Operator Method Research Articles

Bilinear estimates for indexes on Bourgain spaces for the initial boundary-value problem

This paper concerns about the initial boundary-value problem (IBVP) with low regularities via the boundary integral operator method introduced by Bona–Sun–Zhang [Nonhomogeneous boundary-value problems for one-dimensional nonlinear Schrödinger equations. J Math Pures Appl. 2018;109:1–66] on Bourgain-type space, i.e. X s , b − space. Unlike initial value problems, the choice of index b for IBVPs on X s , b − space will need to be less or equal to 1 2 . In addition, for different indexes (i.e. -\\frac {1}{2} $ ]]> s > − 1 2 and s ≤ − 1 2 ), variety of extensions on the boundary integral operator in X s , b − space will be adapted which provides different requirements on b accordingly (i.e. b ≤ 1 2 and b < 1 2 ). In this article, we use the nonlinear Schrödinger equation with different quadratic nonlinearities as examples, 0, \\\\ u(x, 0)=\\varphi(x),\\quad u(0, t)=h(t), \\end{array}\\right. \\] ]]> { i u t + u xx + N i ( u , u ¯ ) = 0 , x , t > 0 , u ( x , 0 ) = φ ( x ) , u ( 0 , t ) = h ( t ) , where N 1 ( u , u ¯ ) = u u ¯ , N 2 ( u , u ¯ ) = u ¯ 2 , to establish well-posed theories for -\\frac {1}{4} $ ]]> s > − 1 4 and -\\frac {3}{4} $ ]]> s > − 3 4 respectively, based on bilinear estimates with different values of b in Bourgain space X s , 1 2 and X s , b ( b < 1 2 ) accordingly. Though similar results have been shown in [Cavalcante M. The initial boundary-value problem for some quadratic nonlinear Schrödinger equations on the half line, 2016] for b < 1 2 , based on Colliander–Kenig–Holmer's approach (see Holmer J. [The initial boundary-value problem for the 1-D nonlinear Schrödinger equation on the half-line. Differ Int Equ. 2005]; Colliander JE, Kenig CE. [The generalized Korteweg–de Vries equation on the half line. arXiv Mathematics e-prints, page math/0111294, Nov. 2001]), our idea follows from Tao's multiplier method [Tao T. Multi-linear weighted convolution of L 2 functions and applications to nonlinear dispersive equations, 2004] and the conclusion is slightly stronger.

Model predictive control parameter optimization method for autonomous vehicles

Aiming at the problem of insufficient tracking accuracy and long computational time of model predictive control algorithm in trajectory tracking of autonomous vehicles, a model predictive control parameter optimization method based on a nondominated sorting whale optimization algorithm was proposed. In this method, the parameter optimization problem of the model predictive control algorithm was transformed into a multiobjective optimization problem, with the predictive horizon, control horizon, and sample time as optimized objectives and the sum of squared lateral trajectory errors and computational time as optimized variables. The multiobjective optimization problem was solved using the nondominated sort whale optimization algorithm, and then the Pareto optimal solution set was obtained. The best solution was determined using the expert scoring method, continuous order weighted average operator method, game theory combination weighting method, and technique for order preference by similarity to the ideal solution method. Finally, the phase plane method is used to analyze the vehicle handling stability. The experimental results show that compared with the initial method, the lateral trajectory errors of the proposed method are reduced by 66.09% on average, and the computational time is reduced by 54.68% on average. Therefore, the proposed method is considered to be an effective method for parameter optimization of model predictive control.

Identifying the onset and decay of quasi-stationary families of almost-invariant sets with an application to atmospheric blocking events.

