CENTRAL ASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES

Algorithms for Automatic Analysis of Human Foot Radiographic Images

Tue, 05 May 2026 00:00:00 +0000

This article provides an overview of algorithms for processing human foot X-ray images, which are essential for diagnosing various foot conditions, including fractures, deformities, and joint diseases. The study explores several image preprocessing techniques, such as detecting structural changes, noise reduction, and contrast enhancement, all of which help improve the quality of radiographic images and increase diagnostic accuracy. In addition, the paper discusses challenges related to noise, distortions, and low contrast in X-ray images, and outlines methods to mitigate these issues. By implementing these algorithms, the study aims to enhance the effectiveness of foot-related diagnoses and support more efficient medical decision-making.

Practical Estimation and Simulation Analysis of the Kolmogorov Constant for Heavy-Tailed Noncritical Markov Branching Systems

Iskandarov S.B , Asirov J.J , Sobirov U.M , Axmedov Q.A — Mon, 11 May 2026 00:00:00 +0000

This paper presents a practical estimation and simulation-based study of the Kolmogorov constant in the context of heavy-tailed, noncritical continuoustime Markov branching systems. Building on the explicit analytic form recently derived for noncritical Markov branching models, we investigate the empirical behaviour of the survival probability and related asymptotic quantities under heavy-tailed offspring distributions using Monte Carlo simulation techniques.

Global Convergence Guarantees for Adaptive Gradient Algorithms with Barzilai–Borwein and Alternative Step-Length Strategies

Alyaqdhan Ammar Abed — Sat, 23 May 2026 00:00:00 +0000

Motivated by recent progress in adaptive schemes for convex optimization, this work develops a proximal-gradient framework that enforces global convergence without resorting to linesearch procedures. The proposed approach accommodates widely used step-length rules, including Barzilai–Borwein updates and one-dimensional Anderson-type acceleration. Importantly, the analysis applies to problems where the smooth component admits only local Hölder continuity of its gradient. The resulting theory unifies and strengthens several existing results, while numerical experiments confirm the practical benefits of coupling aggressive step-length selection with adaptive safeguarding mechanisms.

Applications of Laplace’s Method in Asymptotic Analysis

Iskandarov S.B , Asirov J.J , Sobirov U.M, Yuldashev B.E — Tue, 02 Jun 2026 00:00:00 +0000

This article investigates the application of Laplace’s method in asymptotic analysis. An asymptotic formula is derived showing that, as the parameter increases, the value of the integral involving powers of a function is mainly determined by the behavior of the function near its maximum point. The paper also discusses the asymptotic properties of large-parameter functions and presents related analytical results.

Vibescape: Real-Time Emotion-Based Music Recommendation Using Multimodal Analysis

Tue, 02 Jun 2026 00:00:00 +0000

Vibescape is a novel emotion-based music recommender system that aims to provide a personalised and immersive music streaming experience. This system employs cutting-edge emotion detection technology to analyse the user's emotions in real time and suggest songs that fit their current mood. Vibescape combines popular music platforms such as Spotify, SoundCloud and YouTube to allow users to stream music from their preferred sources seamlessly. The app also provides personalised playlists that match the user’s mood and listening habits. Vibescape’s intuitive and user-friendly interface customises the overall music streaming experience according to the emotional journey of the listener. Vibescape uses advanced algorithms to analyse emotional signals from facial expressions, voice, or text inputs to accurately identify moods. In addition to recommendations based on emotion, the system also adapts to long-term listening patterns, fine-tuning its recommendations to make a more personalised experience over time. Its integration with multiple music sources means the platform can provide a huge library of songs for different tastes and moods. Vibescape is a new way to link emotions and music, turning passive listening into an emotionally resonant and dynamic experience.

Intelligent Hospital Management System Using Machine Learning for Patient Criticality Prediction

R.L. Shyja, K. Senthamilselvan — Sun, 14 Jun 2026 00:00:00 +0000

This project is a Hospital Management System in Python with Machine Learning enhancement to improve the hospital’s operation and patient care. The system has the basic functionalities like registration of patients, maintaining their records and monitoring their real-time status through secure and friendly interface. Its main innovation is the Machine Learning module that predicts the patient criticality level at the time of admission. The system then classifies the patients into low, moderate, and high-risk categories by employing supervised learning algorithms trained on historical medical data such as vital signs and patient history. Such predictive power allows healthcare professionals to make faster, data-driven decisions, ensuring immediate attention for critical patients. Moreover, the system can aid in intelligent ward allocation by prediction of risk levels, available beds and ward specialisation. This makes it possible to optimise hospital resources, reduce delays and to prevent unnecessary patient transfers. Backend is designed to ensure data security and efficient processing, while interface is designed to provide easy access to the hospital staff. The system cuts down significantly on the workload by automating administrative tasks and incorporating predictive analytics, which in turn enhances operational efficiency and overall quality of patient care.

