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We investigate the Sturm-Liouville (S-L) operator with boundary and transfer conditions dependent on the eigen-parameter. By utilizing interval partitioning and factorization techniques of characteristic function, it is proven that this problem has a finite number of eigenvalues when the coefficients of the equation meet certain conditions, and some conditions for determining the number of eigenvalues are provided. The results indicate that the number of eigenvalues in this problem varies when the transfer conditions depend on the eigen-parameter. Furthermore, the equivalence between this problem and matrix eigenvalue problems is studied, and an equivalent matrix representation of the S-L problem is presented.

The virtual synchronous generator (VSG) has been widely used to improve the system inertia and damping in the renewable energy generation system. However, the in-depth understanding of VSG’s stability under disturbances on different control parameters is lacked. In order to solve the problem, the small-signal model of single-VSG is established at first. The influences of key control parameters on the stability of system are analyzed by using the eigenvalue analysis method in detail. On this basis, a novel optimization strategy for control parameters is proposed based on the Particle Swarm Optimization (PSO) algorithm. The control parameters are optimized to realize excellent damping and stability of VSG system. Finally, the simulation and experimental results verify the effectiveness of stability analysis and parameter optimization strategy.

Different from the direct delivery of chemodynamic agents into tumor tissue for chemodynamic therapy (CDT), this work reports the fabrication of heterojunction sonosensitizers (CD/TiSe2) for the in situ generation of chemodynamic agents by responding to tumor microenvironment (TME), realizing the in situ CDT‐enhanced sono‐immunotherapy. The in situ redox of TiSe2 in acidic TME leads to the formation of TiOxSe2−x containing Se (0), selenate, and Ti3+/Ti4+ redox couple, which can facilitate in situ CDT through a Ti3+‐mediated Fenton‐like reaction and consume overexpressed glutathione (GSH) via a Ti4+‐mediated GSH depletion. Moreover, Se ions generated through the in situ redox process promote the maturation of dendritic cells, consequently activating the adaptive immune responses. In another aspect, the construction of heterojunctions within carbon dots and TiSe2 improves the reactive oxygen species (ROS) generation efficiency of TiSe2 in a cascaded manner, which enhances the sonodynamic activity and amplifies the chemodynamic performance. More importantly, the ROS produced by in situ CDT and sonodynamic therapy efficiently triggers immunogenic cell death through a synergistic therapy based on the elicitation of antitumor immunity with the aid of an immune checkpoint blockade. This work thus provides a distinct paradigm of transition metal selenide‐originated in situ Fenton‐like agent generation for in situ CDT‐enhanced sono‐immunotherapy.

On-surface synthesis allows fabrication of nanostructures with atomic precision and may follow different routes compared to in-solution chemistry. Here the authors, using scanning probe microscopy techniques, observe a phenyl group migration reaction on three different metal surfaces forming polycyclic aromatic hydrocarbons, which cannot be accessed by in-solution chemistry.

Abstract Bladder cancer, one of the most prevalent malignant cancers, has high rate of recurrence and metastasis. Owing to genomic instability and high-level heterogeneity of bladder cancer, chemotherapy and immunotherapy drugs sensitivity and lack of prognostic markers, the prognosis of bladder cancer is unclear. Necroptosis is a programmed modality of necrotic cell death in a caspase-independent form. Despite the fact that necroptosis plays a critical role in tumor growth, cancer metastasis, and cancer patient prognosis, necroptosis-related gene sets have rarely been studied in bladder cancer. As a result, the development of new necroptosis-related prognostic indicators for bladder cancer patients is critical. Herein, we assessed the necroptosis landscape of bladder cancer patients from The Cancer Genome Atlas database and classified them into two unique necroptosis-related patterns, using the consensus clustering. Then, using five prognosis-related genes, we constructed a prognostic model (risk score), which contained 5 genes (ANXA1, DOK7, FKBP10, MAP1B and SPOCD1). And a nomogram model was also developed to offer the clinic with a more useful prognostic indicator. We found that risk score was significantly associated with clinicopathological characteristics, TIME, and tumor mutation burden in patients with bladder cancer. Moreover, risk score was a valid guide for immunotherapy, chemotherapy, and targeted drugs. In our study, DOK7 was chosen to further verify our prognosis model, and functional assays indicated that knockdown the expression of DOK7 could prompt bladder cancer proliferation and migration. Our work demonstrated the potential role of prognostic model based on necroptosis genes in the prognosis, immune landscape and response efficacy of immunotherapy of bladder cancer.

