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Keywords = length–weight relationships

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16 pages, 1768 KB  
Article
Body Weight Prediction in Karayaka Lambs Using Morphometric Measurements: A Comparison of Regression and Machine Learning Approaches
by Lütfi Bayyurt
Animals 2026, 16(15), 2288; https://doi.org/10.3390/ani16152288 (registering DOI) - 23 Jul 2026
Abstract
Body weight is one of the important phenotypic traits in sheep breeding for evaluating growth performance, planning flock management practices, and determining economic efficiency. In this study, biometric and machine learning approaches were jointly employed to predict body weight in Karayaka lambs using [...] Read more.
Body weight is one of the important phenotypic traits in sheep breeding for evaluating growth performance, planning flock management practices, and determining economic efficiency. In this study, biometric and machine learning approaches were jointly employed to predict body weight in Karayaka lambs using morphometric characteristics. The research material consisted of a total of 150 Karayaka lambs, including 75 males and 75 females, raised in a private enterprise located in the Erbaa district of Tokat province. The study evaluated body weight (BW), heart girth (HG), abdominal girth (AG), diagonal body length (DBL), body length (BL), withers height (WH), rump height (RH), hip width (HW), chest width (CW), and body condition score (BCS). Relationships among variables were examined using Pearson correlation analysis and principal component analysis (PCA). Multiple linear regression, Ridge Regression, LASSO regression, Random Forest, and Gradient Boosting algorithms were applied to predict body weight. Additionally, variable importance analysis and the SHAP (SHapley Additive Explanations) approach were utilized to enhance model interpretability. The results demonstrated significant differences between sexes in body weight and the majority of morphometric traits (p < 0.05). Correlation analysis revealed that abdominal girth and heart girth had the strongest associations with body weight. According to PCA results, the first principal component explained the majority of the total variance and represented overall body size. Among the evaluated machine learning models, the Gradient Boosting algorithm achieved the highest prediction performance, with a training R2 of 0.962 and a test R2 of 0.862, together with the lowest prediction errors (RMSE = 1.320 kg and MAE = 1.034 kg). The Random Forest model ranked second, achieving a test R2 of 0.828. Variable importance and SHAP analyses indicated that heart girth and abdominal girth were the most influential features in predicting body weight. In conclusion, morphometric traits can be effectively utilized to predict body weight in Karayaka lambs, and the Gradient Boosting algorithm represents a robust approach offering high accuracy and interpretability. Full article
(This article belongs to the Special Issue Current Research in Sheep and Goats Reared for Meat)
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16 pages, 3253 KB  
Article
Transcriptomic Responses of the Endangered Endemic Fish Aspiorhynchus laticeps to Salinity–Alkalinity and Water Flow Stress
by Huanhuan Wang, Liting Yang, Changcai Liu, Wenxia Cai, Yong Song, Xuyuan Lin, Peng Chen, Zhen Sun, Sadia Bibi, Xiao Liang and Shengao Chen
Animals 2026, 16(15), 2281; https://doi.org/10.3390/ani16152281 - 23 Jul 2026
Abstract
To understand the adaptive evolution of endangered plateau freshwater fishes to environmental stress and to better explore the underlying mechanisms in Aspiorhynchus laticeps—a critically endangered fish endemic to the Tarim Basin, Xinjiang, China—a combination of ecological experiments and transcriptome sequencing (RNA-seq) technology [...] Read more.