Macroscopic features of dynamical systems such as almost-invariant sets and coherent sets provide crucial high-level information on how the dynamics organizes phase space. We introduce a method to identify time-parameterized families of almost-invariant sets in time-dependent dynamical systems, as well as the families' emergence and disappearance. In contrast to coherent sets, which may freely move about in phase space over time, our technique focuses on families of metastable sets that are quasi-stationary in space. Our straightforward approach extends successful transfer operator methods for almost-invariant sets to time-dependent dynamics and utilizes the Ulam scheme for the generator of the transfer operator on a time-expanded domain. The new methodology is illustrated with an idealized fluid flow and with atmospheric velocity data. We identify atmospheric blocking events in the 2003 European heatwave and compare our technique to existing geophysical methods of blocking diagnosis.

Asymptotic and Probabilistic Perturbation Analysis of Controllable Subspaces

In this paper, we consider the sensitivity of the controllable subspaces of single-input linear control systems to small perturbations of the system matrices. The analysis is based on the strict component-wise asymptotic bounds for the matrix of the orthogonal transformation to canonical form derived by the method of the splitting operators. The asymptotic bounds are used to obtain probabilistic bounds on the angles between perturbed and unperturbed controllable subspaces implementing the Markoff inequality. It is demonstrated that the probability bounds allow us to obtain sensitivity estimates, which are much tighter than the usual deterministic bounds. The analysis is illustrated by a high-order example.

Modified quantum regression theorem and consistency with Kubo-Martin-Schwinger condition

Abstract We show that the long-time limit of the two-point correlation function obtained via the standard quantum regression theorem, a standard tool to compute correlation functions in open quantum systems, does not respect the Kubo-Martin-Schwinger equilibrium condition to the non-zero order of the system-bath coupling. We then follow the recently developed Heisenberg operator method for open quantum systems and by applying a ``{\it weak}" Markov approximation, derive a new modified version of the quantum regression theorem that not only respects the KMS condition but further predicts exact answers for certain paradigmatic models in specific limits. We also show that in cases where the modified quantum regression theorem does not match with exact answers, it always performs better than the standard quantum regression theorem.

Interpretable machine learning model based on CT semantic features and radiomics features to preoperatively predict Ki-67 expression in gastrointestinal stromal tumors

To develop and validate a machine learning (ML) model which combined computed tomography (CT) semantic and radiomics features to preoperatively predict Ki-67 expression in gastrointestinal stromal tumors (GISTs) patients. We retrospectively collected the clinical, imaging and pathological data of 149 GISTs patients. We randomly assigned the patients in a ratio of 7:3 to a training set (104 cases) and a validation (45 cases) set. We divided the patients into low and high Ki-67 expression group according to postoperative pathology. CT semantic features were analyzed from preoperative enhancement CT images and radiomics features were extracted from venous phase-enhanced images. We used intraclass correlation coefficient, maximal relevance and minimal redundancy and least absolute shrinkage and selection operator method to screen radiomics features and build radiomics label. 6 ML models were used for model construction. Receiver operating characteristic curves were used to evaluate the predictive efficiency of ML models. SHAP analysis was used to explain the contribution of different variables and their risk threshold. AUC of radscores in predicting Ki-67 expression of GIST patients were 0.749 and 0.729 in training and validation set. Among the 6 ML models, SVM exhibited best prediction accuracy. AUC of SVM model in predicting Ki-67 expression of GIST patients were 0.840, 0.767 and 0.832 in training, validation and test set. SHAP analysis showed that radscores and tumor diameter had highly positive contribution to the model. Therefore, the interpretable SVM model can predict Ki-67 expression of GISTs patients individually before surgery, which can provide reliable imaging biomarkers for clinical treatment decisions.

Utility of the 2019 EULAR/ACR SLE classification criteria for predicting mortality and hospitalisation: development and cross-validation of ominosity score

ObjectiveThe 2019 European Alliance of Associations for Rheumatology (EULAR)/American College of Rheumatology (ACR) systemic lupus erythematosus (SLE) classification criteria score (≥20 points) has been associated with poor outcomes. We aimed...

Coexisting metabolic dysfunction-associated steatotic liver disease exacerbates in-hospital outcomes in patients with heat stroke.

