Abstract: The effect of atom size on the shock wave structure in a binary monatomic gas mix with Rydberg atoms has been investigated. The problem was solved numerically using the system of hydrodynamic equations in Argon gas, for the atom size ratios between 2 and 100, T = 1500 K, and the density between 10¹⁷ and 10²⁰ m^-3. It was found that the presence of larger size atoms in the mix results in the shock front splitting that is on the order of mean free path for this component. The results can be of interest in supersonic plasma dynamics and in astrophysics studying shock waves in the environments where high-n Rydberg states are present.

Abstract: In this paper, we propose two novel defective survival models within the Gamma–G family: the Defective Gamma–Gompertz and the Defective Gamma–Da- gum distributions. Unlike classical mixture cure models, our formulation incorporates the cure fraction directly into the survival function through the defective property of the baseline distribution, avoiding the need for an explicit mixing parameter. The motivation for these new models lies in the limited set of defective distributions currently available, despite the increasing demand for flexible and parsimonious cure rate models in biomedical applications. By extending the defective property to the Gamma–G construction, our approach fills this methodological gap while providing models that are both interpretable and computationally efficient. We show that the Gamma–G construction preserves defectiveness whenever the baseline distribution is defective, thus establishing a coherent theoretical foundation. Both models allow covariate effects through regression structures on shape, scale, and, in the case of the Gamma–Dagum distribution, on the cure-fraction parameter, resulting in parsimonious and interpretable specifications. Parameters are estimated via maximum likelihood, and an extensive Monte Carlo study confirms estimator consistency and accurate coverage in finite samples. The practical relevance of the models is illustrated with two large clinical datasets on melanoma and cervical cancer from the São Paulo Cancer Registry. Results reveal that the proposed models not only provide superior goodness-of-fit but also offer clearer insights into long-term survival compared to traditional cure-rate approaches. Overal, this work introduces a unifying and flexible framework for defective survival models, extending their applicability and delivering practical improvements over existing cure models.

Abstract: We introduce a new method of dimensional analysis based on complete systems of units, such as the metric and Planck systems, in which fundamental dimensionless constants arise naturally. In fact, it is the reformulated Planck system that communicates its dimensionless constants to the metric or any other system. The method reveals additional complex dynamical scales and physical effects beyond those amenable to conventional dimensional analysis. We formulate our strategy in simple settings involving pairs of seemingly unrelated constants, and then we extend the analysis to more complicated cases involving combinations of three to five well-known universal constants. In constructions involving several unrelated constants, the method captures increasingly complex effects and places two or more disparate physics areas into a single framework connecting them by never-before-seen combinations of fundamental dimensionless constants, such as the fine-structure constant and the gravitational coupling constant. Thus, this method provides an alternative pathway to unified descriptions of fundamental interactions that have so far eluded a consistent theoretical formulation.

Abstract: Background: Plasma biomarkers are widely promoted as scalable tools for staging Alzheimer’s disease (AD), yet head-to-head comparisons against the clinical scales used to define diagnostic labels remain scarce. Reported gains from machine-learning fusion of clinical and biomarker features may therefore reflect label circularity rather than biological signal. Methods: From the Alzheimer’s Disease Neuroimaging Initiative (ADNI), we assembled 655 participants (CN = 296, MCI = 168, AD = 191) with concurrent plasma biomarkers (pT217, Aβ42/40, NfL, GFAP), clinical scales (MMSE, CDR-SB, FAQ), APOE genotype, and demographics. Three pre-specified feature sets (clinical-only, biomarker-plus-demographic-genetic, and full fusion) were compared across four classifiers (Logistic Regression, SVM, Random Forest, XGBoost) using repeated nested cross-validation (5-fold × 3 outer, 5-fold inner) with balanced class weighting. External validation used the Center for Neurodegeneration and Translational Neuroscience (CNTN) cohort (n=130). Results: Clinical scales alone reached a three-class AUC-OvR of 0.9539±0.0041, and fusion reached 0.9559±0.0046, an indistinguishable gain. Because MMSE, CDR-SB, and FAQ partly determine ADNI diagnostic labels, both estimates are circularity-inflated upper bounds. Independently of this circularity, the plasma-plus-demographic-genetic model still achieved AUC-OvR =0.7455±0.0150, with pT217 the dominant contributor. Pairwise discrimination was excellent for CN vs. AD (1.0000) and MCI vs. AD (0.9739), but markedly weaker for CN vs. MCI (0.9302 fused, 0.69 plasma-only). The reduced biomarker model transferred to CNTN with AUC-OvR =0.702 (95% CI 0.635–0.764). Conclusions: Apparent fusion gains in ADNI are largely a consequence of label circularity. After removing the circular clinical features, plasma pT217 supports three-class CN/MCI/AD screening at AUC ≈0.74 internally and 0.70 externally, which establishes a realistic performance ceiling for blood-based AD staging. MCI detection remains the principal bottleneck.