To understand the adaptive evolution of endangered plateau freshwater fishes to environmental stress and to better explore the underlying mechanisms in Aspiorhynchus laticeps—a critically endangered fish endemic to the Tarim Basin, Xinjiang, China—a combination of ecological experiments and transcriptome sequencing (RNA-seq) technology was used to study the differences in gene expression patterns among individuals under different salinities and flow conditions. This experiment included four treatment groups (CON, H-SA-S, L-SA, L-SA-S). A. laticeps specimens with an average weight of 2.92 ± 0.62 g and a body length of 58.22 ± 5.10 mm were selected, with three biological replicates for a 96 h combined stress treatment. Moreover, the relationships between these differences and the aquatic environment were analyzed. A total of 1847 differentially expressed genes (DEGs), including 935 upregulated genes and 912 downregulated genes, were identified under different aquatic environment stress modes. GO and KEGG enrichment analyses revealed that TNF signal transduction, the NF-κB pathway, and metabolic regulation were significantly enriched among the DEGs (p < 0.05). High salinity–alkali stress significantly activates the TNF/NF-κB pathway, regulates MST1, LOC107702867, LOC113110979 and other genes to enhance the body’s resistance; water flow changes mainly regulate energy metabolism through genes such as NEHOM01_1600 and gptl. These findings provide an important scientific basis for the ecological adaptability, protection, and proliferation of endemic and endangered fish in China, as well as for germplasm innovation to address ecological deterioration in plateau fishes in alpine and arid areas. This study provides a molecular-level theoretical foundation for artificial habitat regulation and the conservation of endangered Aspiorhynchus laticeps populations in the Tarim River. Full article
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18 pages, 3435 KB  
Article
RF-KNN-Assisted Local Gaussian Process Regression for Heat Transfer Coefficient Prediction in Hot Strip Coiling Temperature Control
by Dong Chen, Zhenlei Li, Jian Kang and Guo Yuan
Materials 2026, 19(14), 3096; https://doi.org/10.3390/ma19143096 - 18 Jul 2026
Viewed by 123
Abstract
Accurate prediction of the heat transfer coefficient is essential for improving the coiling temperature control in hot strip rolling, especially under frequent rolling condition changes. Conventional layer-based self-learning methods may lead to boundary discontinuities, insufficient sample support for new gauges, and limited information [...] Read more.
Accurate prediction of the heat transfer coefficient is essential for improving the coiling temperature control in hot strip rolling, especially under frequent rolling condition changes. Conventional layer-based self-learning methods may lead to boundary discontinuities, insufficient sample support for new gauges, and limited information sharing among similar operating conditions. To address these limitations, this paper proposes a random-forest (RF) and K-nearest-neighbor (KNN)-assisted local Gaussian process regression framework for the heat transfer coefficient in hot strip rolling. In the proposed method, RF is first used to select key variables and guide similar-case retrieval. KNN is then employed to retrieve the historical strips most similar to the current strip and to construct a local sample space. Instead of directly using conventional distance-weighted averaging, Gaussian process regression (GPR) is established on the retrieved local samples to model the nonlinear relationship between the process variables and the heat transfer correction coefficient. The proposed method outperforms conventional KNN-based weighting methods in terms of all the evaluation metrics for both first coils and in-lot coils at different speeds. Industrial validation shows that the measured coiling temperature is controlled within ±20 °C over more than 96.5% of the coil length. The results demonstrate that the proposed framework improves the adaptability and online compensation capability of the controlled cooling temperature models. Full article
(This article belongs to the Section Manufacturing Processes and Systems)
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21 pages, 2020 KB  
Article
Determinants of First-Trimester Residual Myometrial Thickness After Previous Cesarean Delivery: A Retrospective Cohort Study
by Coşkun Orhaner and Bilge Çetinkaya Demir
Medicina 2026, 62(7), 1384; https://doi.org/10.3390/medicina62071384 - 17 Jul 2026
Viewed by 142
Abstract
Background and Objectives: To investigate factors associated with first-trimester residual myometrial thickness (RMT) at the site of a previous cesarean section scar and to evaluate the relationship between RMT and selected pregnancy and neonatal outcomes. Materials and Methods: This retrospective cohort study included [...] Read more.
