This study explores how modern human resource strategies empower crisis management through the leadership ability as the effective mediating link. Following recent research on human resource management’s (HRM’s) evolving role in organizational resilience (Sanders et al., 2024), we surveyed 320 senior and middle managers from Jordanian banks using stratified random sampling. From the partial least squares structural equation modeling (PLS-SEM) analysis, three key findings were derived. Following, commitment-based human resources (HR) practices and strategic fit significantly strengthened leadership competencies and crisis management, adding to existing research on HR-crisis relationships (Al-Khrabsheh et al., 2022). Surprisingly, performance-based HR approaches strengthened leadership competencies but undermined crisis preparedness, suggesting potential trade-offs in pressure-intensive contexts. Most importantly, leadership competencies, particularly communication, emotional intelligence, and emergency preparedness — acted as the “missing link” that translated HR policies into successful crisis management. The findings of the study provide pragmatic implications for financial institutions operating in Jordan’s turbulent economic environment: promoting leadership development reinforces the efficacy of human resource systems amidst periods of turbulence. The study ultimately proves that if human resource initiatives are aligned with leadership development, organizations do not just endure crises but come out more robust.

The k-nearest neighbor (KNN) algorithm remains one of the most fundamental and widely-used methods in machine learning. A common rule of thumb sets the number of neighbors as k = √n, where n is the size of the training set. Despite its widespread adoption, the theoretical justification for this choice has remained obscure. We provide a comprehensive rate-based analysis. First, we derive the minimax-optimal exponent β★ = 4/(d+4) for k = n^β under standard Hölder-smoothness assumptions, recovering as a special case Theorem 1: k = √n is minimax-optimal if and only if the feature space has dimensionality d = 4. Second, Theorem 2 quantifies the sub-optimality of any fixed β as R_n(n^β) = Θ(n^(−r(β,d))) with r(β,d) = min{β, 4(1−β)/d}, yielding an asymmetric penalty for the classical rule when d ≠ 4 that we make precise in Corollary 1. The predicted rate is empirically verified across d ∈ {2,…,20} on controlled synthetic data. On 48 datasets from the OpenML-CC18 benchmark suite, the dimension-aware rule k = ⌊n^(4/(d+4))⌋ outperforms the classical √n rule in 32 of 48 head-to-head comparisons (paired Wilcoxon p = 4.6 × 10⁻⁴, mean accuracy gain +2.5 percentage points), demonstrating that the theoretical improvement translates to a practical one. We further test the Hassanat distance metric against Euclidean across all KNN variants on the same 48 datasets, finding that Hassanat outperforms Euclidean in five of six configurations (paired Wilcoxon p < 0.05), with the largest gains on unstandardized data. Cross-validation remains the strongest k-selection strategy when computationally feasible, and the theoretical results provide a principled non-cross-validated alternative.

It is well-known that activation functions are crucial in determining spectral expressiveness, training dynamics, and reconstruction accuracy in implicit neural representations (INRs), which employ coordinate-based multilayer perceptrons to represent continuous signals. Despite showing excellent performance, sinusoidal activations, for example SIREN, are limited in their adaptability to diverse signal types due to their fixed harmonic structure. In this paper, we propose two novel periodic activation functions for INRs. (1) Harmonic generalizes sinusoidal activations by combining the fundamental frequency with learned second and third harmonics through per-neuron trainable amplitude coefficients, resulting in a richer spectral basis within the SIREN initialization framework. (2) PM-FINER (Phase-Modulated FINER) extends the variable-periodic FINER activation by embedding frequency modulation synthesis directly into the instantaneous phase, enabling data-driven phase distortion via a learnable modulation index and carrier ratio. We conducted comprehensive experiments spanning nine architectural configurations (including SIREN, WIRE, FINER, Gaussian, Harmonic, PM-FINER, and an additional direct comparison against the Subtractive Modulative Network (SMN)), using six natural images, three learning rate schedulers, and three random seeds, totaling 486 main training runs (534 runs total including an ${\omega }_0$ sensitivity sweep). Our evaluation combined peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and rigorous statistical analysis, such as paired t-tests, Wilcoxon signed-rank tests, Cohen’s d effect sizes, and Friedman rank tests. Under cosine annealing, Harmonic achieves a mean PSNR gain of 6.08 dB over SIREN and 2.57 dB over FINER (both $p<0.001$, Cohen’s $d>3.7$), while PM-FINER ranks statistically on par with Harmonic (mean difference $0.17$ dB, $p=0.36$), outperforming all of the other baselines. Compared with SMN, Harmonic outperforms it by $+7.94$ dB under cosine annealing (Bonferroni-adjusted $p<{10}^{-5}$, Cohen’s $d=12.3$), winning on all six images. Additionally, the Friedman ranking across the six images confirmed Harmonic (with mean rank $=1.33$) and PM-FINER (with mean rank $=1.67$), being the top two methods under cosine annealing. Our results establish interpretable multi-harmonic and phase-modulated activations as real alternatives to the existing INR activation functions.

The k-nearest neighbor (KNN) algorithm remains one of the most fundamental and widely-used methods in machine learning. A common rule of thumb sets the number of neighbors as $k=\sqrt{n}$, where n is the size of the training set. Despite its widespread adoption, the theoretical justification for this choice has remained obscure. We provide a comprehensive rate-based analysis. First, we derive the minimax-optimal exponent ${\beta }^{*}=4/(d+4)$ for $k=n^{\beta }$ under standard Hölder-smoothness assumptions, recovering as a special case Theorem 1: under these second-order Hölder-smoothness assumptions, $k=\sqrt{n}$ attains the asymptotic minimax-optimal exponent if and only if the feature space has dimensionality $d=4$; this concerns the asymptotic rate exponent, not the finite-sample optimal value of k. Second, Theorem 2 quantifies the sub-optimality of any fixed $\beta$ as $R_n\left(n^{\beta }\right)=\mathrm{\Theta }\left(n^{-r(\beta ,d)}\right)$ with $r(\beta ,d)=min\{\beta ,4(1-\beta )/d\}$, yielding an asymmetric penalty for the classical rule when $d\ne 4$ that we make precise in Corollary 1. The predicted rate is empirically verified across $d\in \{2,\dots ,20\}$ on controlled synthetic data. On 48 datasets from the OpenML-CC18 benchmark suite, the dimension-aware rule $k=\lfloor n^{4/(d+4)}\rfloor$ outperforms the classical $\sqrt{n}$ rule in 32 of 48 head-to-head comparisons (paired Wilcoxon $p=4.6\times {10}^{-4}$, mean accuracy gain $+2.5$ percentage points), demonstrating that the theoretical improvement translates to a practical one. We further test the Hassanat distance metric against Euclidean across all KNN variants on the same 48 datasets, finding that Hassanat outperforms Euclidean in five of six configurations (paired Wilcoxon $p<0.05$), with the largest gains on unstandardized data. Cross-validation remains the strongest k-selection strategy when computationally feasible, and the theoretical results provide a principled non-cross-validated alternative.