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In this study, we derive a simple transportation scheme by post-optimizing the costs of a modified problem. The strategy attempts to make the original (mainly feasible) option more practicable by adjusting the building components' costs. Next, we employ the previously mentioned cell or area cost operators to gradually restore the modified costs to their initial levels, while simultaneously implementing the necessary adjustments to the "optimal" solution. This work presents a multi-goal, multi-item substantial transportation problem with interval-valued fuzzy variables, such as transportation costs, supplies, and demands, as parameters to maintain the transportation cost. This research addresses two circumstances where task ambiguity may occur: the interval solids transportation problem and the fuzzy substantial transportation issue. In the first scenario, we express data problems as intervals instead of exact values using an interval-valued fermatean neutrosophic number; in the second case, the information is not entirely obvious. We address both models when uncertainty solely affects the constraint set. For the interval scenario, we define an additional problem to solve. Our existing efficient systems have dependable transportation, so they are also capable of handling this new problem. In the fuzzy case, a parametric technique generates a fuzzy solution to the preceding problem. Since transportation costs have a direct impact on market prices, lowering them is the primary goal. Using parametric analysis, we provide optimal parameterization solutions for complementary situations. We provide a recommended algorithm for determining the stability set. In conclusion, we offer a sensitivity analysis and a numerical example of the transportation problem involving both balanced and imbalanced loads. [ABSTRACT FROM AUTHOR]

Researchers have created cryptography algorithms that encrypt data using a public or private key to secure it from intruders. It is insufficient to protect the data by using such a key. No research article has identified an algorithm capable of protecting both the data and the associated key, nor has any mechanism been developed to determine whether access to the data is permissible or impermissible based on the authentication of the key. This paper presents a WEDEx-Kerberotic Framework for data protection, in which a user-defined key is firstly converted to a cipher key using the "Secure Words on Joining Key (SWJK)" algorithm. Subsequently, a WEDEx-Kerberotic encryption mechanism is created to protect the data by encrypting it with the cipher key. The first reason for making the WEDEx-Kerberotic Framework is to convert the user-defined key into a key that has nothing to do with the original key, and the length of the cipher key is much shorter than the original key. The second reason is that each ciphertext and key value are interlinked. When an intruder utilizes the snatching mechanism to obtain data, the attacker obtains data or a key unrelated to the original data. No matter how efficient the algorithm is, an attacker cannot access the data when these methods and algorithms are used to protect it. Finally, the proposed algorithm is compared to the previous approaches to determine the uniqueness of the algorithm and assess its superiority to the previous algorithms. [ABSTRACT FROM AUTHOR]

This study formulates a multi-objective, multi-item solid transportation issue with parameters that are neutrosophic Z-number fuzzy variables such as transportation costs, supplies, and demands. This work covers two scenarios where uncertainty in the problem can arise: the fuzzy solid transportation problem and the interval solid transportation problem. The first scenario arises when we represent data problems as intervals instead of exact values, while the second scenario arises when the information is not entirely clear. We address both models when the uncertainty alone impacts the constraint set. In order to find a solution for the interval case, we generate an additional problem. Since this auxiliary problem is typical of solid transportation, we can resolve it using the effective techniques currently in use. In the fuzzy scenario, a parametric method is used to discover a fuzzy solution to the earlier issue. Parametric analysis identifies that the best parameterized approaches to complementary problems are characterized by the application of parametric analysis. We present a suggested algorithm for determining the stability set. Finally, we provide a numerical example and sensitivity analysis for the transportation problem, which is both symmetrical and asymmetrical. [ABSTRACT FROM AUTHOR]

In this paper, we suggest a modification for the residual power series method that is used to solve fractional-order Helmholtz equations, which is called the Shehu-transform residual power series method (S T-RPSM). This scheme uses a combination of the Shehu transform (S T) and the residual power series method (RPSM). The fractional derivatives are taken with respect to Caputo order. The novelty of this approach is that it does not restrict the fractional order and reduces the need for heavy computational work. The results were obtained using an iterative series that led to an exact solution. The 3D graphical plots for different values of fractional orders are shown to compare S T-RPSM results with exact solutions. [ABSTRACT FROM AUTHOR]