Abstract:

Background: Vitamin D–binding protein (DBP) is the principal carrier of circulating 25-hydroxyvitamin D3 [25(OH)D₃] and is independently synthesized by the neonate. Whether neonatal DBP at birth adds predictive value beyond baseline 25(OH)D₃ for supplementation response remains unclear. Methods: This single-center prospective cohort study enrolled 101 neonates. Neonates with 25(OH)D₃ <20 ng/mL (supplementation-response cohort; n = 59: 29 preterm, 30 term) received 800 IU/day oral cholecalciferol for 8 weeks; neonates with 25(OH)D₃ ≥20 ng/mL served as baseline reference controls (n = 42). Serum 25(OH)D₃ and DBP were measured at baseline and week 8 in the supplementation-response cohort. Results: Median baseline 25(OH)D₃ was 8.60 [6.70–12.05] ng/mL and median baseline DBP was 4.97 [3.70–8.19] µg/mL. After supplementation, 25(OH)D₃ increased significantly (median Δ = 17.70 ng/mL; p <0.001), with 55/59 (93.2%) achieving sufficiency. In multivariable regression, gestational age was the strongest independent predictor of Δ25(OH)D3 (β = −0.440, p = 0.001), followed by baseline 25(OH)D3 (β = −0.314, p = 0.015); baseline DBP was not significant (β = 0.072, p = 0.551). Conclusions: Baseline DBP did not independently predict supplementation response. Lower gestational age and lower baseline 25(OH)D₃ were associated with greater increases in 25(OH)D₃ after supplementation, whereas baseline DBP provided no additional predictive value. Supplementation with 800 IU/day for 8 weeks was effective across gestational-age categories. Routine DBP measurement does not appear to provide additional clinical value for guiding neonatal vitamin D supplementation.

Abstract: The paper examines stationary and dynamic gametheoretic models of cooperation formation among agents based on mutual trust. The dynamic model confirms that trust is a critically important factor in economic interactions. Mutual trust can significantly increase the payoffs for all agents, but its achievement is possible only for a certain class of input parameters of the model and requires a significant return on each agent’s investment in the public good. The model uses the value of social trust to describe social norms accepted in society. The study of the dynamic model was conducted based on Nash equilibrium in the static case and via simulation modelling for heterogeneous agents with different objective functionals. In the model, individual states act as agents. It is shown that the payoff of states directly depends on the degree of trust between them and can grow significantly in the presence of trust. Simulation experiments were conducted in the dynamic case, and the results were analysed.

