analysis (CASA). CASA methods often classify sounds from images in the time-frequency (T-F) plane using spectrograms or cochleargrams as the image. In this paper atomic decomposition implemented by matching pursuit performs a transform from time series speech signals to the T-F plane. The atomic decomposition creates a sparsely populated T-F vector in “weight space” where each populated T-F position contains an amplitude weight. The weight space vector along with the atomic dictionary represents a denoised, compressed version of the original signal. The arraignment or of the atomic indices in the T-F vector are used for classification. Unsupervised feature learning implemented by a sparse autoencoder learns a single dictionary of basis features from a collection of envelope samples from all speakers. The approach is demonstrated using pairs of speakers from the TIMIT data set. Pairs of speakers are selected randomly from a single district. Each speak has 10 sentences. Two are used for training and 8 for testing. Atomic index probabilities are created for each training sentence and also for each test sentence. Classification is performed by finding the lowest Euclidean distance between then probabilities from the training sentences and the test sentences. Training is done at a 30dB Signal-to-Noise Ratio (SNR). Testing is performed at SNR’s of 0 dB, 5 dB, 10 dB and 30dB. The algorithm has a baseline classification accuracy of ~93% averaged over 10 pairs of speakers from the TIMIT data set. The baseline accuracy is attributable to short sequences of training and test data as well as the overall simplicity of the classification algorithm. The accuracy is not affected by AWGN and produces ~93% accuracy at 0dB SNR.

Keywords: time-frequency plane, atomic decomposition, envelope sampling, Gabor atoms, matching pursuit, sparse dictionary learning, sparse autoencoder

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Authors: Zhiyong Zheng, Xu Li, Liang Huang, Zhengliang Sun, Jianhua Xu

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Yaw angle plays a significant role in many vehicle safety applications, such as collision avoidance and lane-keeping system. Although the estimation of the yaw angle has been extensively studied in existing literature, it is still the main challenge to simultaneously achieve a reliable and cost-effective solution in complex urban environments. This paper proposes a multi-stage learning framework to estimate the yaw angle with a monocular camera, which can deal with the challenge in a more reliable manner. In the first stage, an efficient road detection network is designed to extract the road region, providing a highly reliable reference for the estimation. In the second stage, a variational auto-encoder (VAE) is proposed to learn the distribution patterns of road regions, which is particularly suitable for modeling the changing patterns of yaw angle under different driving maneuvers, and it can inherently enhance the generalization ability. In the last stage, a gated recurrent unit (GRU) network is used to capture the temporal correlations of the learned patterns, which is capable to further improve the estimation accuracy due to the fact that the changes of deflection angle are relatively easier to recognize among continuous frames. Afterward, the yaw angle can be obtained by combining the estimated deflection angle and the road direction stored in a roadway map. Through effective multi-stage learning, the proposed framework presents high reliability while it maintains better accuracy. Road-test experiments with different driving maneuvers were performed in complex urban environments, and the results validate the effectiveness of the proposed framework.

Keywords: gated recurrent unit, multi-stage learning, reliable estimation, variational auto-encoder, yaw angle

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Authors: Jonathan Gong

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Purpose AI-driven solutions are at the forefront of many pathology and medical imaging methods. Using algorithms designed to better the experience of medical professionals within their respective fields, the efficiency and accuracy of diagnosis can improve. In particular, X-rays are a fast and relatively inexpensive test that can diagnose diseases. In recent years, X-rays have not been widely used to detect and diagnose COVID-19. The under use of Xrays is mainly due to the low diagnostic accuracy and confounding with pneumonia, another respiratory disease. However, research in this field has expressed a possibility that artificial neural networks can successfully diagnose COVID-19 with high accuracy. Models and Data The dataset used is the COVID-19 Radiography Database. This dataset includes images and masks of chest X-rays under the labels of COVID-19, normal, and pneumonia. The classification model developed uses an autoencoder and a pre-trained convolutional neural network (DenseNet201) to provide transfer learning to the model. The model then uses a deep neural network to finalize the feature extraction and predict the diagnosis for the input image. This model was trained on 4035 images and validated on 807 separate images from the ones used for training. The images used to train the classification model include an important feature: the pictures are cropped beforehand to eliminate distractions when training the model. The image segmentation model uses an improved U-Net architecture. This model is used to extract the lung mask from the chest X-ray image. The model is trained on 8577 images and validated on a validation split of 20%. These models are calculated using the external dataset for validation. The models’ accuracy, precision, recall, f1-score, IOU, and loss are calculated. Results The classification model achieved an accuracy of 97.65% and a loss of 0.1234 when differentiating COVID19-infected, pneumonia-infected, and normal lung X-rays. The segmentation model achieved an accuracy of 97.31% and an IOU of 0.928. Conclusion The models proposed can detect COVID-19, pneumonia, and normal lungs with high accuracy and derive the lung mask from a chest X-ray with similarly high accuracy. The hope is for these models to elevate the experience of medical professionals and provide insight into the future of the methods used.

