Search Results (16)

This paper introduces the notion of screen generic lightlike submanifolds (SGLSs) of an indefinite Kaehler statistical manifold equipped with a quarter-symmetric non-metric (QSNM) connection, supported by suitable illustrations. Assertions for induced connection on the lightlike submanifold and integrability of the distributions are proved. The characterization theorems on parallelism and geodesicity of the SGLSs are presented. Results for the totally umbilic screen generic lightlike submanifold with a QSNM connection are also established. Full article

In this paper, different aspects of the concept of spin are studied. The most well-established one is, of course, the quantum mechanical aspect: spin is a broken symmetry in the sense that the solutions of the Dirac equation tend to have directional properties that cannot be seen in the equation itself. It has been clear since the early days of quantum mechanics that this has something to do with the indefinite metric in Lorentz geometry, but the mechanism behind this connection is elusive. Although spin is not the same as rotation in the usual sense, there must certainly be a close relationship between these concepts. And, a possible way to investigate this connection is to instead start from the underlying geometry in general relativity. Is there a reason why rotating motion in Lorentz geometry should be more natural than non-rotating motion? In a certain sense, the answer turns out to be yes. But, it is by no means easy to see what this should correspond to in the usual quantum mechanical picture. On the other hand, it seems very unlikely that the similarities should be just coincidental. The interpretation of the author is that this can be a golden opportunity to investigate the interplay between these two theories. Full article

Cloud organizations now face a challenge in managing the enormous volume of data and various resources in the cloud due to the rapid growth of the virtualized environment with many service users, ranging from small business owners to large corporations. The performance of cloud computing may suffer from ineffective resource management. As a result, resources must be distributed fairly among various stakeholders without sacrificing the organization’s profitability or the satisfaction of its customers. A customer’s request cannot be put on hold indefinitely just because the necessary resources are not available on the board. Therefore, a novel cloud resource allocation model incorporating security management is developed in this paper. Here, the Deep Linear Transition Network (DLTN) mechanism is developed for effectively allocating resources to cloud systems. Then, an Adaptive Mongoose Optimization Algorithm (AMOA) is deployed to compute the beamforming solution for reward prediction, which supports the process of resource allocation. Moreover, the Logic Overhead Security Protocol (LOSP) is implemented to ensure secured resource management in the cloud system, where Burrows–Abadi–Needham (BAN) logic is used to predict the agreement logic. During the results analysis, the performance of the proposed DLTN-LOSP model is validated and compared using different metrics such as makespan, processing time, and utilization rate. For system validation and testing, 100 to 500 resources are used in this study, and the results achieved a make-up of 2.3% and a utilization rate of 13 percent. Moreover, the obtained results confirm the superiority of the proposed framework, with better performance outcomes. Full article

The software defined network (SDN) collects network traffic data and proactively manages networks. SDN’s programmability makes it excellent for developing distributed applications, cybersecurity, and decentralized network control in multitenant data centers. This exceptional architecture is vulnerable to security concerns, such as distributed denial of service (DDoS) attacks. DDoS attacks can be very serious due to the fact that they prevent authentic users from accessing, temporarily or indefinitely, resources they would normally expect to have. Moreover, there are continuous efforts from attackers to produce new techniques to avoid detection. Furthermore, many existing DDoS detection methods now in use have a high potential for producing false positives. This motivates us to provide an overview of the research studies that have already been conducted in this area and point out the strengths and weaknesses of each of those approaches. Hence, adopting an optimal detection method is necessary to overcome these issues. Thus, it is crucial to accurately detect abnormal flows to maintain the availability and security of the network. In this work, we propose hybrid deep learning algorithms, which are the long short-term memory network (LSTM) and convolutional neural network (CNN) with a stack autoencoder for DDoS attack detection and checkpoint network, which is a fault tolerance strategy for long-running processes. The proposed approach is trained and tested with the aid of two DDoS attack datasets in the SDN environment: the DDoS attack SDN dataset and Botnet dataset. The results show that the proposed model achieves a very high accuracy, reaching 99.99% in training, 99.92% in validation, and 100% in precision, recall, and F1 score with the DDoS attack SDN dataset. Also, it achieves 100% in all metrics with the Botnet dataset. Experimental results reveal that our proposed model has a high feature extraction ability and high performance in detecting attacks. All performance metrics indicate that the proposed approach is appropriate for a real-world flow detection environment. Full article

