Non-Abelian Topological Bound States in the Continuum.

Bound states in the continuum (BICs), which are spatially localized states with energies lying in the continuum of extended modes, have been widely investigated in both quantum and classical systems. Recently, the combination of topological band theory with BICs has led to the creation of topological BICs that exhibit extraordinary robustness against disorder. However, the previously proposed topological BICs are only limited in systems with Abelian gauge fields. Whether non-Abelian gauge fields can induce topological BICs and how to experimentally explore these phenomena remains unresolved. Here, we report the theoretical and experimental realization of non-Abelian topological BICs, which are generated by the interplay between two inseparable pseudospins and can coexist in each pseudospin subspace. This unique characteristic necessitates non-Abelian couplings that lack any Abelian counterparts. Furthermore, the non-Abelian couplings can also offer a new avenue for constructing topological subspace-induced BICs at bulk dislocations. Those exotic phenomena are observed by non-Abelian topolectrical circuits. Our results establish the connection between topological BICs and non-Abelian gauge fields, and serve as the catalyst for future investigations on non-Abelian topological BICs across different platforms.

Non-Abelian Inverse Anderson Transitions.

Inverse Anderson transitions, where the flat-band localization is destroyed by disorder, have been wildly investigated in quantum and classical systems in the presence of Abelian gauge fields. Here, we report the first investigation on inverse Anderson transitions in the system with non-Abelian gauge fields. It is found that pseudospin-dependent localized and delocalized eigenstates coexist in the disordered non-Abelian Aharonov-Bohm cage, making inverse Anderson transitions depend on the relative phase of two internal pseudospins. Such an exotic phenomenon induced by the interplay between non-Abelian gauge fields and disorder has no Abelian analogy. Furthermore, we theoretically design and experimentally fabricate non-Abelian Aharonov-Bohm topolectrical circuits to observe the non-Abelian inverse Anderson transition. Through the direct measurements of frequency-dependent impedance responses and voltage dynamics, the pseudospin-dependent non-Abelian inverse Anderson transitions are observed. Our results establish the connection between inverse Anderson transitions and non-Abelian gauge fields, and thus comprise a new insight on the fundamental aspects of localization in disordered non-Abelian flat-band systems.

Remote Sensing Image of The Landsat 8-9 Compressive Sensing via Non-Local Low-Rank Regularization with the Laplace Function.

Utilizing low-rank prior data in compressed sensing (CS) schemes for Landsat 8-9 remote sensing images (RSIs) has recently received widespread attention. Nevertheless, most CS algorithms focus on the sparsity of an RSI and ignore its low-rank (LR) nature. Therefore, this paper proposes a new CS reconstruction algorithm for Landsat 8-9 remote sensing images based on a non-local optimization framework (NLOF) that is combined with non-convex Laplace functions (NCLF) used for the low-rank approximation (LAA). Since the developed algorithm is based on an approximate low-rank model of the Laplace function, it can adaptively assign different weights to different singular values. Moreover, exploiting the structural sparsity (SS) and low-rank (LR) between the image patches enables the restored image to obtain better CS reconstruction results of Landsat 8-9 RSI than the existing models. For the proposed scheme, first, a CS reconstruction model is proposed using the non-local low-rank regularization (NLLRR) and variational framework. Then, the image patch grouping and Laplace function are used as regularization/penalty terms to constrain the CS reconstruction model. Finally, to effectively solve the rank minimization problem, the alternating direction multiplier method (ADMM) is used to solve the model. Extensive numerical experimental results demonstrate that the non-local variational framework (NLVF) combined with the low-rank approximate regularization (LRAR) method of non-convex Laplace function (NCLF) can obtain better reconstruction results than the more advanced image CS reconstruction algorithms. At the same time, the model preserves the details of Landsat 8-9 RSIs and the boundaries of the transition areas.

Moiré Quasibound States in the Continuum.