Abstract Background Bladder cancer (BC) is one of the most common malignancies of the genitourinary system. Animal models offer an important tool to explore tumour initiation, progression, and therapeutic mechanisms. Our aim is to construct an optimized orthotopic BC model which is predictable, reproducible, and convenient. Methods The optimized orthotopic BC model was constructed in male C57BL/6 mice utilizing microsyringes to inoculate them with a murine BC cell line (MB49). Anesthetised mice were inoculated with an MB49 cell suspension (10 µL) at approximately 5 × 106/mL. The whole process of modelling was observed and monitored every 3 days for 21 days utilizing HE staining and transabdominal ultrasonography (TUS). Results In this study, the model showed excellent success rates for tumour formation (96.67%) and metastatic rate (89.66%). Compared to the control group (sham operation), mice in the modelling group had serous cachexia, visible haematuresis and weight loss (all P

Abstract Background Enolase is an essential enzyme in the process of glycolysis and has been implicated in cancer progression. Though dysregulation of ENOs has been reported in multiple cancers, their prognostic value and specific role in bladder cancer (BLCA) remain unclear. Methods Multiple databases were employed to examine the expression of ENOs in BLCA. The expression of ENO1 was also validated in BLCA cell lines and tissue samples by western blotting and immunohistochemistry. Kaplan–Meier analysis, ROC curve, univariate and multivariate Cox regression were performed to evaluate the predictive capability of the ENO1. Gene ontology (GO) and Gene Set Enrichment Analyses (GSEA) analysis were employed to perform the biological processes enrichment. Function experiments were performed to explore the biological role of ENO1 in BLCA. The correlation of ENO1 with immune cell infiltration was explored by CIBERSORT. Results By analyzing three ENO isoforms in multiple databases, we identified that ENO1 was the only significantly upregulated gene in BLCA. High expression level of ENO1 was further confirmed in BLCA tissue samples. Aberrant ENO1 overexpression was associated with clinicopathological characteristics and unfavorable prognosis. Functional studies demonstrated that ENO1 depletion inhibited cancer cell aggressiveness. Furthermore, the expression level of ENO1 was correlated with the infiltration levels of immune cells and immune-related functions. Conclusions Taken together, our results indicated that ENO1 might serve as a promising prognostic biomarker for prognosticating prognosis associated with the tumor immune microenvironment, suggesting that ENO1 could be a potential immune-related target against BLCA.

Abstract Background The current drug treatments for benign prostatic hyperplasia (BPH) have negative side effects. Therefore, it is important to find effective alternative therapies with significantly fewer side effects. Our previous study revealed that Rauwolfia vomitoria (RWF) root bark extract reversed BPH development in a rat model. However, the molecular mechanism of its inhibitory effects on BPH remains largely unknown. Methods BPH-1 and WPMY-1 cell lines derived from BPH epithelial and prostatic stromal compartments were selected to investigate how RWF extract inhibits BPH in vitro by MTT and flow cytometry assays. Microarray, quantitative real-time PCR, immunoblotting, and GFP-LC3 immunofluorescence assays were performed to evaluate the effects of RWF extract on endoplasmic reticulum stress (ER stress) and autophagic apoptosis pathways in two cell lines. A human BPH ex vivo explant assay was also employed for validation. Results RWF extract treatment decreased cell viability and induced apoptotic cell death in both BPH-1 and WPMY-1 cells in a concentration-dependent manner with the increase of pro-apoptotic PCDC4 protein. RWF extract induced autophagy by enhancing the levels of autophagic genes (ULK2 and SQSTM1/p62) and the LC3II:LC3I ratio, with the increase of GFP-LC3 puncta. Moreover, RWF extract activated PERK- and ATF6-associated ER stress pathways by inducing the transcriptional levels of EIF2AK3/PERK, DDIT3/CHOP and ATF6, accompanied by the reduction of BiP protein level, but not its mRNA level. Another ER stress pathway was not induced by RWF extract, as manifested by the lack of XBP1 splicing. Pharmacological inhibition of autophagy by 3-methyladenine abrogated apoptosis but not ER stress; while inhibition of ER stress by 4-phenylbutyrate alleviated the induction of autophagy and apoptosis. In addition, pretreatments with either 3-methyladenine or 4-phenylbutyrate suppressed RWF extract-induced cytotoxicity. Notably, the inductions of PERK- and ATF6-related stress pathways and autophagic apoptosis were confirmed in a human BPH ex vivo explant. Conclusions Our data have demonstrated that RWF extract significantly suppressed the viabilities of BPH epithelial cells and BPH myofibroblasts by inducing apoptosis via upregulating ER stress and autophagy. These data indicate that RWF extract is a potential novel alternative therapeutic approach for BPH.

