A Semi-Implicit Scheme for Stationary Statistical Properties of the Infinite Prandtl Number Model

We propose a semisecret in time semi-implicit numerical scheme for the infinite Prandtl model for convection. Besides the usual finite time convergence, this scheme enjoys the additional highly desirable feature that the stationary statistical properties of the scheme converge to those of the infinite Prandtl number model at vanishing time stop. One of the key characteristics of the scheme is that it preserves the dissipativity of the infinite Prandtl number model uniformly in terms of the time stop. So far as wo know, this is the first rigorous result on convergence of stationary statistical properties of numerical schemes for infinite dimensional dissipative complex systems. © 2008 Society for Industrial and Applied Mathematics

A Uniformly Dissipative Scheme for Stationary Statistical Properties of the Infinite Prandtl Number Model

The purpose of this short communication is to announce that a class of numerical schemes, uniformly dissipative approximations, which uniformly preserve the dissipativity of the continuous infinite dimensional dissipative complex (chaotic) systems possess desirable properties in terms of approximating stationary statistics properties. in particular, the stationary statistical properties of these uniformly dissipative schemes converge to those of the continuous system at vanishing mesh size. the idea is illustrated on the infinite Prandtl number model for convection and semi-discretization in time, although the general strategy works for a broad class of dissipative complex systems and fully discretized approximations. as far as we know, this is the first result on rigorous validation of numerical schemes for approximating stationary statistical properties of general infinite dimensional dissipative complex systems. © 2008 Elsevier Ltd. All rights reserved

T-COL: Generating Counterfactual Explanations for General User Preferences on Variable Machine Learning Systems

Machine learning (ML) based systems have been suffering a lack of interpretability. To address this problem, counterfactual explanations (CEs) have been proposed. CEs are unique as they provide workable suggestions to users, in addition to explaining why a certain outcome was predicted. However, the application of CEs has been hindered by two main challenges, namely general user preferences and variable ML systems. User preferences, in particular, tend to be general rather than specific feature values. Additionally, CEs need to be customized to suit the variability of ML models, while also maintaining robustness even when these validation models change. To overcome these challenges, we propose several possible general user preferences that have been validated by user research and map them to the properties of CEs. We also introduce a new method called \uline{T}ree-based \uline{C}onditions \uline{O}ptional \uline{L}inks (T-COL), which has two optional structures and several groups of conditions for generating CEs that can be adapted to general user preferences. Meanwhile, a group of conditions lead T-COL to generate more robust CEs that have higher validity when the ML model is replaced. We compared the properties of CEs generated by T-COL experimentally under different user preferences and demonstrated that T-COL is better suited for accommodating user preferences and variable ML systems compared to baseline methods including Large Language Models

6-[3-(2,4-Dimethyl­anilino)-2-hydroxy­prop­oxy]-1,8-dihydr­oxy-3-methyl-9,10-dihydro­anthracene-9,10-dione

In the title compound, C26H25NO6, the anthraquinone ring system forms a dihedral angle of 15.5 (1)° with the benzene ring of the dimethyl­aniline group. Intra­molecular O—H⋯O hydrogen bonding is observed between the carbonyl and two hydroxyl groups. The mol­ecules are linked into a ribbon-like structure along the [100] direction by O—H⋯N and C—H⋯O hydrogen bonds. The crystal used was twinned via a 180° rotation about [100]. The ratio of the two twin components is 0.947 (1):0.053 (1)

Adaptive Waveform Design for Multiple Radar Tasks Based on Constant Modulus Constraint

Cognitive radar is an intelligent system, and it can adaptively transmit waveforms to the complex environment. The intelligent radar system should be able to provide different trade-offs among a variety of performance objectives. In this paper, we investigate the mutual information (MI) in signal-dependent interference and channel noise. We propose a waveform design method which can efficiently synthesize waveforms and provide a trade-off between estimation performance and detection performance. After obtaining a local optimal waveform, we apply the technique of generating a constant modulus signal with the given Fourier transform magnitude to the waveform. Finally we obtain a waveform that has constant modulus property

From a Spatial Structure Perspective : Spatial-Temporal Variation of Climate Redistribution of China Based on the Köppen–Geiger Classification

https://doi.org/10.1029/2022GL099319Shifting climate zones are widely used to diagnose and predict regional climate change. However, few attempts have been made to measure the spatial redistribution of these climate zones from a spatial structure perspective. We investigated changes in spatial structure of Köppen climate landscape in China between 1963 and 2098 with a landscape aggregation index. Our results reveal an apparent signal from fragmentation to aggregation, accompanied by the intensification of areal dispersion between cold and warm climate types. Our attribution analysis indicates that anthropogenic forcings have a larger influence on changes of spatial structure than natural variation. We also found that topographical heterogeneity is likely to contribute to the regional spatial fragmentation, especially in the Qinghai-Tibet Plateau. However, we also found that the spatial fragmentation will be weakened around the mid-2040s. We argue that biodiversity is likely to be mediated by spatial structure of future climate landscapes in China.Peer reviewe

Nonlinear optical properties in a quantum well with the hyperbolic confinement potential

We have performed theoretical calculation of the nonlinear optical properties in a quantum well (QW) with the hyperbolic confinement potential. Calculation results reveal that the transition energy, oscillator strength, second-order nonlinear optical rectification (OR), geometric factor and nonlinear optical absorption (OA) are strongly affected by the parameters ($\alpha, \sigma$) of the hyperbolic confinement potential. And an increment of the parameter $\alpha$ reduces all these physical quantities, while an increment of the parameter $\sigma$ enhances them, but not for geometric factor. In addition, it is found that one can control the optical properties of QW by tuning these parameters.Comment: 16pages,6 figures,Accepted for publication in Physica