Novel Formulae for Digit Frequency Analysis in Natural Numbers: Positional Counting and Computational Applications

Plithogenic cubic sets extend the cubic set framework into new mathematical territory that enables superior handling of decision-making and pattern recognition when dealing with uncertainty. Through Plithogenic logic researchers could develop advanced methods to represent complex patterns by supporting inconsistent and self-contradictory or combined features. This research paper explores the schematic explanation of Plithogenic cubic sets and their use in pattern recognition applications. The strong nature of pattern recognition emerge from Plithogenic logic's dimensionality flexibility when combined with a two-member structure in cubic sets while resolving imprecision and vagueness and the complexity of information aspects. Through theoretical foundations and illustrative examples the author presented their capability to employ Plithogenic cubic sets successfully in pattern recognition and classification applications. The schematic method delivers a complete grasp of Plithogenic cubic sets as an enabling instrument for pattern recognition research.

A new kind of Computer, called Attribute Grid Computer based on Qualitative Mapping is presented in this paper, It is shown that a series of intelligent methods, such as Production System, Artificial Neural Network, and Support Vector Machine can be fused in the framework of qualitative criterion transformation of qualitative mapping and can be implemented by attribute grid computer. And some examples of application in pattern recognition are given too.

This paper presents an evaluation of the novel Beagle-Inspired Optimization Algorithm (BIOA), inspired by the scent detection and rabbit hunting strategies of beagle dogs, such as scent detection, tracking, trail following, pattern recognition, continuous adaptation, persistent and exhaustive search, and escape and retrieval. BIOA is compared with well-established algorithms, including Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), Ant Colony Optimization (ACO), and Cuckoo Search (CS), across a set of benchmark functions, including Sphere, Rosenbrock, Rastrigin, Griewank, Ackley, Levy, and Schwefel functions. The results demonstrate BIOA's superior performance, achieving the lowest mean fitness values and best solutions across most test cases. Its balanced exploration and exploitation phases enable effective optimization. While BIOA excels in many instances, it requires further improvements in computational efficiency, particularly for high-dimensional problems. Future research should focus on enhancing BIOA's performance through advanced models, hybrid optimization techniques, and real-world problem applications, thus broadening its practical impact in solving complex optimization tasks.

Computational algebraic geometry has experienced significant advancements in recent years, driven by both theoretical breakthroughs and practical applications comprehensive review of the latest techniques in computational algebraic geometry, highlighting their development and impact on various domains. We begin by discussing foundational methods, including Gröbner bases, resultants, and elimination theory, which have been pivotal in solving polynomial systems and understanding algebraic varieties emerging algorithms that leverage improvements in computational efficiency, such as homotropy continuation methods and numerical algebraic geometry techniques. the applications of these advancements across different fields. In robotics and computer vision, for example, algebraic geometry methods are applied to solve problems related to motion planning and object recognition. In cryptography, recent developments in computational algebraic geometry offer new approaches to designing secure cryptographic systems resistant to quantum attacks. We also discuss the integration of algebraic geometry with machine learning and data science, emphasizing its role in improving predictive modeling and pattern recognition.

This article conducts a thermoelastic analysis of an infinite space embedded with multiple ellipsoidal inhomogeneities, which exhibit different thermal conductivity, stiffness, and thermal expansion ratios. Using the dual equivalent inclusion method (DEIM), the inhomogeneities are replaced by a matrix containing two continuously distributed eigen-fields: eigen-temperature-gradient (ETG) and eigenstrain. Unlike conventional numerical methods that rely on the volume integrals of temperature, the thermo-mechanical fields are expressed by volume integrals of eigen-fields and three Green’s functions over the inhomogeneity domains only, which exhibit significant improvement in computational efficiency. Through the DEIM, this article proves that the uniform ETG and linear eigenstrain, and linear ETG and quadratic eigenstrain are the exact solutions when an ellipsoidal inhomogeneity is subjected to a uniform far-field temperature gradient and a uniform volumetric heat source, respectively. The accuracy of the DEIM is verified via the finite element method through comparisons of thermoelastic fields.