Background and Objectives: To investigate factors associated with first-trimester residual myometrial thickness (RMT) at the site of a previous cesarean section scar and to evaluate the relationship between RMT and selected pregnancy and neonatal outcomes. Materials and Methods: This retrospective cohort study included 80 pregnant women with at least one previous CS who attended the Department of Obstetrics and Gynecology, Uludağ University Faculty of Medicine, between July 2017 and December 2018. RMT at the cesarean scar site was measured by transvaginal ultrasonography (TVUS) during the first trimester. After exclusion of 15 women because of incomplete records or missing follow-up data, 65 patients were included in the final analysis. Participants were categorized according to first-trimester RMT as a thin scar group (RMT ≤ 8 mm, n = 37) and a control group (RMT > 8 mm, n = 28). Demographic characteristics, obstetric history, cesarean-related variables, postpartum hemorrhage (PPH) history, ultrasonographic findings, and neonatal outcomes were analyzed. Statistical analyses included Student’s t-test, chi-square test, one-way analysis of variance (ANOVA), and Spearman correlation analysis. Results: Women with thinner residual myometrium had significantly higher parity (p = 0.003), a greater number of previous cesarean deliveries (p = 0.016), and a higher frequency of previous PPH (p = 0.037) compared with controls. Mean RMT was significantly lower in women with parity ≥ 2 than in women with parity 1 (6.39 ± 2.76 mm vs. 8.51 ± 2.81 mm, p = 0.003). Similarly, women with a history of PPH demonstrated significantly lower RMT than those without such a history (5.67 ± 2.11 mm vs. 7.82 ± 2.98 mm, p = 0.037). Correlation analysis revealed a moderate inverse relationship between the number of previous cesarean deliveries and RMT (r = −0.463, p < 0.001). No significant group differences were observed regarding cervical length, placental location, gestational age at delivery, 5 min Apgar score, or birth weight. Conclusions: First-trimester RMT was significantly associated with parity, previous cesarean delivery number, and a history of PPH. Among the evaluated variables, the number of previous cesarean deliveries demonstrated the strongest independent association with reduced RMT. These findings suggest that early transvaginal ultrasonographic assessment of RMT may serve as a useful sonographic marker of cesarean scar morphology and healing characteristics in pregnancies following cesarean delivery. Larger prospective studies are needed to determine the clinical significance of first-trimester RMT measurements for subsequent obstetric outcomes. Full article
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20 pages, 2047 KB  
Article
A Beta Function-Based Model for Predicting Leaf Appearance and Expansion in Romaine Lettuce
by Jaehyung Ko, Joonwoo Lee, Wonyong Yang, Jong-Suk Park, Teag Kwon, Sewoong An and Kyoung Sub Park
Horticulturae 2026, 12(7), 865; https://doi.org/10.3390/horticulturae12070865 - 16 Jul 2026
Viewed by 222
Abstract
A process-based developmental model was developed to predict leaf appearance and expansion in romaine lettuce (Lactuca sativa L. var. longifolia) using hourly air temperature and daily light integral as environmental inputs. The model consisted of two linked modules representing leaf appearance [...] Read more.
A process-based developmental model was developed to predict leaf appearance and expansion in romaine lettuce (Lactuca sativa L. var. longifolia) using hourly air temperature and daily light integral as environmental inputs. The model consisted of two linked modules representing leaf appearance and individual leaf expansion as distinct biological processes. The leaf appearance module calculated the hourly leaf tip appearance rate as the product of a beta-type nonlinear temperature response function and a developmental stage weighting function based on growing degree days accumulated above a base temperature of 4 °C. The leaf expansion module estimated individual leaf expansion using photothermal age, a Gompertz growth function, and a leaf length–area allometric relationship, with potential leaf length determined by the mean growing temperature and leaf rank. The optimum temperatures for leaf appearance rate and potential leaf length differed by approximately 6 °C (26.7 °C vs. 20.4 °C), indicating distinct temperature response patterns between the two developmental processes. Model calibration was performed using datasets (n = 437) collected from a temperature-gradient greenhouse with a nutrient film technique hydroponic system across the spring, summer, and autumn growing seasons, yielding an overall model efficiency (EF) of 0.92 and a root mean square error (RMSE) of 4.26 leaves for leaf appearance, and an EF of 0.80 and an RMSE of 448.1 cm2 for leaf expansion. Independent model evaluation was also performed using datasets (n = 132) obtained from a commercial greenhouse with either a deep flow technique hydroponic system or a perlite-based substrate system across the same three growing seasons, yielding an EF of 0.96 and an RMSE of 2.24 leaves for leaf appearance, and an EF of 0.92 and an RMSE of 216.8 cm2 for leaf expansion. These results demonstrate that the model effectively described leaf appearance and expansion in romaine lettuce across the tested soilless culture systems under greenhouse conditions, highlighting its potential as a leaf development module for integration into canopy photosynthesis and biomass production models. Full article
(This article belongs to the Section Protected Culture)
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27 pages, 2872 KB  
Article
Post-Translocation Establishment of the Endemic Cyprinid Squalidus multimaculatus Under Favorable Biogeochemical Conditions and Regional Winter Warming
by Sun Kyeong Choi, Seul Yi, Samuel Praveen, Young Baek Son and Seonggil Go
Biology 2026, 15(14), 1140; https://doi.org/10.3390/biology15141140 - 13 Jul 2026
Viewed by 272
Abstract
Human-mediated species translocations are increasingly interacting with global climate change, yet empirical insights into how introduced populations achieve long-term demographic stability in new frontiers remain limited. This study systematically investigates the post-translocation establishment and multi-generational persistence of the endemic cyprinid Squalidus multimaculatus at [...] Read more.
