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We obtain several convexity statements involving positive definite matrices. In particular, if $A,B,X,Y$ are invertible matrices and $A,B$ are positive, we show that the map \[ (s,t) \mapsto \mathrm{Tr}\,\log \left(X^*A^sX + Y^*B^tY\right) \] is jointly convex on $\mathbb{R}^2$. This is related to some exotic matrix Hölder inequalities such as \[ \left\Vert \sinh \left(\sum _{i=1}^m A_iB_i\right) \right\Vert \le \left\Vert \sinh \left(\sum _{i=1}^m A_i^p\right) \right\Vert ^{1/p} \left\Vert \sinh \left(\sum _{i=1}^m B_i^q\right) \right\Vert ^{1/q} \] for all positive matrices $A_i, B_i$, such that $A_iB_i=B_iA_i$, conjugate exponents $p,q$ and unitarily invariant norms $\Vert \cdot \Vert $. Our approach to obtain these results consists in studying the behaviour of some functionals along the geodesics of the Riemanian manifold of positive definite matrices.

Background: Soil available phosphorus (AP) deficiency significantly limits cotton production, particularly in arid and saline-alkaline regions. Screening cotton cultivars for low phosphorus (P) tolerance is crucial for the sustainable development of cotton production. However, the effect of different growth media on the screening outcomes remains unclear. To address this, we evaluated the low P tolerance of 25 cotton cultivars through hydroponic culture at two P levels (0.01 and 0.5 mmol•L−1 KH2PO4) in 2018 and field culture with two P rates (0 and 90 kg•hm−2, in P2O5) in 2019. Results: In the hydroponic experiments, principal component analysis (PCA) showed that shoot dry weight (SDW) and P utilization efficiency in shoots (PUES) of cotton seedlings explained over 45% of the genetic variation in P nutrition. Cotton cultivars were subjected to comprehensive cluster analysis, utilizing agronomic traits (SDW and PUES) during the seedling stage (hydroponic) and yield and fiber quality traits during the mature stage (in field). These cultivars were grouped into four clusters: resistant, moderately resistant, moderately sensitive, and sensitive. In low P conditions (0.01 mmol•L−1 KH2PO4 and 4.5 mg•kg−1 AP), the low-P-resistant cluster showed significantly smaller reductions in SDW (54%), seed cotton yield (3%), lint yield (− 2%), fiber length (− 1%), and fiber strength (− 3%) compared with the low-P-sensitive cluster (75%, 13%, 17%, 7%, and 9%, respectively). The increase in PUES (299%) in the resistant cluster was also significantly higher than in the sensitive cluster (131%). Four of the eight low-P-tolerant cotton cultivars identified in the field and six in the hydroponic screening overlapped in both screenings. Two cultivars overlapped in both screening in the low-P-sensitive cluster. Conclusion: Based on the screenings from both field and hydroponic cultures, ZM-9131, CCRI-79, JM-958, and J-228 were identified as low-P-tolerant cotton cultivars, while JM-169, XM-33B, SCRC-28, and LNM-18 were identified as low-P-sensitive cotton cultivars. The relationship between field and hydroponic screening results for low-P-tolerant cotton cultivars was strong, although field validation is still required. The low P tolerance of these cultivars was closely associated with SDW and PUES. [ABSTRACT FROM AUTHOR]

Background: Endothelial cells are integral components of the tumor microenvironment and play a multifaceted role in tumor immunotherapy. Targeting endothelial cells and related signaling pathways can improve the effectiveness of immunotherapy by normalizing tumor blood vessels and promoting immune cell infiltration. However, to date, there have been no comprehensive studies analyzing the role of endothelial cells in the diagnosis and treatment of prostate adenocarcinoma (PRAD). Method: By integrating clinical and transcriptomic data from TCGA-PRAD, we initially identified key endothelial cell-related genes in PRAD samples through single-cell analysis. Subsequently, cluster analysis was employed to classify PRAD samples based on the expression of these endothelial cell-related genes, allowing us to explore their correlation with patient prognosis and immunotherapy outcomes. A diagnostic model was then constructed and validated using a combination of 108 machine learning algorithms. The XGBoost and Random Forest algorithms highlighted the significant role of COL1A1, and we further analyzed the expression and correlation of COL1A1, AR, and EGFR through multiplex immunofluorescence staining. In vitro experimental analysis of the impact of COL1A1 on the progression of PRAD. Results: Single-cell analysis identified 12 differential prognostic genes associated with endothelial cells. Cluster analysis confirmed a strong correlation between endothelial cell-related genes and both prostate cancer prognosis and immunotherapy responses. Diagnostic models developed using various machine learning techniques demonstrated the significant predictive capability of these 12 genes in the diagnosis of prostate cancer. Furthermore, based on patients' prognostic information, multiple machine learning analyses highlighted the critical role of COL1A1. Immunofluorescence analysis results confirmed that COL1A1 is highly expressed in prostate cancer and is positively correlated with both AR and EGFR. In vitro experiments confirm that reducing COL1A1 expression levels can inhibit PRAD progression. Conclusion: This study provides a comprehensive analysis of the role of endothelial cell-related genes in the diagnosis, prognosis, and immunotherapy of prostate cancer. The findings, supported by various machine learning algorithms and experimental results, highlight COL1A1 as a significant target for the diagnosis and immunotherapy of PRAD. [ABSTRACT FROM AUTHOR]

