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In this paper, we consider the inverse problem for identifying the initial value problem of the time–space fractional nonlinear diffusion equation. The uniqueness of the solution is proved by taking the fixed point theorem of Banach compression, and the ill-posedness of the problem is analyzed through the exact solution. The quasi-boundary regularization method is chosen to solve the ill-posed problem, and the error estimate between the regularization solution and the exact solution is given. Moreover, several numerical examples are chosen to prove the effectiveness of the quasi-boundary regularization method. Finally, our method can be used to solve high dimensional time–space fractional nonlinear diffusion equation, especially in cylindrical and spherical symmetric regions. [ABSTRACT FROM AUTHOR]

The task of analyzing sentiment has been extensively researched for a variety of languages. However, due to a dearth of readily available Natural Language Processing methods, Urdu sentiment analysis still necessitates additional study by academics. When it comes to text processing, Urdu has a lot to offer because of its rich morphological structure. The most difficult aspect is determining the optimal classifier. Several studies have incorporated ensemble learning into their methodology to boost performance by decreasing error rates and preventing overfitting. However, the baseline classifiers and the fusion procedure limit the performance of the ensemble approaches. This research made several contributions to incorporate the symmetries concept into the deep learning model and architecture: firstly, it presents a new meta-learning ensemble method for fusing basic machine learning and deep learning models utilizing two tiers of meta-classifiers for Urdu. The proposed ensemble technique combines the predictions of both the inter- and intra-committee classifiers on two separate levels. Secondly, a comparison is made between the performance of various committees of deep baseline classifiers and the performance of the suggested ensemble Model. Finally, the study's findings are expanded upon by contrasting the proposed ensemble approach efficiency with that of other, more advanced ensemble techniques. Additionally, the proposed model reduces complexity, and overfitting in the training process. The results show that the classification accuracy of the baseline deep models is greatly enhanced by the proposed MLE approach. [ABSTRACT FROM AUTHOR]

In this manuscript, we study the inverse problem for identifying the initial value of a time-fractional diffusion equation in an axisymmetric region. This is an ill-posed problem, i.e., the solution does not depend continuously on the data. We choose the Landweber iterative regularization method to solve this problem. Under the a priori and the a posteriori regularization parameter choice rules, we present the error estimates between the regularization solutions and the exact solution. We present some examples to show this method's effectiveness. [ABSTRACT FROM AUTHOR]

News media agencies are known to publish misinformation, disinformation, and propaganda for the sake of money, higher news propagation, political influence, or other unfair reasons. The exponential increase in the use of social media has also contributed to the frequent spread of fake news. This study extends the concept of symmetry into deep learning approaches for advanced natural language processing, thereby improving the identification of fake news and propaganda. A hybrid HyproBert model for automatic fake news detection is proposed in this paper. To begin, the proposed HyproBert model uses DistilBERT for tokenization and word embeddings. The embeddings are provided as input to the convolution layer to highlight and extract the spatial features. Subsequently, the output is provided to BiGRU to extract the contextual features. The CapsNet, along with the self-attention layer, proceeds to the output of BiGRU to model the hierarchy relationship among the spatial features. Finally, a dense layer is implemented to combine all the features for classification. The proposed HyproBert model is evaluated using two fake news datasets (ISOT and FA-KES). As a result, HyproBert achieved a higher performance compared to other baseline and state-of-the-art models. [ABSTRACT FROM AUTHOR]

In this paper, the inverse problem for identifying the initial value of a time fractional nonhomogeneous diffusion equation in a columnar symmetric region is studied. This is an ill-posed problem, i.e., the solution does not depend continuously on the data. The fractional Tikhonov regularization method is applied to solve this problem and obtain the regularization solution. The error estimations between the regularization solution and the exact solution are also obtained under the priori and the posteriori regularization parameter choice rules, respectively. Some examples are given to show this method's effectiveness. [ABSTRACT FROM AUTHOR]