Human-mediated species translocations are increasingly interacting with global climate change, yet empirical insights into how introduced populations achieve long-term demographic stability in new frontiers remain limited. This study systematically investigates the post-translocation establishment and multi-generational persistence of the endemic cyprinid Squalidus multimaculatus at its newly identified northern distribution limit in Goseong, Republic of Korea, following historical human-mediated introduction. Utilizing nationwide multi-decadal occurrence records, we mapped the species’ spatio-temporal dynamics across three temporal phases (T0, T1, and T2). Long-term biogeochemical water quality indices and thermal regimes were compared between the native baseline (Yeongdeok) and Goseong. Furthermore, demographic shifts and growth trajectories were evaluated using 676 field-sampled specimens through length–weight relationships, condition factor (KF) analysis, age structure mixture modeling, and the von Bertalanffy growth function (VBGF). Our results indicate that the Goseong habitat provides generally favorable biogeochemical conditions characterized by low nutrient loading and high dissolved oxygen stability. Crucial to this transition, a distinct winter warming shift expanded the available thermal window, reducing the frequency of extreme winter cold-stress events (≤2.0 °C) from 40.0% to 6.9%. Concurrently, the post-translocation population exhibited successful demographic stability, characterized by a self-sustaining age structure (ages 0+ to 4+), an inferred spawning window during June–July, and a growth trajectory (L = 95.69 mm) broadly comparable to native benchmarks. These findings establish a reliable empirical baseline framework linking human-mediated introductions with long-term environmental transitions. Globally, this case study suggests that post-translocation success depends on the interplay between introduction pathways and climate suitability, offering key insights into population survival and ecosystem evolution under global change. Full article
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15 pages, 3628 KB  
Article
Age and Growth of Pointhead Flounder, Cleistenes pinetorum, in the West Sea of Korea
by Dong Hyuk Choi, Seulhee Lee, Dae Hyeon Kwon and Soo Jeong Lee
J. Mar. Sci. Eng. 2026, 14(13), 1254; https://doi.org/10.3390/jmse14131254 - 7 Jul 2026
Viewed by 276
Abstract
To investigate the age and growth characteristics of the pointhead flounder (Cleisthenes pinetorum) in the West Sea (Yellow Sea) of Korea, samples were collected from bottom trawl vessels throughout 2019. A total of 1116 individuals (1015 females and 101 males) were [...] Read more.
To investigate the age and growth characteristics of the pointhead flounder (Cleisthenes pinetorum) in the West Sea (Yellow Sea) of Korea, samples were collected from bottom trawl vessels throughout 2019. A total of 1116 individuals (1015 females and 101 males) were analyzed. Because specimens were obtained from commercial landings, only fish of approximately 20 cm or larger were available due to marketability constraints. The body weight (BW) − total length (TL) relationships were BW = 0.00001TL3.3443 (R2 = 0.9279) for females and BW = 0.000002TL3.2659 (R2 = 0.9347) for males. The observed sex ratio (male:female = 1:10) was strongly female-biased; however, this likely reflected the underrepresentation of smaller males in commercial catches rather than the natural population structure. Females also exhibited larger body lengths than males. Otoliths were generally round, with a slightly elongated anterior region, and measurements were taken along the longest axis from the core to the margin. The relationship between TL and otolith radius (R) was expressed as TL = 8.0342R + 5.6218 (R2 = 0.8408). Growth equations were estimated for both sexes; however, because older males were poorly represented, the male von Bertalanffy growth function was fitted with the asymptotic length fixed to 43.3 cm (110% of the observed maximum male TL). Annuli were formed annually in November, and the spawning season was identified as September–November, suggesting a close association between annulus formation and the spawning period. The von Bertalanffy growth equations were Lt = 57.66(1 − exp[−0.1865(t + 0.46)]) for females and Lt = 43.3(1 − exp[−0.2679(t + 0.5490)]) for males. Full article
(This article belongs to the Section Marine Biology)
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21 pages, 4192 KB  
Article
Dust Concentration Forecasting Method for Intermittent Processing of Powder and Granular Materials
by Mingming Wang, Zhiyuan Li, Chaobo Li, Xiaoyun Sun, Yi Wang and Zhaofeng He
Sensors 2026, 26(13), 4207; https://doi.org/10.3390/s26134207 - 3 Jul 2026
Viewed by 188
Abstract
Dust concentration during intermittent processing of powder and granular materials is characterized by high-frequency abrupt changes, local accumulation, and complex coupling among multiple sensors. Existing forecasting models still exhibit limitations in modeling global dependencies and characterizing local trends. To address these issues, this [...] Read more.
