Search Results (96)

This paper investigates the nonlinear dynamics of a decision delay duopoly model that characterizes the competitive landscape within China’s Low-Temperature Milk market. These dynamics include equilibrium points, period-doubling bifurcations, complex torus-like motions, and closed invariant curves induced by Neimark–Sacker bifurcation. Then the Neimark–Sacker bifurcation phenomenon is analyzed. Next, to further stabilize the nonlinear dynamics, an improved impulsive control strategy is introduced. Sufficient conditions for the asymptotic stability of the controlled system are derived using Lyapunov stability theory. Numerical simulations demonstrate that, under appropriate impulsive control, an originally divergent system can converge to equilibrium, effectively stabilizing market profits. This research provides a theoretical reference for oligopolistic firms to optimize their marketing rhythm and for policymakers to maintain market stability. Full article

This study presents a mathematical model for the coupled growth of two interacting wax particles in a non-isothermal laminar flow. The formulation is based on a diffusion-controlled framework, in which the particle evolution is governed by a Stefan-type moving boundary condition with temperature-dependent interfacial concentration. An asymptotic analysis is developed in the limit where the particles’ size is small compared to their separation distance. This leads to a reduced system of nonlinear ordinary differential equations that captures the combined effects of particle interaction and thermal asymmetry. The analysis reveals that both mechanisms enter at leading order and jointly determine the growth dynamics. Numerical simulations are performed to investigate symmetric and asymmetric configurations. The results demonstrate that temperature differences induce a symmetry-breaking mechanism, leading to distinct growth rates even for initially identical particles. Furthermore, the interaction between particles amplifies this asymmetry through a competitive growth process. A key finding is the monotonic increase in the asymmetry ratio, reflecting progressive divergence driven by thermal effects. The proposed model extends the classical method of reflections for interacting Stefan problems to account for thermally induced asymmetry, incorporating non-identical boundary conditions governed by a prescribed temperature field. Full article

The attribution of systemic financial stress to specific market sectors requires metrics that are faithful to the model’s computations, statistically consistent, and connected to a physically meaningful measure of directed information flow. This paper addresses all three requirements through information geometry, contributing to SDGs 7, 8, 9, and 17 through an entropic causal chain linking energy infrastructure failure to financial market stress. We conjecture and empirically verify the Entropy–Saliency Equivalence: Metabolic Saliency is an asymptotically unbiased estimator of the local Kullback–Leibler divergence between stressed and resting sector return distributions, with bias decaying at a parametric rate under Gaussian regularity conditions. The finite-sample bias–variance decomposition of the Kraskov–Stögbauer–Grassberger transfer entropy estimator is derived, establishing a minimax-optimal convergence rate. A novel metric, the Spatio-Temporal Information Flux (STIF), quantifies directed inter-sector stress transmission in bits per trading day, providing a bootstrap-calibrated audit trail aligned with the South African Financial Sector Regulation Act and MiFID II. Empirical validation on the JSE canonical panel (87 securities, 2857 trading days, 2015–2026) with Eskom load-shedding stages as exogenous stress injectors confirms the equivalence ($R^2=0.810$, $\widehat{\rho }=0.90$), with walk-forward $R^2=0.789$ and placebo $R^2=0.081$ ruling out estimation artefacts. The energy sector is identified as the primary stress transmitter during Stage 4+ Eskom events (STIF rising from 0.14 to 0.43 bits/day, directional asymmetry ratio 4.7). Robustness checks confirm stability across non-Gaussian securities and rolling transfer entropy windows. Full article