Keywords: artificial intelligence, convolutional neural networks, deep learning, image processing, machine learning

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Authors: Jun Ming Moey, Zhiyaun Chen, David Nicholson

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Bad actors are often hard to detect in data that imprints their behaviour patterns because they are comparatively rare events embedded in non-bad actor data. An unsupervised machine learning framework is applied here to detect bad actors in financial crime datasets that record millions of transactions undertaken by hundreds of actors (<0.01% bad). Specifically, the framework combines ‘shallow’ (PCA, Isolation Forest) and ‘deep’ (Autoencoder) methods to detect outlier patterns. Detection performance analysis for both the individual methods and their combination is reported.

Keywords: detection, machine learning, deep learning, unsupervised, outlier analysis, data science, fraud, financial crime

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Authors: Varun Agarwal

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Introduction: With the advent of personalized medicine, histopathological review of whole slide images (WSIs) for cancer diagnosis presents an exceedingly time-consuming, complex task. Specifically, detecting metastatic regions in WSIs of sentinel lymph node biopsies necessitates a full-scanned, holistic evaluation of the image. Thus, digital pathology, low-level image manipulation algorithms, and machine learning provide significant advancements in improving the efficiency and accuracy of WSI analysis. Using Camelyon16 data, this paper proposes a deep learning pipeline to automate and ameliorate breast cancer metastasis localization and WSI classification. Methodology: The model broadly follows five stages -region of interest detection, WSI partitioning into image tiles, convolutional neural network (CNN) image-segment classifications, probabilistic mapping of tumor localizations, and further processing for whole WSI classification. Transfer learning is applied to the task, with the implementation of Inception-ResNetV2 - an effective CNN classifier that uses residual connections to enhance feature representation, adding convolved outputs in the inception unit to the proceeding input data. Moreover, in order to augment the performance of the transfer learning CNN, a stack of convolutional denoising autoencoders (CDAE) is applied to produce embeddings that enrich image representation. Through a saliency-detection algorithm, visual training segments are generated, which are then processed through a denoising autoencoder -primarily consisting of convolutional, leaky rectified linear unit, and batch normalization layers- and subsequently a contrast-normalization function. A spatial pyramid pooling algorithm extracts the key features from the processed image, creating a viable feature map for the CNN that minimizes spatial resolution and noise. Results and Conclusion: The simplified and effective architecture of the fine-tuned transfer learning Inception-ResNetV2 network enhanced with the CDAE stack yields state of the art performance in WSI classification and tumor localization, achieving AUC scores of 0.947 and 0.753, respectively. The convolutional feature retention and compilation with the residual connections to inception units synergized with the input denoising algorithm enable the pipeline to serve as an effective, efficient tool in the histopathological review of WSIs.

Keywords: breast cancer, convolutional neural networks, metastasis mapping, whole slide images

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Authors: Francesco Marotti de Sciarra, Raffaele Barretta

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Starting from nonlocal continuum mechanics, a thermodynamically new nonlocal model of Euler-Bernoulli nanobeams is provided. The nonlocal variational formulation is consistently provided and the governing differential equation for transverse displacement are presented. Higher-order boundary conditions are then consistently derived. An example is contributed in order to show the effectiveness of the proposed model.

Keywords: Bernoulli-Euler beams, nanobeams, nonlocal elasticity, closed-form solutions

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Authors: Sai Maniveer Adapa, Sai Guptha Perla, Adithya Reddy P.