Dust concentration during intermittent processing of powder and granular materials is characterized by high-frequency abrupt changes, local accumulation, and complex coupling among multiple sensors. Existing forecasting models still exhibit limitations in modeling global dependencies and characterizing local trends. To address these issues, this paper proposes an iTransformer-based dust concentration forecasting model that integrates a dual-stage feed-forward network and a DLinear branch. With iTransformer as the backbone network, the proposed model captures the coupling relationships among multi-source sensing signals through variate-wise modeling. A progressive dual-stage feed-forward feature refinement mechanism is constructed to enhance the model’s representation capability for transient variations and peak fluctuations in dust concentration. In addition, a collaborative modeling framework consisting of an iTransformer main branch and a DLinear auxiliary branch is designed to jointly learn global nonlinear features and local linear trends. An adaptive gated fusion mechanism is further introduced to dynamically allocate the contribution weights of different branches according to sequential characteristics. Experiments were conducted on a public 1 Hz smoke-sensing dataset, which was used as a proxy benchmark for high-frequency multivariate PM2.5 forecasting rather than direct industrial dust data. Under the setting of a 300-step input length and a 60-step forecasting horizon, the proposed model achieves an MSE of 1.8292 × 10−3, an MAE of 0.0334, an RMSE of 0.0428, an MAPE of 0.0177, and an R2 of 0.9744, outperforming the compared baseline models in overall performance. The results indicate that the proposed method improves overall forecasting accuracy and provides a methodological reference for sensor-driven particulate concentration forecasting and early warning, while further validation using field data from actual powder and granular material processing workshops is still required before practical deployment. Full article
(This article belongs to the Section Industrial Sensors)
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20 pages, 4849 KB  
Article
Reassessment of Growth and Exploitation of Portunus trituberculatus in Laizhou Bay: Legacy of Historical Overfishing
by Shihao Chen, Jilong Chen, Sihan Zhang, Fan Li, Xiaomin Zhang and Haixia Su
Animals 2026, 16(13), 2021; https://doi.org/10.3390/ani16132021 - 2 Jul 2026
Viewed by 268
Abstract
To investigate growth trends of Portunus trituberculatus in Laizhou Bay, this study fitted the Von Bertalanffy growth model using FiSAT II based on carapace width frequency data from 2023 to 2025. Growth parameters and mortality coefficients were estimated, and natural mortality was evaluated [...] Read more.
To investigate growth trends of Portunus trituberculatus in Laizhou Bay, this study fitted the Von Bertalanffy growth model using FiSAT II based on carapace width frequency data from 2023 to 2025. Growth parameters and mortality coefficients were estimated, and natural mortality was evaluated using eight empirical formulas. A total of 2240 individuals (1117 females, 1123 males) were captured. The carapace width–weight relationships were W = 7.145 × 10−5L2.9153 (total), W = 1.208 × 10−4L2.8051 (females), and W = 3.209 × 10−5L3.0809 (males), indicating negative allometric growth in females and near-isometric growth in males. Asymptotic carapace widths (L) were 228.32, 227.23, and 215.25 mm; growth rates (k) were 0.43, 0.49, and 0.44; and the total mortalities (Z) were 1.41, 1.44, and 1.30 for total, female, and male, respectively. Recruitment occurred from April to August (spring–summer). Mean natural mortality (M) was 0.70, and exploitation rate (E) was 0.50. Compared with historical data, the current exploitation rate has decreased from the severely overexploited levels observed historically, approaching the commonly used MSY reference point of E = 0.50. This decline reflects the positive effects of summer fishing moratoriums and stock enhancement in reducing fishing pressure. However, this apparent stabilization in exploitation rate has not translated into biological recovery. Declining growth parameters and continued population decline indicate that the stock remains vulnerable, and current pressure may still exceed the ecosystem’s degraded carrying capacity. Future efforts should strengthen the monitoring and recovery of genetic diversity in P. trituberculatus, extend the study period of length–frequency data, and construct ecosystem models to assess the impacts of food competition and habitat changes, thereby providing a scientific basis for stock enhancement and resource assessment of P. trituberculatus in Laizhou Bay. Full article
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22 pages, 29544 KB  
Article
Dose-Dependent Effects of Branched-Chain Amino Acid Supplementation on Skeletal Muscle Morphology and Ultrastructure in Exercise-Trained Mice
by Yuhang Zhou, Xiaojuan Guo, Hai He, Yufei Yang, Yixin Zhang, Haiyue Feng and Zhiqiang Li
Nutrients 2026, 18(13), 2124; https://doi.org/10.3390/nu18132124 - 1 Jul 2026
Viewed by 369
Abstract
Background: Branched-chain amino acids (BCAAs) regulate muscle protein metabolism, yet the systematic characterization of their dose-dependent morphological effects on exercised skeletal muscle remains limited. This study investigated the dose–response relationship between BCAA supplementation and skeletal muscle adaptations in exercise-trained mice. Methods: Seventy male [...] Read more.