We propose a new class of spatio-temporal GARCH models designed to capture volatility dynamics that propagate jointly across time and space. Existing spatio-temporal GARCH formulations typically account for either lagged spatial spillovers or contemporaneous interactions separately, and therefore fail to capture the combined effect of instantaneous spatial volatility feedback and its propagation over time. To address this gap, we introduce a unified framework that incorporates both contemporaneous and lagged spatial volatility interactions within a single coherent model. At each time point, conditional variances evolve according to a temporal GARCH recursion combined with both contemporaneous and lagged spatial volatility interactions defined on a lattice. This structure allows volatility shocks to diffuse instantaneously across neighboring locations and persist over time through spatially structured feedback mechanisms, extending existing spatial and spatio-temporal GARCH formulations. We establish sufficient conditions for the existence of a unique strictly stationary and ergodic solution based on contraction properties of a combined spatial–temporal operator. Statistical inference is conducted via Gaussian quasi-maximum likelihood estimation (QMLE). We derive consistency and asymptotic normality of the QMLE under two asymptotic regimes: (i) increasing temporal domain with fixed spatial size, and (ii) joint asymptotics where both the number of time periods and spatial locations diverge. In both cases, the asymptotic covariance matrix admits a standard sandwich form and can be consistently estimated. An extensive Monte Carlo study confirms the theoretical results. The simulations show that the QMLE performs well even under strong spatial and temporal persistence and remains robust to heavy-tailed innovations. In particular, increasing the spatial domain substantially improves estimation accuracy, highlighting the efficiency gains induced by spatial information. The proposed model provides a flexible and tractable framework for analyzing volatility processes evolving jointly in time and space. Full article

Quantitative trading systems require predictive models that simultaneously deliver accurate forecasts, calibrated uncertainty quantification, and actionable risk measures. This paper proposes an information-theoretic semiparametric regression framework combining a convolutional neural network–Transformer (CNN–Transformer) network for nonlinear temporal dependencies with a Gaussian process (GP) prior for residual autocorrelation and calibrated predictive distributions. Three theoretical results are established: an identifiability theorem guarantees joint recoverability of the nonparametric and GP components; a consistency theorem showing that the penalised maximum likelihood estimator converges at a rate $n^{-1/(2+d_{\mathrm{eff}})}$; and a coverage theorem proving asymptotic nominal coverage of the GP’s credible intervals. The framework enables an entropy-regulated trading module where predictive differential entropy informs position sizing via an uncertainty-penalised Kelly criterion, Kullback–Leibler divergence quantifies model uncertainty, and CVaR-constrained optimisation controls the tail risk. Simulations show the method outperforms the CNN, long short-term memory (LSTM), Transformer, XGBoost, random forest, least absolute shrinkage and selection operator (LASSO), and standard GP regression approaches. Backtesting on four Chinese A-share stocks yielded annualised returns of 15.9–22.4% with Sharpe ratios of 0.49–0.62, maximum drawdowns below 15%, and daily 95% CVaR reductions of 28–31% relative to a full-Kelly baseline, confirming both predictive accuracy and risk management effectiveness. Full article

In this work, a formal asymptotic framework based on infinite number expressions is employed to investigate structural relations associated with the Dirichlet representation of the Riemann zeta function. Within this framework, infinite number objects are interpreted through asymptotic representatives and serve as symbolic encodings of asymptotic behavior in the regime x → ∞. A divergent real series is constructed from the sum of entries of an n × n matrix in the asymptotic limit n → ∞ and analyzed in relation to the squared modulus of a Dirichlet-type series. When the common parameter coincides with the imaginary part of a nontrivial zero of the Riemann zeta function on the critical line, the framework yields a structured cancellation mechanism, leading to parameter-dependent decay or convergence toward the constant −γ/2. Additional formal asymptotic relations are derived linking nontrivial zeros, divergent expressions, and the Euler–Mascheroni constant. The theoretical analysis is accompanied by numerical computations in double-precision arithmetic, which serve as consistency checks of the predicted asymptotic behavior. The proposed approach provides a coherent representative asymptotic methodology for organizing and analyzing identities involving divergent expressions arising in analytic number theory. The resulting relations are interpreted within this representative framework and are intended as structural asymptotic identities rather than classical equalities of divergent series. Full article

