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Towards a Unified Recurrent Neural Network Theory： The Uniformly Pseudo-Projection-Anti-Monotone Net

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Acta Mathematica Sinica,English Series 2011年第2期27卷 377-396页

作者： zong Ben xu Chen QIAO Institute for Information and System Science Faculty of Science MOE Key Lab for Intelligent Networks and Network Security Xi'an Jiaotong University Xi'an 710049 P. R. China qiaochen @mail.xjtu. edu. cn

In the past decades, various neural network models have been developed for modeling the behavior of human brain or performing problem-solving through simulating the behavior of human brain. The recurrent neural networks are the type of neural networks to model or simulate associative memory behavior of human being. A recurrent neural network （RNN） can be generally formalized as a dynamic system associated with two fundamental operators： one is the nonlinear activation operator deduced from the input-output properties of the involved neurons, and the other is the synaptic connections （a matrix） among the neurons. Through carefully examining properties of various activation functions used, we introduce a novel type of monotone operators, the uniformly pseudo-projectionanti-monotone （UPPAM） operators, to unify the various RNN models appeared in the literature. We develop a unified encoding and stability theory for the UPPAM network model when the time is discrete. The established model and theory not only unify but also jointly generalize the most known results of RNNs. The approach has lunched a visible step towards establishment of a unified mathematical theory of recurrent neural networks.

关键词： Feedback neural networks essential characteristics uniformly pseudo-projection-anti- monotone net unified theory dynamics

Generalization Bounds of ERM Algorithm with Markov Chain Samples

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Acta Mathematicae Applicatae Sinica 2014年第1期30卷 223-238页

作者： Bin ZOU zong-ben xu Jie xu Faculty of Mathematics and Computer Science Hubei University Institute for Information and System Science School of Mathematics and StatisticsXi’an Jiaotong University

One of the main goals of machine learning is to study the generalization performance of learning algorithms. The previous main results describing the generalization ability of learning algorithms are usually based on independent and identically distributed （i.i.d.） samples. However, independence is a very restrictive concept for both theory and real-world applications. In this paper we go far beyond this classical framework by establishing the bounds on the rate of relative uniform convergence for the Empirical Risk Minimization （ERM） algorithm with uniformly ergodic Markov chain samples. We not only obtain generalization bounds of ERM algorithm, but also show that the ERM algorithm with uniformly ergodic Markov chain samples is consistent. The established theory underlies application of ERM type of learning algorithms.

关键词： generalization bounds ERM algorithm relative uniform convergence uniformly ergodic Markovchain learning theory

Low temperature s＇ynthesis of visible light responsive rutile TiO2 nanorods from TiC precursor

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Frontiers of Chemical Science and Engineering 2012年第1期6卷 53-57页

作者： John TELLAM xu zong, Lianzhou WANG ARC Centre of Excellence for Functional Nanomaterials School of Chemical Engineering and AIBN the University of Queensland Brisbane 4072 Australia

A nano-structured YiO2 wkh rutile phase was synthesized by using the hydrothermal method from a titanium carbide （TIC） nano-powder precursor at low temperature to produce a stable visible light responsive photoeatalyst. The rutile phase was formed at temperature as low as 100℃, and both synthesis time and temperature affected its formation. The rutile particles showed a faceted nano-rod structure, and were tested fbr absorption and photo-degradation ability under visible light. Particles with shorter synthesis times showed higher visible light absorption and corresponding photo-degradation ability, while those synthesized at lower tempe, ratures had lower, but still evident, degradation ability under visible light.

