A globally consistent nonlinear least squares estimator for identification of nonlinear rational systems

© 2016 Elsevier Ltd This paper considers identification of nonlinear rational systems defined as the ratio of two nonlinear functions of past inputs and outputs. Despite its long history, a globally consistent identification algorithm remains illusive. This paper proposes a globally convergent identification algorithm for such nonlinear rational systems. To the best of our knowledge, this is the first globally convergent algorithm for the nonlinear rational systems. The technique employed is a two-step estimator. Though two-step estimators are known to produce consistent nonlinear least squares estimates if a N consistent estimate can be determined in the first step, how to find such a N consistent estimate in the first step for nonlinear rational systems is nontrivial and is not answered by any two-step estimators. The technical contribution of the paper is to develop a globally consistent estimator for nonlinear rational systems in the first step. This is achieved by involving model transformation, bias analysis, noise variance estimation, and bias compensation in the paper. Two simulation examples and a practical example are provided to verify the good performance of the proposed two-step estimator

LncRNA MALAT1 Promotes Cancer Metastasis in Osteosarcoma via Activation of the PI3K-Akt Signaling Pathway

Background/Aims: LncRNAs have been reported to be vital regulators of the progression of osteosarcoma, although the underlying mechanisms are not completely understood. Methods: The levels of MALAT1 and miR-129-5p expression were measured using qRT-PCR. Cell growth was determined using the CCK-8 and colony formation assays. Cell migration and invasion were detected using the wound healing and Transwell invasion assays, respectively. Tumor growth was determined with a xenograft model. Results: MALAT1 was significantly up-regulated in osteosarcoma tissues compared with adjacent non-tumor soft tissues. Overexpression of MALAT1 promoted osteosarcoma cell proliferation, migration, and invasion in vitro and enhanced tumor growth in a tumor xenograft mouse model. MALAT1 promoted osteosarcoma progression by modulating stem cell-like properties. Moreover, rescue experiment and luciferase reporter assay results indicated that MALAT1 modulates RET expression by sponging miR-129-5p in osteosarcomas. Furthermore, MALAT1 augmented the expression of downstream proteins of the RET-Akt pathway. MALAT1 was consistently significantly increased in osteosarcoma tissues and MALAT1 expression was positively correlated with tumor size and metastasis. High expression of MALAT1 was significantly associated with poor outcomes in patients with osteosarcomas. MALAT1 expression was positively related to RET and negatively related to miR-129-5p in osteosarcoma samples and xenograft tumors. MALAT1 functioned as an oncogenic lncRNA in osteosarcomas and was as an independent prognostic indicator. Conclusion: Our data revealed for the first time that MALAT1 increases stem cell-like properties by up-regulating RET via sponging miR-129-5p, and thus activates the PI3K-Akt signaling pathway and provides potential therapeutic targets for osteosarcoma treatment

Global and asymptotically efficient identification of nonlinear rational systems via a two-step method

Identification of nonlinear rational systems defined as the ratio of two nonlinear functions of past inputs and outputs is considered in this paper. Although this problem has a long history, there is still lack of a globally consistent identification algorithm for such identification problem. This paper develops a globally consistent algorithm by the following steps: model transformation, bias analysis, noise variance estimation, and compensation. First, the paper studies the prediction error type estimator (nonlinear least square estimators) and the corresponding solving algorithm (Gauss-Newton algorithms). It is shown that the Gauss-Newton algorithm is locally convergent but actually asymptotically efficient by calculating the Cramér-Rao lower bound under Gaussian observation noises. This motivates that a global and asymptotically efficient estimator can be constructed by combining the proposed globally consistent estimator with the Gauss-Newton algorithm. So, a two-step method is proposed, which consists of first executing the globally consistent algorithm and then applying the Gauss-Newton algorithm with the consistent estimate serving as the initial value. A simulation example is provided to verify the good performance of the proposed two-step method

Consistent variable selection for high-dimensional nonparametric additive nonlinear systems

