生成学习系统的混沌与设计

认知学习是一种高度复杂的非线性现象.试图依据生成学习理论和经验学习的思想,建构含有记忆效应的生成学习系统动力学模型,探讨认知学习过程的复杂现象和变化特征,揭示学习系统波动的内生机制和学生认知的混沌规律,并在此基础上提出基于学习混沌的教学系统设计模式,期望能促进学生认知结构的发展.     

基于鲁棒最优控制的在线机器学习方法

基于再生核Hilbert空间(reproducing kernel Hilbert space,RKHS)的统计学习模型被广泛应用于函数逼近、图像处理、模式识别和回归分析等领域,并且也在非线性随机动力学系统的辨识问题中有着很好的表现.本文提出一个基于鲁棒最优控制的RKHS模型学习方法,来实现对非线性随机动力学系统的高效在线建模.利用本文得到的关于再生核空间的一些理论结果,本文将随机动力学系统的在线学习问题转化为一组具有有界随机扰动的离散时变线性系统的输出反馈镇定问题,并利用模型预测控制技术来设计相应的控制算法和学习算法.与现有的RKHS模型学习方法相比,在不引入任何数据窗口原理、剪枝技术、学习步长的调整机制以及对噪声统计性质的假设的情形下,新方法可以在保证模型参数快速且鲁棒收敛的同时,实现对动力学系统的自适应高精度建模.此外,本文首次从最优控制的视角出发,研究动力学系统的在线核学习问题.在本文提出的研究框架下,现有各种控制技术可以被利用起来开发新的鲁棒学习方法,这也为核学习理论的研究和算法的开发提供一些新的思路.本文亦给出了数值算例和对比结果,用来说明新方法的有效性.     

具有随机干扰的时滞车辆跟随控制

考虑信息传输和车辆动力学行为对控制指令具有时间滞后因素和车辆动力学系统建模中忽略的随机因素,建立了一类具有时间滞后的随机车辆跟随系统,并研究了该系统的稳定性和控制器设计.根据Ito(伊藤)随机微分方程建立随机车辆动力学模型.利用滑模控制设计了系统的控制策略,并运用系统的稳定性判据得到了系统控制参数的收敛区域.数值仿真试验结果表明:各跟随车辆的加速度、速度和位移等状态能在较短的时间内迫近领头车辆;各车辆的车间距误差有较快的收敛速度,均能在10 s内收敛于0.     

商品价格极端波动影响期现价格联动及套期保值吗?

试图将极端价格波动成因归结于系统惯性因素和极端随机冲击因素,借助Copulas-GARCH模型,将其引入期货和现货价格联动的计量模型之中,以持有便利收益高的沪铜作为研究样本,实证研究发现:1)引入极端价格波动因素后将显著提升价格联动计量模型的解释能力;2)当负向基差扩大,系统惯性因素引起商品价格剧烈变动,将导致市场联动性下降,而极端随机冲击却具有正向效应,即市场受到极端随机冲击时会增强期现价格联动关系;3)极端随机冲击效应中正向冲击和负向冲击的非对称性特征不显著;4)考虑极端价格波动效应可明显降低生产企业的套期保值成本.研究结论对于商品期货市场套期保值等期货交易具有重要管理启示.     

随机时滞教学系统的最优习得策略

认识非线性随机时滞现象的内在机理、运演性态和掌握其内在规律己成为当今非线性随机动力学理论分析与数值分析的重要主题.基于教学论、自组织理论和非线性随机时滞动力学等理论及其有关研究成果,构建教学系统的非线性随机时滞Logistic模型,寻求教学系统的演化规律,并在此基础上研究教学系统的最优习得策略和提出相应教学建议,期望能促进教学系统有序发展;同时,也期望能促使教学论与非线性随机动力学等理论"联姻",拓展与丰富教学论的研究领域,为教学论研究提供一个新的学科视角的支持与论证.     