Abstract Quarteranthene is predicted to manifest nontrivial edge states as the competition from the hybridization of localized frontier states and the Coulomb repulsion between valence electrons, which hosts much research potential in memory, spintronic devices fabrication, and quantum computation. The fabrication of ribbon‐like structures with up‐mentioned edge states, such as chiral graphene nanoribbon, possesses a high significance in the topological phase transition investigation. However, the synthesis of chiral graphene nanoribbon is limited in reactive substrate or with the edge‐brominated precursor. Here, the fabrication of quarteranthene and its chiral graphene nanoribbon segment on Au(111) substrate is reported. A combined bond‐resolved scanning tunneling microscopy, noncontact atomic force microscopy characterization, and corresponding density functional theory calculations confirm the chemical structure of fabricated products on the Au(111) substrate. The detailed analysis of the laterally extended products reveals that the lateral‐extended structures are acquired via the linkage of the hydrocarbon quarter‐anthryl. In addition, several strategies are used to modulate the yield of quarteranthene and its lateral‐extended products. These findings provide a new insight into the lateral extension strategy on metal substrates and provide another possible fabrication strategy of chiral graphene nanoribbons on the relative inert Au(111) substrate.

This paper is concerned with a fourth-order differential operator with eigenparameter dependent boundary conditions. We prove that each of the eigenvalues of the problem can be embedded in a continuous eigenvalue branch. Furthermore, the differential expressions of the eigenvalues with respect to each of parameters are given.

Bladder cancer (BC) ranks the tenth in the incidence of global tumor epidemiology. LncRNAs and cuproptosis were discovered to regulate the cell death. Herein, we downloaded transcriptome profiling, mutational data, and clinical data on patients from The Cancer Genome Atlas (TCGA). High- and low-risk BC patients were categorized. Three CRLs (AL590428.1, AL138756.1 and GUSBP11) were taken into prognostic signature through least absolute shrinkage and selection operator (LASSO) Cox regression. Worse OS and PFS were shown in high-risk group (p < 0.05). ROC, independent prognostic analyses, nomogram and C-index were predicted via CRLs. Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) analysis indicated IncRNAs play a biological role in BC progression. Immune-related functions showed the high-risk group received more benefit from immunotherapy and had stronger immune responses, and the overall survival was better (p < 0.05). Finally, a more effective outcome (p < 0.05) was found from clinical immunotherapy via the TIDE algorithm and many potential anti-tumor drugs were identified. In our study, the cuproptosis-related signature provided a novel tool to predict the prognosis in BC patients accurately and provided a novel strategy for clinical immunotherapy and clinical applications.

Matrix representations for a class of Sturm–Liouville problems with eigenparameters contained in the boundary and interface conditions were studied. Given any matrix eigenvalue problem of a certain type and an eigenparameter-dependent condition, a class of Sturm–Liouville problems with this specified condition was constructed. It has been proven that each Sturm–Liouville problem is equivalent to the given matrix eigenvalue problem.

