Electroencephalography (EEG) signals are the primary source for discriminating the preictal from the interictal stage, enabling early warnings before the seizure onset. The epileptic seizure prediction models face significant challenges due to data scarcity, diversity, and privacy. This paper proposes a three-tier architecture for epileptic seizure prediction associated with the Federated Learning (FL) model that enhances the capability by utilizing the significant amount of seizure patterns from globally distributed patients with data privacy. The determination of the preictal state is influenced by global and local model-assisted decision-making by modeling the two-level edge layer. Integrating the Spiking Encoder (SE) with Graph Convolutional Neural Network (Spiking-GCNN) works as the local model trained using the bi-timescale approach. Each local model utilizes the aggregated seizure knowledge from the different medical centers through FL and determines the preictal probability in the coarse-grained personalization. The Adaptive Neuro-Fuzzy Inference System (ANFIS) is utilized in fine-grained personalization to recognize epileptic seizure patients by examining the outcomes of the FL model, heart rate variability features, and patient-specific clinical features. The proposed seizure prediction is evaluated using benchmark datasets by comparing them with the existing works to demonstrate the potential results.

The accurate prediction of molecular properties such as lipophilicity and aqueous solubility are of great importance and pose challenges in several stages of the drug discovery pipeline. Machine learning methods like graph-based neural networks (GNNs) have shown exceptionally good performance in predicting these properties. In this work, we introduce a novel GNN architecture, called directed edge graph isomorphism network (D-GIN). It is composed of two distinct sub-architectures (D-MPNN, GIN) and achieves an improvement in accuracy over its sub-architectures employing various learning, and featurization strategies. We argue that combining models with different key aspects help make graph neural networks deeper and simultaneously increase their predictive power. Furthermore, we address current limitations in assessment of deep-learning models, namely, comparison of single training run performance metrics, and offer a more robust solution.

Social media platforms are entirely an undeniable part of the lifestyle from the past decade. Analyzing the information being shared is a crucial step to understand humans behavior. Social media analysis is aiming to guarantee a better experience for the user and risen user satisfaction. But first, it is necessary to know how and from which aspects to compare users with each other. In this paper, an intelligent system has been proposed to measure the similarity of Twitter profiles. For this, firstly, the timeline of each profile has been extracted using the official Twitter API. Then, all information is given to the proposed system. Next, in parallel, three aspects of a profile are derived. Behavioral ratios are time-series-related information showing the consistency and habits of the user. Dynamic time warping has been utilized for comparison of the behavioral ratios of two profiles. Next, Graph Network Analysis is used for monitoring the interactions of the user and its audience; for estimating the similarity of graphs, Jaccard similarity is used. Finally, for the Content similarity measurement, natural language processing techniques for preprocessing and TF-IDF for feature extraction are employed and then compared using the cosine similarity method. Results have presented the similarity level of different profiles. As the case study, people with the same interest show higher similarity. This way of comparison is helpful in many other areas. Also, it enables to find duplicate profiles; those are profiles with almost the same behavior and content.

The purpose of water treatment through ultraviolet (UV) radiation is to interrupt the development and multiplication of microorganisms by preventing their growth and reproduction.Ultraviolet treatment has become a very affordable solution to produce clean water of optimal quality in regions where access to drinking water is essential. The experimental water treatment unit is powered by a photovoltaic (PV) source. It incorporates a discharge lamp used to generate ultraviolet radiation, which is harnessed to address bacteriological issues related to water quality. This lamp is continuously powered by a photovoltaic (PV) source through an inverter and an electronic ballast. The water treatment system also includes a motor pump designed to draw contaminated water from the input reservoir, a flow control valve to adjust flow rates as needed, and a filter aimed at enhancing the quality of the contaminated water. The water circulates between the input reservoir (contaminated water) and the output reservoir (treated water) through the UV lamp. The relationship between the intensity of the UV lamp and the water flow rate can ensure an adequate water quality.

