Current Issue : April-June Volume : 2026 Issue Number : 2 Articles : 5 Articles
Currently, Kronecker Matrix–Matrix Multiplication play a crucial role in many advanced applications across science and engineering, such as Quantum Computing (Tensor Representation of Quantum States, Quantum Gate Construction), Machine Learning and Data Science (Kernel Methods, Tensor Decompositions), and Signal and Image Processing (Multidimensional Filtering, Compression Algorithms). However, the implementation of the Kronecker Matrix–Matrix Multiplication increasingly relies on systems with enhanced computational capabilities. Specifically, current implementations expend large amounts of external memory and requires a large number of processing units to perform this operation. As is commonly acknowledged, cutting-edge high-performance computing schemes still faces limitations in terms of energy and performance due to the bottleneck in data transfer between processing units and memory. To mitigate this limitation, memory processing units (MPUs) enable direct computation on in-memory data, reducing latency and eliminating the need for data transfer. On the other hand, spiking neural P systems, with their inherent parallelism and distributed processing capabilities, are therefore well-suited as foundational components for implementing such memory architectures efficiently. From the mathematical point of view, we present for the first time a neural, synaptic, and dendritic model to support the Kronecker Matrix–Matrix multiplication. To this end, the proposed spiking neural P system with their cutting-edge variants, such as anti-spikes, communication on request, synaptic weights, and dendritic–axonal delays, facilitates the creation of neural memory cells and spike-based routers. Hence, these elements potentially allow the design of novel processing memory architectures that markedly enhance data transfer efficiency between computational units and memory....
We obtain an infinite series expression for the joint probability density function of occupation times in a Three-State Markov chain. By extending the identity given by Darroch, we demonstrate that Pedler’s technique of employing moment generating functions can be applied to the three-state case as well....
We investigate the interplay between monomial first integrals, polynomial invariants of certain group action, and the Poincaré–Dulac normal forms for autonomous systems of ordinary differential equations with a diagonal matrix of the linear part. Using tools from computational algebra, we develop an algorithmic approach for identifying generators of the algebras of monomial and polynomial first integrals, which works in the general case where the matrix of the linear part includes algebraic complex eigenvalues. Our method also provides a practical tool for exploring the algebraic structure of polynomial invariants and their relation to the Poincaré-Dulac normal forms of the underlying vector fields....
Heart disease remains one of the leading causes of mortality worldwide, accounting for millions of deaths annually. Early detection of individuals at risk is essential for reducing complications and improving patient outcomes. This study applies logistic regression, a supervised machine learning algorithm, to predict the likelihood of heart disease based on clinical and demographic features such as age, sex, chest pain type, resting blood pressure, cholesterol level, fasting blood sugar, and maximum heart rate achieved. The dataset obtained from Kaggle’s Heart Disease Dataset, comprises 1025 patient records with 14 attributes. Following data preprocessing including handling missing values, feature scaling using StandardScaler, and categorical encoding, the data were divided into training (80%) and testing (20%) subsets. A logistic regression model with the liblinear solver and L2 regularization was trained and evaluated using multiple performance metrics. The model achieved 85.24% accuracy on the training set and 80.49% accuracy on the test set, with a ROC-AUC score of 0.86 and consistent results from 5-fold cross-validation. These findings demonstrate that logistic regression provides a robust, interpretable, and computationally efficient approach for binary classification in healthcare. The model’s high recall indicates its reliability in identifying patients at risk of heart disease, supporting its potential application in clinical decision-support systems for early diagnosis and intervention....
This report is a follow-up to the previously published article. The scope of the purely numeric study of the previous report is augmented and formulated analytically. The main objective is to analytically formulate the capacitance of a non-concentric, asymmetric, long cylindrical capacitor. It is proven that the capacitance is a function of the radii of the cylinders and the separation distance between the circular centers. It is also shown that the numeric conformal mapping of the previous work is closely related to the bipolar coordinate system. To accomplish the set goal, we utilized one of the popular Computer Algebra Systems (CAS), especially Mathematica . To underline the usefulness of the CAS, the analytic formulation, its associated numeric and graphical outputs are bundled into one file. It is shown under special conditions that the presented format approaches the well-known characteristic of the symmetric capacitor. Application-wise, the impact of the non-concentric cylindrical capacitor in an RC DC-driven electric circuit is reported. The report embodies the essential Mathematica codes, readily making the reproduction of the results attainable....
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