Abstract The chromobox (CBX) proteins mediate epigenetic gene silencing and have been implicated in the cancer development. By analyzing eight CBX family members in TCGA dataset, we found that chromobox 7 (CBX7) was the most strikingly downregulated CBX family member in urinary bladder cancer (UBC), as compared to normal tissues. Though dysregulation of CBX7 has been reported in multiple cancers, its specific role and clinical relevance in UBC remain unclear. Herein, we found that frequent downregulation of CBX7 in UBC specimens, which was due to its promoter hypermethylation, was correlated with poor prognosis. The ectopic expression of CBX7 suppressed UBC cell proliferation, migration, invasion, and cancer stemness, whereas CBX7 depletion promoted cancer cell aggressiveness. Importantly, CBX7 overexpression in UBC cells inhibited tumorigenicity, whereas CBX7 depletion promoted the tumor development, indicating its tumor-suppressive role in UBC. Using RNA-seq and chromosome immunoprecipitation (ChIP) assays, we identified aldo-keto reductase family 1 member 10 (AKR1B10) as a novel downstream target of CBX7, which was negatively modulated by CBX7 in a PRC1-dependent manner and involved in stimulating ERK signaling. Consistently, AKR1B10 overexpression induced cancer cell aggressiveness, whereas suppression of AKR1B10 by siRNA or its small molecular inhibitor, oleanolic acid, reversed the CBX7 deficiency-induced cellular effects. AKR1B10 overexpression was negatively associated with CBX7 downregulation and predicted poor clinical outcomes in UBC patients. Taken together, our results indicate that CBX7 functions as a tumor suppressor to downregulate AKR1B10 and further inactivates ERK signaling. This CBX7/AKR1B10/ERK signaling axis may provide a new therapeutic strategy against UBC.

Background: Bladder cancer (BC) is a leading cause of death from malignancy, with significant heterogeneity in the immunotherapeutic responsiveness of advanced status. Pyroptosis, a newly discovered inflammatory programmed cell death, is confirmed to play an indispensable role in tumorigenesis and anti-tumor activity. However, the effect of pyroptosis on the tumor-immune landscape remodeling and immunotherapy in BC remains elusive.Methods: We comprehensively evaluated the mRNA expression and genomic alterations of 33 pyroptosis-related genes (PRGs) in BC and evaluated the patterns of pyroptosis in publicly available BC datasets. An unsupervised clustering method was used to classify patients into distinct patterns. Then, we established a pyroptosis-related signature score (PS-score) model to quantify the pyroptosis-related patterns of individual BC patients using principal component analysis. Furthermore, we correlated the patterns with the immune landscape and response efficacy of immunotherapy.Results: Two pyroptosis-related patterns were identified in BC, and distinct patterns showed various immune characteristics. Patterns with a high expression level of PRGs exhibited a survival advantage and showed higher infiltration of cytotoxic lymphocytes. Tumors with a low PS-score were characterized by high tumor-infiltrating lymphocytes and considered “hot.” Further analysis revealed that the PS-score was an independent prognostic factor and could predict the response to immunotherapy for patients with advanced BC. We found a significant positive association between AHNAK2, AHNAK nucleoprotein 2, expression, and PS-score. Functional assays showed that AHNAK2 knockdown was correlated with attenuated invasive ability.Conclusion: This work comprehensively demonstrated the potential function of pyroptosis-related patterns in the bladder tumor-immune landscape and identified their therapeutic liability in immunotherapy. Our study enhanced our understanding of the immune landscape and provided a new approach toward more effective immunotherapy strategies.

In this paper, we study a singular Sturm–Liouville problem with an eigenparameter-dependent boundary condition and transmission conditions at two interior points. Using an operator-theoretical formulation, we transfer the problem to an operator in an appropriate Hilbert space. It is proved that the operator is self-adjoint. We also give the asymptotic formulas of the eigenvalues of the problem. Moreover, Green’s function is also discussed.