Estimating the Effectiveness of University Training Programs on Student Achievement Using Generalized Linear Models (GLM): An Applied Evaluation Study

Thu, 11 Jun 2026 00:00:00 +0000

Generalized Linear Models (GLM) is applied in this paper as a statistical assessment framework to estimate the effect of university training programs on student achievements. The study seeks to know the effects that well-structured training programs have on the academic achievements of undergraduate students from different fields. Data used in this research was achieved through academic records and post-training performance survey data from three public universities with 500 students. GLM permits both continuous and categorical dependent variables, therefore making provisions for more flexible modeling of academic achievement data.[1] Training duration, type of program, previous GPA, gender, and academic department were used as predictor variables in the study. There was an explicitly significant positive relationship between the intensity of training and post-program academic achievement. Students who have attended more than 40 hours of structured training showed by a mean GPA improvement of 0.35 points that GPAs compared to untrained peers. Besides, gender and academic discipline showed moderating effects on the relationship between training and performance (see Table 1). The findings highlight structured skill-based university programs aimed at In conclusion, the results of this study draw attention to the effectiveness of structured skill-based university programs on improving learning outcomes and students’ academic record. Furthermore, we specifically recommend the universities to implement a system of continuous assessment as a part of the training curriculum and to adopt the evaluation and monitoring systems based on Generalized Linear Models. This particular model used in our research provides an example of statistically sound and reproducible approach for educational administrators who search for data-driven continuous quality improvement solutions.

Best Proximity Point Theorem for Non-Cyclic Geraghty Contractions Mappings of Generalized Metric Space

Hanan A. A. Asaad Al-Ukaily — Fri, 12 Jun 2026 00:00:00 +0000

The approaches for finding an idea approximate solution, known as a best proximity point, to the equation , which is certainly unsolvable when is a non-self mapping, can be determined by best proximity point theorems. This paper establishes adequate requirements for the existence of a uniqueness best (optimum) proximity point for Geraghty contractions mappings in double controlled metric space. for new classes of non-self mappings known as generalized proximal contractions. Furthermore, the aforementioned best proximity point theorems can be realized as specific cases of the well-known Banach's contraction principle and more than of its expansions and modifications

An Interpretable Optimized Artificial Neural Network Framework for Concrete Compressive Strength Prediction

Taisir Mohsin, Duaa Muhsin, Waffaa Mohammed — Fri, 19 Jun 2026 00:00:00 +0000

Predicting concrete compressive strength is paramount to the structural safety, quality control and sustainable mix design processes. Although artificial neural networks (ANNs) are powerful nonlinear modeling capabilities , their performance is sensitive to data quality, and hyper-parameter configuration. This paper proposes a strong and full framework for automated machine learning that combines rigorous data preprocessing with full Bayesian hyper-parameter optimization. The proposed framework employs interquartile range (IQR)-based outlier removal on all eight input features (cement, blast furnace slag, fly ash, water, superplasticizer, coarse aggregate, fine aggregate, and curing age) and the target compressive strength, before removing duplicate mixture designs. After cleaning, the dataset is normalized to [−1, 1] and split into training, validation and test sets. A feedforward neural network is then searched over a wide hyper-parameter space, including network depth, neurons per layer, learning rate, training algorithm and activation function, with validation mean squared error as the objective .The optimized model achieves strong predictive performance on an independent test set : R=0.939 ,RMSE=5.304 MPa ,MAE=4.167 MPa and MAPE=14.832. Critically, the optimization process selected logsig as the best activation function, which is appropriate due to the positive, saturating nature of concrete strength growth. The study simultaneously performs statistical data cleansing and tuning of the model hyper-parameters to provide a clear and robust AI-based system for predicting the concrete compressive strength in smart construction projects.

Spatial Pattern Formation and Synchronization in Engineered Gene Networks: Insights from Reaction-Diffusion Modeling

