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中国科学院数学与系统科学研究院Sun, 26 Mar 2023 19:39:28 GMT2023-03-26T19:39:28ZEddy heat exchange at the boundary under white noise turbulence
http://ir.amss.ac.cn:80/handle/2S8OKBNM/61575
Title: Eddy heat exchange at the boundary under white noise turbulence
Authors: Flandoli; Galeati, L; Luo, DJ
Description: <p>We prove the existence of an eddy heat diffusion coefficient coming from an idealized model of turbulent fluid. A difficulty lies in the presence of a boundary, with also turbulent mixing and the eddy diffusion coefficient going to zero at the boundary. Nevertheless, enhanced diffusion takes place. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.</p>Tue, 14 Mar 2023 04:37:46 GMThttp://ir.amss.ac.cn:80/handle/2S8OKBNM/615752023-03-14T04:37:46ZON IDENTIFICATION OF BOOLEAN CONTROL NETWORKS
http://ir.amss.ac.cn:80/handle/2S8OKBNM/61572
Title: ON IDENTIFICATION OF BOOLEAN CONTROL NETWORKS
Authors: Wang, Biao; Feng, Jun-e; Cheng, Daizhan
Description: A new analytical framework consisting of two phenomena, a single sample and multiple samples, is proposed to formulate the identification problem of Boolean control networks (BCNs) systematically and comprehensively. Under this framework, the existing works on identification can be categorized as special cases of these two phenomena. Several effective criteria for determining the identifiability and the corresponding identification algorithms are proposed. Two novel and important results are derived for the multiple-samples case: (1) A Boolean network is identifiable if and only if it is observable. (2) A BCN is identifiable if it is O1-observable, where O1-observability is the most general form of the existing observability terms. In addition, remarks present some challenging future research and contain a preliminary attempt about how to identify unobservable systems.Tue, 07 Feb 2023 00:57:00 GMThttp://ir.amss.ac.cn:80/handle/2S8OKBNM/615722023-02-07T00:57:00ZVortex patch problem for steady lake equation
http://ir.amss.ac.cn:80/handle/2S8OKBNM/61569
Title: Vortex patch problem for steady lake equation
Authors: Cao, Daomin; Qin, Guolin; Zou, Changjun
Description: We study the vortex patch problem for the steady lake equation in a bounded domain and construct three different kinds of solutions where the vorticity concentrates in the domain or near the boundary. Our approach is based on the Lyapunov-Schmidt reduction, which transforms the construction into a problem of seeking critical points for a function related to the kinetic energy. The method in this paper has a wide applicability and can be used to deal with general elliptic equations in divergence form with Heaviside nonlinearity. Published under an exclusive license by AIP Publishing.Tue, 07 Feb 2023 00:57:00 GMThttp://ir.amss.ac.cn:80/handle/2S8OKBNM/615692023-02-07T00:57:00ZStudy on convex optimization with least constraint violation under a general measure
http://ir.amss.ac.cn:80/handle/2S8OKBNM/61566
Title: Study on convex optimization with least constraint violation under a general measure
Authors: Dai, Yu-Hong; Zhang, Liwei
Description: Optimization problems with least constraint violation have many important practical backgrounds. The related works in the literature normally focus on the norm square measure function and the classical augmented Lagrangian method is proved to be suitable for finding an approximate solution. This paper considers the constrained convex optimization problem with the least constraint violation under a general measure function. The properties of the conjugate dual associated with the measure function of the shifted problem are discussed through the relations between the dual function and the optimal value function. The differentiability of the dual function associated with the measure function is proved. The properties of augmented Lagrangian method induced by the measure function are characterized in terms of the dual function. The optimality conditions for the problem with the least constraint violation are established in term of the augmented Lagrangian. It is shown that the augmented Lagrangian method has the properties that the sequence of shift measure values is decreasing, the sequence of multipliers is unbounded, and the sequence of shifts converges to the least violated shift under an extra assumption.Tue, 07 Feb 2023 00:57:00 GMThttp://ir.amss.ac.cn:80/handle/2S8OKBNM/615662023-02-07T00:57:00ZStable solitons and interactions of the logarithmic nonlinear Schrodinger equation with two PT-symmetric non-periodic potentials<br>
