Research Article
Neural Network Axiomatic Solver Coaching AGI Method for Solving Scientific and Practical Problems
Evgeny Bryndin*
Issue:
Volume 10, Issue 4, December 2025
Pages:
110-120
Received:
2 September 2025
Accepted:
13 September 2025
Published:
9 October 2025
Abstract: Modern neural network methods combine work with an axiomatic mathematical description (laws, equations, invariants, logical rules) and the power of neural networks for learning from data, pattern recognition and differentiation through complex spaces. This combination produces systems that can learn from data, observe given laws and, as a result, make predictions, solve problems and even discover new hypotheses. Quality depends on the formulation of axioms and the presence of correct formulations, the complexity of scaling to very large axiomatic bases, trade-offs between the accuracy of fitting to data and compliance with laws, interpretation and verification of results. Modern neural network methods with an axiomatic mathematical description have better generalization and physical interpretability due to compliance with axioms, the ability to work with small data due to built-in laws and the ability to discover new dependencies within the framework of formalized rules. Theoretical principles and formal axioms set requirements for neural networks and their training so that solutions to scientific problems correspond to the laws of nature, invariances, data characteristics and other desired properties. Power: an axiomatic neural network tends to be accurately modeled given its sufficient complexity and large scientific data and knowledge. The author proposes a neural network axiomatic solver coaching AGI method for solving scientific and practical problems according to their formulations and developed systems of axioms.
Abstract: Modern neural network methods combine work with an axiomatic mathematical description (laws, equations, invariants, logical rules) and the power of neural networks for learning from data, pattern recognition and differentiation through complex spaces. This combination produces systems that can learn from data, observe given laws and, as a result, m...
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Research Article
Modeling Pulmonary Tuberculosis-Pneumonia Co-dynamics Incorporating Drug Resistance with Optimal Control
Issue:
Volume 10, Issue 4, December 2025
Pages:
121-144
Received:
9 August 2025
Accepted:
21 August 2025
Published:
14 October 2025
Abstract: In this paper, a deterministic mathematical model illustrating the transmission dynamics of pulmonary tuberculosis and pneumonia co-infection is formulated, incorporating a drug-resistant strain. The model employs a Holling-type functional response to capture the impact of natural immunity on the progression from latent tuberculosis infection to active disease, as well as its role in controlling drug-resistant pulmonary tuberculosis-pneumonia co-infections. The model is extended to include optimal control theory, aimed at identifying strategies to minimize co-infections using prevention, screening of latently infected individuals, and treatment as control variables. Pontryagin’s Maximum Principle is applied to characterize the optimal control system. The resulting optimality system is then solved numerically using the Runge-Kutta-based forward-backward sweep method. Numerical simulations demonstrate that enhancing natural immunity among latently infected individuals significantly reduces the number of co-infected cases. The optimal control analysis indicates that the most effective strategy for controlling or reducing co-infections of drug-resistant tuberculosis and pneumonia is the combined optimization of infection prevention and screening of latently infected individuals. These findings underscore the importance of scaling up preventive measures against pulmonary tuberculosis and opportunistic pneumonia, alongside screening efforts, to effectively control co-infections. Additionally, the study recommends strengthening immunity among latently infected populations to further reduce the prevalence of co-infections.
Abstract: In this paper, a deterministic mathematical model illustrating the transmission dynamics of pulmonary tuberculosis and pneumonia co-infection is formulated, incorporating a drug-resistant strain. The model employs a Holling-type functional response to capture the impact of natural immunity on the progression from latent tuberculosis infection to ac...
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Research Article
An Alternate Formulation for Computing/Validating the Shannon Entropy of Probability Distributions
Parthasarathy Srinivasan*
Issue:
Volume 10, Issue 4, December 2025
Pages:
145-150
Received:
10 November 2025
Accepted:
21 November 2025
Published:
24 December 2025
Abstract: One of the most pervasive applications in Computing, is the generation of Random numbers, which belong to a certain probability distribution such as a Gaussian (normal) distribution. These probability distributions possess statistical properties such as expected values (mean), variance (standard deviation), p-value, Entropy etc.; out of which Entropy is significant, for quantifying the amount of (useful) information, that a particular instance of a distribution embodies. This quantification of Entropy is of value as a characterizing metric, which determines the amount of randomness/uncertainty and/or redundancy that can be achieved using a particular distribution instance. This is particularly useful for communication, cryptographic and astronomical applications in this day and age. In the present work the Author introduces an alternate way to calculate the approximate value of the Information Entropy (with a variation to the formulation of Information Entropy by Claude Shannon, as known by the scientific community); by observing that a Takens embedding of the probability distribution yields a simple measure of the Entropy; by taking into consideration only four critical/representative points of the embedding. By comparative experimentation, the Author has been able to empirically verify that this alternate formulation is consistently valid: The baseline experiment chosen relates to Discrete Task Oriented Joint Source Channel Coding (DT-JSCC) which utilizes entropy computation to perform efficient and reliable task oriented communication (transmission and reception) as will be elaborated further. The author performed the comparison by employing the Shannon formulation for Entropy computation in the baseline DT-JSCC experiment and then repeating the experiment by employing the Entropy formulation, introduced in this work. Eventually, the accuracy of results obtained (data models generated) were almost identical (differing in accuracy by only ~ 1% overall). Thus, the alternate formulation introduced in this work, provides a reliable means of validating the random numbers obtained from the Shannon formulation and also potentially serves as a simpler, faster, and more computationally optimal method. This is particularly useful in applications, where there is a constraint on the computational resources available, such as mobile and limited devices. The method is also useful as a way of uniquely identifying and characterizing Random probability sources, such as those from astronomical and/or optical (photonic) phenomenon. The author also investigates the impact of incorporating the above notion of Entropy into the Mars Rover IER software and confirms the conclusions in the original article from Jet Propulsion Laboratories, NASA, which describes the ICER Progressive Wavelet Image Compressor.
Abstract: One of the most pervasive applications in Computing, is the generation of Random numbers, which belong to a certain probability distribution such as a Gaussian (normal) distribution. These probability distributions possess statistical properties such as expected values (mean), variance (standard deviation), p-value, Entropy etc.; out of which Entro...
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