Feature Papers in AppliedMath

This study presents an ideal-cycle thermodynamic analysis of an advanced compressed air energy storage (A-CAES) system with single thermal energy storage (TES) and an external heat boost. The additional heat is represented by a solar heat source, although the analysis is equally applicable to other forms of externally supplied thermal energy. Following the classical thermodynamic approach used for ideal cycles such as the Brayton, Otto and Diesel cycles, the objective is to establish analytical relationships and performance bounds for the integrated system rather than to model a specific engineering configuration. Three principal performance measures are examined: the electrical round-trip coefficient of performance (CoP), the marginal thermal coefficient of performance associated with external heat addition, and the overall second-law efficiency. Closed-form analytical expressions are derived for these quantities under idealised but still practically relevant assumptions. The analysis identifies distinct operating regimes governed by the level of external heat input and establishes analytical transition conditions between them. It is shown that external heat addition can substantially increase the round-trip coefficient of performance and lead to high marginal heat-utilisation effectiveness. A rigorous upper bound on the second-law efficiency is also obtained from a complete-cycle exergy analysis, demonstrating consistency with the laws of thermodynamics. The results provide analytical insight into the fundamental thermodynamic structure of solar-assisted A-CAES systems and establish performance bounds that are independent of any particular engineering implementation. Full article

This study proposes a transformed two-part bootstrap confidence interval (TTB-CI) for zero-inflated count data. The method combines a standard zero-inflated mixture formulation, parametric bootstrap, and monotone transformations to improve inference for practically meaningful estimands, including the marginal mean, zero probability, and positive-part mean. Simulation studies under zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) data-generating processes show that the proposed method maintains nominal or near-nominal coverage while reducing interval width, particularly for the positive-part mean. Compared with conventional Poisson- and negative binomial-based confidence intervals, the proposed TTB-CI provides a more favorable coverage and width tradeoff and yields more informative intervals for positive count inference. These results indicate that the proposed method offers a practical and efficient confidence interval framework for zero-inflated count data. Full article

We compare classical and modern regression models for next-day cryptocurrency forecasting on 14 USD-denominated coins across three liquidity tiers from 2018 through 2025, and we use the resulting panel to formally test three pre-specified hypotheses. The features are a strictly past-only 28-element set; the evaluation uses expanding-window walk-forward cross-validation with nested hyperparameter tuning, stationary block-bootstrap 95% confidence intervals, and pairwise Diebold–Mariano tests. Methodologically, we derive a bias-variance bound that turns the ‘no model beats the mean’ observation from a null finding into a predicted outcome under weak-form market efficiency. Empirically, (H1) the threshold–effect interaction is not supported (slope −1.7 × 10⁻⁴, 95% CI [−4.8 × 10⁻⁴, +1.4 × 10⁻⁴], p = 0.25). (H2) Statistical loss minimisation is decoupled from risk-adjusted economic outcome: the cluster-bootstrapped 95% CI for the Spearman rank correlation between the within-ticker MAE rank and within-ticker post-cost Sharpe rank is [−0.39, +0.10] overall, lies *strictly below zero* on the mid-cap (CI [−0.71, −0.04]) and long-tail (CI [−0.26, −0.09]) tiers, and decisively rejects perfect alignment (ρ = +1) on every tier. None of the seven (ticker, model) pairs with annualised Sharpe ≥ 0.5 has a hit rate significantly different from 0.5; high-Sharpe outcomes reflect return skew, not directional skill—formally predicted by a closed-form Sharpe–MSE decoupling proposition we derive in Section 3.6 under non-zero return skewness. (H3) Lo–MacKinlay variance ratio tests show top-tier coins are indistinguishable from a random walk (|z| ≤ 1.5 at q ∈ {2, 5, 10}), while mid- and long-tail tiers reject the random-walk null at q = 2 (z = −2.36, z = −2.60). The findings extend across two robustness layers. An AR(1)-GARCH(1,1) baseline produces R² ≈ −0.005 on every tier and is indistinguishable from Lasso, supporting the bias-variance bound; Giacomini–White conditional predictive ability tests reject equal predictive ability between Lasso and tree-based models on every coin in every tier, complicating naive DM interpretations; and a forward-walking 2026-Q1 holdout—83 daily observations per coin entirely outside the training window—confirms that H1 is even more decisively null on unseen data and that the H3 efficiency conclusion holds. Together, these results give a formally tested EMH-style picture for daily crypto: no model meaningfully forecasts log-returns; statistical accuracy and trading P&L are decoupled by an analytically derived mechanism; and weak-form efficiency is approximately satisfied in most liquid coins and in the convergence across the cross-section. Full article

