Application of the Conditional Nonlinear Local Lyapunov Exponent to Second-Kind Predictability

In order to quantify the influence of external forcings on the predictability limit using observational data,the author introduced an algorithm of the conditional nonlinear local Lyapunov exponent(CNLLE)method.The effectiveness of this algorithm is validated and compared with the nonlinear local Lyapunov exponent(NLLE)and signal-to-noise ratio methods using a coupled Lorenz model.The results show that the CNLLE method is able to capture the slow error growth constrained by external forcings,therefore,it can quantify the predictability limit induced by the external forcings.On this basis,a preliminary attempt was made to apply this method to measure the influence of ENSO on the predictability limit for both atmospheric and oceanic variable fields.The spatial distribution of the predictability limit induced by ENSO is similar to that arising from the initial conditions calculated by the NLLE method.This similarity supports ENSO as the major predictable signal for weather and climate prediction.In addition,a ratio of predictability limit(RPL)calculated by the CNLLE method to that calculated by the NLLE method was proposed.The RPL larger than 1 indicates that the external forcings can significantly benefit the long-term predictability limit.For instance,ENSO can effectively extend the predictability limit arising from the initial conditions of sea surface temperature over the tropical Indian Ocean by approximately four months,as well as the predictability limit of sea level pressure over the eastern and western Pacific Ocean.Moreover,the impact of ENSO on the geopotential height predictability limit is primarily confined to the troposphere.

Conditional Generative Adversarial Network Enabled Localized Stress Recovery of Periodic Composites

Structural damage in heterogeneousmaterials typically originates frommicrostructures where stress concentration occurs.Therefore,evaluating the magnitude and location of localized stress distributions within microstructures under external loading is crucial.Repeating unit cells(RUCs)are commonly used to represent microstructural details and homogenize the effective response of composites.This work develops a machine learning-based micromechanics tool to accurately predict the stress distributions of extracted RUCs.The locally exact homogenization theory efficiently generates the microstructural stresses of RUCs with a wide range of parameters,including volume fraction,fiber/matrix property ratio,fiber shapes,and loading direction.Subsequently,the conditional generative adversarial network(cGAN)is employed and constructed as a surrogate model to establish the statistical correlation between these parameters and the corresponding localized stresses.The stresses predicted by cGAN are validated against the remaining true data not used for training,showing good agreement.This work demonstrates that the cGAN-based micromechanics tool effectively captures the local responses of composite RUCs.It can be used for predicting potential crack initiations starting from microstructures and evaluating the effective behavior of periodic composites.

Existence and Uniqueness of Solution for a Fractional Order Integro-Differential Equation with Non-Local and Global Boundary Conditions

In this paper, we prove an important existence and uniqueness theorem for a fractional order Fredholm – Volterra integro-differential equation with non-local and global boundary conditions by converting it to the corresponding well known Fredholm integral equation of second kind. The considered in this paper has been solved already numerically in [1].

Existence and Uniqueness Theorem for the Cauchy Problem of Fuzzy Differential Equations under Non-Lipschitz Conditions

Solutions of fuzzy differential equations provide a noteworthy example of time-dependent fuzzy sets The purpose of this paper is to introduce functions of a suitable Lyapunov-like type and to show the existence and uniqueness theorem for the Cauchy problem of fuzzy differential equations under non-Lipschitz conditions The comparison principles and the existence and uniqueness theorems of this paper generalize many well-known results up to now

Multiplicity of Solutions for Fractional Hamiltonian Systems under Local Conditions

Under some local superquadratic conditions on W (t, u) with respect to u, the existence of infinitely many solutions is obtained for the nonperiodic fractional Hamiltonian systems, where L (t) is unnecessarily coercive.