Decarbonizing the construction sector requires high-volume replacement of Portland clinker with non-calcined supplementary cementitious materials (SCMs). This study investigates white cement pastes incorporating raw Algerian diatomite—a silica-rich biogenic mineral—at substitution levels from 40% to 95% (5% increments) and a fixed water-to-binder ratio of 0.5. The target application is ultra-lightweight, multifunctional composites for non-structural uses such as decorative panels and partition elements. Increasing diatomite content progressively reduced bulk density from 1.483 g/cm³ (D40) to 0.557 g/cm³ (D95) and increased porosity. 28-day compressive strength decreased monotonically from 16 MPa (D40) to 2.4 MPa (D95) as clinker dilution intensified. Ultrasonic pulse velocity dropped from 6205 m/s to 1495 m/s, reflecting progressive pore development and confirming the material’s lightweight potential. Statistically significant strength gains beyond 28 days were recorded ($+25.87\%$ for compression, p-value $< 0.05$), evidencing delayed pozzolanic activity. These results confirm that raw, non-calcined diatomite is a viable SCM for eco-efficient, low-density construction systems. To overcome the extrapolation instability of purely data-driven approaches, a Meta-Avrami Hybrid Framework was developed. It anchors Gradient Boosting residual learning to a sigmoidal Avrami hydration kernel. The model achieved high predictive accuracy ($R^2\approx 0.999$, $\mathrm{RMSE}\approx 0.010$) under 10-fold cross-validation. Generalization was well-controlled, with a low overfitting gap ($\Delta R^2=0.0226$) and stable fold-to-fold performance ($\mathrm{Std}=0.0204$). These metrics confirm suitability for unseen mix designs. This is particularly relevant for service-life assessment of partition panels and lightweight façade elements, where long-term performance guarantees are required. The physics-informed architecture ensures asymptotic strength stabilization up to a 10-year horizon (amplification ratios 1.03–1.05). This prevents the non-physical divergence observed in polynomial and power-law hybrids (ratios 1.36–1.70). The framework provides a reliable and interpretable tool for service-life design of sustainable low-carbon cementitious systems. Full article

We investigate the combined effects of spatial curvature and topology on the properties of the vacuum state for a charged scalar field localized on the (2 + 1)-dimensional Beltrami pseudosphere, assuming that the field obeys the quasiperiodicity condition with constant phase. As important local characteristics of the vacuum state, the vacuum expectation values (VEVs) of the field squared and energy–momentum tensor are evaluated. The contributions in the VEVs coming from geometry with an uncompactified azimuthal coordinate are divergent, whereas the compact counterparts are finite and are analyzed both numerically and asymptotically. For small values of the proper radius of the compactified dimension, the leading terms of topological contributions are independent of the field mass and curvature coupling parameter, increasing by a power law. In the opposite limit, the VEVs decay following a power law in the general case. In the special case of a conformally coupled massless field, the behavior is different. Unlike the VEV of field squared and vacuum energy density, the radial and azimuthal stresses are increasing by absolute value. As a consequence, the effects of nontrivial topology are strong for the stresses, in this case, at small values of the radial coordinate. Full article

The density power divergence (DPD) is a well-studied member of the Bregman divergence family and forms the basis of widely used minimum divergence estimators that balance efficiency and robustness. In this paper, we introduce and study a new sub-class of Bregman divergences, termed the exponentially weighted divergence (EWD), designed to generate competitive and practically interpretable inference procedures. The EWD is constructed so that its associated weight function remains bounded within the interval $[0, 1]$, which facilitates a transparent interpretation of robustness through controlled downweighting of low-density observations and avoids excessive influence from high-density points. We develop minimum EWD estimators (MEWDEs) within a general framework accommodating independent but non-homogeneous data, thereby extending classical minimum divergence theory beyond the i.i.d. setting. Under standard regularity conditions, we establish Fisher consistency and asymptotic normality, and we analyze robustness properties through influence function calculations. The EWD framework is further extended to parametric hypothesis testing, for which we derive the asymptotic null distribution of a Bregman divergence-based test statistic. Extensive simulation studies and real-data applications demonstrate that the proposed estimators perform comparably to, and often more robustly than, existing DPD-based procedures, particularly under moderate to heavy contamination, while retaining high efficiency under clean data. Overall, the EWD provides a tractable and interpretable alternative within the Bregman divergence class for robust parametric estimation and testing. Full article

