This work introduces an immersed boundary method for two-dimensional simulation of incompressible Navier-Stokes equations. The method uses flow field mapping on the immersed boundary and performs a contour integration to calculate immersed boundary forces. This takes into account the relative location of the immersed boundary inside the background grid elements by using inverse distance weights, and also considers the curvature of the immersed boundary edges. The governing equations of the fluid mechanics are solved using a Galerkin-Least squares finite element formulation. The model is validated against a stationary and a vertically oscillating circular cylinder in a cross flow. The results of the model show acceptable accuracy when compared to experimental and numerical results.

This study examines the dynamic impact of geopolitical risk (GPR) and renewable energy consumption (RENE) on energy security in Egypt from 2000 to 2023. Given the increasing regional instability and Egypt’s strategic pivot toward a green economy, this research employs the Autoregressive Distributed Lag (ARDL) bounds testing approach, which is robust for small sample sizes and mixed integration levels. The empirical results provide preliminary evidence of a long-run negative relationship between geopolitical risk and energy security (coefficient: −11.92), suggesting that external political shocks may act as a deterrent to energy stability. Conversely, renewable energy is found to exert an indicative positive influence (coefficient: +1.17) on the energy security index. Notably, these long-run coefficients are significant at the 10% level, implying that while these variables represent emerging structural trends, they remain sensitive to high regional volatility and the evolving nature of the Egyptian energy sector. Diagnostic tests, including Jarque–Bera (0.92) and Breusch–Pagan–Godfrey (0.94) tests, support the model’s reliability, while CUSUM and CUSUMSQ tests indicate general parameter stability. The study suggests that while renewable energy integration shows potential for enhancing resilience, its current scale may not yet be sufficient to fully counterbalance the potential pressures of geopolitical shocks. Policy implications point toward the strategic value of “geopolitical hedging” through continued green investment, the expansion of strategic reserves, and the adoption of de-risking financial instruments like Green Sukuk to support long-term energy sovereignty as a precautionary measure.

Probabilistic artificial-intelligence (AI) models in sports are often reused across seasons despite changes in teams and context. We develop Monotone Empirical-Bayes Transport Recalibration (MEBTR), a model-agnostic maintenance layer that partially pools local calibration maps, requires a prespecified worthwhile Brier-risk improvement before updating, and monitors gains with anytime-valid e-processes. A predictable-support construction sharpens the universal Brier-difference bound using outcome-free bounds known once both forecasts are frozen. Across logistic regression, random forest, histogram gradient boosting (HGB), and multilayer perceptron learners, 400 paired replications retain Raw AI in 94.25–96.00% of exact-identity runs and select local MEBTR in 82.50–85.50% of affine-shift runs, improving guarded Brier risk by 3.27–3.47% under shift. In leakage-audited NCAA basketball, prospective HGB recalibration improves Brier from 0.224853 to 0.224395, calibration slope from 0.9489 to 0.9883, and ICI from 0.02182 to 0.02050. A 10,000-game bootstrap confirms positive average gain, but the prespecified δ = 0.0005 threshold is not anytime certified. Whole-game-disjoint and repeated-season audits show why the risk guard is necessary: candidate improvements can be small and finite-sample action selection is not oracle model selection.

This paper proposes the Poisson-Emrem (PEm) distribution, a new one-parameter discrete probability model obtained by compounding the Poisson and Emrem distributions. The model preserves the mathematical tractability of the Poisson law while offering greater flexibility for analyzing count data in health and biological sciences. A theoretical study establishes its principal properties, showing that increases in the parameter lead to systematic reductions in the mean, variance, and interquartile range, with a corresponding increase in skewness. Additional features such as moments, dispersion index, and the hazard rate function are derived, the latter characterized by a bathtub-shaped form that is particularly suitable for lifetime studies. Parameters are estimated using maximum likelihood, and Monte Carlo simulations confirm the accuracy and efficiency of the estimator. The applicability of the PEm distribution is demonstrated through two empirical datasets involving cytogenetic abnormalities in rabbit lymphoid cells under streptogramin treatment and daily COVID-19 mortality counts in South Korea. Comparative goodness-of-fit analyses show that the proposed model consistently provides superior performance over competing discrete distributions. Owing to its ability to effectively capture skewness, over-dispersion, and zero inflation, the PEm distribution offers a flexible and reliable framework for modeling complex count data arising in health and biological sciences. These findings highlight its potential usefulness in public health monitoring and related statistical applications.

Continuous dequantization embeds discrete data into a continuous space, but relaxation can alter the statistical information carried by the original categories. We study a complementary regime in which a specified weighted discrete law is the target and the dequantizer is required to be lossless under a prescribed quantizer. Any partition-respecting, parameter-independent kernel produces a continuous experiment Blackwell equivalent to the original discrete one, so likelihood ratios, maximum-likelihood estimators, score and Fisher information, Bayes posteriors, and optimal risks are unchanged before downstream approximation. We then characterize what happens after a finite-capacity continuous model is fitted. A Kullback–Leibler (KL) chain rule separates continuous approximation error into the categorical error of the requantized model plus a within-cell shape term; the information-preservation guarantee therefore does not extend automatically to an arbitrary fitted downstream model. We also provide a plug-in analysis for empirically estimated weights, showing that dequantization preserves rather than removes the discrete estimation error. Within each cell, maximizing entropy minus a displacement penalty yields a truncated Gibbs kernel. The apparent concentration and geometric-scale parameters reduce exactly to one effective concentration, $\alpha =\lambda /s_c^2$. We further derive exact transport costs, a sharp $W_1=\Theta \left(h^2\right)$ reconstruction rate for the special reconstruction-from-exact-bin-masses setting, leakage-specific and geometry-perturbation bounds, and a bounded-domain multidimensional formulation. A finite-candidate Monte Carlo selector satisfies a nonasymptotic $O\left(m^{-1/2}\right)$ oracle inequality. Experiments verify the identities and show that exact dequantization can materially reduce requantized error when a smooth continuous downstream model is imposed; this is a conditional representational advantage, not a claim that dequantization dominates an unrestricted categorical model.