Robust Damage Detection and Localization Under Complex Environmental Conditions Using Singular Value Decomposition-based Feature Extraction and One-dimensional Convolutional Neural Network

Ultrasonic guided wave is an attractive monitoring technique for large-scale structures but is vulnerable to changes in environmental and operational conditions(EOC),which are inevitable in the normal inspection of civil and mechanical structures.This paper thus presents a robust guided wave-based method for damage detection and localization under complex environmental conditions by singular value decomposition-based feature extraction and one-dimensional convolutional neural network(1D-CNN).After singular value decomposition-based feature extraction processing,a temporal robust damage index(TRDI)is extracted,and the effect of EOCs is well removed.Hence,even for the signals with a very large temperature-varying range and low signal-to-noise ratios(SNRs),the final damage detection and localization accuracy retain perfect 100%.Verifications are conducted on two different experimental datasets.The first dataset consists of guided wave signals collected from a thin aluminum plate with artificial noises,and the second is a publicly available experimental dataset of guided wave signals acquired on a composite plate with a temperature ranging from 20℃to 60℃.It is demonstrated that the proposed method can detect and localize the damage accurately and rapidly,showing great potential for application in complex and unknown EOC.

Overcoming Investment Risks Chinese investors need to thoroughly understand local conditions before investing in Africa

With abundant labor resources and the increase in policy sup port for economie development and loreign investment, Africa is becoming a new sought-after destination for investment by multinational companics.

Conditional Diagnosability of the Locally Twisted Cubes under the PMC Model

In a multiprocessor systems, it is important to local and to replace the faulty processors to maintain systempsilas high reliability. The fault diagnosis, which is the process of identifying fault processors in a multiprocessor system through testing. The conditional diagnosis requires that for each processor u in a system, all the processors that are directly connected to u do not fail at the same time. In this paper, we study the conditional diagnosability of the n-dimensional locally twisted cubes. After showing some properties of the locally twisted cubes, we prove that it under the PMC model is 4n – 7 for n ≥ 5.

Multiple Solutions for a Class of Semilinear Elliptic Equations with Nonlinear Boundary Conditions

In this paper, using Local Linking Theorem, we obtain the existence of multiple solutions for a class of semilinear elliptic equations with nonlinear boundary conditions, in which the nonlinearites are compared with higher Neumann eigenvalue and the first Steklov eigenvalue.

Existence and Uniqueness of the Nonlinear BSDEs with a Small Parameter under Locally Lipschitz Condition

In this paper we study the following nonlinear BSDE：y（t） ＋ ∫1 t f（s,y（s）,z（s））ds ＋ ∫1 t [z（s） ＋ g 1 （s,y（s）） ＋ εg 2 （s,y（s）,z（s））]dW s=ξ,t ∈ [0,1],where ε is a small parameter.The coefficient f is locally Lipschitz in y and z,the coefficient g 1 is locally Lipschitz in y,and the coefficient g 2 is uniformly Lipschitz in y and z.Let L N be the locally Lipschitz constant of the coefficients on the ball B（0,N） of R d × R d×r.We prove the existence and uniqueness of the solution when L N ～ √ log N and the parameter ε is small.

NONLINEAR APPROXIMATION OF A VARIATION OF L^1 UNDER THE LOCAL HAAR CONDITION

In this paper, we discuss the nonlinear approximation of a variation of L1 under the local Haar condition. Theorems on characterizations (including alternations), unicity and strong unicity of the nonlinear approximation are obtained, the associated linear problem equivalent to the nonlinear approximation are given.

Blow-up of Solutions to Porous Medium Equations with a Nonlocal Boundary Condition and a Moving Localized Source

This paper is devoted to the blow-up properties of solutions to the porous medium equations with a nonlocal boundary condition and a moving localized source. Conditions for the existence of global or blow-up solutions are obtained. Moreover, we prove that the unique solution has global blow-up property whenever blow-up occurs.

ONSET CONDITION OF STRAIN LOCALIZATION IN MATRIX OF SATURATED POROUS MEDIA

Based on governing equations of saturated porous media and Liapunov＇ s stability here, onset conditions matrix of porous media used by solid stress and Terzaghi＇s effective stress constitutive description under seepage flow state, are presented, which have different forms with different representation of the solid phase, matrix or skeleton, constitutive model of porous media. The main difference relates with how to describe the interaction between solid phase and liquid phase in constitutive model. The derived onset condition of strain localization under Terzaghi＇ s effective stress description can be used to interpret different failure types, piping effect, landslides and mudflows, by means of the type and the magnitude ratio of relative movement between solid phase and liquid phase. Examples here illuminate the onset condition of how to work.