Every biological image contains quantitative data that can be used to test hypotheses about how patterns were formed, what entities are associated with one another, and whether standard mathematical methods inform our understanding of biological phenomena. In particular, spatial point distributions and polygonal tessellations are particularly amendable to analysis with a variety of graph theoretic, computational geometric, and spatial statistical tools such as: Voronoi Polygons; Delaunay Triangulations; Perpendicular Bisectors; Circumcenters; Convex Hulls; Minimal Spanning Trees; Ulam Trees; Pitteway Violations; Circularity; Clark-Evans spatial statistics; Variance to Mean Ratios; Gabriel Graphs; and, Minimal Spanning Trees. Furthermore, biologists have developed a number of empirically related correlations for polygonal tessellations such as: Lewis’s Law (the number of edges of convex polygons are positively correlated with the areas of these polygons): Desch’s Law (the number of edges of convex polygons are positively correlated with the perimeters of these polygons); and Errara’s Law (daughter cell areas should be roughly half that of their parent cells’ areas). We introduce a new Pitteway Law that the number of sides of the convex polygons in a Voronoi tessellation of biological epithelia is proportional to the minimal interior angle of the convex polygons as angles less than 90 degrees result in Pitteway violations of the Delaunay dual of the Voronoi tessellation.

Traffic shaping is a critical task in software-defined -IoT networks (SDN-IoTs) to efficiently manage network resources and ensure Quality of Service (QoS) for end-users. However, traditional traffic shaping approaches based on queuing theory or static policies may not be effective due to the dynamic and unpredictable nature of network traffic. In this paper, we propose a novel approach that leverages Graph Neural Networks (GNNs) and Multi-arm Bandit algorithms to dynamically optimize traffic shaping policies based on real-time network traffic patterns. Specifically, our approach uses a GNN model to learn and predict network traffic patterns and a Multi-arm Bandit algorithm to optimize traffic shaping policies based on these predictions. We evaluate the proposed approach on three different datasets, including a simulated corporate network (KDD Cup 1999), a collection of network traffic traces (CAIDA), and a simulated network environment with both normal and malicious traffic (NSL-KDD). The results demonstrate that our approach outperforms other state-of-the-art traffic shaping methods, achieving higher throughput, lower packet loss, and lower delay, while effectively detecting anomalous traffic patterns. The proposed approach offers a promising solution to traffic shaping in SDNs, enabling efficient resource management and QoS assurance

In this paper, we demonstrate a useful interaction between the theory of clique partitions, edge clique covers of a graph, and the spectra of graphs. Using a clique partition and an edge clique cover of a graph we introduce the notion of a vertex-clique incidence matrix for a graph and produce new lower bounds for the negative eigenvalues and negative inertia of a graph. Moreover, utilizing these vertex-clique incidence matrices, we generalize several notions such as the signless Laplacian matrix, and develop bounds on the incidence energy and the signless Laplacian energy of the graph. %The tight upper bounds for the energies of a graph and its line graph are given. More generally, we also consider the set $S(G)$ of all real-valued symmetric matrices whose off-diagonal entries are nonzero precisely when the corresponding vertices of the graph are adjacent. An important parameter in this setting is $q(G)$, and is defined to be the minimum number of distinct eigenvalues over all matrices in $S(G)$. For a given graph $G$ the concept of a vertex-clique incidence matrix associated with an edge clique cover is applied to establish several classes of graphs with $q(G)=2$.

Given several nonnegative matrices with a single pattern of allocation among their zero/nonzero elements, the average matrix should have the same pattern, too. This is the first tenet of the pattern-multiplicative average (PMA) concept, while the second one suggests the multiplicative (or geometric) nature of averaging. The original concept of PMA was motivated by the practice of matrix population models as a tool to assess the population viability from long-term monitoring data. The task has reduced to searching for an approximate solution to an overdetermined system of polynomial equations for unknown elements of the average matrix (G), hence to a nonlinear constrained minimization problem for the matrix norm. Former practical solutions faced certain technical problems, which required sophisticated algorithms but returned acceptable estimates. Fresh idea to use the eigenvalue approximation ensues also from the basic equation of averaging, which determines the exact value of λ1(G), the dominant eigenvalue of matrix G, too, and the corre-sponding eigenvector. These are bound by the well-known linear equations, which reduce the task to a standard problem of linear programing (LP). The LP approach is realized for 13 fixed-pattern matrices gained in a case study of Androsace albana, an alpine short-lived perennial, monitored on permanent plots during 14 years. A standard software routine reveals the unique exact solution, rather than an approximate one, to the PMA problem, which turns the LP approach into ‘’the best of versatile optimization tools”. The exact solution turns out to be peculiar in reaching zero bounds for certain nonnegative entries of G, which deserves a modified problem formulation separating the lower bounds from zero.