Long-termrotary tillage has led to a deterioration in cotton production. It remains unclear whether soil inversion with subsoiling could halt the deterioration. Here, a field experiment was set from 2015 to 2017 with three treatments: CK, 15 cm rotary tillage; T1, replace the top 20 cm soil layer with the 20–40 cm soil layer and loosen the 40–55 cm soil layer; T2, replace the top 20 cm soil layer with the 20–40 cm soil layer and loosen the 40–70 cm soil layer. The results showed that the total nitrogen(N) content, alkaline N content, total phosphorous(P) content, available P content, and available potassium(K) content of T1 and T2 in the 20–40 cm soil layer were significantly higher than those in the top 20 cm soil layer in 2017, and the soil nutrient contents in the top 20 cm soil layer increased with each planting season. Compared with CK, the root dry matter of T1 and T2 increased by 13.1% and 15.2%, respectively, and the boll number and boll weight were also significantly higher, and the seed cotton yield under T1 for the three years increased by 7.7%, 7.6%, and 6.1%, respectively, and the seed cotton yield under T2 for the three years increased by 6.1%, 8.6%, and 8.2%, respectively. The results suggest that soil inversion with subsoiling is a continuously effective tillage practice for increasing the output of cotton in the North China Plain. [ABSTRACT FROM AUTHOR]

Background: Liver hepatocellular carcinoma (LIHC) ranks as the foremost cause of cancer-related deaths worldwide, and its early detection poses considerable challenges. Current prognostic indicators, including alpha-fetoprotein, have notable limitations in their clinical utility, thereby underscoring the necessity for discovering new biomarkers to improve early diagnosis and enable personalized treatment options. Method: This investigation employed single-cell analysis techniques to identify stem cell-associated genes and assess their prognostic significance for LIHC patients, as well as the efficacy of immunotherapy, utilizing nonnegative matrix factorization (NMF) cluster analysis. A diagnostic model for LIHC was developed and validated through multiple datasets and various machine learning clustering methods. The XGBOOST algorithm identified MRPL17 as the most significant prognostic gene among those associated with stem cells. Additionally, the research explores the relationship between MRPL17 expression and immune cell infiltration. Immunofluorescence staining of LIHC tissue samples was conducted to evaluate the expression and prognostic value of MRPL17, as well as its correlation with KI67. Results: Through single-cell analysis, this study identified 14 essential stem cell-related genes, highlighting their significance in the diagnosis, prognostication, and potential treatment strategies for LIHC patients. Various machine learning algorithms indicated that MRPL17 is particularly associated with patient prognosis and responses to immunotherapy. Furthermore, experimental results demonstrate that MRPL17 is upregulated in LIHC and correlates with poor prognosis, as well as positively correlating with KI67. Conclusion: Cancer stem cells are pivotal in the mechanisms of immune evasion within the tumor microenvironment and have a substantial impact on treatment results. This study experimentally validated MRPL17 as a promising prognostic biomarker, emphasizing the need to target liver cancer stem cells to improve patient prognosis and enhance treatment effectiveness. [ABSTRACT FROM AUTHOR]

Although peer feedback has been proposed as an instructional strategy for cultivating critical thinking, high-quality peer feedback is difficult to obtain. Regulation scripts are a promising scaffold for this activity. Besides, few previous studies have explored the dynamic relationship between feedback content and critical thinking. Therefore, this study investigated the effects of peer feedback with regulation scripts on students' critical thinking, cognitive and affective feedback content, and how feedback content is related to critical thinking. Thirty-four students were randomly divided into nine groups and assigned to one of two conditions: regulation scripts (experimental groups, EGs) and general scripts (control groups, CGs). EGs' students were instructed to argue about the feedback content with prompting questions, and CGs' students completed the tasks with task-related hints. The results revealed that peer feedback with regulation scripts is effective in promoting critical thinking, suggestive comments on cognitive content and positive comments on affective content. Moreover, the epistemic network analysis results indicated that the EGs showed a stronger connection between suggestive/informative comments and creating for cognitive content, while regarding affective content, they showed stronger connections between various affective comments and higher-order critical thinking. Overall, the study yields new insights into the relationship between feedback content and critical thinking. [ABSTRACT FROM AUTHOR]