In nature, symmetry is all around us. The symmetry framework represents integer partial differential equations and their fractional order in the sense of Caputo derivatives. This article suggests a semi-analytical approach based on Aboodh transform (A T) and the homotopy perturbation scheme (HPS) for achieving the approximate solution of time-fractional porous media and heat transfer equations. The A T converts the fractional problems into simple ones and obtains the recurrence relation without any discretization or assumption. This nonlinear recurrence relation can be decomposed via the use of the HPS to obtain the iterations in terms of series solutions. The initial conditions play an important role in determining the successive iterations and yields towards the exact solution. We provide some numerical applications to analyze the accuracy of this proposed scheme and show that the performance of our scheme has strong agreement with the exact results. [ABSTRACT FROM AUTHOR]

Symmetries are crucial to the investigation of nonlinear physical processes, particularly the evaluation of a differential problem in the real world. This study focuses on the investigation of the Kadomtsev–Petviashvili (KP) model within a (3+1)-dimensional domain, governing the behavior of wave propagation in a medium characterized by both nonlinearity and dispersion. The inquiry employs two distinct analytical techniques to derive multiple soliton solutions and multiple solitary wave solutions. These methods include the modified Sardar sub-equation technique and the Darboux transformation (DT) . The modified Sardar sub-equation technique is used to obtain multiple soliton solutions, while the DT is introduced to develop two bright and two dark soliton solutions. These solutions are presented alongside their corresponding constraint conditions and illustrated through 3-D, 2-D, and contour plots to physically portray the derived solutions. The results demonstrate that the employed analytical techniques are useful and have not yet been explored in the context of the analyzed models. The proposed methodologies are valuable and can be applied to additional nonlinear evolutionary models employed to describe nonlinear physical models within the domain of nonlinear science. [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]

Graphs are useful for analysing the structure models in computer science, operations research, and sociology. The word metric dimension is the basis of the distance function, which has a symmetric property. Moreover, finding the resolving set of a graph is NP-complete, and the possibilities of finding the resolving set are reduced due to the symmetric behaviour of the graph. In this paper, we introduce the idea of the edge-multiset dimension of graphs. A representation of an edge is defined as the multiset of distances between it and the vertices of a set, B ⊆ V (Γ) . If the representation of two different edges is unequal, then B is an edge-multiset resolving a set of Γ. The least possible cardinality of the edge-multiset resolving a set is referred to as the edge-multiset dimension of Γ. This article presents preliminary results, special conditions, and bounds on the edge-multiset dimension of certain graphs. This research provides new insights into structure models in computer science, operations research, and sociology. They could have implications for developing computer algorithms, aircraft scheduling, and species movement between regions. [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]

The study of dynamic systems appears in various aspects of dynamical structures such as decomposition, decoupling, observability, and controllability. In the present research, we study the controllability of fractional stochastic systems (FSF) and examine the Poisson jumps in finite dimensional space where the fractional impulsive neutral stochastic system is controllable. Sufficient conditions are demonstrated with the aid of fixed point theory. The Mittag-Leffler (ML) matrix function defines the controllability of the Grammian matrix (GM). The relation to symmetry is clear since the controllability Grammian is a hermitian matrix (since the integrand in its definition is hermitian) and this is the complex version of a symmetric matrix. In fact, such a Grammian becomes a symmetric matrix in the specific scenario where the controllability Grammian is a real matrix. Some examples are provided to demonstrate the feasibility of the present theory. [ABSTRACT FROM AUTHOR]