Creating self-learning algorithms, developing deep neural networks and improving other methods that "learn" for various areas of human activity is the main goal of the theory of machine learning. It helps to replace the human with a machine, aiming to increase the quality of production. The theory of artificial neural networks, which already have replaced the humans in problems of detection of moving objects, recognition of images or sounds, time series prediction, big data analysis and numerical methods remains the most dispersed branch of the theory of machine learning. Certainly, for each area of human activity it is necessary to select appropriate neural network architectures, methods of data processing and some novel tools from applied mathematics. But the universal problem for all these neural networks with specific data is the achieving the highest accuracy in short time. Such problem can be resolved by increasing sizes of architectures and improving data preprocessing, where the accuracy rises with the training time. But there is a possibility to increase the accuracy without time growing, applying optimization methods. In this survey we demonstrate existing optimization algorithms of all types, which can be used in neural networks. There are presented modifications of basic optimization algorithms, such as stochastic gradient descent, adaptive moment estimation, Newton and quasi-Newton optimization methods. But the most recent optimization algorithms are related to information geometry, for Fisher-Rao and Bregman metrics. This approach in optimization extended the theory of classic neural networks to quantum and complex-valued neural networks, due to geometric and probabilistic tools. There are provided applications of all introduced optimization algorithms, what delighted many kinds of neural networks, which can be improved by including any advanced approaches in minimization of the loss function. Afterwards, we demonstrated ways of developing optimization algorithms in further researches, engaging neural networks with progressive architectures. Classical gradient based optimizers can be replaced by fractional order, bilevel and, even, gradient free optimization methods. There is a possibility to add such analogues in graph, spiking, complex-valued, quantum and wavelet neural networks. Besides the usual problems of image recognition, time series prediction, object detection, there are many are other tasks for modern theory of machine learning, such as solving problem of quantum computations, partial differential and integro-differential equations, stochastic processes and Brownian motion, making decisions and computer algebra.

We prove a version of Ekeland Variational Principle (EkVP) in a weighted graph $G$ and its equivalence to Caristi fixed point theorem and to Takahashi minimization principle. The usual completeness and topological notions are replaced with some weaker versions expressed in terms of the graph $G$. The main tool used in the proof is the OSC property for sequences in a graph. Converse results, meaning the completeness of graphs for which one of these principles holds is also considered.

This paper presents a novel approach to demonstrate the Collatz Conjecture, an unsolved problem in mathematics stating that all positive integers will eventually converge to 1 when subjected to a recursive sequence of operations. We introduce Algebraic Inverse Trees (AITs), innovative data structures that characterize relationships within the Collatz sequence by tracing inverse transformations back to the origin. Leveraging properties unveiled through this inverted representation, including absence of non-trivial cycles and guaranteed convergence of paths, we construct a topological framework to formally prove that all trajectories invariably lead to 1 under the Collatz iterative process. This modern technique provides not only the machinery to manifest a rigorous proof, but also grants intuitive insights into the deep complexity of this notorious yet elementary conjecture.

Maintaining a healthy cyber society is a big challenge due to the users’ freedom of expression and behaving. It can be solved by monitoring and analyzing the users’ behavior and taking proper actions towards them. This research aims to present a platform that monitors the public content on Twitter by extracting tweet data. After maintaining the data, the users’ interactions are analyzed using Graph Analysis methods. Then the users’ behavioral patterns are analyzed by applying Metadata Analysis, in which the timeline of each profile is obtained; also, the time-series behavioral features of users are investigated. Then in the Abnormal Behavior Detection Filtering component, the interesting profiles are selected for further examinations. Finally, in the Contextual Analysis component, the contents will be analyzed using natural language processing techniques; A binary text classification model (SVM + TF-IDF with 88.89% accuracy) for detecting if the tweet is related to crime or not. Then, a sentiment analysis method is applied to the crime-related tweets to perform aspect-based sentiment analysis (DistilBERT + FFNN with 80% accuracy); because sharing positive opinions about a crime-related topic can threaten society. This platform aims to provide the end-user (Police) suggestions to control hate speech or terrorist propaganda.