BackgroundBladder cancer is a common malignant type in the world, and over 90% are transitional cell carcinoma. While the impact of inflammatory response on cancer progression has been reported, the role of inflammatory response-associated genes (IRAGs) in transitional bladder cancer still needs to be understood.MethodsIn this study, IRAGs were download from Molecular Signature Database (MSigDB). The transcriptional expression and matched clinicopathological data were separately obtained from public databases. The TCGA-BLCA cohort was used to identify the differentially expressed IRAGs, and prognostic IRAGs were filtrated by univariate survival analysis. The intersection between them was displayed by Venn diagram. Based on least absolute shrinkage and selection operator (LASSO) regression analysis method, the TCGA-BLCA cohort was used to construct a risk signature. Survival analysis was conducted to calculate the overall survival (OS) in TCGA and GSE13507 cohort between two groups. We then conducted univariate and multivariate survival analyses to identify independently significant indicators for prognosis. Relationships between the risk scores and age, grade, stage, immune cell infiltration, immune function, and drug sensitivity were demonstrated by correlation analysis. The expression level of prognostic genes in vivo and in vitro were determined by qRT-PCR assay.ResultsComparing with normal tissues, there were 49 differentially expressed IRAGs in cancer tissues, and 12 of them were markedly related to the prognosis in TCGA cohort for transitional bladder cancer patients. Based on LASSO regression analysis, a risk model consists of 10 IRAGs was established. Comparing with high-risk groups, survival analysis showed that patients in low-risk groups were more likely to have a better survival time in TCGA and GSE13507 cohorts. Besides, the accuracy of the model in predicting prognosis is acceptable, which is demonstrated by receiver operating characteristic curve (ROC) analysis. Age, stage, and risk scores variables were identified as the independently significant indicators for survival in transitional bladder cancer. Correlation analysis represented that the risk score was identified to be significantly related to the above variables except gender variable. Moreover, the expression level of prognostic genes in vivo and in vitro was markedly upregulated for transitional bladder cancer.ConclusionsA novel model based on the 10 IRAGs that can be used to predict survival time for transitional bladder cancer. In addition, this study may provide treatment strategies according to the drug sensitivity in the future.

Bladder cancer (BC) belongs to one of the most common and highly heterogeneous malignancies. Ferroptosis is a newly discovered regulated cell death (RCD), characterized by accumulation of toxic lipid peroxides, and plays a crucial role in tumor progression. Here, we conducted a comprehensive analysis on the transcriptomics data of ferroptosis-related genes in BC based on The Cancer Genome Atlas (TCGA) and three Gene Expression Omnibus (GEO) datasets. In our study, a 6-gene signature was identified based on the potential prognostic ferroptotic regulatory genes. Furthermore, our signature revealed a good independent prognostic ability in BC. Patients with low-risk score exhibited higher FGFR3 mutation rates while high risk score had a positive association with higher RB1 mutation rates. Meanwhile, higher proportions of macrophages were observed in high BC risk group simultaneously with four methods. Unexpectedly, the risk score showed a significant positive correlation with epithelial-mesenchymal transition (EMT) status. Functional assays indicated that CRYAB and SQLE knockdown was associated with attenuated invasion capacity. Our study revealed a ferroptosis-related risk model for predicting prognostic and BC progression. Our results indicate that targeting ferroptosis may be a therapeutic strategy for BC.

This paper deals with a singular (Weyl’s limit circle case) non-self-adjoint (dissipative) Dirac operator with eigenparameter dependent boundary condition and finite general transfer conditions. Using the equivalence between Lax-Phillips scattering matrix and Sz.-Nagy-Foiaş characteristic function, the completeness of the eigenfunctions and associated functions of this dissipative operator is discussed.

Abstract The present paper deals with a class of discontinuous Sturm–Liouville problems with boundary conditions rationally dependent on the eigenparameter. Operator formulation is built and asymptotic formulas for eigenvalues and eigenfunctions are given. Moreover, the completeness of its eigenfunctions is also discussed.