This study aimed to investigate the impact of coexisting metabolic dysfunction-associated steatotic liver disease (MASLD) on in-hospital mortality and organ injury markers in patients with heat stroke (HS). HS patients were retrospectively identified between July 1, 2022 and September 30, 2023 at West China Hospital, Sichuan University. Baseline characteristics, such as demographics, initial vital signs, and organ functional indicators were collected. Outcome events included organ injury and in-hospital mortality. The Least Absolute Shrinkage and Selection Operator (Lasso) method was employed to identify the optimal predictors for in-hospital mortality in HS patients. Subsequently, multivariable logistic regression analysis was performed to assess the relationship between the presence of MASLD and in-hospital mortality as well as organ function indicators. A total of 112 patients were included in the study, in which 27 (24.1%) had coexisting MASLD. Compared to those without MASLD, patients with MASLD had higher levels of various organ injury markers such as aspartate aminotransferase, urea nitrogen, serum cystatin C, creatinine, uric acid, myoglobin, creatine kinase and its isoenzymes upon admission (P < 0.05). The multivariable Logistic regression analysis indicated that the presence of MASLD is an independent risk factor for in-hospital mortality in HS patients. This study firstly indicated that coexisting MASLD may exacerbate organ injury in HS patients and serve as an independent risk factor for in-hospital mortality.

Predicting thyroid involvement in primary Sjögren's syndrome: development and validation of a predictive nomogram.

Patients with Primary Sjögren's syndrome (pSS) are at a higher risk of thyroid disorders than the general population. This retrospective analysis of 202 patients with pSS was conducted to uncover risk factors associated with thyroid involvement and to create a predictive model for this condition. We analyzed 202 patients with pSS from Guang'anmen Hospital, China Academy of Chinese Medical Sciences, with 105 cases of thyroid involvement and 97 without. The Least Absolute Shrinkage and Selection Operator method was used to identify key variables for our risk model. These variables were then subjected to multivariate logistic regression to develop the model. The accuracy of the model was assessed through the C-index, receiver operating characteristic curves, calibration plots, and decision curve analysis, with internal validation via bootstrapping. High-sensitivity C-reactive protein (HCRP), pulmonary disease, pharyngeal dryness, forgetfulness, night sweats, hyperuricemia, nasal dryness, anxiety, Ro52, and aspartate aminotransferase (AST) were incorporated into the nomogram. The model showed robust discrimination and calibration abilities. Decision curve analysis indicated the clinical utility of our nomogram in intervening on the probability thresholds of thyroid disease. By integrating HCRP, pulmonary disease, pharyngeal dryness, forgetfulness, night sweats, hyperuricemia, nasal dryness, anxiety, Ro52, and AST, our thyroid risk nomogram can predict the risk of thyroid involvement in patients with pSS, aiding in more informed treatment strategies.

Computational Study of Carbon Dioxide Capture by Tertiary Amines.

The reaction mechanisms and corresponding structure-activity relationships of tertiary amines with respect to CO2 capture have been investigated using density functional theory (DFT) calculations. The reaction mechanism for CO2 capture via base-catalyzed hydration to form bicarbonate is proposed to proceed in a single step involving proton transfer and the formation of a carbon-oxygen bond. Based on the height of the reaction barriers, we suggest that amines containing side chains with the ethyl group, along with a single hydroxyl group, and cyclic structures, are especially active for CO2 capture. The activation barrier is shown to be a descriptor for predicting the experimental CO2 loading values. To enhance the prediction accuracy for CO2 loading, we employ the sure-independence screening and sparsifying operator (SISSO) method, which can scan a large pool of mathematical terms stemming from combining DFT-derived descriptors to select the superior ones. Thus, we can predict the CO2 loading with acceptable accuracy from the obtained mathematical expression. Since the computational workload of applying this expression is negligible, this facilitates high-throughput screening and accelerates the design of tertiary amines for CO2 capture.