Graphical methods of correlation analysis, such as correlation n-ptychs or hotspots, focus on the identification of the strength and direction of functional relationships between sets of attributes in multidimensional datasets. Since these correlation structures only take into account values of the attributes, situations arise when the relationship is coincidental, meaning that there is no real-world causality between the values of the observed attributes but these values still exhibit significant correlation. This problem of correlation analysis as a whole motivates the need for semantic evaluation of significant relationships identified using its methods—a task that could potentially be time- and resource-intensive when conducted manually. However, modern results in the large language model area provide tools for the automatization of such tasks. Hence, this work focuses on the design and implementation of a novel large language model-based method for semantic evaluation of correlation structures embedded in a correlation graph, specifically correlation n-ptychs for $n\in \{3, 4, 5\}$ and correlation hotspots. In the method, the large language model is automatically prompted to assess the semantic nature of relationships in the set of correlation substructures of the dataset, identify their real-world relevance, and visualize the result in the form of a Semantic evaluation card. The proposed approach is evaluated using two benchmarking datasets focusing on the visualization method used in the model, large language model interaction with the correlation substructures, and comparative analysis with previously used tools in the area. Full article

We present a review on the application of the mathematical models for research on social processes, social structures, and actors in social systems. The scope of the review is not restricted to the classical applications of mathematics such as theory of probability, statistics, stochastic processes, differential equations, and game theory. We also discuss applications of the theory of networks for social network analysis and the numerical research on dynamics of social systems. The number of these applications has increased very fast in recent years. Special attention is given to the results from the area of sociophysics, where mathematical methodology is used to analyze social systems in cooperation with the models and concepts of physics. Another special topic in his review is connected to the results from econophysics, where the mathematical methodology and theories and methods of physics are used in the studies on the dynamics of economic systems. In addition, we give several examples for the application of mathematical methods to social systems: (a) application of difference equations to model the flow of substances in channels of networks; (b) analytical solution of nonlinear equations connected to the model of waves of popularity; (c) numerical results of the waves of popularity in a model that accounts for the change in the opinion of the supporters of the ideas for positive or negative popularity of a person, material item, or a piece of information (idea, theory, ideology, etc.) In the last case, we illustrate the effectiveness of the numerical analysis to discover new effects on the studied social system. The review ends with a large list of references. These references can be used as a guide of the way of new researchers to the large field of mathematical social dynamics. Full article

The increasing need for high-resolution, real-time radiative transfer (RT) modeling in climate science, remote sensing, and planetary exploration has exposed limitations of traditional solvers such as the Discrete Ordinate Radiative Transfer (DISORT) and Rapid Radiative Transfer Model for General Circulation Models (RRTMG), particularly in handling spectral complexity, non-local thermodynamic equilibrium (non-LTE) conditions, and computational scalability. Quantum-Inspired Neural Radiative Transfer (QINRT) frameworks, combining tensor-network parameterizations and quantum neural operators (QNOs), offer efficient approximation of high-dimensional radiative fields while preserving key physical correlations. This review highlights the advances of QINRT in enhancing spectral fidelity and computational efficiency, enabling energy-efficient, real-time RT inference suitable for satellite constellations and unmanned aerial vehicle (UAV) platforms. By integrating physics-informed modeling with scalable neural architectures, QINRT represents a transformative approach for next-generation Earth-system digital twins and autonomous climate intelligence. Full article