http://ir.amss.ac.cn:80/handle/2S8OKBNM/61560
Title: Stable solitons and interactions of the logarithmic nonlinear Schrodinger equation with two PT-symmetric non-periodic potentials<br>
Authors: Zhou, Zijian; Song, Jin; Weng, Weifang; Yan, Zhenya
Description: In this paper, we consider two types of PT-symmetric non-periodic potentials (PT symmetric harmonic potential and harmonic-Gaussian potential) in the logarithmic nonlinear Schrodinger (LNLS) equation. The exact solitons are found, and shown to be stable for some parameter regions. The interactions are studied between two solitons in the LNLS equation with the two types of PT-symmetric potentials. Moreover, we also study the excitations of solitons in the LNLS equation with the PT-symmetric potentials containing the time-dependent functions. (C) 2022 Elsevier Ltd. All rights reserved.Tue, 07 Feb 2023 00:56:59 GMThttp://ir.amss.ac.cn:80/handle/2S8OKBNM/615602023-02-07T00:56:59ZDISTRIBUTED ORDER ESTIMATION OF ARX MODEL UNDER
http://ir.amss.ac.cn:80/handle/2S8OKBNM/61563
Title: DISTRIBUTED ORDER ESTIMATION OF ARX MODEL UNDER
Authors: Gan, D. I. E.; Liu, Zhixin
Description: In this paper, we consider the distributed estimation problem of a linear stochastic system described by an autoregressive model with exogenous inputs when both the system orders and parameters are unknown. We design distributed algorithms to estimate the unknown orders and parameters by combining the proposed local information criterion with the distributed least squares method. The simultaneous estimation for both the system orders and parameters brings challenges for the theoretical analysis. Some analysis techniques, such as double array martingale limit theory, stochastic Lyapunov functions, and martingale convergence theorems are employed. For the case where the upper bounds of the true orders are available, we introduce a cooperative excitation condition, under which the strong consistency of the estimation for the orders and parameters is established. Moreover, for the case where the upper bounds of true orders are unknown, a similar distributed algorithm is proposed to estimate both the orders and parameters, and the corresponding convergence analysis for the proposed algorithm is provided. We remark that our results are obtained without relying on the independency or stationarity assumptions of regression vectors, and the cooperative excitation conditions can show that all sensors can cooperate to fulfill the estimation task even though any individual sensor cannot.Tue, 07 Feb 2023 00:56:59 GMThttp://ir.amss.ac.cn:80/handle/2S8OKBNM/615632023-02-07T00:56:59ZOn arithmetic properties of Cantor sets
http://ir.amss.ac.cn:80/handle/2S8OKBNM/61557
Title: On arithmetic properties of Cantor sets
Authors: Cui, Lu; Ma, Minghui
Description: In this paper, we study three types of Cantor sets. For any integer m >= 4, we show that every real number in [0, k] is the sum of at most k m-th powers of elements in the Cantor ternary set C for some positive integer k, and the smallest such k is 2(m). Moreover, we generalize this result to the middle-1/alpha Cantor set for 1 < alpha < 2 + root 5 and m sufficiently large. For the naturally embedded image W of the Cantor dust C x C into the complex plane C, we prove that for any integer m >= 3, every element in the closed unit disk in C can be written as the sum of at most 2(m+8) m-th powers of elements in W. At last, some similar results on p-adic Cantor sets are also obtained.Tue, 07 Feb 2023 00:56:58 GMThttp://ir.amss.ac.cn:80/handle/2S8OKBNM/615572023-02-07T00:56:58ZPrediction of the transcription factor binding sites with meta-learning
http://ir.amss.ac.cn:80/handle/2S8OKBNM/61554
Title: Prediction of the transcription factor binding sites with meta-learning
Authors: Jing, Fang; Zhang, Shao-Wu; Zhang, Shihua
