AppliedMath, Volume 5, Issue 1 (March 2025) – 8 articles

Optimizing learning rates (LRs) in deep learning (DL) has long been challenging. Previous solutions, such as learning rate scheduling (LRS) and adaptive learning rate (ALR) algorithms like RMSProp and Adam, added complexity by introducing new hyperparameters, thereby increasing the cost of model training through expensive cross-validation experiments. These methods mainly focus on local gradient patterns, which may not be effective in scenarios with multiple local optima near the global optimum. A new technique called Learning Rate Tuner with Relative Adaptation (LRT-RA) is introduced to tackle these issues. This approach dynamically adjusts LRs during training by analyzing the global loss curve, eliminating the need for costly initial LR estimation through cross-validation. This method reduces training expenses and carbon footprint and enhances training efficiency. It demonstrates promising results in preventing premature convergence, exhibiting inherent optimization behavior, and elucidating the correlation between dataset distribution and optimal LR selection. The proposed method achieves 84.96% accuracy on the CIFAR-10 dataset while reducing the power usage to 0.07 kWh, $C{O}_2$ emissions to 0.05, and both $S{O}_2$ and $N{O}_x$ emissions to 0.00003 pounds, during the whole training and testing process. Full article

Haberman linking is a widely used method for comparing groups using the two-parameter logistic item response model. However, the traditional Haberman linking approach relies on joint item parameter estimation, which prevents the application of standard M-estimation theory for linking error calculation in the presence of differential item functioning. To address this limitation, a novel pairwise Haberman linking method is introduced. Pairwise Haberman linking aligns with Haberman linking when no items are missing but eliminates the need for joint item parameters, allowing for the use of M-estimation theory in linking error computation. Theoretical derivations and simulation studies show that pairwise Haberman linking delivers reliable statistical inferences for items and persons, particularly in terms of coverage rates. Furthermore, using a bias-corrected linking error is recommended to reduce the influence of sample size on error estimates. Full article

The stock market index future price forecasting is one of the imperative financial time series problems. Accurately estimated future closing prices can play important role in making trading decisions and investment plannings. This work proposes a new multi-output ensemble framework that integrates the hybrid systems generated through importance score based feature weighted learning models through a continuous multi-colony ant colony optimization technique (MACO-LD) for multi-day ahead index future price forecasting. Importance scores are obtained through four different importance score generation strategies (F-test, Relief, Random Forest, and Grey correlation). Multi-output variants of three baseline learning algorithms are brought in to address multi-day ahead forecasting. This study uses three learning algorithms namely multi-output least square support vector regression (MO-LSSVR), multi-output proximal support vector regression (MO-PSVR) and multi-output $\epsilon$-twin support vector regression (MO-$\epsilon$-TSVR) as the baseline methods for the feature weighted hybrid models. For the purpose of forecasting the future price of an index, a comprehensive collection of technical indicators has been taken into consideration as the input features. The proposed study is tested over eight index futures to explore the forecasting performance of individual hybrid predictors obtained after incorporating importance scores over baseline methods. Finally, multi-colony ant colony optimization algorithm is employed to construct the ensemble results from the feature weighted hybrid models along with baseline algorithms. The experimental results for all the eight index futures established that the proposed ensemble of importance score based feature weighted models exhibits superior performance in index future price forecasting compared to the baseline methods and that of importance score based hybrid methods. Full article

We present the derivation of generic equations describing the long gravity waves in incompressible fluid with a decaying effect. We show that in this theory, the only restriction to the surface deviation is connected to the stability condition for the waves. Derivation of these generic equations is based on Euler equations for inviscid incompressible fluid and the definition of dynamic pressure which leads to a correct dispersion equation for gravity waves. These derived generic equations for the velocity of fluid and the surface deviation describe the propagation of long gravity waves in incompressible fluid with finite amplitude. We also find the necessary and sufficient conditions for generic equations with dissipation of energy or a decaying effect. The developed approach can significantly improve the accuracy of theory for long gravity waves in incompressible fluid. We also find the quasi-periodic and solitary wave solutions for generic equations with a decaying effect. Full article

The information paradox suggests that the black hole loses information when it emits radiation. In this way, the spectrum of radiation corresponds to a mixed (non-pure) quantum state even if the internal state generating the black hole is expected to be pure in essence. In this paper we propose an argument solving this paradox by developing an understanding of the process by which spontaneous symmetry breaks when a black hole selects one of the many possible ground states and emits radiation as a consequence of it. Here, the particle operator number is the order parameter. This mechanism explains the connection between the density matrix, corresponding to the pure state describing the black hole state, and the density matrix describing the spectrum of radiation (mixed quantum state). From this perspective, we can recover black hole information from the superposition principle, applied to the different possible order parameters (particle number operators). Full article

According to the latest data from CryptoSlam, as of November 2024, NFT sales have approached USD 7.43 billion, with trading profits exceeding USD 33.303 million. In the buyer–seller market, the potential demand for NFT transactions continues to grow, leading to rapid development in the NFT market and giving rise to various issues, such as price manipulation, counterfeit products, hacking of investment platforms, identity verification errors, data leaks, and wallet security failures, all of which have caused significant financial losses for investors. Currently, the NFT investment market faces challenges such as legal uncertainty, information security, and high price volatility due to speculation. This study conducted expert interviews and adopted a two-stage research methodology to analyze the most common risk factors when selecting NFT investments. It employed the Decision-Making Trial and Evaluation Laboratory (DEMATEL) and the Analytic Network Process (ANP) to explore risk factors such as legal issues, security concerns, speculation, and price volatility, aiming to understand how these factors influence investors in choosing the most suitable NFT investment platform. The survey was conducted between February and June 2023, targeting professionals and scholars with over 10 years of experience in the financial market or financial research, with a total of 13 participants. The empirical results revealed that speculation had the greatest impact compared to legal issues, security concerns, and NFT price volatility. Speculation and price volatility directly influenced other risk factors, potentially increasing the risks faced by NFT investment platforms. In contrast, legal and security issues had less influence on other factors and were more affected by them, indicating a relatively lower likelihood of occurrence. Thus, investors must be cautious of short-term speculation, particularly when dealing with rare NFTs. The best approach is to set an exit price to minimize potential losses if the investment does not proceed as planned. Full article

Given the fundamental importance of the power grid in both supply and demand, frequency stability is critical to the reliable and stable function of energy systems. When energy is stored in the system, it mitigates problems caused by various disturbances that interrupt the energy system’s operation. The energy storage system (ESS) stores excess energy and returns it to the system by reducing power oscillations and improving stability and dependability. Superconducting magnetic energy storage (SMES) is one strategy for storing energy in the power system. As a rotational storage system, its quick dynamic response is a significant advantage. This device can quickly release a substantial amount of energy. A gas power plant in one area, along with a steam and a hydropower plant in another, constitute a multi-resource energy system. This paper’s primary objective is to study and model how SMES affects the dynamic behavior of this energy system. The state-space representation of the power system’s dynamic behavior is given by first-order differential equations. This power system has a complexity of fifteen orders. The outcomes of the simulation using MATLAB software are presented in the time domain, and its correctness is shown by analyzing the power system’s modes. The results show that placing an SMES unit not only eliminates oscillations and frequency deviation but also reduces the induction time in the time responses of power in the connection line and frequency deviation. Different modes are considered for the energy system, and the effect of the power storage unit is shown by presenting the simulation results. Full article