Abstract: Background/Objectives: Chromosomal microarray analysis (CMA) is an essential tool in modern cytogenetics for detecting copy number alterations and copy-neutral loss of heterozygosity (CN-LOH). As optical genome mapping (OGM) emerges as a potential replacement for traditional cytogenetic methods, the extent to which CMA remains necessary in routine diagnostic workflows remains to be elucidated. Methods: We retrospectively reviewed 53 primary neoplastic cases in which CMA identified one or more CN-LOH events. Event size, genomic content, and correlation with next-generation sequencing (NGS) findings were assessed. A separate cohort of newly diagnosed B-cell acute lymphoblastic leukemia (B-ALL) was analyzed to evaluate disease-specific CN-LOH frequency. Results: Nearly half of CN-LOH events detected were &lt;25 Mb, below the current detection threshold of OGM. Many encompassed clinically relevant genes, including FLT3, JAK2, TET2, TP53, and RUNX1. Additionally, two-thirds of cases harbored pathogenic or likely pathogenic variants by NGS within the corresponding CN-LOH regions, further underscoring the clinical value of detecting these copy-neutral events. In contrast, CN-LOH was uncommon in B-ALL, and most alterations identified by CMA would be detectable by OGM. Many of these patients also harbored complex structural rearrangements that required multiple conventional assays for full characterization; these could be resolved by OGM in a single analysis. Conclusions: Our findings indicate that although OGM excels at resolving complex structural variants, CMA remains essential for detecting copy-neutral events. Until OGM achieves improved sensitivity for CN-LOH, an integrated approach utilizing conventional cytogenetics, CMA, NGS, and OGM provides the most reliable framework for comprehensive genomic assessment across cancer types.

Abstract: Marginal ice zone (MIZ) is a transitional region between dense pack ice and open water. It is a highly dynamic zone under strong interactions between the atmosphere, ocean, sea ice and waves, playing a crucial role in the polar climate and ecosystem. Accurate determination of MIZ is therefore essential for advancing our understanding, modeling and prediction of the polar climate system. In this paper, we introduce and apply a suite of MIZ-related metrics to evaluate the performance of four satellite-derived high-resolution operational sea ice concentration (SIC) products in determination of the MIZs around Svalbard, using the Norwegian ice chart as reference. The metrics used for evaluation include sea ice extent (SIE), MIZ extent (MIZE), length of ice edge (LIE), integrated ice edge error (IIEE), integrated MIZ error (IME), ice edge distance error (IEDE), and MIZ width error (MWE). The evaluation is based on three years of daily SIC data (2023-2025) from four products, including the Bremen AMSR2 SIC data from the University of Bremen (Bremen SIC), the Resolution-enhanced AMSR2 SIC (RE SIC) and Multisensor SIC products (Multisensor SIC) from the Norwegian Meteorological Institute, and the Automated Sea Ice Product (ASIP) from the Copernicus Marine Environment and Monitoring Service (CMEMS) (ASIP SIC). To be consistent with the Norwegian ice chart, the MIZ is defined as MIZ70 and MIZ90, corresponding to SIC thresholds of up to 0.7 and 0.9, respectively. IEDE and MWE are calculated using two types of LIE, the reference LIE (LIEr) from the Norwegian ice chart and the average LIE (LIEa) by averaging the ice chart LIE and the concerned LIE from the four satellite products. The results demonstrate that all four satellite SIC products generally capture the evolution of the sea ice conditions around Svalbard well, but differ in their accuracy when determining the ice edge and MIZs. The Bremen SIC product tends to overlook areas with low SIC, leading to a significant underestimation of SIE and a large IIEE. However, it provides an overall close agreement with the ice chart for the MIZ90 metrics (MIZE, IME and MWE). The RE and ASIP SIC products exhibit strong performance in capturing the ice edge and total SIE, with the ASIP product particularly excelling in accurately representing the ice edge and MIZ70. The Multisensor provides the closest agreement with the ice chart for the IME90, MWE90 and MWEa70, and ranks as the second-best product for the IIEE, IME70 and MWEr70. These results suggest that SAR and Low-frequency AMSR2 channels are especially effective for capturing the lower bounds of the MIZ, while high-frequency channels are more suitable for defining the upper bounds. Despite these strengths, the complex summer surface conditions pose significant challenges for satellite sensors in determining the ice edge and the MIZ, resulting in higher IEDE and MWE values during this period. These results highlight both the capabilities and limitations of satellite-based data in determining the MIZ, particularly under challenging summer conditions. Accurate determination of MIZs may require significant advancements in satellite observation technologies, retrieval algorithms, and more robust methods for integrating multiple sources.