Description: With the accumulation of ChIP-seq data, convolution neural network (CNN)-based methods have been proposed for predicting transcription factor binding sites (TFBSs). However, biological experimental data are noisy, and are often treated as ground truth for both training and testing. Particularly, existing classification methods ignore the false positive and false negative which are caused by the error in the peak calling stage, and therefore, they can easily overfit to biased training data. It leads to inaccurate identification and inability to reveal the rules of governing protein-DNA binding. To address this issue, we proposed a meta learning-based CNN method (namely TFBS_MLCNN or MLCNN for short) for suppressing the influence of noisy labels data and accurately recognizing TFBSs from ChIP-seq data. Guided by a small amount of unbiased meta-data, MLCNN can adaptively learn an explicit weighting function from ChIP-seq data and update the parameter of classifier simultaneously. The weighting function overcomes the influence of biased training data on classifier by assigning a weight to each sample according to its training loss. The experimental results on 424 ChIP-seq datasets show that MLCNN not only outperforms other existing state-of-the-art CNN methods, but can also detect noisy samples which are given the small weights to suppress them. The suppression ability to the noisy samples can be revealed through the visualization of samples' weights. Several case studies demonstrate that MLCNN has superior performance to others.Tue, 07 Feb 2023 00:56:58 GMThttp://ir.amss.ac.cn:80/handle/2S8OKBNM/615542023-02-07T00:56:58ZLithology Classification Based on Set-Valued Identification Method
http://ir.amss.ac.cn:80/handle/2S8OKBNM/61548
Title: Lithology Classification Based on Set-Valued Identification Method
Authors: Li Jing; Wu Lifang; Lu Wenjun; Wang Ting; Kang Yu; Feng Deyong; Zhou Hansheng
Description: Lithology classification using well logs plays a key role in reservoir exploration. This paper studies the problem of lithology identification based on the set-valued method (SV), which uses the SV model to establish the relation between logging data and lithologic types at a certain depth point. In particular, the system model is built on the assumption that the noise between logging data and lithologic types is normally distributed, and then the system parameters are estimated by SV method based on the existing identification criteria. The logging data of Shengli Oilfield in Jiyang Depression are used to verify the effectiveness of SV method. The results indicate that the SV model classifies lithology more accurately than the Logistic Regression model (LR) and more stably than uninterpretable models on imbalanced dataset. Specifically, the Macro-F1 of the SV models (i.e., SV(3), SV(5), and SV(7)) are higher than 85%, where the sandstone samples account for only 22%. In addition, the SV(7) lithology identification system achieves the best stability, which is of great practical significance to reservoir exploration.Tue, 07 Feb 2023 00:56:57 GMThttp://ir.amss.ac.cn:80/handle/2S8OKBNM/615482023-02-07T00:56:57ZLarge N Limit of the O(N) Linear Sigma Model in 3D
http://ir.amss.ac.cn:80/handle/2S8OKBNM/61551
Title: Large N Limit of the O(N) Linear Sigma Model in 3D
Authors: Shen, Hao; Zhu, Rongchan; Zhu, Xiangchan
Description: In this paper we study the large N limit of the O( N)-invariant linear sigma model, which is a vector-valued generalization of the Phi(4) quantum field theory, on the three dimensional torus. We study the problem via its stochastic quantization, which yields a coupled system of N interacting SPDEs. We prove tightness of the invariant measures in the large N limit. For large enough mass or small enough coupling constant, they converge to the (massive) Gaussian free field at a rate of order 1/root N with respect to the Wasserstein distance. We also obtain tightness results for certain O( N) invariant observables. These generalize some of the results in Shen et al. (Ann Probab 50(1):131202, 2022) from two dimensions to three dimensions. The proof leverages the method recently developed by Gubinelli and Hofmanova (Commun Math Phys 384(1):1-75, 2021) and combines many newtechniques such as uniform in N estimates on perturbative objects as well as the solutions.Tue, 07 Feb 2023 00:56:57 GMThttp://ir.amss.ac.cn:80/handle/2S8OKBNM/615512023-02-07T00:56:57Z