Nada Abdul-Hassan Atiyah — Sat, 20 Jun 2026 00:00:00 +0000

Synthetic biology constructs with distinctly different scenarios for approaches to synthetic gene regulation — Background systematic control of when and where synthetic genes are activated in apparently identical cells has result_fulltext Tired mechanisms generally see cells as sitting in an ideally mixed soup. That blatantly dismisses the fact that true biosynthetic tissue is loopy, clunky, thready reality. Objective would like to create a mathematical model, that is PDE based to predict the behavior of these spatial patterns against some change in physical environment. Methods created a reaction-diffusion model for two bodies. The first is about how activator interacts and repress quorum-sensing signals. I numerically solved the equations using a finite difference method and parameterized diffusion rates (speed of cell spreading) and numbers of cells. Fast Fourier Transforms were also used to interpret the periodic spatial patterns and measure Pearson correlation coefficients to quantify cell synchrony coordination. Results The three spatial behaviors were simulated. At a low level D = 0.01 the chemicals are fixed in stiff, stagnant configurations -- Add some diffusion (D = 0.10): chemical waves undulate through space in periodic waves -- Crank it to full throttle (D = 0.50, r=0.91) and we have a synchronized blinking population! Now strap a backwards feedback loop to that élan and it drops the spatial disorder 60%. I discovered how a neoburst of chemicals could change the system for all time from one state to another. It turns out that the speed of diffusion and how tightly cells pile one next to one other determines what your gene circuit does. Contrary to the deceptive complexity of heterogenous geometry, the maps I wrote up that reconcile this data would here be a primitive framework for biologically-inspired design—self-organizing systems or precise applications.

The Role of Mathematics in Motion: An Analysis of Speed and Distance

Omar Ahmed Abbas — Sat, 20 Jun 2026 00:00:00 +0000

Mathematics permeates almost every aspect of our daily lives. It is fundamental to our understanding of the motion of humans and the earth around us. This paper aims to evaluate the motion from various points of view through basic mathematical concepts such as speed, time, and distance. It starts with introducing and comparing the average speed with instantaneous speed, gives some equations that relate distance to time, and supports that with analysis of practical examples of vehicles motion, pedestrians' motion, and freely falling objects motion to ensure the veracity of these equations. Moreover, it discusses the significance of viewing motion as a change with graphical representations in a way that enhances readers' understanding of mathematical relationships. It also aims to enhance our mathematical thinking in the study of motion and show how to utilize mathematics to promote our vigour in explaining the natural world and the human mutual action.

Smart Compiler: An AI-Powered IDE for Intelligent Code Analysis and Execution

V. Chrysolite, K. Senthamilselvan — Wed, 24 Jun 2026 00:00:00 +0000

Smart Compiler is an AI based Integrated Development Environment (IDE) to enhance the coding experience of both beginners and professionals. It supports a number of programming languages such as Java, C and Python so that users are able to write, compile and run programs all in one place. The system, powered by Google’s Gemini API, analyses code intelligently, assisting users in identifying syntax errors and providing optimised solutions with detailed explanations for novices. This feature helps programmers to understand mistakes better and improve their coding skills over time. The IDE has a built-in terminal where you can see the output of your program as it happens, so testing and debugging is easy. The graphical user interface is developed with Java Swing providing interactive and user-friendly environment and OkHttp is used to communicate with APIs efficiently. Gemini AI improves code readability, suggests performance improvement and enforces better programming standards. The Smart Compiler connects learning platforms and professional development tools by integrating code execution with AI-powered feedback. Thus the system provides efficient coding, less time spent on debugging and continuous learning and is a valuable tool for modern software development.

An Intelligent Real-Time Credit Card Fraud Detection Framework Using Machine Learning

R. Sivakani, S. Tamil Selvam, N. Steevan D’Souza — Tue, 30 Jun 2026 00:00:00 +0000

In this report, we present the development and implementation of a Real-Time Credit Card Fraud Detection System using machine learning techniques. The exponential growth of electronic transactions demands robust and instantaneous fraud detection mechanisms. The main aim of the project was to construct a highly scalable and accurate system for real-time classification of transactions as legit or fraudulent. The methodology We had a very imbalanced transaction dataset. We did feature engineering to extract contextual variables like transaction history, a custom risk score. To tackle the class imbalance problem, ADASYN oversampling technique was applied. We chose the Light Gradient Boosting Machine (LGBM) model as it performed best for binary classification problems in both speed and accuracy. The model was then trained and deployed using a FastAPI web service with a PostgreSQL database for prediction logging and Redis caching to enhance performance and latency in production. The validation results showed high Recall and F1-scores, indicating that the system is effective in detecting fraudulent activities with low false negatives. -scores which proved that the system is capable of detecting fraudulent activities with low false negatives.

Study of The Ant Colony With Its Application to The Traveling Salesman Problem

Sami Nazim Hussein — Wed, 01 Jul 2026 00:00:00 +0000

Ant Colony Optimization (ACO) is one of the most known nature inspired metheuristic techniques, which is basically based on the simulation of the social behaviour of ants when searching for the shortest paths between their colony and their food source. The algorithm was originally introduced in 1992 by Marco Dorigo to solve NP-hard combinatorial optimization problems which are hard to solve with traditional algorithms because of their large search space and high computational complexity. The research shows that the ant algorithm is a flexible yet powerful mathematical model that can adapt to changes occurring in dynamically changing complex systems, and that new opportunities for hybridizing with techniques of artificial intelligence/machine learning emerge for further increasing the convergence speed and the efficiency of the system. It has been used to solve the travelling salesman problem and has proved to be successful.