Abstract: The sealing behavior of fracture-filling minerals in the near-field of the deep geological repository (DGR) is critical for the safe disposal of high-level radioactive waste (HLW). In granite host rocks, natural fractures are often filled with polymineralic assemblages of calcite, quartz, and clay minerals; however, their coupled compaction–pressure solution mechanisms under thermal–hydraulic–mechanical–chemical (THMC) conditions remain poorly understood. In this study, 12 fracture sealing experiments were conducted on Beishan granite and its typical fracture fillings at 90 °C and 15 MPa effective stress, using different pore fluids and systematically varying grain size (75–250 μm), mineral proportions, and clay content. The results demonstrate that pressure solution–precipitation of calcite in saturated CaCO3 solution is the key mechanism for long-term fracture sealing, achieving a compaction strain of 24.6%—substantially higher than those obtained in deionized water (20.6%) and under dry conditions (14.8%). Fine-grained calcite compacts more effectively than its coarse-grained counterpart, reaching a porosity as low as 4.8%; rigid quartz accelerates calcite pressure solution via stress concentration at grain contacts; and a moderate amount of clay minerals (~20 wt%) further reduces porosity to 2.1% through lubrication and micropore filling. The study reveals a multi-stage process transitioning from mechanical compaction to pressure solution–precipitation, and a synergistic sealing mechanism dominated by calcite compaction–pressure solution, augmented by quartz stress transfer and clay lubrication. These findings revise the traditional monomineralic understanding and provide a scientific basis for safety assessment of HLW disposal and the design of natural sealing materials.

Abstract: Introduction: Transepithelial photorefractive keratectomy (Trans-PRK) offers superior re-epithelialization and visual recovery. This study evaluates the impact of preoperative refractive status on clinical outcomes and identifies prognostic factors across varying myopic severities. Methods: This retrospective observational study included 125 eyes [64 patients; age > 20 years; best-corrected visual acuity (BCVA) ≥ 20/25] that underwent Trans-PRK between March and December 2022. Patients were stratified into low myopia (LM: > -5.0 D), moderate-to-high myopia (MHM: ≤ -5.0 D to > -8.0 D) extremely high myopia (EHM: ≤ -8.0 D) groups. Analysis focused on preoperative refraction, intraoperative parameters, postoperative uncorrected visual acuity (UCVA) and corneal conditions of superficial punctate keratitis (SPKs) and haze. Results: The mean age was 30.20 ± 6.34 years, with a mean initial manifest sphere (MS) of -6.42 ± 2.27 Diopter (D) overall and -3.73 ± 0.15 D, -6.28 ± 0.13 D and -9.17 ± 0.15 D in the LM, MHM and EHM groups, respectively. At a mean follow-up of 6.69 ± 3.73 months, the overall mean final manifest spherical equivalent (MSE) was -0.12 ± 0.73 D and mean final UCVA was 0.01 [Snellen equivalent (SE), 205/200] ± 0.08 logMAR. Predictability was 94.4%, 88.88% and 94.3% for the final MS ≤ -1.0 D, final MSE ≤ -1.0 D and UCVA ≥ 0.8, respectively. In the LM and MHM groups, cycloplegic and subjective refractions showed the highest concordance with emmetropia, whereas initial manifest refractions were most accurate for the EHM group. Corneal SPK incidence declined from 32.2% (1 month) to 1.6% (6 months), primarily localized to EHM eyes. Corneal haze peaked at 28.2% at three months before receding to 9.4% by 6 months. Conclusions: Refractive and visual stability were achieved by the third month for the LM and MHM groups, whereas the EHM group required six months to reach both refractive and visual plateaus. Despite transiently higher rates of corneal SPKs and haze in EHM eyes, final visual outcomes remained excellent (UCVA 18/20).