Inverted oscillator: quantum discrete spectrum

Abstract We use the invariant operator method to investigate the quantum characteristics of the inverted oscillator. We introduce a unitary transformation that maps a time-dependent general Hermitian linear invariant operator to a time-independent one, which describes a harmonic oscillator with a unit mass and a constant frequency. Our investigation includes three distinguished cases: negative frequency, zero frequency, and positive frequency. Our most interesting result concerns the last case. For the case of negative frequency, we propose a new inner product by the introduction of the new metric operator η. Coherent state for this case will be constructed.

Simulating the Landau-Zener sweep in deeply sub-Ohmic environments.

With the goal to study dissipative Landau-Zener (LZ) sweeps in realistic solid-state qubits, we utilize novel methods from non-Markovian open quantum system dynamics that enable reliable long-time simulations for sub-Ohmic environments. In particular, we combine a novel representation of the dynamical propagator, the uniform time evolving matrix product operator method, with a stochastic realization of finite temperature fluctuations. The latter greatly reduces the computational cost for the matrix product operator approach, enabling convergence in the experimentally relevant deeply sub-Ohmic regime. Our method allows the exact simulation of dynamical protocols with long operation times, such as the LZ sweep, in challenging parameter regimes that are realized in current experimental platforms.

Novel insights of disulfidptosis-mediated immune microenvironment regulation in atherosclerosis based on bioinformatics analyses

Atherosclerosis (AS) is the leading cause of coronary heart disease, which is the primary cause of death worldwide. Recent studies have identified disulfidptosis as a new type of cell death that may be involved in onset and development of many diseases. However, the role of disulfidptosis in AS is not clear. In this study, bioinformatics analysis and experiments in vivo and in vitro were performed to evaluate the potential relationship between disulfidptosis and AS. AS-related sequencing data were obtained from the Gene Expression Omnibus (GEO). Bioinformatics techniques were used to evaluate differentially expressed genes (DEGs) associated with disulfidptosis-related AS. Hub genes were screened using least absolute shrinkage and selection operator (LASSO) and random forests (RF) methods. In addition, we established a foam cell model in vitro and an AS mouse model in vivo to verify the expressions of hub genes. In addition, we constructed a diagnostic nomogram with hub genes to predict progression of AS. Finally, the consensus clustering method was used to establish two different subtypes, and associations between subtypes and immunity were explored. As the results, 9 disulfidptosis-related AS DEGs were identified from GSE28829 and GSE43292 datasets. Evaluation of DEGs using LASSO and RF methods resulted in identification of 4 hub genes (CAPZB, DSTN, MYL6, PDLIM1), which were analyzed for diagnostic value using ROC curve analysis and verified in vitro and in vivo. Furthermore, a nomogram including hub genes was established that accurately predicted the occurrence of AS. The consensus clustering algorithm was used to separate patients with early atherosclerotic plaques and patients with advanced atherosclerotic plaques into two disulfidptosis subtypes. Cluster B displayed higher levels of infiltrating immune cells, which indicated that patients in cluster B may have a positive immune response for progression of AS. In summary, disulfidptosis-related genes including CAPZB, DSTN, MYL6, and PDLIM1 may be diagnostic markers and therapeutic targets for AS. In addition, these genes are closely related to immune cells, which may inform immunotherapy for AS.

Investigation of risk signatures associated with anoikis in thyroid cancer through integrated transcriptome and Mendelian randomization analysis.