The novel physics of twisted bilayer graphene has motivated extensive studies of magic-angle flat bands hosted by moiré structures in electronic, photonic, and acoustic systems. On the other hand, bound states in the continuum (BICs) have also attracted great attention in recent years because of their potential applications in the field of designing superior optical devices. Here, we combine these two independent concepts to construct a new optical state in a twisted bilayer photonic crystal slab, which is called as moiré quasi-BIC, and numerically demonstrate that such an exotic optical state possesses dual characteristics of moiré flat bands and quasi-BICs. To illustrate the mechanism for the formation of moiré flat bands, we develop an effective model at the center of the Brillouin zone and show that moiré flat bands could be fulfilled by balancing the interlayer coupling strength and the twist angle around the band edge above the light line. Moreover, by decreasing the twist angle of moiré photonic crystal slabs with flat bands, it is shown that the moiré flat-band mode at the Brillouin center gradually approaches a perfect BIC, where the total radiation loss from all diffraction channels is significantly suppressed. To clarify the advantage of moiré quasi-BICs, enhanced second-harmonic generation (SHG) is numerically proven with a wide-angle optical source. The efficiency of SHG assisted by designed moiré quasi-BICs can be greatly improved compared with that based on dispersive quasi-BICs with similar quality factors.

Prognostic Value of HLA Class I in Patients with Hepatocellular Carcinoma.

BACKGROUND: Downregulation of HLA class I molecules is a major tumor escape mechanism from immune attack. However, its prognostic impact for patients with hepatocellular carcinoma is still unclear. This study aimed to investigate whether HLA class I has prognostic significance in patients with hepatocellular carcinoma. METHODS: A cohort of 132 patients with hepatocellular carcinoma was enrolled. HLA class I expression was detected by immunohistochemistry. Levels of HLA class I expression were dichotomized as low and high according to staining intensity or staining percentage of positive tumor cells, respectively. Association of HLA class I expression with clinical characteristics and survival was analyzed. RESULTS: None of the clinical characteristics, including gender, age, virus infection, cirrhosis, AFP, vascular invasion, tumor size and number, was significantly associated with staining percentage of HLA class I or staining intensity (p > 0.05). Low staining percentage of HLA class I was significantly associated with a worse survival (p = 0.011), which was further confirmed by Cox regression hazards model in multivariate analysis (HR 0.416, 95% CI 0.204 - 0.849, p = 0.016). Staining intensity of HLA class I was not significantly associated with survival (p > 0.05). CONCLUSIONS: Expression of HLA class I might be a significant prognostic factor in hepatocellular carcinoma, and downregulation of HLA class I was significantly associated with a worse survival in terms of expression percentage of HLA class I.

Characterizing core-shell nanostructures through photoacoustic response based on theoretical model in the frequency domain.

Core-shell nanostructures are widely used, and their photoacoustic (PA) properties are important for applications. However, the relations between their structural parameters and the properties of the PA spectrum are indirect because most theoretical models have been reported for them in the time domain. In this study, we develop a complete model in the frequency domain to analyze the PA response of core-shell particles. As in the case of solid spheres, the core-shell particles have pronounced resonant modes. The PA mode varies with the thickness of the shell and the radius of the core. Under single-pulse irradiation, PA signals of gold-silica nanospheres obtained by our theory agreed with those of the theory in the time domain and experiments. Under multi-pulse irradiation, the magnitude of the PA signals peaked whether the repeated excitation itself or its harmonic was equal to the PA mode. The structure could thus be monitored by the PA signals. These findings enrich PA theory and may inspire new techniques for the noninvasive characterization of nanoparticles.

Optimization and robustness of the topological corner state in second-order topological photonic crystals.

The second-order topological photonic crystal with the 0D corner state provides a new way to investigate cavity quantum electrodynamics and develop topological nanophotonic devices with diverse functionalities. Here, we report on the optimization and robustness of the topological corner state in the second-order topological photonic crystal both in theory and in experiment. The topological nanocavity is formed based on the 2D generalized Su-Schrieffer-Heeger model. The quality factor of the corner state is optimized theoretically and experimentally by changing the gap between two photonic crystals or just modulating the position or size of the airholes surrounding the corner. The fabricated quality factors are further optimized by the surface passivation treatment which reduces surface absorption. A maximum quality factor of the fabricated devices is about 6000, which is the highest value ever reported for the active topological corner state. Furthermore, we demonstrate the robustness of the corner state against strong disorders including the bulk defect, edge defect, and even corner defect. Our results lay a solid foundation for further investigations and applications of the topological corner state, such as the investigation of a strong coupling regime and the development of optical devices for topological nanophotonic circuitry.

Experimental Observation of Higher-Order Topological Anderson Insulators.