Abstract: Active asset managers are increasingly including cryptocurrencies in their alternative asset allocations, highlighting their speculative and volatile nature. The aim of this research is to examine trends in the returns and volatility of cryptocurrencies while accounting for the depegging of stablecoins driven by speculative trading macroeconomic shocks, and technological shifts. It builds a sample, by market capitalisation, using data from the daily closing prices of Bitcoin (BTC), Ethereum (ETH), Binance (BNB), and Ripple (XRP), two fiat-backed stablecoins (USDT and USDC) and a cryptocurrency-collateralised stablecoin (DAI). As a first step, Granger causality tests were applied to examine the influence of stablecoin depegging events on crypto returns during financial market stress. The results indicate that DAI exhibits the most consistent Granger-causal relationship with cryptocurrency returns; whereas, the predictive power of USDT and USDC depegging events varies across assets. The analysis was extended by modelling volatility using an EGARCH-X model to study whether depegs also affect crypto during periods of market stress. In this case, the evidence for statistically significant effects is limited. Nevertheless, in the instances where significance is detected, the results are consistently linked to USDC.

Abstract: To identify the key factors influencing the cracking behavior of fully ceramic microencapsulated (FCM) fuel, this study employed the MOOSE multi-physics coupling platform and the cohesive phase-field fracture theory to simulate crack initiation and propagation in FCM fuel, with particular attention to the effects of particle spacing and residual pore in the matrix. Results showed that during early irradiation stages, in the absence of matrix defects, particle spacing had minimal influence on the distribution of the maximum principal stress. However, when residual pore was present in the SiC matrix, significant stress concentration occurred at the porosity sites, where the maximum principal stress was localized. Smaller particle spacing promoted crack initiation in the SiC matrix between adjacent particles and led to a higher number of cracks under the same fast neutron fluence. In the presence of residual pore, crack nucleation occurred at porosity sites even at low neutron fluence; at a fluence of 2.3 dpa, through-thickness cracks formed in FCM fuel containing residual pore, resulting in the loss of fission product containment capability.

Abstract: Federated learning lets organizations train a shared model without pooling private data. The standard method, Federated Averaging, requires all participants to use the same input features, a condition that fails in cross-sector phishing detection, where banks analyze URL structure and hospitals analyze email content. We present RankBridge, a system that groups participants by comparing ranked lists of SHapley Additive exPlanations (SHAP) feature importance rather than model weights or gradients. Each participant trains a local LightGBM model, extracts the top-K features by SHAP importance, and sends only 60 bytes of ranked indices to a central server. The server applies rank correlation and Ward’s hierarchical clustering to identify similarly threatened organizations, then combines models only within each discovered group. Across 32 participants in five organization types, RankBridge achieves F1 =0.854 on synthetic data and F1 =0.775 on real phishing data. Federated Averaging collapses to F1 =0.278 on the same data. RankBridge recovers the correct organizational groupings with Normalized Mutual Information (NMI) =0.978 while each participant transmits roughly 10,000× less data per round than a full model upload.

Abstract: Plant-derived exosome-like nanoparticles (PELNs), a subset of extracellular vesicle (EV) secreted by plant cells, have emerged as revolutionary biomaterial with broad applications in biomedicine, agriculture, and nanotechnology. Structurally, PELNs feature with phospholipid bilayer homologous to plant cell membranes, encapsulating bioactive components such as proteins, nucleic acids, lipids, and secondary metabolites. The native structure of PELNs endows them with enhanced bioavailability, reduced immunogenicity, and improved barrier penetration for precise tissue delivery. Recent researches highlight the cross-kingdom therapeutic potential of PELNs in mammals, including antitumor, anti-inflammatory, tissue repair, immunomodulation and so on. This review comprehensively summarized recent advancements in PELNs researches, including innovative isolation techniques, molecular characterization, their roles in drug delivery and disease therapy. We also discussed challenges in standardization, scalability, and regulatory frameworks which could provide future perspectives for translating PELNs into clinical and industrial applications.