Analysis of Probabilistic Models in Artificial Intelligence Using Mathematical Statistical Methods

Zainab A. Khudhair — Tue, 07 Jul 2026 00:00:00 +0000

Today’s AI Must Use Probabilistic Models. AI is applying probabilistic models more often so it can work in the real world. The artificial intelligence application of probability models helps mathematical statisticians to formulate, estimate and evaluate bases. We will use essential ideas from Mathematical Statistics and Probability Theory to analyze models such as Bayes’ networks, Hidden Markov Models, Gaussian Mixture Model and more.

The study employs a systematic computation method. This study analyses a range of mathematical formulations of selective probability models in conjunction with a critique of brute force statistical estimation conclusions. It uses maximum likelihood and Bayesian methods. A synthetic dataset can facilitate easy control of experiments. Models that use probabilities yield successful predictions by taking into account their uncertainty. Still, estimating parameters and assuming distributions is the basis for the model functionality.

According to the text, three tables as well as three figures offer comparisons among the models on accuracy, convergence behaviour and likelihood estimation. Bayesian-based model outperform classical ones when data is lacking, and likelihood-based models do when data is plentiful. This researcher seeks to reduce the gap between theory and application in statistics.

This article will set up the statistical framework in which probablisitic models operate. Considering data and computational restrictions, we advise on a probabilistic model.

Wave Transport and the Effects of Magnetohydrodynamics on a Non-Newtonian Biological Fluid

Amal Nouman Khalaf, Omar Ahmed Abbas, Huda Fadil Khudair — Mon, 13 Jul 2026 00:00:00 +0000

In this article, the effect of hydromagnetic dynamics on blood circulation within a non-Newtonian fluid characterised by specific mathematical properties was investigated. The wavelength and flow regime were modelled using an analysis of ordinary differential equations, leading to the derivation of a closed-form solution. Following the application of the theories, results were obtained showing that the magnetic field increases the temperature distribution, leading to a decrease in pressure. The coefficients leading to a decrease in temperature distribution were also studied; The increase in the number of particles in the cycle is caused by the effect of the magnetic field, whilst the increase in the slip coefficient and porosity leads to an increase in the volume of the cycle.

Computational Simulation of Equitable Topological Graphs

Hanady F. Khudhair, Mohammed A. Abdlhusein — Mon, 13 Jul 2026 00:00:00 +0000

This study presents a computational simulation of the equitable topological graph G_q, which is constructed from a finite non-empty set endowed with the discrete topology. The vertices of the graph correspond to all non-empty proper subsets of the underlying set, while adjacency is defined according to a complementary-cardinality rule. The main objective of this work is to provide computational verification of the theoretical properties previously established for this class of graphs. An exact python-based algorithm was developed to generate the graph and compute its principal parameters, including the order, size, degree distribution, number of connected components, clique number, radius, and diameter. In addition, growth behavior was analyzed for increasing values of n, and monte carlo sampling techniques were employed to estimate graph size in cases where exact construction becomes computationally expensive. The computational results show complete agreement with the theoretical formulas and structural decomposition of the equitable topological graph. The study confirms that vertex degrees depend solely on subset cardinality and that the graph is connected only for small values of n, becoming disconnected for larger values. Furthermore, the simulations verify the decomposition of G_q into complete bipartite components and, in the even case, an additional complete graph corresponding to the middle cardinality class. Monte carlo experiments produced highly accurate estimates with very small relative errors, demonstrating the effectiveness of sampling methods for large-scale instances. The findings highlight the usefulness of computational techniques in validating theoretical results and investigating the structural properties of topological graphs when direct analytical or manual construction becomes impractical.

A Semi-Analytical Hybrid Methodology for Studying Mathematical Models of Cancer and Immune Dynamics

Saadallah Hazem Al-Rawi, Abdul Sattar Jaber Ali Al-Safi — Wed, 15 Jul 2026 00:00:00 +0000

In this paper, we present a new method for result analytical approximate solutions to systems of cancer and immune dynamics. The new method is developed by combining the Akbari-Gangi method with an external modification of Atkin. The proposed method was tested by applying it to solve nonlinear mathematical models describing cancer and immune dynamics. To demonstrate the effectiveness of the new method in improving results, it was compared with the Akbari-Gangi method and other methods presented in the literature. The obtained results show that this method has high accuracy, good convergence, and acceptable stability, which were illustrated in the form of tables and graphical representations of the solutions and error estimates.