Anoikis is intricately associated with the malignant progression of cancer. Thyroid cancer (THCA) is the most common endocrine tumor, metastasis is closely related to treatment response and prognosis of THCA. Hence, it is imperative to comprehensively identify predictive prognostic genes and novel molecular targets for effective THCA therapy. Differential expression analysis and weighted gene co-expression network analysis (WGCNA) were utilized to mine differentially expressed anoikis-related (DE-ARGs). Then, the prognostic genes were identified and a risk signature was constructed for THCA using univariate Cox analysis and least absolute shrinkage and selection operator (LASSO) method. Furthermore, the associations between risk signature and immune infiltration, immunotherapy, as well as potential mechanisms of action were determined using multiple R packages and Wilcoxon test. Finally, Mendelian randomized (MR) analysis was conducted to investigate the causal relationship between the prognostic genes and THCA. In total, six prognostic genes (LRRC75A, METTL7B, ADRA1B, TPD52L1, TNFRSF10C, and CXCL8) related to anoikis were identified, and the corresponding risk signature were constructed to assess the survival time of THCA patients. Immunocorrelation analysis demonstrated the anoikis-relevant risk signature could be used to evaluate immunotherapy effects in THCA patients, and the infiltration of immune cells was correlated with the degree of risk in THCA patients. According to two-sample MR analysis, there was the significant causal relationship between CXCL8 and THCA (odds ratio [OR] > 1 & p< 0.05), and the increase of its gene expression would lead to an increased risk of THCA. Furthermore, real-time quantitative polymerase chain reaction (RT-qPCR) confirmed the upregulated expression patterns of these prognostic genes in THCA tissues. In conclusion, we constructed the risk signature related to anoikis for THCA, which might have important clinical significance for improving the quality of life and treatment effect of THCA patients.

Radiomics analysis in differentiating osteosarcoma and chondrosarcoma based on T2-weighted imaging and contrast-enhanced T1-weighted imaging

This study was performed to investigate the diagnostic value of radiomics models constructed by fat suppressed T2-weighted imaging (T2WI-FS) and contrast-enhanced T1-weighted imaging (CET1) based on magnetic resonance imaging (MRI) for differentiation of osteosarcoma (OS) and chondrosarcoma (CS). In this retrospective cohort study, we included all inpatients with pathologically confirmed OS or CS from Second Xiangya Hospital of Central South University (Hunan, China) as of October 2020. Demographic and imaging variables were extracted from electronic medical records and compared between OS and CS group. Totals of 530 radiomics features were extracted from CET1 and T2WI-FS sequences based on MRI. The least absolute shrinkage and selection operator (LASSO) method was used for screening and dimensionality reduction of the radiomics model. Multivariate logistic regression analysis was performed to construct the radiomics model, and receiver operating characteristic curve (ROC) was generated to evaluate the diagnostic accuracy of the radiomics model. The training cohort and validation cohort included 87 and 29 patients, respectively. 8 CET1 features and 15 T2WI-FS features were screened based on the radiomics features. In the training group, the area under the receiver-operator characteristic curve (AUC) value for CET1 and T2WI-FS sequences in the radiomics model was 0.894 (95% CI 0.817–0.970) and 0.970 (95% CI 0.940–0.999), respectively. In the validation group, the AUC value for CET1 and T2WI-FS sequences in the radiomics model was 0.821 (95% CI 0.642–1.000) and 0.899 (95% CI 0.785–1.000), respectively. In this study, we developed a radiomics model based on T2WI-FS and CET1 sequences to differentiate between OS and CS. This model exhibits good performance and can help clinicians make decisions and optimize the use of healthcare resources.

Research on Grading Method for Jin Guan Apples based on Machine Vision

As the demand for apples increases, so do the expectations for apple quality. To address the time-consuming and labor-intensive nature of apple grading, this paper focuses on the Jin-Guan apple variety and applies machine vision techniques to extract three key features: maximum transverse diameter, shape index, and surface color. A backpropagation neural network (BP neural network) is employed to achieve accurate grading of the apples. First, by analyzing the relationships between the RGB color space components in the original images, the apple images are extracted using the method of comparing the R channel value to the B channel value. Gaussian filtering is then applied to remove image noise. Second, the complete apple contour is extracted using an improved Sobel operator method. The maximum transverse diameter and shape index of the apple are calculated based on the pixel coordinates along the contour, and the apple's surface color is determined using a nearest-neighbor classifier. Finally, a BP neural network model is established and trained to perform the grading. A total of 160 apples were used for training, and 140 for testing. The results show that the grading accuracy reached 92.14%, and the grading efficiency was approximately 1.7 times that of a skilled human grader. This grading method provides a technical reference for apple grading processes.