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Thyroid nodules can often be diagnosed with ultrasound imaging, although differentiating between benign and malignant nodules can be challenging for medical professionals. This work suggests a novel approach to increase the precision of thyroid nodule identification by combining machine learning and deep learning. The new approach first extracts information from the ultrasound pictures using a deep learning method known as a convolutional autoencoder. A support vector machine, a type of machine learning model, is then trained using these features. With an accuracy of 92.52%, the support vector machine can differentiate between benign and malignant nodules. This innovative technique may decrease the need for pointless biopsies and increase the accuracy of thyroid nodule detection.

Keywords: thyroid tumor diagnosis, ultrasound images, deep learning, machine learning, convolutional auto-encoder, support vector machine

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Authors: Khaled I. Nawafleh

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In this work, we apply the method of Hamilton-Jacobi to obtain solutions of Hamiltonian systems in classical mechanics with two certain structures: the first structure plays a central role in the theory of time-dependent Hamiltonians, whilst the second is used to treat classical Hamiltonians, including dissipation terms. It is proved that the generalization of problems from the calculus of variation methods in the nonstationary case can be obtained naturally in Hamilton-Jacobi formalism. Then, another expression of geometry of the Hamilton Jacobi equation is retrieved for Hamiltonians with time-dependent and frictional terms. Both approaches shall be applied to many physical examples.

Keywords: Hamilton-Jacobi, time dependent lagrangians, dissipative systems, variational principle

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Authors: Maria Hussin, Malik Zawwar Hussain, Mubashrah Saddiqa

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We present a trigonometric scheme to approximate a circular arc with its two end points and two end tangents/unit tangents. A rational cubic trigonometric Bézier curve is constructed whose end control points are defined by the end points of the circular arc. Weight functions and the remaining control points of the cubic trigonometric Bézier curve are estimated by variational approach to reproduce a circular arc. The radius error is calculated and found less than the existing techniques.

Keywords: control points, rational trigonometric Bézier curves, radius error, shape measure, weight functions

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Authors: Rashini Maduka, C. R. Wijesinghe, A. R. Weerasinghe

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Drug-drug interactions (DDIs) can happen when two or more drugs are taken together. Today DDIs have become a serious health issue due to adverse drug effects. In vivo and in vitro methods for identifying DDIs are time-consuming and costly. Therefore, in-silico-based approaches are preferred in DDI identification. Most machine learning models for DDI prediction are used chemical and biological drug properties as features. However, some drug features are not available and costly to extract. Therefore, it is better to make automatic feature engineering. Furthermore, people who have diabetes already suffer from other diseases and take more than one medicine together. Then adverse drug effects may happen to diabetic patients and cause unpleasant reactions in the body. In this study, we present a model with a graph convolutional autoencoder and a graph decoder using a dataset from DrugBank version 5.1.3. The main objective of the model is to identify unknown interactions between antidiabetic drugs and the drugs taken by diabetic patients for other diseases. We considered automatic feature engineering and used Known DDIs only as the input for the model. Our model has achieved 0.86 in AUC and 0.86 in AP.

Keywords: drug-drug interaction prediction, graph embedding, graph convolutional networks, adverse drug effects

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Authors: Debajyoti Choudhuri, Ratan Kumar Giri, Shesadev Pradhan

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The perturbed nonlinear Schrodinger equation involving the p-biharmonic and the p-Laplacian operators involving a real valued parameter and a continuous real valued potential function defined over the N- dimensional Euclidean space has been considered. By the variational technique, an existence result pertaining to a nontrivial solution to this non-linear partial differential equation has been proposed. Further, by the Concentration lemma, the concentration of solutions to the same problem defined on the set consisting of those elements where the potential function vanishes as the real parameter approaches to infinity has been addressed.

Keywords: p-Laplacian, p-biharmonic, elliptic PDEs, Concentration lemma, Sobolev space

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Authors: Ram Kishor

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The Lyapunov characteristic exponent (LCE) is an important tool to describe behavior of a dynamical system, which measures the average rate of divergence (or convergence) of a trajectory emanating in the vicinity of initial point. To analyze the behavior of nearby trajectory emanating in the neighborhood of an equilibrium point in the restricted three-body problem under the influence of perturbations in the form of radiation pressure and oblateness, we compute LCEs of first order with the help of slandered method which is based on variational equation of the system. It is observed that trajectories are chaotic in nature due positive LCEs. Also, we analyze the effect of radiation pressure and oblateness on the LCEs. Results are applicable to study the behavior of more generalized RTBP in the presence of perturbations such as PR drag, solar wind drag etc.