Background: Branched-chain amino acids (BCAAs) regulate muscle protein metabolism, yet the systematic characterization of their dose-dependent morphological effects on exercised skeletal muscle remains limited. This study investigated the dose–response relationship between BCAA supplementation and skeletal muscle adaptations in exercise-trained mice. Methods: Seventy male Kunming mice were randomly assigned to seven groups (n = 10): a background group (no exercise), a control group (exercise + saline), and five exercise groups receiving BCAAs at 1–5 g/kg/day via intragastric gavage. Mice in the exercise groups performed 45 min of swimming daily (6 days/week) for 50 days. Gastrocnemius muscles were processed using hematoxylin–eosin staining, Masson trichrome staining, Gomori aldehyde fuchsin staining, and transmission electron microscopy. Data were analyzed using one-way ANOVA with Dunnett’s post hoc test. Results: BCAA supplementation increased gastrocnemius wet weight-to-body weight ratios and promoted denser fiber packing in a dose-dependent manner up to 3–4 g/kg/day. Deep-staining fiber proportion (putatively type II-like) increased progressively with BCAA concentration, plateauing at doses ≥ 3 g/kg/day, while elastic fiber content continued to rise through 5 g/kg/day. Mitochondrial size decreased as mitochondrial number increased; membrane and cristae thickness peaked at 3 g/kg/day. Sarcomere length, myofibril diameter, sarcoplasmic reticulum size, and transverse tubule diameter exhibited increasing trends. Conclusions: These findings establish a parameter-specific dose–response framework for BCAA-induced muscle remodeling. A supplemental dose of 3 g/kg/day above background dietary intake represents an effective threshold for maximizing indices of hypertrophic gains and mitochondrial structural maturation potentially indicative of functional enhancement. Higher doses (≥4 g/kg/day) elicited additional benefits in fiber density, mitochondrial proliferation, and elastic fiber content. Supplemental BCAA dosing strategies above constant background intake should be tailored to target specific structural outcomes, with functional validation required to confirm physiological relevance. Full article
(This article belongs to the Section Proteins and Amino Acids)
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23 pages, 1801 KB  
Article
In-Orchard Sizing of Mango Fruit: 3. Allometry and Growth Model
by Maisa Pereira and Kerry Brian Walsh
Horticulturae 2026, 12(7), 806; https://doi.org/10.3390/horticulturae12070806 - 30 Jun 2026
Viewed by 521
Abstract
The forecast of fruit weight at harvest requires (i) a non-destructive method for assessment of weight (Fw) of fruit-on-tree and (ii) the knowledge of fruit growth dynamics. To address the first issue for mango fruit, several allometric relationships between [...] Read more.
The forecast of fruit weight at harvest requires (i) a non-destructive method for assessment of weight (Fw) of fruit-on-tree and (ii) the knowledge of fruit growth dynamics. To address the first issue for mango fruit, several allometric relationships between Fw and fruit-lineal dimensions of length (L), width (W), and thickness (T) were considered, with the relationship Fw=kLWT recommended. A k value of 0.5146 was established for fruit of the cultivar Honey Gold for fruit past the stone-hardening stage, based on assessment of 1091 fruit from 13 season/orchard populations and preliminary values of 0.5376, 0.5151, and 0.5239 for the Keitt, Kensington Pride, and R2E2, respectively, on the basis of more limited datasets. A combined cultivar model was recommended across all cultivars considered, except Keitt. The variation in k between populations of Keitt and Honey Gold fruit was due to the difference in fruit density, rather than shape. This conclusion should be tested in context of other cultivars and fruit development. A correction for developmental age was established for Honey Gold fruit, viz., kcorr=0.0009× DAFB+0.5975 for fruit up to ~1224 growing degree days. The need for similar corrections for other cultivars should be investigated. For the second issue, the use of a linear function based on measurements of Fw in the weeks immediately before harvest was recommended for forecasting harvest-time weight to an accuracy of approximately 10%. A Logistic function described Fw increase better than a Gompertz function; however, a change in growing conditions during fruit development limits the reliability of such models for forecasting fruit weight at harvest maturity. Rather, it is proposed that a set of reference models based on a set of reference Logistic model parameters for a suite of growing conditions be developed for use in guiding agronomic interventions earlier in fruit development to maintain growth on a trajectory to achieve a desired weight at harvest. Full article
(This article belongs to the Section Fruit Production Systems)
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15 pages, 4476 KB  
Article
Baseline Morphometric Assessment and Sexual Dimorphism of Three Freshwater Mollusks in a Tropical Floodplain Wetland
by Mohammad Amzad Hossain, Rafiul Islam and Mohammed Mahbub Iqbal
Hydrobiology 2026, 5(3), 20; https://doi.org/10.3390/hydrobiology5030020 - 30 Jun 2026
Viewed by 412
Abstract
This study examined the morphometric variability and sex-related patterns in three freshwater mollusk species, Pila globosa, Lamellidens marginalis, and Parreysia corrugata from the Hakaluki Haor ecosystem, Bangladesh. All species showed strong linear relationships between shell length and body weight (p [...] Read more.