Sufficient Conditions of Optimality for Convex Differential Inclusions of Elliptic Type and Duality

This paper deals with the Dirichlet problem for convex differential (PC) inclusions of elliptic type. On the basis of conjugacy correspondence the dual problems are constructed. Using the new concepts of locally adjoint mappings in the form of Euler-Lagrange type inclusion is established extremal relations for primary and dual problems. Then duality problems are formulated for convex problems and duality theorems are proved. The results obtained are generalized to the multidimensional case with a second order elliptic operator.

An Image Segmentation Algorithm Based on a Local Region Conditional Random Field Model

To reduce the computation cost of a combined probabilistic graphical model and a deep neural network in semantic segmentation, the local region condition random field (LRCRF) model is investigated which selectively applies the condition random field (CRF) to the most active region in the image. The full convolutional network structure is optimized with the ResNet-18 structure and dilated convolution to expand the receptive field. The tracking networks are also improved based on SiameseFC by considering the frame relations in consecutive-frame traffic scene maps. Moreover, the segmentation results of the greyscale input data sets are more stable and effective than using the RGB images for deep neural network feature extraction. The experimental results show that the proposed method takes advantage of the image features directly and achieves good real-time performance and high segmentation accuracy.

Modeling the Spatio-Temporal Dynamics of Local Context for a Contextualized Diffusion of Agroecological Intensification Options in Niger

Spatio-temporal variability and dynamics in Sahelian agro-pastoral zones make each local situation a special case. These specificities must be considered to guide the dissemination of agricultural options with a view to sustainable development. The territorial scale of municipalities is not sufficient for this necessary contextualization;the scale of the “village terroir” seems to be a better option. This is the hypothesis we put forward in the framework of the Global Collaboration for Resilient Food Systems program (CRFS), i.e. local context is spatially defined by village terroir. The study is based on data collected through participatory mapping and surveys in “village terroirs” in three regions of Niger (Maradi, Dosso and Tillabéri). Then the links between farm managers and their cultivated land, as well as the spatio-temporal dynamics of local context are analyzed. This study provides evidence of the existence and functional usefulness of the village terroir for farmers, their land management and their activities. It demonstrates the usefulness of contextualizing agricultural options at this scale. Their analysis elucidates the links between “terroirs village” and the specific functioning of the agrosocio-ecosystems acting on each of them, thus laying the systemic and geographical foundations for a model of the spatio- temporal dynamics of “village terroirs”. This initial work has opened up new perspectives in modeling and sustainable development.

Locally varying geostatistical machine learning for spatial prediction

Machine learning methods dealing with the spatial auto-correlation of the response variable have garnered significant attention in the context of spatial prediction.Nonetheless,under these methods,the relationship between the response variable and explanatory variables is assumed to be homogeneous throughout the entire study area.This assumption,known as spatial stationarity,is very questionable in real-world situations due to the influence of contextual factors.Therefore,allowing the relationship between the target variable and predictor variables to vary spatially within the study region is more reasonable.However,existing machine learning techniques accounting for the spatially varying relationship between the dependent variable and the predictor variables do not capture the spatial auto-correlation of the dependent variable itself.Moreover,under these techniques,local machine learning models are effectively built using only fewer observations,which can lead to well-known issues such as over-fitting and the curse of dimensionality.This paper introduces a novel geostatistical machine learning approach where both the spatial auto-correlation of the response variable and the spatial non-stationarity of the regression relationship between the response and predictor variables are explicitly considered.The basic idea consists of relying on the local stationarity assumption to build a collection of local machine learning models while leveraging on the local spatial auto-correlation of the response variable to locally augment the training dataset.The proposed method’s effectiveness is showcased via experiments conducted on synthetic spatial data with known characteristics as well as real-world spatial data.In the synthetic(resp.real)case study,the proposed method’s predictive accuracy,as indicated by the Root Mean Square Error(RMSE)on the test set,is 17%(resp.7%)better than that of popular machine learning methods dealing with the response variable’s spatial auto-correlation.Additionally,this method is not only valuable for spatial prediction but also offers a deeper understanding of how the relationship between the target and predictor variables varies across space,and it can even be used to investigate the local significance of predictor variables.