Keywords: Lyapunov characteristic exponent, RTBP, radiation pressure, oblateness

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Authors: Mohammad Moezzibadi, Isabelle Charpentier, Adrien Wanko, Robert Mosé

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The calibration of hydrodynamic parameters for subsurface constructed wetlands (CWs) is a sensitive process since highly non-linear equations are involved in unsaturated flow modeling. CW systems are engineered systems designed to favour natural treatment processes involving wetland vegetation, soil, and their microbial flora. Their significant efficiency at reducing the ecological impact of urban runoff has been recently proved in the field. Numerical flow modeling in a vertical variably saturated CW is here carried out by implementing the Richards model by means of a mixed hybrid finite element method (MHFEM), particularly well adapted to the simulation of heterogeneous media, and the van Genuchten-Mualem parametrization. For validation purposes, MHFEM results were compared to those of HYDRUS (a software based on a finite element discretization). As van Genuchten-Mualem soil hydrodynamic parameters depend on water content, their estimation is subject to considerable experimental and numerical studies. In particular, the sensitivity analysis performed with respect to the van Genuchten-Mualem parameters reveals a predominant influence of the shape parameters α, n and the saturated conductivity of the filter on the piezometric heads, during saturation and desaturation. Modeling issues arise when the soil reaches oven-dry conditions. A particular attention should also be brought to boundary condition modeling (surface ponding or evaporation) to be able to tackle different sequences of rainfall-runoff events. For proper parameter identification, large field datasets would be needed. As these are usually not available, notably due to the randomness of the storm events, we thus propose a simple, robust and low-cost numerical method for the inverse modeling of the soil hydrodynamic properties. Among the methods, the variational data assimilation technique introduced by Le Dimet and Talagrand is applied. To that end, a variational data assimilation technique is implemented by applying automatic differentiation (AD) to augment computer codes with derivative computations. Note that very little effort is needed to obtain the differentiated code using the on-line Tapenade AD engine. Field data are collected for a three-layered CW located in Strasbourg (Alsace, France) at the water edge of the urban water stream Ostwaldergraben, during several months. Identification experiments are conducted by comparing measured and computed piezometric head by means of the least square objective function. The temporal variability of hydrodynamic parameter is then assessed and analyzed.

Keywords: automatic differentiation, constructed wetland, inverse method, mixed hybrid FEM, sensitivity analysis

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Authors: Saghar Heidari

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In this paper, we study the valuation problem of European continuous-installment options under Markov-modulated models with a partial differential equation approach. Due to the opportunity for continuing or stopping to pay installments, the valuation problem under regime-switching models can be formulated as coupled partial differential equations (CPDE) with free boundary features. To value the installment options, we express the truncated CPDE as a linear complementarity problem (LCP), then a finite element method is proposed to solve the resulted variational inequality. Under some appropriate assumptions, we establish the stability of the method and illustrate some numerical results to examine the rate of convergence and accuracy of the proposed method for the pricing problem under the regime-switching model.

Keywords: continuous-installment option, European option, regime-switching model, finite element method

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Authors: Elisa Boatti, Ulisse Stefanelli, Alessandro Reali, Ferdinando Auricchio

