The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition

In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.

Variational Calculus With Conformable Fractional Derivatives

Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of invariance are obtained. As particular cases, we prove fractional versions of Noether's symmetry theorem. Invariant conditions for fractional optimal control problems, using the Hamiltonian formalism, are also investigated. As an example of potential application in Physics, we show that with conformable derivatives it is possible to formulate an Action Principle for particles under frictional forces that is far simpler than the one obtained with classical fractional derivatives.

A unified analysis of a micro-beam,droplet and CNT ring adhered on a substrate:Calculation of variation with movable boundaries

In this study, we developed a general method to analytically tackle a kind of movable boundary problem from the viewpoint of energy variation. Having grouped the adhesion of a micro-beam, droplet and carbon nanotube （CNT） ring on a substrate into one framework, we used the developed line of reasoning to investigate the adhesion behaviors of these systems. Based upon the derived governing equations and transversality conditions, explicit solutions involving the critical parameters and morphologies for the three systems are successfully obtained, and then the parameter analogies and common characteristics of them are thor- oughly investigated. The presented method has been verified via the concept of energy release rate in fracture mechanics. Our analyses provide a new approach for exploring the mechanism of different systems with similarities as well as for understanding the unity of nature. The analysis results may be beneficial for the design of nano-structured materi- als, and hold potential for enhancing their mechanical, chemical, optical and electronic properties.

A semantic and emotion-based dual latent variable generation model for a dialogue system

With the development of intelligent agents pursuing humanisation,artificial intelligence must consider emotion,the most basic spiritual need in human interaction.Traditional emotional dialogue systems usually use an external emotional dictionary to select appropriate emotional words to add to the response or concatenate emotional tags and semantic features in the decoding step to generate appropriate responses.However,selecting emotional words from a fixed emotional dictionary may result in loss of the diversity and consistency of the response.We propose a semantic and emotion-based dual latent variable generation model(Dual-LVG)for dialogue systems,which is able to generate appropriate emotional responses without an emotional dictionary.Different from previous work,the conditional variational autoencoder(CVAE)adopts the standard transformer structure.Then,Dual-LVG regularises the CVAE latent space by introducing a dual latent space of semantics and emotion.The content diversity and emotional accuracy of the generated responses are improved by learning emotion and semantic features respectively.Moreover,the average attention mechanism is adopted to better extract semantic features at the sequence level,and the semi-supervised attention mechanism is used in the decoding step to strengthen the fusion of emotional features of the model.Experimental results show that Dual-LVG can successfully achieve the effect of generating different content by controlling emotional factors.

Potential of rooftop rainwater harvesting to meet outdoor water demand in arid regions

The feasibility of rooftop rainwater harvesting （RRWH） as an alternative source of water to meet the outdoor water demand in nine states of the U.S. was evaluated using a system dynamics model developed in Systems Thinking, Experimental Learning Laboratory with Animation. The state of Arizona was selected to evaluate the effects of the selected model parameters on the efficacy of RRWH since among the nine states the arid region of Arizona showed the least potential of meeting the outdoor water demand with rain harvested water. The analyses were conducted on a monthly basis across a 10-year projected period from 2015 to 2024. The results showed that RRWH as a potential source of water was highly sensitive to certain model parameters such as the outdoor water demand, the use of desert landscaping, and the percentage of existing houses with RRWH. A significant difference （as high as 37.5%） in rainwater potential was observed between the projected wet and dry climate conditions in Arizona. The analysis of the dynamics of the storage tanks suggested that a 1.0-2.0 m3 rainwater barrel, on an average, can store approximately 80% of the monthly rainwater generated from the rooftops in Arizona, even across the high seasonal variation. This interactive model can be used as a quick estimator of the amount of water that could be generated, stored, and utilized through RRWH systems in the U.S. under different climate conditions. The findings of such comprehensive analyses may help regional policymakers, especially in arid regions, to develop a sustainable water management infrastructure.

Generating diverse clothed 3D human animations via a generative model

Data-driven garment animation is a current topic of interest in the computer graphics industry.Existing approaches generally establish the mapping between a single human pose or a temporal pose sequence,and garment deformation,but it is difficult to quickly generate diverse clothed human animations.We address this problem with a method to automatically synthesize dressed human animations with temporal consistency from a specified human motion label.At the heart of our method is a twostage strategy.Specifically,we first learn a latent space encoding the sequence-level distribution of human motions utilizing a transformer-based conditional variational autoencoder(Transformer-CVAE).Then a garment simulator synthesizes dynamic garment shapes using a transformer encoder-decoder architecture.Since the learned latent space comes from varied human motions,our method can generate a variety of styles of motions given a specific motion label.By means of a novel beginning of sequence(BOS)learning strategy and a self-supervised refinement procedure,our garment simulator is capable of efficiently synthesizing garment deformation sequences corresponding to the generated human motions while maintaining temporal and spatial consistency.We verify our ideas experimentally.This is the first generative model that directly dresses human animation.

An inverse design method for supercritical airfoil based on conditional generative models

Inverse design has long been an efficient and powerful design tool in the aircraft industry.In this paper,a novel inverse design method for supercritical airfoils is proposed based on generative models in deep learning.A Conditional Variational Auto Encoder(CVAE)and an integrated generative network CVAE-GAN that combines the CVAE with the Wasserstein Generative Adversarial Networks(WGAN),are conducted as generative models.They are used to generate target wall Mach distributions for the inverse design that matches specified features,such as locations of suction peak,shock and aft loading.Qualitative and quantitative results show that both adopted generative models can generate diverse and realistic wall Mach number distributions satisfying the given features.The CVAE-GAN model outperforms the CVAE model and achieves better reconstruction accuracies for all the samples in the dataset.Furthermore,a deep neural network for nonlinear mapping is adopted to obtain the airfoil shape corresponding to the target wall Mach number distribution.The performances of the designed deep neural network are fully demonstrated and a smoothness measurement is proposed to quantify small oscillations in the airfoil surface,proving the authenticity and accuracy of the generated airfoil shapes.

Some Inequalities for Tree Martingales

In this paper we study tree martingales and proved that if 1≤α,β〈∞,1≤p〈∞ then for every predictable tree martingale f=（ft,t∞T）and E[σ^（P）（f）]〈∞,E[S^（P）（f）]〈∞,it holds that ‖（St^（p）（f）,t∈T）‖M^α∞≤Cαβ‖f‖p^αβ,‖（σt^（p）（f）,t∈T）‖M^α,β‖f‖P^αβ,where Cαβ depends only on α and β.