Recently, a new family of symmetry-protected higher-order topological insulators has been proposed and was shown to host lower-dimensional boundary states. However, with the existence of the strong disorder in the bulk, the crystal symmetry is broken, and the associated corner states are disappeared. It is well known that the emergence of robust edge states and quantized transport can be induced by adding sufficient disorders into a topologically trivial insulator, that is the so-called topological Anderson insulator. The question is whether disorders can also cause the higher-order topological phase. This is not known so far, because interactions between disorders and the higher-order topological phases are completely different from those with the first-order topological system. Here, we demonstrate theoretically that the disorder-induced higher-order topological corner state and quantized fraction corner charge can appear in a modified Haldane model. In experiments, we construct the classical analog of such higher-order topological Anderson insulators using electric circuits and observe the disorder-induced corner state through the voltage measurement. Our work defies the conventional view that the disorder is detrimental to the higher-order topological phase, and offers a feasible platform to investigate the interaction between disorders and higher-order topological phases.

Simulate Deutsch-Jozsa algorithm with metamaterials.

During the past few years, a lot of efforts have been devoted in studying optical analog computing with artificial structures. Up to now, much of them are primarily focused on classical mathematical operations. How to use artificial structures to simulate quantum algorithm is still to be explored. In this work, an all-dielectric metamaterial-based model is proposed and realized to demonstrate the quantum Deutsch-Jozsa algorithm. The model is comprised of two cascaded functional metamaterial subblocks. The oracle subblock encodes the detecting functions (constant or balanced), onto the phase distribution of the incident wave. Then, the original Hadamard transformation is performed with a graded-index subblock. Both the numerical and experimental results indicate that the proposed metamaterials are able to simulate the Deutsch-Jozsa problem with one round operation and a single measurement of the output eletric field, where the zero (maximum) intensity at the central position results from the destructive (constructive) interference accompanying with the balance (constant) function marked by the oracle subblock. The proposed computational metamaterial is miniaturized and easy-integration for potential applications in communication, wave-based analog computing, and signal processing systems.

Vector Exceptional Points with Strong Superchiral Fields.

Exceptional points (EPs), branch points of complex energy surfaces at which eigenvalues and eigenvectors coalesce, are ubiquitous in non-Hermitian systems. Many novel properties and applications have been proposed around the EPs. One of the important applications is to enhance the detection sensitivity. However, due to the lack of single-handed superchiral fields, all of the proposed EP-based sensing mechanisms are only useful for the nonchiral discrimination. Here, we propose theoretically and demonstrate experimentally a new type of EP, which is called a radiation vector EP, to fulfill the homogeneous superchiral fields for chiral sensing. This type of EP is realized by suitably tuning the coupling strength and radiation losses for a pair of orthogonal polarization modes in the photonic crystal slab. Based on the unique modal-coupling property at the vector EP, we demonstrate that the uniform superchiral fields can be generated with two beams of lights illuminating the photonic crystal slab from opposite directions. Thus, the designed photonic crystal slab, which supports the vector EP, can be used to perform surface-enhanced chiral detection. Our findings provide a new strategy for ultrasensitive characterization and quantification of molecular chirality, a key aspect for various bioscience and biomedicine applications.

Prognostic Value of PD-L1 in Patients with Hepatocellular Carcinoma.

BACKGROUND: The aim of the study is to investigate whether programmed death ligand l (PD-L1) on tumor cells has prognostic significance in patients with hepatocellular carcinoma. METHODS: A cohort of 143 patients with hepatocellular carcinoma was enrolled. PD-L1 expression was detected by immunohistochemistry. The association of PD-L1 expression with clinical characteristics and survival was analyzed. RESULTS: PD-L1 positive rate in our study was 13.3% (19/143). None of clinical characteristics, including gender, age, virus infection, AFP, vascular invasion, tumor size, and number, was significantly associated with PD-L1 expression (p > 0.05). PD-L1 expression was significantly associated with cirrhosis (p = 0.016). PD-L1 expression was not significantly associated with survival (Log-rank p = 0.076; HR: 0.363 p = 0.091). CONCLUSIONS: PD-L1 expression failed to have a markedly significant prognostic association with survival in patients with hepatocellular carcinoma.

Tunable superradiance and quantum phase gate based on graphene wrapped nanowire.