Macro-Driven Stock Market Volatility Prediction: Insights from a New Hybrid Machine Learning Approach

This study comprehensively investigates stock market volatility based on over one hundred monthly macroeconomic variables, applying machine learning models. Methodological contribution integrating the random forest (RF) with the least absolute shrinkage and selection operator methods (LASSO). Importantly, the RF-LASSO model can robustly achieve the best forecasting performance under different circumstances. In addition, we focus on model explanation from different perspectives based on permutation importance and shapley additive explanation (SHAP) methods. This study illuminates novel insights into the realm of stock market volatility, harnessing the transformative potential of machine learning methodologies.

Can we skip invasive biopsy of sentinel lymph nodes? A preliminary investigation to predict sentinel lymph node status using PET/CT-based radiomics

BackgroundSentinel lymph node (SLN) biopsy (SLNB) is considered the gold standard for detecting SLN metastases in patients with invasive ductal breast cancer (IDC). However, SLNB is invasive and associated with several complications. Thus, this study aimed to evaluate the diagnostic performance of a non-invasive radiomics analysis utilizing 2-deoxy-2-[18F]fluoro-d-glucose positron emission tomography/computed tomography (18F-FDG-PET/CT) for assessing SLN metastasis in IDC patients.MethodsThis retrospective study included 132 patients with biopsy-confirmed IDC, who underwent 18F-FDG PET/CT scans prior to mastectomy or breast-conserving surgery with SLNB. Tumor resection or SLNB was conducted within one-week post-scan. Clinical data and metabolic parameters were analyzed to identify independent SLN metastasis predictors. Radiomic features were extracted from each PET volume of interest (VOI) and CT-VOI. Feature selection involved univariate and multivariate logistic regression analysis, and the least absolute shrinkage and selection operator (LASSO) method. Three models were developed to predict SLN status using the random forest (RF), decision tree (DT), and k-Nearest Neighbors (KNN) classifiers. Model performance was assessed using the area under the receiver operating characteristic curve (AUC).ResultsThe study included 91 cases (32 SLN-positive and 59 SLN-negative patients) in the training cohort and 41 cases (29 SLN-positive and 12 SLN-negative patients) in the validation cohort. Multivariate logistic regression analysis identified Ki 67 and TLG as independent predictors of SLN status. Five PET-derived features, three CT-derived features, and two clinical variables were selected for model development. The AUC values of the RF, KNN, and DT models for the training cohort were 0.887, 0.849, and 0.824, respectively, and for the validation cohort were 0.856, 0.830, and 0.819, respectively. The RF model demonstrated the highest accuracy for the preoperative prediction of SLN metastasis in IDC patients.ConclusionThe PET-CT radiomics approach may offer robust and non-invasive predictors for SLN status in IDC patients, potentially aiding in the planning of personalized treatment strategies for IDC patients.

Exactly solvable time-dependent oscillator family

This paper proposes a method for constructing exactly solvable time-dependent oscillator families based on the invariant operator method and the duality method. An exactly solvable time-dependent oscillator family contains an infinite number of exactly solvable time-dependent oscillators. As a byproduct, we also construct exactly solvable Ermakov–Pinney equation families.

Generalized Langevin dynamics for single beads in linear elastic networks.

We derive generalized Langevin equations(GLEs) for single beads in linear elastic networks. In particular, the derivations of the GLEs are conducted without employing normal modes, resulting in two distinct representations in terms of resistance and mobility kernels. The fluctuation-dissipation relations are also confirmed for both GLEs. Subsequently, we demonstrate that these two representations are interconnected via Laplace transforms. Furthermore, another GLE is derived by utilizing a projection operator method, and it is shown that the equationobtained through the projection scheme is consistent with the GLE with the resistance kernel. As simple examples, the general theory is applied to the Rouse model and the ring polymer, where the GLEs with the resistance and mobility kernels are explicitly derived for arbitrary positions of the tagged bead in these models. Finally, the GLE with the mobility kernel is also derived for the elastic network with hydrodynamic interactions under the pre-averaging approximation.