Let F be a field and P is an element of F [x(1), ... , x(n)] be a homogeneous polynomial such that | F | > deg(P) and phi, psi : F-n -> F-n be two maps such that P(x + lambda y) = P(phi(x) + lambda(y)) for all lambda is an element of F and x,y is an element of F (n). We provide the characterization of all such phi and psi for all polynomials in the case if char(F) = 0 and for all polynomials satisfying certain condition in the case if char( F) > 0. This characterization generalizes the existing results regarding the linear maps on matrices preserving the determinant, the immanant and other homogeneous polynomial functions of matrix entries. To obtain the main result of this paper, we introduce the vector space L-P subset of F-n & lowast; spanned by the range of the gradient field of P is an element of F [x(1), ... , x(n)]. Being a linear invariant associated with P, this space has several remarkable properties and may also be used for studying the linear maps preserving P. In addition, we demonstrate how the main result could be applied to the particular polynomial matrix invariants. Namely, we provide an explicit description of corresponding pairs of nonlinear maps phi, psi for the case where P is equal to the Cullis' determinant of n >< k rectangular matrix (with the assumption that n >= k + 2 and k >= 3). (c) 2026 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).
Nuclear forensics depends on accurate identification of fissile isotopes for security and nonproliferation purposes. However, traditional fission track analysis (FTA) is largely manual, operator-dependent, and incapable of distinguishing isotopes based on track features. This research aims to modernize FTA by developing a physics-informed, automated framework that combines Monte Carlo simulations (GEANT4), synthetic data generation, and image-processing algorithms for isotope differentiation. Simulations were performed for 233U, 235U, and 229Th using a LEXAN (R) polycarbonate solid-state nuclear track detector (SSNTD) with Aerogel spacers of various densities to improve track resolution. Synthetic datasets were analyzed through the newly developed FTA-Finder application. Results indicate that a 50 mu m aerogel spacer enhances the separation of light and heavy fission fragment clusters. Image-processing algorithms successfully differentiated isotopes in synthetic data by reconstructing isotope-specific track-length distributions and angular spreads. These findings demonstrate that morphology-based parameters can serve as isotopic fingerprints, paving the way for automated, reproducible, and high-accuracy nuclear forensic analysis. The framework's integration into practical safeguards investigations could improve the reliability and speed of fissile material identification worldwide.
Microalgal strains are engineered and benchmarked under fixed conditions, yet industrial cultures experience light, temperature, CO₂, salinity and nutrient regimes that shift from seconds to seasons. Programmable microalgae, cells that sense environmental change, integrate signals and adjust their physiology (Sense–Decide–Adapt, SDA), could close this gap. Native nutrient-sensing, photoprotective, carbon-concentrating and osmotic programs already approximate SDA architectures, and genome editing, biosensors and single-cell screening make them tractable to rewire, although direct evidence that altering response dynamics raises productivity remains sparse. Here, we introduce the Environmental Performance Envelope (EPE), a framework defining the region of environmental space in which a strain retains a defined fraction of its reference productivity under realistic trajectories. The EPE turns a design question into an experiment: does engineering expand the operating space or merely relocate the optimum? A staged roadmap, including CO₂-fluctuation trials and evolutionary stability testing, shifts engineering targets from static traits to response kinetics, recovery, heterogeneity and stability, and couples cellular control to bioprocess design, pointing toward more robust algal biomanufacturing. Because environmental variability constrains any living system deployed outside the laboratory, the same logic may extend to other microbial cell factories, crops and engineered organisms.
Women frequently initiate divorce, yet their post-divorce experiences are shaped by gender norms and societal expectations surrounding marriage and motherhood. In Israel, where liberal-secular values coexist with familistic and religious norms, initiating divorce may be perceived as a deviation from the social order. This study examines how women who initiate divorce perceive societal attitudes toward themselves and their decision, and how these attitudes shape their post-divorce social position. Drawing on semi-structured in-depth interviews with 38 mostly secular, heterosexual, Jewish-Israeli mothers aged 25–70 who initiated divorce, this thematic analysis revealed five central themes: repositioning in the social arena: loss of belonging and social status; reconfiguring support networks from couple-based ties to alternative sources of support; navigating social norms as part of the complex journey of divorce initiators; the attribution of blame and responsibility to the initiator; and societal attitudes that foster self-blame and weaken the initiator's social confidence. The study demonstrates that stigma and moral judgment directed at women who initiate divorce function as informal sanctions that regulate gender norms, weaken women's social capital in the post-divorce period and sustain patriarchal power relations. The findings highlight the need for supportive frameworks that validate women's autonomy and mitigate post-divorce social exclusion.
Purpose of research Long COVID (LC) risk varies across SARS-CoV-2 variants, but causal inference is complicated by rising vaccine coverage coinciding with viral evolution. We examined how pre-infection vaccination status modified LC risk across different pandemic periods dominated by different variants, to disentangle the contributions of viral evolution and vaccine-induced immunity.In this prospective cohort study of Israeli adults with SARS-CoV-2 infections from July 2021–March 2023, participants completed baseline and follow-up online surveys ≥60 days post-infection. LC was defined as ≥3 symptoms within validated symptom clusters. Infections were assigned to an infection period corresponding to the predominant circulating variant (Wild type, Alpha, Delta, Omicron) at onset time. Pre-infection vaccination was categorized as unvaccinated (0–1 doses), partially vaccinated (2 doses), or fully vaccinated (≥3 doses). Generalized estimating equations estimated multivariable risk ratios, adjusted for age, sex, and follow-up time. Among 1715 participants reporting 2018 infections, LC was reported following 30·4% of infections. In models adjusted for vaccination, LC risk did not differ between the Delta and Omicron-dominant periods (aRR 1·01, 95% CI 0·80–1·26). Among partially vaccinated individuals, infections during the Omicron-dominant period carried lower LC risk than during Delta (aRR 0·62, 95% CI 0·40–0·98). LC risk did not differ by variant-dominant periods among unvaccinated or fully vaccinated individuals. Major conclusions Observed differences in LC risk at various periods of the pandemic dominated by different variants may be largely explained by concurrent increases in vaccine coverage rather than intrinsic changes in variant pathogenicity. Full pre-infection vaccination conferred consistent protection against LC regardless of the period of variant dominance.