The interaction between quantum emitters and graphene wrapped nanowire has been investigated using a Green's function technique. The eigenmodes for the graphene wrapped nanowire at various Fermi levels in graphene have been solved exactly. The Dicke subradiance and superradiance resulting from the graphene-mediated interaction have been observed. Based on these phenomena, we have proposed a scheme for a deterministic tunable two-qubit quantum phase gate. The "switching" effect for the quantum phase gate has been realized theoretically by changing an external voltage, which is very beneficial for the quantum-information processing.

An exosome-derived lncRNA signature identified by machine learning associated with prognosis and biomarkers for immunotherapy in ovarian cancer.

Background: Ovarian cancer (OC) has the highest mortality rate among gynecological malignancies. Current treatment options are limited and ineffective, prompting the discovery of reliable biomarkers. Exosome lncRNAs, carrying genetic information, are promising new markers. Previous studies only focused on exosome-related genes and employed the Lasso algorithm to construct prediction models, which are not robust. Methods: 420 OC patients from the TCGA datasets were divided into training and validation datasets. The GSE102037 dataset was used for external validation. LncRNAs associated with exosome-related genes were selected using Pearson analysis. Univariate COX regression analysis was used to filter prognosis-related lncRNAs. The overlapping lncRNAs were identified as candidate lncRNAs for machine learning. Based on 10 machine learning algorithms and 117 algorithm combinations, the optimal predictor combinations were selected according to the C index. The exosome-related LncRNA Signature (ERLS) model was constructed using multivariate COX regression. Based on the median risk score of the training datasets, the patients were divided into high- and low-risk groups. Kaplan-Meier survival analysis, the time-dependent ROC, immune cell infiltration, immunotherapy response, and immune checkpoints were analyzed. Results: 64 lncRNAs were subjected to a machine-learning process. Based on the stepCox (forward) combined Ridge algorithm, 20 lncRNA were selected to construct the ERLS model. Kaplan-Meier survival analysis showed that the high-risk group had a lower survival rate. The area under the curve (AUC) in predicting OS at 1, 3, and 5 years were 0.758, 0.816, and 0.827 in the entire TCGA cohort. xCell and ssGSEA analysis showed that the low-risk group had higher immune cell infiltration, which may contribute to the activation of cytolytic activity, inflammation promotion, and T-cell co-stimulation pathways. The low-risk group had higher expression levels of PDL1, CTLA4, and higher TMB. The ERLS model can predict response to anti-PD1 and anti-CTLA4 therapy. Patients with low expression of PDL1 or high expression of CTLA4 and low ERLS exhibited significantly better survival prospects, whereas patients with high ERLS and low levels of PDL1 or CTLA4 exhibited the poorest outcomes. Conclusion: Our study constructed an ERLS model that can predict prognostic risk and immunotherapy response, optimizing clinical management for OC patients.

Reversal of tamoxifen resistance by artemisinin in ER+ breast cancer: bioinformatics analysis and experimental validation.

Breast cancer is the leading cause of cancer-related deaths in women worldwide, with Hormone Receptor (HR)+ being the predominant subtype. Tamoxifen (TAM) serves as the primary treatment for HR+ breast cancer. However, drug resistance often leads to recurrence, underscoring the need to develop new therapies to enhance patient quality of life and reduce recurrence rates. Artemisinin (ART) has demonstrated efficacy in inhibiting the growth of drug-resistant cells, positioning art as a viable option for counteracting endocrine resistance. This study explored the interaction between artemisinin and tamoxifen through a combined approach of bioinformatics analysis and experimental validation. Five characterized genes (ar, cdkn1a, erbb2, esr1, hsp90aa1) and seven drug-disease crossover genes (cyp2e1, rorc, mapk10, glp1r, egfr, pgr, mgll) were identified using WGCNA crossover analysis. Subsequent functional enrichment analyses were conducted. Our findings confirm a significant correlation between key cluster gene expression and immune cell infiltration in tamoxifen-resistant and -sensitized patients. scRNA-seq analysis revealed high expression of key cluster genes in epithelial cells, suggesting artemisinin's specific impact on tumor cells in estrogen receptor (ER)-positive BC tissues. Molecular target docking and in vitro experiments with artemisinin on LCC9 cells demonstrated a reversal effect in reducing migratory and drug resistance of drug-resistant cells by modulating relevant drug resistance genes. These results indicate that artemisinin could potentially reverse tamoxifen resistance in ER-positive breast cancer.

Hyperbolic photonic topological insulators.

