This paper studies the boundary observer design problem for the state estimation of the thermoacoustic system in a Rijke tube with nonlinear Heckl heat release. Firstly, the one-dimensional gas dynamics model of the Rijke tube with nonlinear Heckl heat release is set up to describe the thermoacoustic dynamic system. It can be transformed into a group of first-order hyperbolic partial differential equations with coupling boundary conditions through Riemann coordinate transformation and folding transformation. Then, a boundary observer based on in-domain point-wise pressure and velocity measurements is proposed, in which the boundary conditions are injected into a series of functions to be designed. Accordingly, the boundary conditions of the estimation error system can be decoupled by the design of boundary functions, thereby ensuring the global asymptotic stability of the estimation error system. Furthermore, the proposed design approach remains applicable even in a scenario where only the in-domain point-wise pressure measurements are available. Finally, the feasibility of the proposed boundary observer is verified by numerical simulations.

Recent studies of the emergent capabilities of transformer-based Natural Language Understanding (NLU) models have indicated that they have an understanding of lexical and compositional semantics.We provide evidence that suggests these claims should be taken with a grain of salt: we find that state-of-the-art Natural Language Inference (NLI) models are sensitive towards minor semantics preserving surface-form variations, which lead to sizable inconsistent model decisions during inference.Notably, this behaviour differs from valid and in-depth comprehension of compositional semantics, however does neither emerge when evaluating model accuracy on standard benchmarks nor when probing for syntactic, monotonic, and logically robust reasoning.We propose a novel framework to measure the extent of semantic sensitivity.To this end, we evaluate NLI models on adversarially generated examples containing minor semantics-preserving surface-form input noise.This is achieved using conditional text generation, with the explicit condition that the NLI model predicts the relationship between the original and adversarial inputs as a symmetric equivalence entailment.We systematically study the effects of the phenomenon across NLI models for in-and outof domain settings.Our experiments show that semantic sensitivity causes performance degradations of 12.92% and 23.71% average over in-and out-of-domain settings, respectively.We further perform ablation studies, analysing this phenomenon across models, datasets, and variations in inference and show that semantic sensitivity can lead to major inconsistency within model predictions.

MOTIVATION: In prognosis and survival studies, an important goal is to identify multi-biomarker panels with predictive power using molecular characteristics or clinical observations. Such analysis is often challenged by censored, small-sample-size, but high-dimensional genomic profiles or clinical data. Therefore, sophisticated models and algorithms are in pressing need. RESULTS: In this study, we propose a novel Area Under Curve (AUC) optimization method for multi-biomarker panel identification named Nearest Centroid Classifier for AUC optimization (NCC-AUC). Our method is motived by the connection between AUC score for classification accuracy evaluation and Harrell's concordance index in survival analysis. This connection allows us to convert the survival time regression problem to a binary classification problem. Then an optimization model is formulated to directly maximize AUC and meanwhile minimize the number of selected features to construct a predictor in the nearest centroid classifier framework. NCC-AUC shows its great performance by validating both in genomic data of breast cancer and clinical data of stage IB Non-Small-Cell Lung Cancer (NSCLC). For the genomic data, NCC-AUC outperforms Support Vector Machine (SVM) and Support Vector Machine-based Recursive Feature Elimination (SVM-RFE) in classification accuracy. It tends to select a multi-biomarker panel with low average redundancy and enriched biological meanings. Also NCC-AUC is more significant in separation of low and high risk cohorts than widely used Cox model (Cox proportional-hazards regression model) and L1-Cox model (L1 penalized in Cox model). These performance gains of NCC-AUC are quite robust across 5 subtypes of breast cancer. Further in an independent clinical data, NCC-AUC outperforms SVM and SVM-RFE in predictive accuracy and is consistently better than Cox model and L1-Cox model in grouping patients into high and low risk categories. CONCLUSION: In summary, NCC-AUC provides a rigorous optimization framework to systematically reveal multi-biomarker panel from genomic and clinical data. It can serve as a useful tool to identify prognostic biomarkers for survival analysis. AVAILABILITY AND IMPLEMENTATION: NCC-AUC is available at http://doc.aporc.org/wiki/NCC-AUC. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.