Background: The Sella Turcica is a critical structure from an orthodontic perspective, and its morphological characteristics can help in understanding craniofacial deformities. However, accurately extracting Sella Turcica shapes can be challenging due to the indistinct edges and indefinite boundaries present in X-ray images. This study aimed to develop and validate an automated Sella Morphology Network (SellaMorph-Net), a hybrid deep learning pipeline for segmenting Sella Turcica structure and extracting different morphological types; Methods: The SellaMorph-Net model proposed in this study combined attention-gating and recurrent residual convolutional layers (AGM and RrCL) to enhance the encoder’s abilities. The model’s output was then passed through a squeeze-and-excitation (SE) module to improve the network’s robustness. In addition, dropout layers were added to the end of each convolution block to prevent overfitting. A Zero-shot classifier was employed for multiple classifications, and the model’s output layer used five colour codes to represent different morphological types. The model’s performance was evaluated using various quantitative metrics, such as global accuracy and mean pixel-wise Intersection over Union (IoU) and dice coefficient, based on qualitative results; Results: The study collected 1653 radiographic images and categorised them into four classes based on the predefined shape of Sella Turcica. These classes were further divided into three subgroups based on the complexity of the Sella structures. The proposed SellaMorph-Net model achieved a global accuracy of 97.570, mean pixel-wise IoU scores of 0.7129, and a dice coefficient of 0.7324, significantly outperforming the VGG-19 and InceptionV3 models. The publicly available IEEE ISBI 2015 challenge dataset and our dataset were used to evaluate the test performance between the state-of-the-art and proposed models. The proposed model provided higher testing results, which were 0.7314 IoU and 0.7768 dice for our dataset and 0.7864 IoU and 0.8313 dice for the challenge dataset; Conclusions: The proposed hybrid SellaMorph-Net model provides an accurate and reliable pipeline for detecting morphological types of Sella Turcica using full lateral cephalometric images. Future work will focus on further improvement and utilisation of the developed model as a prognostic tool for predicting anomalies related to Sella structures. Full article

Our research focuses on the tangent space of a point on a four-dimensional Riemannian manifold. Besides having a positive definite metric, the manifold is endowed with an additional tensor structure of type $(1,1)$, whose fourth power is minus the identity. The additional structure is skew-circulant and compatible with the metric, such that an isometry is induced in every tangent space on the manifold. Both structures define an indefinite metric. With the help of the indefinite metric, we determine circles in different two-planes in the tangent space on the manifold. We also calculate the length and area of the circles. On a smooth closed curve, such as a circle, we define a vector force field. Further, we obtain the circulation of the vector force field along the curve, as well as the flux of the curl of this vector force field across the curve. Finally, we find a relation between these two values, which is an analog of the well-known Green’s formula in the Euclidean space. Full article

Different hypotheses of carcinogenesis have been proposed based on local genetic factors and physiologic mechanisms. It is assumed that changes in the metric invariants of a biologic system (BS) determine the general mechanisms of cancer development. Numerous pieces of data demonstrate the existence of three invariant feedback patterns of BS: negative feedback (NFB), positive feedback (PFB) and reciprocal links (RL). These base patterns represent basis elements of a Lie algebra $sl\left(2,R\right)$ and an imaginary part of coquaternion. Considering coquaternion as a model of a functional core of a BS, in this work a new geometric approach has been introduced. Based on this approach, conditions of the system are identified with the points of three families of hypersurfaces in R⁴₂: hyperboloids of one sheet, hyperboloids of two sheets and double cones. The obtained results also demonstrated the correspondence of an indefinite metric of coquaternion quadratic form with negative and positive entropy contributions of the base elements to the energy level of the system. From that, it can be further concluded that the anabolic states of the system will correspond to the points of a hyperboloid of one sheet, whereas catabolic conditions correspond to the points of a hyperboloid of two sheets. Equilibrium states will lie in a double cone. Physiologically anabolic and catabolic states dominate intermittently oscillating around the equilibrium. Deterioration of base elements increases positive entropy and causes domination of catabolic states, which is the main metabolic determinant of cancer. Based on these observations and the geometric representation of a BS’s behavior, it was shown that conditions related to cancer metabolic malfunction will have a tendency to remain inside the double cone. Full article