Abstract: The calculation of gas properties from the gas composition is an activity that occurs frequently in gas analysis. Such calculations play an important role in the transmission and distribution of energy gases, carbon dioxide and other commodities. They also occur in monitoring air quality. Applications include the calculation of compressibility factors of natural gas to convert metered gas volumes from actual to reference conditions, the conversion of amount fractions into mass concentrations and calculations in process design and optimisation. Evaluating measurement uncertainty is important, as usually there are legislative, regulatory and commercial requirements to be met. Assessing and demonstrating compliance with such requirements requires knowledge about the uncertainty of the measurement result. It is shown how the well-known law of propagation of uncertainty can be used with models from which it is not evident how to calculate partial derivatives, such as equations of state, which are used to calculate, e.g., compressibility factors, densities and energies. Furthermore, it is shown how to calculate time averages from measurement data in grids and networks.

Abstract: Existing radio environment map (REM)-based emitter detection methods suffer from high false positives and missed detections in blurred or conjoined structures, or require large annotated datasets and heavy computation. This paper proposes an unsupervised method, persistent homology with agglomerative clustering (PH-AC), based on an improved persistent homology algorithm. A simulated spaceborne REM dataset is constructed via synthetic aperture passive interferometric imaging, covering isolated, adjacent-pair, and complex emitter distributions. Persistent homology tracks the birth, death, and merging of zero-dimensional connected components as the intensity threshold varies. To address missed detections for spatially proximate emitters, multidimensional topological features are constructed via feature contribution analysis. Agglomerative clustering with Ward linkage then adaptively separates emitters from noise without supervision. Experimental results show that PH-AC achieves a perfect F1 score of 1.000 in isolated scenarios; for adjacent emitters, it improves F1 by 15.7% over the best image processing method and stays within 4% of supervised deep learning methods, while requiring no annotations. In complex environments, it attains an F1 of 0.937, outperforming all compared methods. Its computational complexity is only 3.18e7 FLOPs, two orders lower than YOLO-based detectors. This work offers a lightweight, annotation-free topological paradigm for spaceborne REM emitter detection.

Abstract: Glioblastoma multiforme (GBM) remains one of the most aggressive and treatment-resistant brain tumors, characterized by rapid proliferation and poor patient prognosis. Novel therapeutic strategies are urgently needed to improve clinical outcomes. In this study, we investigated the cytotoxic and pro-apoptotic effects of bortezomib (BORT), a proteasome inhibitor, and graphene oxide (GO), a nanomaterial with known anticancer potential, on human glioblastoma cell lines. Treatment with BORT and GO, both individually and in combination, significantly reduced cell viability in a dose-dependent manner, as determined by MTT. In this study we observed revealed enhanced apoptotic cell death, accompanied by increased activation of both caspase-8 and caspase-9, indicating simultaneous engagement of extrinsic and intrinsic apoptotic pathways. Western blot analysis demonstrated downregulation of anti-apoptotic proteins Bcl-2 and upregulation of pro-apoptotic markers (NOXA, cleaved PARP). A central finding of this work is the pronounced increase in intracellular reactive oxygen species (ROS) levels following BORT–GO treatment. The elevated ROS levels observed in BORT–GO–treated cells compared with free bortezomib therefore suggest a synergistic mechanism in which GO-mediated oxidative stress amplifies proteasome inhibition–induced apoptosis, which is particularly visible in the LN-229 line. Notably, the combination of BORT and GO exhibited synergistic effects, suggesting a potential cooperative mechanism through proteasome inhibition and oxidative stress induction. These findings indicate that graphene oxide may potentiate the antitumor efficacy of bortezomib and support further investigation of this combination as a promising therapeutic approach for glioblastoma.