If our observable Universe is only a tiny region of a vastly larger and conformally older spacetime, then the usual formulations of the classical flatness and horizon problems of the Hot Big Bang can be reinterpreted as artifacts manifesting an observational selection effect; we occupy a small causal domain of a much larger causally-connected and possibly non-flat spacetime. A sufficiently large positive cosmological constant, $\Lambda$, sets the future asymptotic horizon scale of the observable Universe, ∼${\Lambda }^{-1/2}$, thereby implying that the observable Universe may simply be a minute patch of a far larger pre-existing one, hereafter a Small Patch Hypothesis. Importantly, this observational bound is purely geometric; regardless of when the Universe is observed, the maximum accessible scale is finite and fixed by $\Lambda$, independent of inflationary dynamics, anthropic arguments, or assumptions about the global hosting spacetime. The externally possibly frozen past-eternal state implied by a pre-existing, causally connected spacetime motivates, but does not strictly require, viewing the perturbation field as being in (or arbitrarily close to) a coarse-grained maximum-entropy—equilibrium—configuration. Conditionalizing only on fixed mean and variance, a Gaussian distribution uniquely emerges, while the absence of entropy gradients corresponds to adiabaticity. In this work these features are therefore treated as plausible maximum-ignorance priors for super-horizon perturbations, rather than as rigorously derived consequences of a fully developed microscopic notion of gravitational entropy. In this sense, inflation becomes one viable realization of the proposed Small Patch Hypothesis. Here, one particular non-inflationary alternative is considered for illustrative purposes in which a primordial spectrum $P_{\zeta }\left(k\right)$ of the gauge-invariant perturbation $\zeta$ that pre-dates the Big Bang grows logarithmically toward large scales, $k\to 0$, and in fact diverges at some finite $k_c$. If $k_c\ll {\Lambda }^{-1/2}$, then our local cosmic patch probes only the regime where $\zeta \ll 1$ and appears exceptionally smooth. Over the comparatively narrow observable window, this $P_{\zeta }\left(k\right)$ mimics a slightly red-tilted, inflation-like spectrum. Rather than introducing high-energy new fields, this perspective frames large-scale homogeneity, isotropy, Gaussianity, adiabaticity, and the observed thermodynamic Arrow of Time as possible consequences of restricted observational access to a much larger Universe in equilibrium, rather than signatures of a unique early-Universe mechanism. Current observations cannot distinguish this logarithmically running spectrum from the standard power-law one, but future probes—for example high-resolution 21-cm measurements of the Dark Ages—may be able to falsify it. Full article

Evaluating artificial intelligence (AI) models in clinical medicine requires more than conventional metrics such as accuracy, Area Under the Receiver Operating Characteristic (AUROC), or F1-score, which often overlook key considerations such as fairness, reliability, and real-world utility. We introduce CUES as a multiplicative composite score for clinical prediction models; it is defined as $\mathrm{CUES}=(C\cdot U\cdot E\cdot S{)}^{1/4}$, where C represents calibration, U integrated clinical utility, E equity across patient subpopulations, and S sampling stability. We formally establish boundedness, monotonicity, and differentiability on the domain ${\left(\mathrm{0,1}\right]}^4$, derive first-order sensitivity relations, and provide asymptotic approximations for its sampling distribution via the delta method. To facilitate inference, we propose bootstrap procedures for constructing confidence intervals and for comparative model evaluation. Analytic examples illustrate how CUES can diverge from traditional metrics, capturing dimensions of predictive performance that are essential for clinical reliability but often missed by AUROC or F1-score alone. By integrating multiple facets of clinical utility and robustness, CUES provides a comprehensive tool for model evaluation, comparison, and selection in real-world medical applications. Full article