In recent years, q-rung orthopair fuzzy sets (q-ROFSs), a novel and rigorous generalization of the fuzzy set (FS) coined by Yager in 2017, have been used to manage inexplicit and indefinite information in daily life with a high precision and greater accuracy than intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFSs). The characterization of a measure of similarity between q-ROFSs is important, as they have applications in different areas, including pattern recognition, clustering, image segmentation and decision making. Therefore, this article is dedicated to the construction of a measure of similarity between q-ROFSs based on the Hausdorff metric. This is a very useful tool for establishing the similarity between two objects. Furthermore, some axiomatic definitions of the distances and similarity measures of q-ROFSs are also presented. In this article, we first present a novel method to calculate the distance between q-ROFSs based on the Hausdorff metric. We then utilize our proposed distance measure to construct the degree of similarity between q-ROFSs. We provide some properties for the proposed similarity measures. We offer several numerical examples related to pattern recognition and characterization linguistic variables to demonstrate the usefulness of the proposed similarity measures. We construct an algorithm for orthopair fuzzy TODIM (interactive and multi-criteria decision making, in Portuguese) based on our proposed methods. Finally, we use the constructed orthopair fuzzy TODIM method to address problems related to daily life settings involving multi-criteria decision making (MCDM). The numerical results show that the proposed similarity measures are suitable, applicable and well-suited to the contexts of pattern recognition, queries with fuzzy linguistic variables and MCDM. Full article

In this paper, we study the properties of $ϵ$-Kenmotsu manifolds if its metrics are $*\eta$-Ricci-Yamabe solitons. It is proven that an $ϵ$-Kenmotsu manifold endowed with a $*\eta$-Ricci-Yamabe soliton is $\eta$-Einstein. The necessary conditions for an $ϵ$-Kenmotsu manifold, whose metric is a $*\eta$-Ricci-Yamabe soliton, to be an Einstein manifold are derived. Finally, we model an indefinite Kenmotsu manifold example of dimension 5 to examine the existence $*\eta$-Ricci-Yamabe solitons. Full article

We study the semi-Riemannian geometry of the foliation $\mathcal{F}$ of an indefinite locally conformal Kähler (l.c.K.) manifold M, given by the Pfaffian equation $\omega =0$, provided that $\nabla \omega =0$ and $c=\parallel \omega \parallel \ne 0$ ($\omega$ is the Lee form of M). If M is conformally flat then every leaf of $\mathcal{F}$ is shown to be a totally geodesic semi-Riemannian hypersurface in M, and a semi-Riemannian space form of sectional curvature $c/4$, carrying an indefinite c-Sasakian structure. As a corollary of the result together with a semi-Riemannian version of the de Rham decomposition theorem any geodesically complete, conformally flat, indefinite Vaisman manifold of index $2s$, $0<s<n$, is locally biholomorphically homothetic to an indefinite complex Hopf manifold $\mathbb{C}{H}_s^n\left(\lambda \right)$, $0<\lambda <1$, equipped with the indefinite Boothby metric $g_{s,n}$. Full article