关键词： photocatalysis mtile TiO2 hydrothermal,visible titanium carbide

Adistributedeco-hydrologicalmodelanditsapplication

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Water Science and Engineering 2017年第4期10卷 257-264页

作者： zong-xue xu Lei Li Jie Zhao College of Water Sciences Beijing Normal UniversityBeijing 100875China Beijing Key Laboratory of Urban Hydrological Cycle and Sponge City Technology Beijing 100875China Bureau of Hydrology Ministry of Water Resources of ChinaBeijing 100053China

Eco-hydrological processes in arid areas are the focus of many hydrological and water resources studies. However, the hydrological cycle and the ecological system have usually been considered separately in most previous studies, and the correlation between the two has not been fully understood. Interdisciplinary research on eco-hydrological processes using multidisciplinary knowledge has been insufficient. In order to quantitatively analyze and evaluate the interaction between the ecosystem and the hydrological cycle, a new kind of eco-hydrological model, the ecology module for a grid-based integrated surface and groundwater model(Eco-GISMOD), is proposed with a two-way coupling approach,which combines the ecological model(EPIC) and hydrological model(GISMOD) by considering water exchange in the soil layer. Water interaction between different soil layers is simply described through a generalized physical process in various situations. A special method was used to simulate the water exchange between plants and the soil layer, taking into account precipitation, evapotranspiration, infiltration, soil water replenishment, and root water uptake. In order to evaluate the system performance, the Heihe River Basin in northwestern China was selected for a case study. The results show that forests and crops were generally growing well with sufficient water supply, but water shortages,especially in the summer, inhibited the growth of grass and caused grass degradation. This demonstrates that water requirements and water consumption for different kinds of vegetation can be estimated by considering the water-supply rules of Eco-GISMOD, which will be helpful for the planning and management of water resources in the future.

关键词： Ecologicalmodel Distributed hy drologicalmodel EPIC GISMOD Heihe River Basin

Temporal variations of reference evapotranspiration and its sensitivity to meteorological factors in Heihe River Basin, China

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Water Science and Engineering 2015年第1期8卷 1-8页

作者： Jie Zhao zong-xue xu De-peng Zuo xu-ming Wang College of Water Sciences Beijing Normal University

On the basis of daily meteorological data from 15 meteorological stations in the Heihe River Basin （HRB） during the period from 1959 to 2012, long-term trends of reference evapotranspiration （ET0） and key meteorological factors that affect ET0 were analyzed using the Mann- Kendall test. The evaporation paradox was also investigated at 15 meteorological stations. In order to explore the contribution of key meteo- rological factors to the temporal variation of ET0, a sensitivity coefficient method was employed in this study. The results show that：（1） mean annual air temperature significantly increased at all 15 meteorological stations, while the mean annual ET0 decreased at most of sites; （2） the evaporation paradox did exist in the HRB, while the evaporation paradox was not continuous in space and time; and （3） relative humidity was the most sensitive meteorological factor with regard to the temporal variation of ET0 in the HRB, followed by wind speed, air temperature, and solar radiation. Air temperature and solar radiation contributed most to the temporal variation of ETo in the upper reaches; solar radiation and wind speed were the determining factors for the temporal variation of ET0 in the middle-lower reaches.

关键词： Reference evapotranspiration Evaporation paradox Meteorological factor Heihe River Basin

Reduction of the Differential Light Shift by the Spatial Periodicity in an Optical Lattice

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Chinese Physics Letters 2013年第10期30卷 85-88页

作者： YUE xu-Guang xu Xia CHEN xu-zong ZHOU Xiao-Ji School of Electronics Engineering&Computer Science Peking UniversityBeijing 100871

We study the spatial periodicity effects on the differential light shift of noninteracting atoms in an optical *** the Rabi-spectrum approach,when the wavelength of the optical lattice is not magic,a reduction to the differential light shift is *** reduction results from the Bloch bands induced by the quantized motion in the periodic *** the microwave transition of rubidium atoms as an example,this reduction at some wavelengths can reach one order of magnitude,compared to the data without considering the spatial profile of the optical *** the atomic temperature is considered,the differential light shift increases or decreases with temperature,depending on the wavelength of the *** results should be beneficial for microwave optical lattice clock and precision measurements.