During the last few decades, there has been a considerable growth of interest in pattern recognition in the field of robotics. An application of pattern recognition in robotics includes mobile robots and service robots. Visual and signal recognition of patterns enables the robots to perform a variety of tasks such as object and target recognition, navigation, grasping, and manipulation, assisting physically challenged people. This chapter surveys trends in robotics with pattern recognition that focuses more on the interaction between robot assistive device and human with signal pattern recognition. This interaction helps to enhance the capability of people in rehabilitation and in the field of medicine. Finally, this chapter includes the application of pattern recognition in the development of a prosthetic hand.

Historically, geoscience has been a prominent domain for applications of computer vision and pattern recognition. The numerous challenges associated with geoscience-related imaging data, which include poor imaging quality, noise, missing values, lack of precise boundaries defining various geoscience objects and processes, as well as non-stationarity in space and/or time, provide an ideal test bed for advanced computer vision techniques. On the other hand, the developments in pattern recognition, especially with the rapid evolution of powerful graphical processing units (GPUs) and the subsequent deep learning breakthrough, enable valuable computational tools, which can aid geoscientists in important problems, such as land cover mapping, target detection, pattern mining in imaging data, boundary extraction and change detection. In this landscape, classical computer vision approaches, such as active contours, superpixels, or descriptor-guided classification, provide alternatives that remain relevant when domain expert labelling of large sample collections is often not feasible. This issue persists, despite efforts for the standardization of geoscience datasets, such as Microsoft’s effort for AI on Earth, or Google Earth. This work covers developments in applications of computer vision and pattern recognition on geoscience-related imaging data, following both pre-deep learning and post-deep learning paradigms. Various imaging modalities are addressed, including: multispectral images, hyperspectral images (HSIs), synthetic aperture radar (SAR) images, point clouds obtained from light detection and ranging (LiDAR) sensors or digital elevation models (DEMs).

The ionosphere is an important component of the near Earth space environment. The three common methods for detecting the ionosphere with high frequency (HF) radio signals are vertical detection, oblique detection, and oblique backscatter detection. The ionograms obtained by these detection methods can effectively reflect a large amount of effective information in the ionosphere. The focus of this article is on the oblique backscatter ionogram obtained by oblique backscatter detection. By extracting the leading edge of the oblique backscatter ionogram, effective information in the ionosphere can be inverted. The key issue is how to accurately obtain the leading edge of the oblique backscatter ionogram. In recent years, the application of pattern recognition has become increasingly widespread, and the YOLO model is one of the best fast object detection algorithms in one-stage. Therefore, the core idea of this article is to use the newer YOLOX object detection algorithm in the YOLO family to perform pattern recognition on the F and Es layers echoes in the oblique backscatter ionogram. After image processing, a single-layer oblique backscatter echoes are obtained. It can be found that the leading edge extraction of the oblique backscatter ionogram obtained after pattern recognition and image processing by the YOLOX model is more fitting to the actual oblique backscatter leading edge.

The field of pattern recognition has emerged as one of the most challenging and important endeavours in the area of information technology research. Research in the area of pattern recognition has benefits for improving many areas of human endeavour, including medicine, the economy, the environment, and security. This book presents some of the latest advances in the area of pattern recognition theory and applications. The first half of the book discusses novel pattern classification and matching schemes, and the second half describes the application of novel tools in biometrics and digital multimedia. The applications included, such as face/iris recognition, handwriting recognition, surveillance, human dynamics, sensor fusion, etc., provide a detailed insight into how to build real pattern recognition systems and how to evaluate them. Given the dynamic nature of technology evolution in this area, this book provides the latest algorithms and concepts that can be used to build real systems. Features and topics: Provides state-of-the art algorithms, as well as presents cutting-edge applications within the field Introduces achievements in theoretical pattern recognition, including statistical and Bayesian pattern recognition, structural pattern recognition, neural networks, classification and data mining, evolutionary approaches to optimisation, and knowledge based systems Offers insights and support to practitioners concerned with the state-of-the art technology in the area Progress in Pattern Recognition addresses the needs of postgraduate students, researchers, and practitioners in the areas of computer science, engineering and mathematics where pattern recognition techniques are widely used. Professor Sameer Singh is Director of the Research School of Informatics, Loughborough University, UK, and serves as Editor-in-Chief of the Springer journal, Pattern Analysis and Applications

Pattern recognition is easy. Doing it well is hard. Communicating across disciplines is even more difficult. This paper reports on efforts to reduce the communication issues across researchers. Currently, the social network data is being exploited by a number of academics to understand interactions among individuals. Assessing interactions among individuals is an application of pattern recognition, a science that for over 40 years has received a huge financial investment from the research and development community. This paper provides a lexicon that has been developed from the pattern recognition community and applies it to the current tasks of social network interactions. Two case studies will be used: reconnaissance imagery from the Cold War and text from social networks that includes both posting messages and instant messaging.