This study examined the morphometric variability and sex-related patterns in three freshwater mollusk species, Pila globosa, Lamellidens marginalis, and Parreysia corrugata from the Hakaluki Haor ecosystem, Bangladesh. All species showed strong linear relationships between shell length and body weight (p < 0.001). The R2 values indicated moderate association in P. globosa (0.57) and L. marginalis (0.59) and a high association in P. corrugata (0.80). Most traits were similar across sexes; however, females of P. corrugata had significantly higher body weight and slightly wider shells, suggesting mild sexual dimorphism. Condition indices were species-specific, with males generally higher, notably in P. corrugata (p < 0.05). Violin box plots showed minor sex differences in P. globosa aperture and spire, with overlap. PCA revealed that size traits were major contributors, explaining 60–75% of the variation. Females of P. globosa scored higher on the size axis, indicating sexual size dimorphism, while L. marginalis and P. corrugata showed significant overlap. Overall, results highlight strong allometric scaling, limited species-specific sexual dimorphism, and body size as the main determinants of morphology. Full article
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23 pages, 2760 KB  
Article
Comparative Evaluations of Commercial Seaweed Extract Formulations on Germination, Biomass Accumulation and Early Seedling Growth in Capsicum annuum
by Prabhaharan Renganathan, Kristina Borisovna Ukhatkina, Ilya Isidorovich Van Erp, Alfia Mufazalova, Natalia V. Sukhanova and Lira A. Gaysina
Horticulturae 2026, 12(7), 799; https://doi.org/10.3390/horticulturae12070799 - 30 Jun 2026
Viewed by 511
Abstract
Seaweed-derived biostimulants are increasingly used to improve seed germination and early seedling development in horticultural crops. This study evaluated the effects of five commercially available seaweed extract (SWE) formulations (ASCO, AQUA, KAT, SAGA, and BIO) applied at 2 mL L−1 on germination, [...] Read more.
Seaweed-derived biostimulants are increasingly used to improve seed germination and early seedling development in horticultural crops. This study evaluated the effects of five commercially available seaweed extract (SWE) formulations (ASCO, AQUA, KAT, SAGA, and BIO) applied at 2 mL L−1 on germination, seedling growth, biomass accumulation, moisture-related traits, and biomass allocation indices of Capsicum annuum L. under controlled conditions. A 10-day in vitro Petri dish bioassay was conducted using five experimental replicates for each treatment. Significant differences among the treatments were observed for several germination, growth, biomass, and moisture-related parameters. KAT exhibited the highest final germination percentage, whereas SAGA exhibited the fastest germination response and the highest seedling vigor index. SAGA was associated with higher root length and total dry weight, whereas AQUA exhibited among the highest root biomass values. BIO recorded the highest moisture content, leaf length, and shoot-to-root ratio. Correlation analysis identified significant relationships among growth and biomass traits, whereas principal component analysis revealed distinct multivariate response patterns among the evaluated formulations. Overall, the commercial SWE formulations showed different response profiles during the early seedling development of C. annuum under the conditions of present study. Further studies are required to evaluate the consistency of these responses across different concentrations, cultivars, and growing environments. Full article
(This article belongs to the Topic Applications of Biotechnology in Food and Agriculture)
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14 pages, 3439 KB  
Article
Determination of the Reproductive Status of the Female Round Goby Neogobius melanostomus (Pallas, 1814) in Southwestern Lake Michigan
by Meghan A. Kline, Piotr Hliwa and Sergiusz J. Czesny
Animals 2026, 16(13), 1999; https://doi.org/10.3390/ani16131999 - 29 Jun 2026
Viewed by 259
Abstract
The successful invasion of the round goby, Neogobius melanostomus (Pallas, 1814), in European and North American water ecosystems is assisted by its reproductive strategy, including high fecundity, multiple spawning events over an extended spawning season, and male parental care of offspring. In this [...] Read more.