In this paper, we first prove (Theorem 1) that any two inputs producing the same output in a symmetric pair of discrete skew tent maps always have the same parity, meaning that they are either both even or both odd. Building on this property, we then propose (Definition 1) a new discrete chaotic map and prove that (Theorem 2) the proposed map is a bijection for all control parameters. We further prove that (Theorem 3) the discrete Lyapunov exponent (dLE) of the proposed map is not only positive but also approaches the maximum value among all permutation maps over the integers $\{0,1,\dots ,2^m-1\}$ as m gets larger. In other words, (Corollary 1) the proposed map asymptotically achieves the highest possible chaotic divergence among the permutation maps over the integers $\{0,1,\dots ,2^m-1\}$. To provide some further evidence that the proposed map is highly chaotic, we present at the end some results from the numerical experiments. We calculate the approximation and permutation entropy of the output integer sequences. We also show the NIST SP800-22 tests results and correlation properties of some derived binary sequences. Full article

In this work, we introduce a new four-parameter distribution, called the integrated linear–Weibull (ILW) model, constructed by embedding a dynamic linear component within the Weibull framework. The ILW distribution is capable of capturing a wide variety of symmetric and asymmetric density shapes and accommodates diverse failure-rate behaviors. We derive several of its key mathematical and statistical properties, including moments, extropy, cumulative residual entropy, order statistics, and their asymptotic forms. The mean residual life function and its reciprocal relationship with the failure rate are also obtained. An algorithm for generating random samples from the ILW distribution is provided, and model identifiability is examined numerically through the Kullback–Leibler divergence. Parameter estimation is carried out via maximum likelihood, and a simulation study is conducted to assess the accuracy of the estimators; the results show improvements in estimator performance as sample size increases. Finally, three real datasets involving failure-time observations and one describing hydrological and epidemiological data are analyzed to demonstrate the practical usefulness of the ILW model. In these applications, the proposed model exhibits competitive or superior performance relative to several existing lifetime distributions based on standard model selection criteria and goodness-of-fit measures. Full article

Controllability metrics based on system Gramians have been widely adopted to provide quantitative measures of the degree of controllability (DoC) and the disturbance rejection capability (DoDR) of dynamical systems. While steady-state Gramian formulations offer closed-form tractability, they are not applicable when rigid-body modes are present, as the associated poles at the origin cause the conventional Gramians to diverge. This paper presents a novel steady-state DoDR metric for linear time-invariant systems with a rigid-body mode. By block-diagonalizing the dynamics through a similarity transformation and analyzing the asymptotic behavior of the Gramian matrices, we derive an exact closed-form expression for the steady-state DoDR. The resulting formulation is numerically stable and enables systematic evaluation of disturbance-rejection capability even in the presence of a rigid-body mode. The proposed metric is validated using a mass–spring–damper chain model, where its effectiveness is demonstrated in actuator placement problems. The results show that the metric not only remains computationally well-posed but also provides physically meaningful interpretations consistent with modal characteristics. This study establishes a foundation for extending disturbance-rejection metrics to systems with multiple rigid-body modes, thereby broadening the applicability of Gramian-based controllability analysis. Full article

Accurate estimation of tail dependence is difficult due to model misspecification and data contamination. This paper introduces a class of minimum f-divergence estimators for the tail dependence coefficient that unifies robust estimation with extreme value theory. I establish strong consistency and derive the semiparametric efficiency bound for estimating extremal dependence, the extremal Cramér–Rao bound. I show that the estimator achieves this bound if and only if the second derivative of its generating function at unity equals one, formally characterizing the trade-off between robustness and asymptotic efficiency. An empirical application to systemic risk in the US banking sector shows that the robust Hellinger estimator provides stability during crises, while the efficient maximum likelihood estimator offers precision during normal periods. Full article