In this paper, the problem of variable selection is addressed for high-dimensional nonparametric additive nonlinear systems. The purpose of variable selection is to determine contributing additive functions and to remove non-contributing ones from the underlying nonlinear system. A two-step method is developed to conduct variable selection. The first step is concerned with estimating each additive function by virtue of kernel-based nonparametric approaches. The second step is to apply a nonnegative garrote estimator to identify which additive functions are nonzero in terms of the obtained non-parametric estimates of each function. The proposed variable selection method is workable without suffering from the curse of dimensionality, and it is able to find the correct variables with probability one under weak conditions as the sample size approaches infinity. The good performance of the proposed variable selection method is demonstrated by a numerical example

Variable selection and identification of high-dimensional nonparametric additive nonlinear systems

This paper considers variable selection and identification of dynamic additive nonlinear systems via kernel-based nonparametric approaches, where the number of variables and additive functions may be large. Variable selection aims to find which additive functions contribute and which do not. The proposed variable selection consists of two successive steps. At the first step, one estimates each additive function by kernel-based nonparametric identification approaches without suffering from the curse of dimensionality. At the second step, a nonnegative garrote estimator is applied to identify which additive functions are nonzero by utilizing the obtained nonparametric estimates of each function. Under weak conditions, the nonparametric estimates of each additive function can achieve the same asymptotic properties as for one-dimensional nonparametric identification based on kernel functions. It is also established that the nonnegative garrote estimator turns a consistent estimate for each additive function into a consistent variable selection with probability one as the number of samples tends to infinity. Two simulation examples are presented to verify the effectiveness of the variable selection and identification approaches proposed in the paper

Establishment of a staging system for visceral sarcoma

Abstract Background Visceral sarcoma is a rare malignancy with a poor prognosis. However, there is no recommended prognostic staging system for the malignant disease. Method We analyzed the data of patients diagnosed with primary soft tissue sarcoma (STS) of the abdomen and thoracic visceral organs between 2006 and 2017 at our hospital. Prognostic factors (size, tumor grade, and lymph node metastasis) were analyzed in our cohort (n = 203) and the SEER validation cohort (n = 5826). Results Tumor size, grade, and lymph node metastasis were important prognostic factors for visceral sarcoma in both our and the SEER cohorts. Based on these prognostic factors, we established a new staging system for visceral sarcoma, by which patients could be stratified into clinically meaningful and non‐overlapping stages in both our cohort and the SEER validation series. Moreover, the area under the curve (AUC) value of the staging system for 5‐year survival was 0.84 (95% CI: 0.78–0.89) in our series and 0.80 (95% CI: 0.79–0.81) in SEER series, respectively. In addition, compared with the widely used FIGO staging system for female genital sarcoma, the visceral sarcoma staging system could more effectively and reliably stratify patients into four different prognostic groups. Conclusions The visceral sarcoma staging system is applicable for STS of the abdomen and thoracic visceral organs and is better than the current FIGO staging system for female genital sarcoma and should be incorporated into the AJCC Cancer Staging Manual

(Variable selection in nonlinear non-parametric system identification)

This paper considers a problem of variable selection for a high dimensional nonlinear non-parametric system. Different algorithms are proposed for cases when the number of observed data increasing to infinity, being finite, and the nonlinear system being additive. The theoretical properties of the proposed algorithms are obtained, which are validated by simulation examples. The algorithms find the relationship between the input and output variables, and further the inter-dependence of input variables so that the importance of the input variables can be established

Recursive identification of Hammerstein systems : convergence rate and asymptotic normality

In this work, recursive identification algorithms are developed for Hammerstein systems under the conditions considerably weaker than those in the existing literature. For example, orders of linear subsystems may be unknown and no specific conditions are imposed on their moving average part. The recursive algorithms for estimating both linear and nonlinear parts are based on stochastic approximation and kernel functions. Almost sure convergence and strong convergence rates are derived for all estimates. In addition, the asymptotic normality of the estimates for the nonlinear part is also established. The nonlinearity considered in the paper is more general than those discussed in the previous papers. A numerical example verifies the theoretical analysis with simulation results