Abstract: Background: Healthcare systems are organized around traditional levels of care (primary, secondary, tertiary), activated only when a patient enters the formal system. Translational medicine typically moves from bench to bedside. Here we propose a reverse translational step: patient-led self-management as a pre-clinical level of care – LINE ZERO. Objective: To introduce and test LINE ZERO – self-management, prevention, and self-care – as an extension of the traditional care model. Methods: An 11-month longitudinal self-experiment (n=1) in a 55-65 year old man with adjustment disorder. Interventions included breathing exercises, light therapy, music therapy, gentle stretching, moderate dietary changes, and self-monitoring of blood pressure, deep sleep, and blood glucose. Results: Deep sleep increased 3-fold (p < 0.001). Blood pressure stabilized. Glycemic variability decreased after an acute stress-related peak. A subsequent work stress episode caused a 30% drop in deep sleep, followed by rapid recovery within 48 hours. Conclusion: LINE ZERO extends the traditional care model by adding a pre-clinical self-management space. It aligns with Future Medicine (predictive, preventive, personalized, participatory) and represents a reverse translational contribution – from patient observation to a conceptual framework applicable to health systems.

Abstract: Special Economic Zones (SEZs) are widely promoted as catalysts for industrialization and export growth in developing countries, yet their capacity to generate sustainable and inclusive regional development remains debated, particularly in sub-Saharan Africa. This study investigates the impact of the Nkok SEZ in Gabon on the forestry sector—a novel case study—by analyzing the resulting economic and spatial disparities between the SEZ (homogeneous space) and its periphery (heterogeneous space). Combining robust econometric methods (Bias-Corrected Fixed Effects, OLS) and principal component analysis (PCA) on time-series data (2014–2022), we show that while the SEZ has significantly boosted export revenues (84%–97% growth) and industrial production through agglomeration and scale economies, these benefits remain largely concentrated. The periphery experiences weaker growth, reinforcing center-periphery dependencies and extractive specialization. Export revenues from the homogeneous space exhibit strong autoregressive effects (77%–94%) but limited macroeconomic diffusion (6%–25%), whereas the heterogeneous space shows lower autoregressive growth but a stronger historical influence on national aggregates, highlighting a structural polarization trap. To address these persistent imbalances, this paper introduces the SEMD model (Segmentation, Evaluation, and Multi-level Disparities Management). This operational framework proposes a six-fold territorial typology (from SEZs to informal circuits), hybrid quantitative-qualitative indicators, and proactive rebalancing mechanisms (vertical and horizontal channels) to institutionalize the diffusion of growth. The SEMD model offers a strategic tool for policymakers in the Global South to reconcile industrial performance with territorial cohesion, moving beyond the mere diagnosis of inequalities toward adaptive, real-time management of polarized development dynamics.

Abstract: For a fixed integer \( n\ge2 \), let \( \Delta_{n-1} \) denote the standard probability simplex in $\( \mathbb R^n \)$. We introduce and analyze the self-power escort transformation \( T_n:\Delta_{n-1}\to\Delta_{n-1} \) defined by \( \begin{equation*}T_n(p)_i=\frac{p_i^{p_i}}{\sum_{j=1}^n p_j^{p_j}},\qquad i=1,\ldots,n,\end{equation*} \) with the continuous boundary convention \( 0^0=1 \). Unlike the usual power escort transformation, whose exponent is an external parameter, the exponent here is the coordinate itself; equivalently, each coordinate is reweighted by \( \exp(p_i\log p_i) \). The paper proves that this elementary self-feedback rule has a rigid global dynamics. Every boundary point is immediately activated, every orbit enters an explicitly described compact core after one step, the uniform distribution is the unique fixed point, and the Hilbert log-diameter contracts exponentially after core entrance. Consequently every orbit converges exponentially to the uniform distribution, and no nontrivial periodic orbit exists. We then compute the complete linear spectrum and second-order normal form at the uniform state, obtaining a sign transition between the binary and higher-dimensional systems. For \( n\ge4 \), the post-core Hilbert contraction constant is sharpened to a two-variable min--max problem involving only the smallest and largest coordinates. We also classify the entire one-step uniformization fiber \( T_n^{-1}(\nu_n) \): besides the vertices and the uniform point, each dimension \( n\ge3 \) has exactly one nonuniform interior orbit type, up to permutation. Finally, in the binary case we prove global contraction in logit coordinates and an arithmetic escape phenomenon: algebraic irrational inputs become transcendental after one step, while rational nonuniform inputs become transcendental after two steps.