The successful invasion of the round goby, Neogobius melanostomus (Pallas, 1814), in European and North American water ecosystems is assisted by its reproductive strategy, including high fecundity, multiple spawning events over an extended spawning season, and male parental care of offspring. In this study, we investigated female spawning effort and the determination of their reproductive status. The analysis was based on 552 females caught from May to September in Jackson Harbor (JH) and Waukegan Harbor (WH) in southwestern Lake Michigan (USA). The total length of females ranged from 62.6 to 160.0 mm, and the weight was between 3.47 and 59.8 g. Significantly different maximum mean values of the gonadosomatic index (GSI) in both localities were noted in early June (8.62% for JH) and in mid-June (7.82% for WH), associated with differing thermal regimes. Fecundity exhibited a significant linear relationship with the total length of females at both sites (Jackson Harbor, p < 0.0001, R2 = 0.5861; Waukegan Harbor, p < 0.0001, R2 = 0.6278) and with the total mass of fish (Jackson Harbor, p < 0.0001, R2 = 0.6614; Waukegan Harbor, p < 0.0001, R2 = 0.6327). Histological examination of ovaries showed that the spawning season of the round goby in southwestern Lake Michigan is prolonged from May to late June. The monthly distribution of the different sexual maturity stages and the frequency distribution of oocyte diameter revealed that this species is a batch spawner. The results expand the current knowledge of reproductive biology and physiology of the round goby. Full article
(This article belongs to the Special Issue Fish Reproductive Biology in a Changing Environment)
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Article
Mathematical Modeling and Generalization Inference Mechanisms of Large Language Models Under Transformer Architecture
by Meng Guo, Huifang Wu and Qinglin Guo
Mathematics 2026, 14(13), 2301; https://doi.org/10.3390/math14132301 - 29 Jun 2026
Viewed by 305
Abstract
Large language models (LLMs) built upon the Transformer architecture have achieved remarkable performance in natural language understanding, text generation and logical reasoning, while their internal working mechanisms remain poorly interpreted. This paper establishes a systematic mathematical analysis framework tailored for decoder-only Transformer LLMs, [...] Read more.
Large language models (LLMs) built upon the Transformer architecture have achieved remarkable performance in natural language understanding, text generation and logical reasoning, while their internal working mechanisms remain poorly interpreted. This paper establishes a systematic mathematical analysis framework tailored for decoder-only Transformer LLMs, based on linear algebra, tensor analysis, probability theory, information theory, optimization dynamics and geometric deep learning. We conduct rigorous mathematical modeling and theoretical deduction on core modules including word embedding, position encoding, self-attention, feed-forward networks, training optimization and generalization reasoning, and explore the mathematical nature of semantic representation, contextual correlation, knowledge storage and logical inference within models. In this paper, we strictly distinguish between classic established Transformer theories and our original mathematical derivations and conclusions. Distinct from existing fragmented theoretical studies, this work presents six targeted novel contributions beyond conventional Transformer theories: (1) we construct the first full-process unified mathematical framework covering all core modules and the entire lifecycle of Transformer-based LLMs; (2) we provide strict mathematical proof to verify that single-head self-attention is essentially a kernel weighted average operation in reproducing kernel Hilbert space and derive the low-rank and sparse properties of attention weights; (3) we establish a high-dimensional non-convex optimization dynamics model for pre-training and mathematically prove that model training converges to flat local minima; (4) we derive a tighter upper bound of generalization error and quantify the quantitative relationship among model parameters, sequence length, training data scale and generalization performance; (5) we characterize the latent space as a low-curvature smooth Riemannian manifold and model logical reasoning as geometric transformation on this manifold; (6) we design multi-group controlled experiments on mainstream datasets to quantitatively validate all above theoretical conclusions. This paper further summarizes the inherent mathematical limitations of current Transformer LLMs and proposes feasible theoretical optimization paths, referring to state-of-the-art research published from 2021 to 2026. The outcomes of this research can provide solid mathematical theoretical support for improving model interpretability, optimizing network structures and boosting practical performance, and facilitate the transition of LLM research from empirical engineering practice to theory-driven development. Full article
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