Various factors, such as uncertainty of component parameters and uncertainty of sensor meas-urement values, contribute to the difficulty of fault detection in the landing gear retrac-tion/extension hydraulic system. In this paper, we introduce linear fractional transformation technology and uncertainty analysis theory for the construction of the diagnostic bond graph of the landing gear retraction/extension hydraulic system. In this way, interval analytical redundancy relations and fault signature matrix can be derived. Using the fault signature matrix, existing faults of the system can be preliminarily detected and isolated. Additionally, interval analytical re-dundancy relations can be used to detect system faults in detail, and cases analysis can be carried out to determine if the actuator is externally or internally leaky, and if the landing gear selector valve is reversing stuck. Compared to the traditional analytical redundancy relations, this method takes into account the negative factors of uncertainty; and compared to the traditional absolute diagnostic threshold, the interval diagnostic threshold is more accurate and sensitive.

With the growth of air traffic demand in busy airspace, there is an urgent need for airspace sectorization to increase air traffic throughput and ease the pressure on controllers. The purpose of this paper is to develop a method framework that can perform airspace sectorization automatically, reasonably, which can be used as an advisory tool for controllers as an automatic system, especially for eliminating irregular sector shapes generated by simulated annealing algorithm (SAA) based on region growth method. Two graph cutting method, dynamic Monte Carlo method by changing location of flexible vertices (MC-CLFV) and Monte Carlo method by radius changing (MC-RC) were developed to eliminating irregular sector shapes generated by SAA in post-processing. The experimental results show that the proposed method framework of AS can automatically and reasonably generate sector design schemes that meet the design criteria. Our methodology framework and software can provide assistant design and analysis tools for airspace planners to design airspace, improve the reliability and efficiency of airspace design, and reduce the burden of airspace planners. In addition, this lays the foundation for reconstructing airspace with more intelligent method.

The influence and importance of research and development (R&D) for business sustainability have gained increasing interests, especially in the high-tech sector. However, the efforts of R&D might cause complex and mixed impacts on the financial results considering the associated expenses. Thus, this study aims to examine how R&D efforts may influence business to improve its financial performance considering the dual objectives: the gross and the net profitability. This research integrated a rough-set-based soft computing technique and multiple criteria decision-making (MCDM) methods to explore this complex and yet valuable issue. A group of public listed companies from Taiwan, all in the semiconductor sector, was analyzed as a case study. Initially, more than 30 variables were considered, and the adopted soft computing technique retrieved 14 core attributes—for the dual profitability objectives—to form the evaluation model. The importance of R&D for pursuing superior financial prospects is confirmed, and the empirical case demonstrates how to guide an individual company to plan for improvements to achieve its long-term sustainability by this hybrid approach.

Smart grid software interconnects multiple Engineering disciplines (power systems, communication, software and hardware technology, instrumentation, big data, etc.). The software architecture is an evolving concept in smart grid systems in which systematic architecture development is a challenging process. The architecture has to realize the complex legacy power grid systems and cope up with current Information and Communication Technologies (ICT). The distributed generation in smart grid environment expects the software architecture to be distributed and to enable local control. Smart grid architecture should also be modular, flexible and adaptable to technology upgrades. In this paper, the authors have made a comprehensive review on architecture for smart grids. An in depth analysis of layered and agent based architectures is presented and compared under various domains.

This paper offers a novel geometric and visual approach to the renowned Four Color Map Theorem and K5 non-planarity problem while unveiling their profound connection to the "kissing number" problem in 2D. We represent planar graphs through circles and tangents, simplifying complex structures and shedding light on these classic problems. Our proofs by contradiction, rooted in the kissing number concept, reveal that both the Four Color Map Theorem and K5 non-planarity are fundamentally linked, as they pivot around the concept of coloring. This study bridges the realms of geometry and graph theory, providing fresh insights and emphasizing the significance of the kissing number problem in various fields.