Topological photonics provides a new degree of freedom to robustly control electromagnetic fields. To date, most of established topological states in photonics have been employed in Euclidean space. Motivated by unique properties of hyperbolic lattices, which are regular tessellations in non-Euclidean space with a constant negative curvature, the boundary-dominated hyperbolic topological states have been proposed. However, limited by highly crowded boundary resonators and complicated site couplings, the hyperbolic topological insulator has only been experimentally constructed in electric circuits. How to achieve hyperbolic photonic topological insulators is still an open question. Here, we report the experimental realization of hyperbolic photonic topological insulators using coupled ring resonators on silicon chips. Boundary-dominated one-way edge states with pseudospin-dependent propagation directions have been observed. Furthermore, the robustness of edge states in hyperbolic photonic topological insulators is also verified. Our findings have potential applications in the field of designing high-efficient topological photonic devices with enhanced boundary responses.

Topologically Protected Quantum Logic Gates with Valley-Hall Photonic Crystals.

Topological photonics provide a promising way to realize more robust optical devices against some defects and environmental perturbations. Quantum logic gates are fundamental units of quantum computers, which are widely used in future quantum information processing. Thus, constructing robust universal quantum logic gates is an important way forward to practical quantum computing. However, the most important problem to be solved is how to construct the quantum-logic-gate-required 2 × 2 beam splitter with topological protection. Here, the experimental realization of the topologically protected contradirectional coupler is reported, which can be employed to realize the quantum logic gates, including control-NOT and Hadamard gates, on the silicon photonic platform. These quantum gates not only have high experimental fidelities but also exhibit a certain degree of tolerances against certain types of defects. This work paves the way for the development of practical optical quantum computations and signal processing.

Large-Scale Synthesis of High-Loading Single Metallic Atom Catalysts by a Metal Coordination Route.

Single atom catalyst (SAC) is one of the most efficient and versatile catalysts with well-defined active sites. However, its facile and large-scale preparation, the prerequisite of industrial applications, has been very challenging. This dilemma originates from the Gibbs-Thomson effect, which renders it rather difficult to achieve high single atom loading (< 3 mol%). Further, most synthesizing procedures are quite complex, resulting in significant mass loss and thus low yields. Herein, a novel metal coordination route is developed to address these issues simultaneously, which is realized owing to the rapid complexation between ligands (e.g., biuret) and metal ions in aqueous solutions and subsequent in situ polymerization of the formed complexes to yield SACs. The whole preparation process involves only one heating step operated in air without any special protecting atmospheres, showing general applicability for diverse transition metals. Take Cu SAC for an example, a record yield of up to 3.565 kg in one pot and an ultrahigh metal loading 16.03 mol% on carbon nitride (Cu/CN) are approached. The as-prepared SACs are demonstrated to possess high activity, outstanding selectivity, and robust cyclicity for CO2 photoreduction to HCOOH. This research explores a robust route toward cost-effective, massive production of SACs for potential industrial applications.

CRP, IL-1α, IL-1ß, and IL-6 levels and the risk of breast cancer: a two-sample Mendelian randomization study.

Epidemiological studies have reported a positive association between chronic inflammation and cancer risk. However, the causal association between chronic inflammation and breast cancer (BC) risk remains unclear. Here, we performed a Mendelian randomization study to investigate the etiological role of chronic inflammation in BC risk. We acquired data regarding C-reactive protein (CRP), interleukin (IL)-1a, IL-1b, and IL-6 expression and BC related to single nucleotide polymorphisms (SNPs) from two larger consortia (the genome-wide association studies and the Breast Cancer Association Consortium). Next, we conducted the two-sample Mendelian randomization study to investigate the relationship of the abovementioned inflammatory factors with the incidence of BC. We found that genetically predicted CRP, IL-6, and IL-1a levels did not increase BC incidence (odds ratio (OR)CRP 1.06, 95% confidence interval (CI) 0.98-1.12, P = 0.2059, ORIL-6 1.05, 95% CI 0.95-1.16, P = 0.3297 and ORIL-1a 1.01, 95% CI 0.99-1.03, P = 0.2167). However, in subgroup analysis, genetically predicted IL-1b levels increased ER + BC incidence (OR 1.15, 95% CI 1.03-1.27, P = 0.0088). Our study suggested that genetically predicted IL-1b levels were found to increase ER + BC susceptibility. However, due to the support of only one SNP, heterogeneity and pleiotropy tests cannot be performed, which deserves further research.