Exploring two-dimensional materials with excellent photoelectricity properties is of great theoretical significance and practical value for developing new photocatalysts, electronics and photonic devices. Here, using first-principle calculations, we designed and analyzed systematically a series of α , β and γ phase structures of two-dimensional group IV-V monolayers (IV-V, IV = C, Si, Ge, Sn, Pb; V = N, P, As, Sb, Bi), most of them are semiconductors. Among them, γ -GeN and α -SnP monolayers with thermodynamic and kinetic stability (at 300 K) have been further studied due to their wide range of energy band gaps ( γ -GeN: 2.54 eV, α -SnP:1.34 eV). The two band gaps are greater than the free energy for water splitting (1.23 eV), which are crucial for photocatalytic decomposition of water. The γ -GeN and α -SnP monolayers present excellent photocatalystics properties in pH = 0/7 and pH = 10 environments, respectively. Moreover, both of the monolayers show strong light absorption coefficients greater than 10 ^5 cm ^−1 in the visible and ultraviolet regions. In addition, it is found that the band edge positions and band gap sizes of γ -GeN and α -SnP monolayers can be regulated by biaxial strain. Benefitting from the wide selection of energy band gaps and high absorption coefficients, the γ -GeN and α -SnP monolayers are the next generation of promising candidate materials for photocatalysts, nanoelectronics and optoelectronics.

Cu _2 Se monolayer (ML) synthesized experimentally is a member of transition metal chalcogenides materials, which has attracted significant attention due to its diversity and unique properties. However, the feature of an indirect band gap of Cu _2 Se ML in the low-temperature phase limits its’ application in electronics devices. Our study results based on the first principle calculations show that indirect-direct band gap transitions can occur in Cu _2 Se ML under appropriate uniaxial or biaxial strains. The band gap of Cu _2 Se ML is controllable due to the different responses of the edge-states near the Fermi level to the strain. The phonon dispersion suggests that the semiconducting Cu _2 Se ML can maintain dynamic stability in a wide range of strains. With the tunable electronic structure, semiconducting Cu _2 Se ML would become a promising candidate for electronic devices.

Acne vulgaris associated with Propionibacterium acnes ( P. acnes ) remains one of the most common skin diseases, while lacking of effective and non-resistant treatments. Graphene inclusing graphene oxide (GO) and reduced graphene oxide (rGO) have been triggering abundant attentions due to their astonishing performances in multi research areas. Here, the GO and rGO suspensions with different concentrations and sizes against P. acnes were investigated. The higher the concentration while the smaller the size distribution led to the better the antibacterial performance. And the loss of viability of P. acnes can surprisely achieve 72% under a 100 μ g 10 000 mesh rGO existed which was induced by physical puncture and oxidative stress. Furthermore, the physiological activities of P. acnes will reduce the GO to rGO which further accelerate its death. This study will provide a rapid, effective and non-resistant method for the treatment of acne.

In this paper, we investigate a class of discontinuous singular Sturm-Liouville problems with limit circle endpoints and eigenparameter dependent boundary conditions. Operator formulation is constructed and asymptotic formulas for eigenvalues and fundamental solutions are given. Moreover, the completeness of eigenfunctions is discussed.

This article investigates the effect of different magnetic fields on modulating the alignment of graphene nanoplatelets (GNPs) and their impact on the thermal conductivity of epoxy nanocomposites. Various nanocomposite specimens were fabricated with different GNP contents by using magnetically fieldaligned GNPs in the fabrication process to enhance the thermal conductivity. The results showed that the in-plane thermal conductivity of the Bmf (Bidirectional magnetic field) sample with 5 wt% GNPs added reached 0.75 W m-1 K-1, which is 276.6% higher than that of pure epoxy resin and the anisotropy coefficient (Kk/K?) reached 3.3. In addition, temperature rise tests were performed to simulate the thermal conductivity of nanocomposites used as an electronic packaging material, and the results indicated that the composites achieved a significant increase in in-plane thermal conductivity with a lower amount of filler. This provides valuable insights into the preparation of thermally conductive composites and demonstrates their potential as a thermal management packaging material for next-generation electronic devices. [ABSTRACT FROM AUTHOR]