Let a topological space. An intersection GRAPH on a topological space, which denoted by , is an undirected GRAPH which whose vertices are open subsets of and two vertices are adjacent if the intersection of them are nonempty. In this paper, the relation between topological properties of and GRAPH properties of are investigated. Also some classifications and REPRESENTATIONs for the GRAPH are introduced and at last some results about dominating sets on are explained.

There are two approaches for simulating memory as well as learning in artificial intelligence; the functionalistic approach and the cognitive approach. The necessary condition to put the second approach into account is to provide a model of brain activity that contains a quite good congruence with observational facts such as mistakes and forgotten experiences. Given that human memory has a solid core that includes the components of our identity, our family and our hometown, the major and determinative events of our lives, and the countless repeated and accepted facts of our culture, the more we go to the peripheral spots the data becomes flimsier and more easily exposed to oblivion. It was essential to propose a model in which the topoGRAPHical differences are quite distinguishable. In our proposed model, we have translated this topoGRAPHical situation into quantities, which are attributed to the nodes. The result is an edge-weighted GRAPH with mass-based values on the nodes which demonstrates the importance of each atomic proposition, as a truth, for an intelligent being. Furthermore, it dynamically develops and modifies, and in successive phases, it changes the mass of the nodes and weight of the edges depending on gathered inputs from the environment.

Feature extraction plays a crucial role in dimensionality reduction in machine learning applications. Nonnegative Matrix Factorization (NMF) has emerged as a powerful technique for dimensionality reduction; however, its equal treatment of all features may limit accuracy. To address this challenge, this paper introduces GRAPH-Regularized Entropy-Weighted Nonnegative Matrix Factorization (GEWNMF) for enhanced feature REPRESENTATION. The proposed method improves feature extraction through two key innovations: optimizable feature weights and GRAPH regularization. GEWNMF uses optimizable weights to prioritize the extraction of crucial features that best describe the underlying data structure. These weights, determined using entropy measures, ensure a diverse selection of features, thereby enhancing the fidelity of the data REPRESENTATION. This adaptive weighting not only improves interpretability but also strengthens the model against noisy or outlier-prone datasets. Furthermore, GEWNMF integrates robust GRAPH regularization techniques to preserve local data relationships. By constructing an adjacency GRAPH that captures these relationships, the method enhances its ability to discern meaningful patterns amid noise and variability. This regularization not only stabilizes the method but also ensures that nearby data points appropriately influence feature extraction. Thus, GEWNMF produces REPRESENTATIONs that capture both global trends and local nuances, making it applicable across various domains. Extensive experiments on four widely used datasets validate the efficacy of GEWNMF compared to existing methods, demonstrating its superior performance in capturing meaningful data patterns and enhancing interpretability.

Precise player localization is the key step for improved analysis such as player tracking in soccer broadcast videos. Extracting player trajectories provides some essencial information for coaches and sport experts to determine weaknesses and strengths of the players and the team and to evaluate overall strategy of the game. As far as previous scenes are missed by camera motion, continuous player trajectory could be depicted by trajectory extraction on constructed mosaic. The goal of this paper is to transform player position to the field model and extract all trajectories in both image and model spaces. Therefore, players are detected using Gaussian Mixture Model and Gentle Adaboost. After removing extra regions such as goal post and lines, isolating occluded players, player labeling and transforming player positions to the same coordinate system, player tracking is carried out. Finally, the proposed player detection and tracking methods are applied for 78 frames taken from six soccer sequences.

Inertial Navigation System (INS) is one of the navigation systems widely used in various land-based, aerial, and marine applications. Among all types of INS, Microelectromechanical System (MEMS)-based INS can be widely utilized, owing to their low cost, lightweight, and small size. However, due to the manufacturing technology, MEMS-based INS suffers from deterministic and stochastic errors, which increase positioning errors over time. In this paper, a new effective noise reduction method is proposed that can provide more accurate outputs of MEMS-based inertial sensors. The intelligent method in this paper is a combined denoising method that combines Wavelet Transform (WT), Permutation Entropy (PE), Support Vector Regression (SVR), and Genetic Algorithm (GA). Firstly, WT is employed to obtain a time-frequency REPRESENTATION of raw data. Secondly, a four-element feature vector is formed. These four features are (1) amplitude of frequency, (2) its ratio to mean of amplitudes of all frequencies, (3) location of frequency in time-frequency REPRESENTATION, and (4) judgment on behaviors of frequency that is obtained by utilizing PE. Thirdly, based on the feature vector, the GA-SVR algorithm predicts amplitudes of all frequencies in the time-frequency REPRESENTATION of the denoised signal. Finally, by employing inverse WT the denoised signal is obtained. In this work, the outputs of the Inertial Measurement Unit (IMU) in ADIS16407 sensor, as a low-cost and MEMS-based INS, have been utilized for data collection. The proposed method has been compared with other noise reduction methods and the achieved results verify superior improvement than other methods.

In some point of view, neither Michel Foucault nor Ibn Khaldun are considered philosophers in the conventional classifications, but both are very  important in intellectual and, of course, in philosophical contexts, especially for those who are interested in the deep study of human life from the perspective of political thought.The main concern of two thinkers, one in the 14th century, the other in the 20th century, is the issue  of power, although neither of them provided a precise definition of it. In this article, an attempt has been made to show the place of power and domination in the political thought of both thinkers by examining the thoughts of two thinkers. And in search of an answer to this question, how did Asabiyyah and industry of religion in Ibn Khaldun's thought and social control through self-technology and discipline in Foucault's thought lead to the expansion of the domination of power? This article is written by analytically comparing the opinions of two thinkers based on Ibn Khaldun's most important book called Muqaddimah and Foucault's late works

The independence GRAPH Ind(G) of a GRAPH G is the GRAPH with vertices as maximum independent sets of G and two vertices are adjacent, if and only if the corresponding maximum independent sets are disjoint. In this work, we find the independence GRAPH of Cartesian product of d copies of complete GRAPHs Kq, which is known as the Hamming GRAPH H(d, q). Greenwell and Lovasz [7] found that the independence number of direct product of d copies of Kq as qd−1. We prove that the independence number of Hamming GRAPH H(d, q), which is cartesian product of d copies of Kq, is also qd−1. As an application of our findings, we find answers for rook problem in higher dimensional square chess board.