In this study, in order to prevent information loss, we propose two dissimilarity measures between intuitionistic fuzzy sets ( IFSs ), which consider membership and non-membership degree and IFSs is farther extension of Fuzzy sets ( FSs ). Additionally, we have examined the characteristics of the proposed metrics to confirm their validity. We then conducted a series of experiments, including numerical experimentation, pattern recognition, and clustering analysis, to evaluate the efficacy of these metrics. The comparative outcomes illustrate that our dissimilarity metrics are more straightforward, easy to understand, and superior to the majority of the existing methods.

Distance is an important fundamental concept of the set theory. Since the intuitionistic fuzzy sets (IFSs) was put forward, distance between IFSs has been widely concerned by some researchers and many types of measures have been proposed. However, although intuitionistic fuzzy sets have the advantage of being able to consider waver (lack of knowledge), existing distance measures have not yet considered waver and most of them have counter-intuitive cases. To deal with this problem, this paper introduces the concept of intuitive distance for IFSs, which embodies the property requirements of classical distance measure and highlights the characteristics of intuitionistic fuzzy information. Then, a new intuitive distance measure for IFSs is proposed along with its proofs. After that, a comparative analysis between the intuitive distance measure and the existing distance measures is conducted based on an extended artificial benchmark test set, in which eleven pairs of single-element IFSs are used as an illustration of six typical counter-intuitive cases. Finally, the proposed distance measure is applied to deal with pattern recognition. Results show that the proposed distance does not provide any counter-intuitive cases and the waver that brought from hesitance index can be well reflected.

Application of pattern recognition and piezoelectric sensor array for the detection of organic compounds

The paper is devoted to the statistical-mechanical description of high-field transport in semiconductors within the semiclassical picture, assuming the band structure and electron-phonon interaction to be known. Our goal is to obtain a physical understanding in simple, universal terms without resorting to specific, simplified models for the band structure and/or the electron-phonon interaction. We first examine the lucky-drift model against an exact (analytical and numerical) solution of the Boltzmann transport equation in the simple parabolic case, and two discrepancies are found. The first stems from an incorrect expression for the drift velocity of a hot electron, while the second is associated with the approximate nature of the statistical device yielding the energy distribution. With the aim of retaining the features of simplicity of the lucky-drift description, another approach to the statistics of transport in the high-field regime is developed, based upon a nonlinear Fokker-Planck equation in energy space. While it gives the exact solution in the parabolic case, it has the ability to take up transport in an arbitrary band structure as well, and accounts for the success of the generalized lucky-drift model. The carrier energy distribution is expressed in terms of integrals over constant-energy surfaces in the Brillouin zone; the integrals involve the electron-phonon interaction and have direct physical meaning. The momentum-space distribution is derived approximately from the energy distribution. A simple comprehensive picture of transport statistics emerges that is not linked to a particular material or to specific assumptions regarding the electron-phonon interaction.

In the author's previous works (1990-1999), a one-layered, hard-limited perceptron can be used to classify analog pattern vectors if the latter satisfy the PLI condition. For most pattern recognition applications, this condition should be satisfied. When this condition is satisfied, then an automatic feature extraction scheme can be derived using some N-dimension Euclidean geometry theories. The scheme will automatically extract the most distinguished parts of the pattern vectors used in the training. It selects the feature vectors automatically according to the descending order of the volumes of the parallelepiped spanned by these sub-vectors. Theoretical derivation and numerical examples revealing the physical nature of this process and its effect in optimizing the robustness of this novel pattern recognition system are reported in detail. An experiment shows that the system gives the learning of 4 handwritten characters near to real time. The recognition of untrained handwritten characters is above 90% correct and the recognition is in real time.