Higher dimensional theories, wherein our four dimensional universe is immersed into a bulk ambient, have received much attention recently, and the directions of investigation had, as far as we can discern, all followed the ordinary Euclidean hypersurface theory’s isometric immersion recipe, with the spacetime metric being induced by an ambient parent. We note, in this paper, that the indefinite signature of the Lorentzian metric perhaps hints at the lesser known equiaffine hypersurface theory as being a possibly more natural, i.e., less customized beyond minimal mathematical formalism, description of our universe’s extrinsic geometry. In this alternative, the ambient is deprived of a metric, and the spacetime metric becomes conformal to the second fundamental form of the ordinary theory, therefore is automatically indefinite for hyperbolic shapes. Herein, we advocate investigations in this direction by identifying some potential physical benefits to enlisting the help of equiaffine differential geometry. In particular, we show that a geometric origin for dark energy can be proposed within this framework. Full article

Social media and other forms of volunteered geographic information (VGI) are used frequently as a source of fine-grained big data for research. While employing geographically referenced social media data for a wide array of purposes has become commonplace, the relevant scales over which these data apply to is typically unknown. For researchers to use VGI appropriately (e.g., aggregated to areal units (e.g., neighbourhoods) to elicit key trend or demographic information), general methods for assessing the quality are required, particularly, the explicit linkage of data quality and relevant spatial scales, as there are no accepted standards or sampling controls. We present a data quality metric, the Spatial-comprehensiveness Index (S-COM), which can delineate feasible study areas or spatial extents based on the quality of uneven and dynamic geographically referenced VGI. This scale-sensitive approach to analyzing VGI is demonstrated over different grains with data from two citizen science initiatives. The S-COM index can be used both to assess feasible study extents based on coverage, user-heterogeneity, and density and to find feasible sub-study areas from a larger, indefinite area. The results identified sub-study areas of VGI for focused analysis, allowing for a larger adoption of a similar methodology in multi-scale analyses of VGI. Full article

We investigate whether Szabo’s metrizability theorem can be extended to Finsler spaces of indefinite signature. For smooth, positive definite Finsler metrics, this important theorem states that, if the metric is of Berwald type (i.e., its Chern–Rund connection defines an affine connection on the underlying manifold), then it is affinely equivalent to a Riemann space, meaning that its affine connection is the Levi–Civita connection of some Riemannian metric. We show for the first time that this result does not extend to general Finsler spacetimes. More precisely, we find a large class of Berwald spacetimes for which the Ricci tensor of the affine connection is not symmetric. The fundamental difference from positive definite Finsler spaces that makes such an asymmetry possible is the fact that generally, Finsler spacetimes satisfy certain smoothness properties only on a proper conic subset of the slit tangent bundle. Indeed, we prove that when the Finsler Lagrangian is smooth on the entire slit tangent bundle, the Ricci tensor must necessarily be symmetric. For large classes of Finsler spacetimes, however, the Berwald property does not imply that the affine structure is equivalent to the affine structure of a pseudo-Riemannian metric. Instead, the affine structure is that of a metric-affine geometry with vanishing torsion. Full article

In the present paper, we study conformal mappings between a connected n-dimension pseudo-Riemannian Einstein manifolds. Let g be a pseudo-Riemannian Einstein metric of indefinite signature on a connected n-dimensional manifold M. Further assume that there is a point at which not all sectional curvatures are equal and through which in linearly independent directions pass n complete null (light-like) geodesics. If, for the function $\psi$ the metric ${\psi }^{-2}g$ is also Einstein, then $\psi$ is a constant, and conformal mapping is homothetic. Note that Kiosak and Matveev previously assumed that all light-lines were complete. If the Einstein manifold is closed, the completeness assumption can be omitted (the latter result is due to Mikeš and Kühnel). Full article

We investigate recurrent, Lie-recurrent, and Hopf lightlike hypersurfaces of an indefinite trans-Sasakian manifold with a semi-symmetric metric connection. In these hypersurfaces, we obtain several new results. Moreover, we characterize that the total space (an indefinite generalized Sasakian space form) with a semi-symmetric metric connection is an indefinite Kenmotsu space form under various lightlike hypersurfaces. Full article