Hyperbolic band topology with non-trivial second Chern numbers.

Topological band theory establishes a standardized framework for classifying different types of topological matters. Recent investigations have shown that hyperbolic lattices in non-Euclidean space can also be characterized by hyperbolic Bloch theorem. This theory promotes the investigation of hyperbolic band topology, where hyperbolic topological band insulators protected by first Chern numbers have been proposed. Here, we report a new finding on the construction of hyperbolic topological band insulators with a vanished first Chern number but a non-trivial second Chern number. Our model possesses the non-abelian translational symmetry of {8,8} hyperbolic tiling. By engineering intercell couplings and onsite potentials of sublattices in each unit cell, the non-trivial bandgaps with quantized second Chern numbers can appear. In experiments, we fabricate two types of finite hyperbolic circuit networks with periodic boundary conditions and partially open boundary conditions to detect hyperbolic topological band insulators. Our work suggests a new way to engineer hyperbolic topological states with higher-order topological invariants.

Comprehensive analysis of a cuproptosis-related ceRNA network implicates a potential endocrine therapy resistance mechanism in ER-positive breast cancer.

BACKGROUND: While adjuvant endocrine therapy (ET) may decrease the mortality rate of estrogen receptor-positive (ER+) breast cancer (BC), the likelihood of relapse and metastasis due to ET resistance remains high. Cuproptosis is a recently discovered regulated cell death (RCD), whose role in tumors has yet to be elucidated. Thus, there is a need to study its specific regulatory mechanism in resistance to ET in BC, to identify novel therapeutic targets. METHODS: The prognostic cuproptosis-related genes (CRGs) in ER+ BC were filtered by undergoing Cox regression and least absolute shrinkage and selection operator (LASSO) regression analyses in TCGA-BRCA, and a CRGs risk signature was constructed using the correlation coefficient. Immune infiltration analysis, immune function analysis, tumor microenvironment (TME) analysis, immune checkpoint analysis, immunotherapy response analysis, drug sensitivity analysis, and pathway activation analysis were carried out among the high- and low-risk groups in turn. The central CRG of cuproptosis in ER+ BC resistance to ET was acquired through the intersection of protein interaction network (PPI) analysis, genes differentially expressed (DEGs) between human BC cells LCC9 and MCF-7 (GSE159968), and CRGs with prognostic significance in TCGA-BRCA ER+ BC. The miRNAs upstream of the core CRGs were predicted based on the intersection of 4 databases, miRDB, RNA22, miRWalk, and RNAlnter. Candidate miRNAs consisted of the intersection of predicted miRNAs and miRNAs differentially expressed in the LCC9 and MCF-7 cell lines (GSE159979). Candidate lncRNAs were the intersection of the differential lncRNAs from the LCC9 and MCF-7 cell lines and the survival-related lncRNAs obtained from a univariate Cox regression analysis. Pearson's correlation analysis was performed between mRNA-miRNA, miRNA-lncRNA, and mRNA-lncRNA expression separately. RESULTS: We constructed A risk signature of 4-CRGs to predict the prognosis of ER+ BC in TCGA-BRCA, a risk score = DLD*0.378 + DBT*0.201 + DLAT*0.380 + ATP7A*0.447 was used as the definition of the formula. There were significant differences between the high- and low-risk groups based on the risk score of 4-CRGs in aspects of immune infiltration, immune function, expression levels of immune checkpoint genes, and signaling pathways. DLD was determined to be the central CRG of cuproptosis in ER+ BC resistance to ET through the intersection of the PPI network analysis, DEGs between LCC9 and MCF-7 and 4-CRGs. Two miRNAs hsa-miR-370-3p and hsa-miR-432-5p were found taking DLD mRNA as a target, and the lncRNA C6orf99 has been hypothesized to be a competitive endogenous RNA that regulates DLD mRNA expression by sponging off hsa-miR-370-3p and hsa-miR-432-5p. CONCLUSION: This study built a prognostic model based on genes related to cuproptosis in ER+ BC. We considered DLD to be the core gene associated with resistance to ET in ER+ BC via copper metabolism. The search for promising therapeutic targets led to the establishment of a cuproptosis-related ceRNA network C6orf99/hsa-miR-370-3p and hsa-miR-432-5p/DLD.