关键词： potential microwave lattice

Characterizations and Extensions of Lipschitz-α Operators

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Acta Mathematica Sinica,English Series 2006年第3期22卷 671-678页

作者： Huai Xin CAO Jian Hua ZHANG zong Ben xu College of Mathematics and Information Science Shaanxi Normal University Faculty of Science Xi'an Jiaotong University

In this work, we prove that a map F from a compact metric space K into a Banach space X over F is a Lipschitz-α operator if and only if for each σ in X^＊ the map σoF is a Lipschitz-α function on K. In the case that K = [a, b], we show that a map f from [a, b] into X is a Lipschitz-1 operator if and only if it is absolutely continuous and the map σ→ （σ o f）＇ is a bounded linear operator from X^＊ into L^∞（[a, b]）. When K is a compact subset of a finite interval （a, b） and 0 〈 α ≤ 1, we show that every Lipschitz-α operator f from K into X can be extended as a Lipschitz-α operator F from [a, b] into X with Lα（f） ≤ Lα（F） ≤ 3^1-α Lα（f）. A similar extension theorem for a little Lipschitz-α operator is also obtained.

关键词： Characterization Extension Lipschitz-α operator

Optimized Degenerate Bose-Fermi Mixture in Microgravity： DSMC Simulation of Sympathetic Cooling

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Chinese Physics Letters 2014年第4期31卷 41-45页

作者： LUAN Tian JIA Tao CHEN xu-zong MA Zhao-Yuan School of Electronics Engineering and Computer Science Peking University Beijing 100871 Shanghai Institute of Optics and Fine Mechanics Chinese Academy of Sciences Shanghai 201800

Applying the direct simulation Monte Carlo （DSMC） method developed for the cold atom system, we explore the possibility of a high-efflciency sympathetic cooling process between 87Rb and 40K without gravitational force in an optical trap. The relation between the pre-cooling of Bosons and the sympathetic cooling efficiency is also studied. We find that the absence of gravitational force is beneficial to the process of sympathetic cooling. fhrthermore, an inefficient pre-cooling process will in fact hamper the creation of Fermi degenerate gases. This suggests the advantages of sympathetic cooling in microgravity.

关键词： MONTE Carlo method GRAVITATIONAL force REDUCED gravity environments PRECOOLING BOSONS

Boosting the Capacitive Performance of Cobalt(Ⅱ) Phthalocyanine by Non-peripheral Octamethyl Substitution for Supercapacitors

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Chinese Journal of Chemistry 2021年第5期39卷 1265-1272页

作者： Minzhang Li Rajendran Ramachandran Yu Wang Qian Chen zong-Xiang xu School of Chemistry and Chemical Engineering Harbin Institute of TechnologyHarbinHeilongjiang 150001China Deportment of Chemistry Southern University of Science and TechnologyShenzhenGuangdong 518055China Guangdong-Hong Kong-Macao Joint Laboratory for Photonic-Thermal-Electricol Energy Materials and Devices Southern University of Science and TechnologyShenzhenGuangdong 518055China

In this paper,pristine cobalt(Ⅱ)phthalocyanine(CoPc)and non-peripheral octamethyl substituted CoPc(N-CoMe_(2)Pc)are the focus of electrochemical *** and N-CoMe_(2)Pc nanorods(NR)were synthesized by a facile precipitation process from sublimated bulk phthalocyanine powders and their electrochemical properties were *** to the large specific surface area,the capacitance performance of the nanorods was significantly higher than that of the sublimated powder sample.N-CoMe_(2)Pc powder exhibited better pseudocapacity compared with CoPc powder and CoPc NR,which is attributed to enhanced charge transfer rate and im-proved redox activity after the introduction of octamethyl substituents on phthalocyanine *** maximum specific capacitance value was achieved by N-CoMe_(2)Pc NR based electrode,exhibiting 210.2 F g^(-1) capacitance at 5 mV s^(-1) scan rate and 156.1 F g^(-1) at 0.25 A g^(-1) current density,and also showing high efficiency and satisfactory *** results indicate that according to proper molecular design,N-CoMe_(2)Pc NR could be applied as the potential candidate for electrode material in supercapacitors.

关键词： Phthalocyanines Methylation Nanostructures Supercapacitors Electrochemistry