高质量发展是全面建设社会主义现代化国家的首要任务

党的二十大报告提出以中国式现代化全面推进中华民族伟大复兴,形成对中国式现代化的系统性认知,强调高质量发展是全面建设社会主义现代化国家的首要任务。改革开放以来,在中国共产党的领导下,我国逐步摆脱观念桎梏和教条约束,坚持一切从国情出发,创造了人类文明新形态。经济全球化势不可挡,世界必然是和而不同的全球格局,不同文明形态、不同经济体制、不同行为方式共存形成人类命运共同体。这是中国式现代化的底层逻辑,体现了中国经济高质量发展的世界意义。从中国式现代化视角透视高质量发展的深刻叙事,有助于深刻诠释中国式现代化的核心意涵。

A stabilized least-squares imaging condition with structure constraints

Conventional shot-gather migration uses a cross-correlation imaging condition proposed by Clarebout （1971）, which cannot preserve imaging amplitudes. The deconvolution imaging condition can improve the imaging amplitude and compensate for illumination. However, the deconvolution imaging condition introduces instability issues. The least-squares imaging condition first computes the sum of the cross-correlation of the forward and backward wavefields over all frequencies and sources, and then divides the result by the total energy of the forward wavefield. Therefore, the least-squares imaging condition is more stable than the classic imaging condition. However, the least-squares imaging condition cannot provide accurate results in areas where the illumination is very poor and unbalanced. To stabilize the least-squares imaging condition and balance the imaging amplitude, we propose a novel imaging condition with structure constraints that is based on the least-squares imaging condition. Our novel imaging condition uses a plane wave construction that constrains the imaging result to be smooth along geological structure boundaries in the inversion frame. The proposed imaging condition improves the stability of the imaging condition and balances the imaging amplitude. The proposed condition is applied to two examples, the horizontal layered model and the Sigsbee 2A model. These tests show that, in comparison to the damped least-squares imaging condition, the stabilized least-squares imaging condition with structure constraints improves illumination stability and balance, makes events more consecutive, adjusts the amplitude of the depth layers where the illumination is poor and unbalanced, suppresses imaging artifacts, and is conducive to amplitude preserving imaging of deep layers.

Relationship between the transition frequency of local fluid flow and the peak frequency of attenuation

Local fluid flow（LFF） at the mesoscopic scale is the main dissipation mechanism of seismic waves in heterogeneous porous media within the seismic frequency band.LFF is easily influenced by the structure and boundary conditions of the porous media,which leads to different behaviors of the peak frequency of attenuation.The associated transition frequency can provide detailed information about the trend of LFF;therefore,research on the transition frequency of LFF and its relationship with the peak frequency of the corresponding attenuation（i.e.,inverse of quality factor） facilitates the detailed understanding of the effect of inner structures and boundary conditions in porous media.In this study,we firstly obtain the transition frequency of fluid flux based on Biot＇s theory of poroelasticity and the fast Fourier transform algorithm in a sample containing one repeating unit cell（RUC）.We then analyze changes of these two frequencies in porous media with different porous properties.Finally,we extend our analysis to the influence of the undrained boundary condition on the transition frequency and peak frequency in porous media with multiple RUCs.This setup can facilitate the understanding of the effect from the undrained boundary condition.Results demonstrate that these two frequencies have the same trend at low water saturation,but amplitude variations differ between the frequencies as the amount of saturation increases.However,for cases of high water saturation,both the trend and the amplitude variation of these two frequencies fit well with each other.