This article presents an idea of a new approach for the solitary wave solution of the modified Degasperis–Procesi (mDP) and modified Camassa–Holm (mCH) models with a time-fractional derivative. We combine Laplace transform (L T) and homotopy perturbation method (HPM) to formulate the idea of the Laplace transform homotopy perturbation method (L HPTM). This study is considered under the Caputo sense. This proposed strategy does not depend on any assumption and restriction of variables, such as in the classical perturbation method. Some numerical examples are demonstrated and their results are compared graphically in 2D and 3D distribution. This approach presents the iterations in the form of a series solutions. We also compute the absolute error to show the effective performance of this proposed scheme. [ABSTRACT FROM AUTHOR]

The critical component of HCI is face recognition technology. Emotional computing heavily relies on the identification of facial emotions. Applications for emotion-driven face animation and dynamic assessment are numerous (FER). Universities have started to support real-world face expression recognition research as a result. Short video clips are continually uploaded and shared online, building up a library of videos on various topics. The enormous amount of movie data appeals to system engineers and researchers of autonomous emotion mining and sentiment analysis. The main idea is that categorizing things may be done by looking at how individuals feel about specific issues. People might choose to have a basic or complex facial appearance. People worldwide continually express their feelings through their faces, whether they are happy, sad, or uncertain. An online user can visually express themselves through a video's editing, music, and subtitles. Additionally, before the video data can be used, noise in the data must frequently be eliminated. Automatically figuring out how someone feels in a video is a challenging task that will only get harder over time. Therefore, this paper aims to show how facial recognition video analysis can be used to show how sentiment analysis can help with business growth and essential decision-making. To determine how people are affected by reviewers' writing, we use a technique for deciding emotions in this analysis. The feelings in movies are assessed using machine learning algorithms to categorize them. A lightweight machine learning algorithm is proposed to help in Aspect-oriented emotion classification for movie reviews. Moreover, to analyze real and published datasets, experimental results are compared with different Machine Learning algorithms, i.e., Naive Bayes, Support Vector Machine, Random Forest, and CNN. The proposed approach obtained 84.72 accuracy and 79.24 sensitivity. Furthermore, the method has a specificity of 90.64 and a precision of 90.2. Thus, the proposed method significantly increases the accuracy and sensitivity of the emotion detection system from facial feature recognition. Our proposed algorithm has shown contribution to detect datasets of different emotions with symmetric characteristics and symmetrically-designed facial image recognition tasks. [ABSTRACT FROM AUTHOR]

The symmetry design of the system contains integer partial differential equations and fractional-order partial differential equations with fractional derivative. In this paper, we develop a scheme to examine fractional-order shock wave equations and wave equations occurring in the motion of gases in the Caputo sense. This scheme is formulated using the Mohand transform (MT) and the homotopy perturbation method (HPM), altogether called Mohand homotopy perturbation transform (MHPT). Our main finding in this paper is the handling of the recurrence relation that produces the series solutions after only a few iterations. This approach presents the approximate and precise solutions in the form of convergent results with certain countable elements, without any discretization or slight perturbation theory. The numerical findings and solution graphs attained using the MHPT confirm that this approach is significant and reliable. [ABSTRACT FROM AUTHOR]

The algebras of the symmetry operators for the Klein–Gordon equation are important for a charged test particle, moving in an external electromagnetic field in a space time manifold on the isotropic hydrosulphate. In this paper, we develop an analytical and numerical approach for providing the solution to a class of linear and nonlinear fractional Klein–Gordon equations arising in classical relativistic and quantum mechanics. We study the Yang homotopy perturbation transform method (Y HPTM), which is associated with the Yang transform (Y T) and the homotopy perturbation method (HPM), where the fractional derivative is taken in a Caputo–Fabrizio (CF) sense. This technique provides the solution very accurately and efficiently in the form of a series with easily computable coefficients. The behavior of the approximate series solution for different fractional-order ℘ values has been shown graphically. Our numerical investigations indicate that Y HPTM is a simple and powerful mathematical tool to deal with the complexity of such problems. [ABSTRACT FROM AUTHOR]