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Thanks to their unusual properties, shape memory alloys (SMAs) are good candidates for advanced applications in a wide range of engineering fields, such as automotive, robotics, civil, biomedical, aerospace. In the last decades, the ever-growing interest for such materials has boosted several research studies aimed at modeling their complex nonlinear behavior in an effective and robust way. Since the constitutive response of SMAs is strongly thermomechanically coupled, the investigation of the non-isothermal evolution of the material must be taken into consideration. The present study considers an existing three-dimensional phenomenological model for SMAs, able to reproduce the main SMA properties while maintaining a simple user-friendly structure, and proposes a variational reformulation of the full non-isothermal version of the model. While the considered model has been thoroughly assessed in an isothermal setting, the proposed formulation allows to take into account the full nonisothermal problem. In particular, the reformulation is inspired to the GENERIC (General Equations for Non-Equilibrium Reversible-Irreversible Coupling) formalism, and is based on a generalized gradient flow of the total entropy, related to thermal and mechanical variables. Such phrasing of the model is new and allows for a discussion of the model from both a theoretical and a numerical point of view. Moreover, it directly implies the dissipativity of the flow. A semi-implicit time-discrete scheme is also presented for the fully coupled thermomechanical system, and is proven unconditionally stable and convergent. The correspondent algorithm is then implemented, under a space-homogeneous temperature field assumption, and tested under different conditions. The core of the algorithm is composed of a mechanical subproblem and a thermal subproblem. The iterative scheme is solved by a generalized Newton method. Numerous uniaxial and biaxial tests are reported to assess the performance of the model and algorithm, including variable imposed strain, strain rate, heat exchange properties, and external temperature. In particular, the heat exchange with the environment is the only source of rate-dependency in the model. The reported curves clearly display the interdependence between phase transformation strain and material temperature. The full thermomechanical coupling allows to reproduce the exothermic and endothermic effects during respectively forward and backward phase transformation. The numerical tests have thus demonstrated that the model can appropriately reproduce the coupled SMA behavior in different loading conditions and rates. Moreover, the algorithm has proved effective and robust. Further developments are being considered, such as the extension of the formulation to the finite-strain setting and the study of the boundary value problem.

Keywords: generalized gradient flow, GENERIC formalism, shape memory alloys, thermomechanical coupling

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Authors: Giovanni Cicceri, Roberta Maisano, Nathalie Morey, Salvatore Distefano

Abstract:

The main goal of this paper is to present a solution for a water purification system based on an Environmental Internet of Things (EIoT) platform to monitor and control water quality and machine learning (ML) models to support decision making and speed up the processes of purification of water. A real case study has been implemented by deploying an EIoT platform and a network of devices, called Gramb meters and belonging to the Gramb project, on wastewater purification systems located in Calabria, south of Italy. The data thus collected are used to control the wastewater quality, detect anomalies and predict the behaviour of the purification system. To this extent, three different statistical and machine learning models have been adopted and thus compared: Autoregressive Integrated Moving Average (ARIMA), Long Short Term Memory (LSTM) autoencoder, and Facebook Prophet (FP). The results demonstrated that the ML solution (LSTM) out-perform classical statistical approaches (ARIMA, FP), in terms of both accuracy, efficiency and effectiveness in monitoring and controlling the wastewater purification processes.

Keywords: environmental internet of things, EIoT, machine learning, anomaly detection, environment monitoring

Procedia PDF Downloads 133

Authors: Nilay K. Doshi

Abstract:

A theoretical probe describing the excited energy states of the electron density surrounding a nanoparticle (NP) is presented. An electromagnetic (EM) wave interacts with a NP much smaller than the incident wavelength. The plasmon that oscillates locally around the NP comprises of excited conduction electrons. The system is based on the Jellium model of a cluster of metal atoms. Hohenberg-Kohn (HK) equations and the variational Kohn-Sham (SK) scheme have been used to obtain the NP electron density in the ground state. Furthermore, a time-dependent density functional (TDDFT) theory is used to treat the excited states in a density functional theory (DFT) framework. The non-interacting fermionic kinetic energy is shown to be a functional of the electron density. The time dependent potential is written as the sum of the nucleic potential and the incoming EM field. This view of the quantum oscillation of the electron density is a part of the localized surface plasmon resonance.

Keywords: electron density, energy, electromagnetic, DFT, TDDFT, plasmon, resonance

Procedia PDF Downloads 310

Authors: Mahasen M. Abdel Mageed, H. S. Zaghloul

Abstract:

Annihilations, phase shifts, scattering lengths, and elastic cross sections of low energy positrons scattering from magnesium atoms were studied using the least-squares variational method (LSVM). The possibility of positron binding to the magnesium atoms is investigated. A trial wavefunction is suggested to represent e+-Mg elastic scattering and scattering parameters were derived to estimate the binding energy and annihilation rates. The trial function is taken to depend on several adjustable parameters and is improved iteratively by increasing the number of terms. The present results have the same behavior as reported semi-empirical, theoretical, and experimental results. Especially, the estimated positive scattering length supports the possibility of positron-magnesium bound state system that was confirmed in previous experimental and theoretical work.

Keywords: bound wavefunction, positron annihilation, scattering phase shift, scattering length

Procedia PDF Downloads 531