We study Geraghty-type non-self mappings within the framework of best proximity point theory. By introducing auxiliary functions with subsequential convergence, we establish general conditions ensuring the existence and uniqueness of best proximity points. Our results extend and unify earlier work on proximal and Kannan-type contractions under a Geraghty setting, and provide counterexamples showing that the auxiliary assumptions are essential. As an illustration, we construct an explicit non-self alignment mapping on subsets of ${\mathbb{R}}^2$ for which all hypotheses can be verified and the unique best proximity point, as well as the convergence of the associated proximal iteration, can be computed in closed form.

We study Geraghty-type non-self mappings within the framework of best proximity point theory. By introducing auxiliary functions with subsequential convergence, we establish general conditions ensuring the existence and uniqueness of best proximity points. Our results extend and unify earlier work on proximal and Kannan-type contractions under a Geraghty setting, and we provide counterexamples showing that the auxiliary assumptions are essential. As an illustration, we construct an explicit non-self alignment mapping on subsets of \( \mathbb{R} \)² for which all hypotheses can be verified and the unique best proximity point, as well as the convergence of the associated proximal iteration, can be computed in closed form.

European grapevine (\textit{Vitis vinifera} L.) is a climate-sensitive perennial whose flowering and ripening govern yield and quality. Phenological records from monitoring programs are typically collected at irregular intervals, so true transition dates are interval-censored, and many site-years are right-censored. We develop a reproducible workflow that treats phenology as a time-to-event outcome: Status \& Intensity observations from the USA-NPN are converted to interval bounds, linked to NASA POWER daily weather, and analyzed with parametric accelerated failure time (AFT) models (Weibull and log-logistic). To avoid outcome-dependent bias from aggregating weather up to the event date, antecedent conditions are summarized in fixed pre-season windows and standardized; quality-control filters ensure adequate within-window data coverage. Applied to flowering and ripening of \textit{V.~vinifera}, the framework yields interpretable time-ratio effects and publication-ready tables and figures. Warmer pre-season conditions are associated with earlier ripening, whereas flowering responses are modest and uncertain in these data; precipitation plays, at most, a secondary role. The approach demonstrates how interval-censored survival models with exogenous weather windows can extract robust climate signals from citizen-science phenology while preserving observation uncertainty, and it generalizes readily to other species and networks.

Social media is a major source of health information, but reproductive-health topics such as polycystic ovary syndrome (PCOS), endometriosis, fertility, and menstruation attract both unsupported claims and stigmatizing framing. We present an evidence-grounded pipeline that combines large language models (LLMs) with biomedical retrieval to assess such claims on Bluesky, and we extend it with a novel layer that scores the stigma framing of each claim independently of its truth. From 991 English-language posts we extracted 937 distinct health claims, grounded each in evidence retrieved from PubMed, openFDA, and authoritative clinical guidelines (ACOG, NICE, NHS, WHO), and classified veracity into five categories using only the retrieved evidence. A parallel module scored six stigma dimensions (shame, secrecy, disgust, fear, blame, empowerment). Most claims (75.2%) were not supported by biomedical evidence, yet the dominant emotional frame across the corpus was empowerment rather than overt shame. Critically, stigma increased monotonically as claims departed from the evidence, from supported to dangerous claims, a graded relationship confirmed by a Kruskal–Wallis test (p <10⁻⁷) and reflected in effect sizes that grew steadily across the veracity scale. Stigma also varied sharply by condition, being highest for infertility and endometriosis and lowest for PCOS. These findings show that misinformation and stigma co-occur in reproductive-health discourse and demonstrate that evidence-grounded LLMs can jointly surface both. A single-coder human validation served as a pilot diagnostic check: stigma scores were directionally aligned with human judgment, while five-way veracity agreement was limited, indicating that categorical veracity labels require calibration against a larger multi-coder reference set. As an exploratory single-platform study, results should be interpreted within the keyword-sampled corpus rather than as platform-wide prevalence estimates.

We investigate the linguistic complexity and emotional valence of popular song lyrics across English ($n=1491$), Spanish ($n=307$), and German ($n=225$), using an analytical corpus of 2023 tracks drawn from 2113 deduplicated tracks on Spotify’s weekly Top 200 charts (2019–2021). Transformer-based sentiment analysis is combined with complexity-science tools to characterize both the affective content and the structural organization of commercially successful lyrics. A multilingual BERT model reveals a mild negative skew across all three languages (63.7% negative overall); the 1.003-point English–German gap observed under the English-centric VADER lexicon collapses to 0.127 points under BERT, indicating that earlier cross-linguistic sentiment differences are largely measurement artifacts. Word frequency distributions follow Zipf’s law in all three languages ($R^2>0.96$), with English steepest ($\alpha =1.409$) and German shallowest ($\alpha =1.181$). Detrended fluctuation analysis indicates persistent long-range correlations ($H\approx 0.66$–$0.76$; none of the 50 shuffled surrogates exceeded the observed values), and multifractal singularity spectra are statistically indistinguishable across languages once corpus size is controlled (all pairwise Mann–Whitney $p>0.13$). Streaming counts within the Top 200 are concentrated (German Gini $=0.556$) but, given the truncated single-snapshot sample, are reported as within-chart descriptors rather than population-level scaling.

European grapevine (\textit{Vitis vinifera} L.) is a climate–sensitive perennial whose flowering and ripening govern yield and quality. Phenological records from monitoring programs are typically collected at irregular intervals, so true transition dates are interval-censored, and many site-years are right-censored. We develop a reproducible workflow that treats phenology as a time–to–event outcome: Status \& Intensity observations from the USA–NPN are converted to interval bounds, linked to NASA POWER daily weather, and analyzed with parametric accelerated failure time (AFT) models (Weibull and log–logistic). To avoid outcome–dependent bias from aggregating weather up to the event date, antecedent conditions are summarized in fixed pre–season windows and standardized; quality–control filters ensure adequate within–window data coverage. Applied to flowering and ripening of \textit{V.~vinifera}, the framework yields interpretable time–ratio effects and publication-ready tables and figures. Warmer pre–season conditions are associated with earlier ripening, whereas flowering responses are modest and uncertain in these data; precipitation plays, at most, a secondary role. The approach demonstrates how interval-censored survival models with exogenous weather windows can extract robust climate signals from citizen-science phenology while preserving observation uncertainty, and it generalizes readily to other species and networks.