Krawtchouk polynomials (KPs) and their moments are promising techniques for applications of information theory, coding theory, and signal processing. This is due to the special capabilities of KPs in feature extraction and classification processes. The main challenge in existing KPs recurrence algorithms is that of numerical errors, which occur during the computation of the coefficients in large polynomial sizes, particularly when the KP parameter (p) values deviate away from 0.5 to 0 and 1. To this end, this paper proposes a new recurrence relation in order to compute the coefficients of KPs in high orders. In particular, this paper discusses the development of a new algorithm and presents a new mathematical model for computing the initial value of the KP parameter. In addition, a new diagonal recurrence relation is introduced and used in the proposed algorithm. The diagonal recurrence algorithm was derived from the existing n direction and x direction recurrence algorithms. The diagonal and existing recurrence algorithms were subsequently exploited to compute the KP coefficients. First, the KP coefficients were computed for one partition after dividing the KP plane into four. To compute the KP coefficients in the other partitions, the symmetry relations were exploited. The performance evaluation of the proposed recurrence algorithm was determined through different comparisons which were carried out in state-of-the-art works in terms of reconstruction error, polynomial size, and computation cost. The obtained results indicate that the proposed algorithm is reliable and computes lesser coefficients when compared to the existing algorithms across wide ranges of parameter values of p and polynomial sizes N. The results also show that the improvement ratio of the computed coefficients ranges from 18.64% to 81.55% in comparison to the existing algorithms. Besides this, the proposed algorithm can generate polynomials of an order ∼8.5 times larger than those generated using state-of-the-art algorithms.
Praise be to God, Lord of the Worlds, and the best blessings and peace be upon our master Muhammad and all his family and companions, and those who follow them with goodness until the Day of Judgment. . And after:
God created man in the best manner, and subjugated the universe to him and favored him over the rest of creation when he gave him a mind to contemplate and know how to distinguish between the harmful and the beneficial, the bad and the good, in order to exploit him in achieving the meaning of worship, because it is the highest goal of his creation. God Almighty said (And I did not create the jinn and mankind. Except that they worship them.” [Al-Dhariyat: 56]
If knowing what is harmful from what is beneficial a
... Show MoreGlobally, Sustainability is very quickly becoming a fundamental requirement of the construction industry as it delivers its projects; whether buildings or infrastructures. Throughout more than two decades, many modeling schemes, evaluation tools, and rating systems have been introduced en route to realizing sustainable construction. Many of these, however, lack consensus on evaluation criteria, a robust scientific model that captures the logic behind their sustainability performance evaluation, and therefore experience discrepancies between rated results and actual performance. Moreover, very few of the evaluation tools available satisfactorily address infrastructure projects. The res
A significant challenge arises in the characterization of urban systems, especially regarding the intricate structures of Central Business Districts (CBDs). Conventional models seem insufficient, failing to comprehend the non-linear, network-oriented structure of the city's economic and social dynamics. This creates a disparity between the city's physical, geographical structure and the unseen processes occurring within it. The fundamental inquiry is thus configurational: how can we systematically examine the inherent spatial logic of the CBD to develop a more efficient and predictive planning model? This paper presents a theoretical and methodological model to explore this inquiry, which focuses on Lower Manhattan as the primary su
... Show MoreA new mathematical model describing the motion of manned maneuvering targets is presented. This model is simple to be implemented and closely represents the motion of maneuvering targets. The target maneuver or acceleration is correlated in time. Optimal Kalman filter is used as a tracking filter which results in effective tracker that prevents the loss of track or filter divergency that often occurs with conventional tracking filter when the target performs a moderate or heavy maneuver. Computer simulation studies show that the proposed tracker provides sufficient accuracy.
The increasing demand for continual learning in sequential data processing has led to progressively complex training methodologies and larger recurrent network architectures. Consequently, this has widened the knowledge gap between continual learning with recurrent neural networks (RNNs) and their ability to operate on devices with limited memory and compute. To address this challenge, we investigate the effectiveness of simplifying RNN architectures, particularly gated recurrent unit (GRU), and its impact on both single-task and multitask sequential learning. We propose a new variant of GRU, namely the minion recurrent unit (MiRU). MiRU replaces conventional gating mechanisms with scaling coefficients to regulate dynamic updates of hidden
... Show MoreWith the continuous progress of image retrieval technology, the speed of searching for the required image from a large amount of image data has become an important issue. Convolutional neural networks (CNNs) have been used in image retrieval. However, many image retrieval systems based on CNNs have poor ability to express image features. Content-based Image Retrieval (CBIR) is a method of finding desired images from image databases. However, CBIR suffers from lower accuracy in retrieving images from large-scale image databases. In this paper, the proposed system is an improvement of the convolutional neural network for greater accuracy and a machine learning tool that can be used for automatic image retrieval. It includes two phases
... Show MoreIn this study, we have created a new Arabic dataset annotated according to Ekman’s basic emotions (Anger, Disgust, Fear, Happiness, Sadness and Surprise). This dataset is composed from Facebook posts written in the Iraqi dialect. We evaluated the quality of this dataset using four external judges which resulted in an average inter-annotation agreement of 0.751. Then we explored six different supervised machine learning methods to test the new dataset. We used Weka standard classifiers ZeroR, J48, Naïve Bayes, Multinomial Naïve Bayes for Text, and SMO. We also used a further compression-based classifier called PPM not included in Weka. Our study reveals that the PPM classifier significantly outperforms other classifiers such as SVM and N
... Show More