分子刚度对膜锚定受体-配体结合动力学影响的理论与模拟研究

人体内大部分生物学过程都离不开细胞黏附.细胞黏附行为主要由锚定于细胞膜上的特异性分子（又称受体和配体）的结合动力学关系来决定.已有研究表明，特异性分子的结合关系受外力及细胞膜波动等多种因素影响.然而，特异性分子刚度对细胞膜锚定受体 配体结合关系的影响机制仍不清楚.近期关于新冠病毒强传染力的研究表明，特异性黏附分子刚度对病毒与细胞结合具有重要影响.该文通过建立生物膜黏附的粗粒度模型，借助分子模拟和理论分析来研究分子刚度在黏附中的作用.结果表明，始终存在一个最佳膜间距及最佳分子刚度值，使得黏附分子亲和力和结合动力学参数达到最大值.这项研究不仅能加深人们对细胞黏附的认知，还有助于指导药物设计、疫苗研发等.     

Knight不确定及机制转换环境下带通胀的最优投资问题研究

本文研究了投资者在Knight不确定及机制转换环境下带通胀的最优投资决策问题.利用Ito公式、α-最大最小预期效用偏好模型、随机分析等方法,得出了机制转换环境下利润流的动力学方程,Knight不确定及机制转换条件下考虑通胀因素的投资预期价值公式,利润流临界现值及不同参数对投资的影响.     

基于MASIM的社会推理与计算系统

随着计算机和信息技术的发展,信息科学技术的研究越来越重视与社会科学的交叉,社会计算已成为国内外计算机及相关领域的最新研究热点.社会计算与社会智能研究的核心之一是社会因果关系推理和行为评判问题.基于认知和心理学理论,介绍一个社会推理计算模型MASIM以及基于MASIM的社会计算系统实例,并以此阐述建立社会推理机制和社会计算系统的若干技术方面.     

一类具有非线性发生率的随机SIS传染病模型阈值动力学行为研究

考虑到环境波动对传染病传播过程的影响,该文研究了一类具有非线性发生率的SIS随机传染病动力学模型的阈值动力学行为.利用Feller检测和随机比较原理得到了决定疾病绝灭或持久的随机基本再生数R_0~s,即当R_0~s1时,疾病将趋于绝灭;当R_0~s=1时,疾病也将趋于绝灭,这一结论补充了已有随机阈值结果;当R_0~s1时,疾病将随机持续下去,并给出了最终传染规模的范围估计.最后,利用数值仿真验证了文中所得出的结论并根据实际生物参数说明了环境波动对不同大小尺度群体中SIS传染病传播的影响.     

“一带一路”背景下云南省区域物流发展研究——基于系统动力学的仿真研究

基于系统动力学相关理论,分析云南区域物流的动力学机制,构建区域物流系统动力学模型,探讨云南区域物流未来的发展态势.利用系统动力学模型的“战略与策略实验室”功能,通过考虑四种政策方案分析,模拟不同影响因素对云南物流业以及经济的促进作用,根据模型模拟的结果,有针对性地提出云南省发展物流业的对策建议:增强云南省区域竞争力,优化资源配置,为打造云南省为面向东南亚、南亚“一带一路”的桥梁枢纽提供理论支撑和政策指导.     

Deep learning for energy markets

Deep Learning (DL) is combined with extreme value theory (EVT) to predict peak loads observed in energy grids. Forecasting energy loads and prices is challenging due to sharp peaks and troughs that arise due to supply and demand fluctuations from intraday system constraints. We propose a deep temporal extreme value model to capture these effects, which predicts the tail behavior of load spikes. Deep long‐short‐term memory architectures with rectified linear unit activation functions capture trends and temporal dependencies, while EVT captures highly volatile load spikes above a prespecified threshold. To illustrate our methodology, we develop forecasting models for hourly price and demand from the PJM interconnection. The goal is to show that DL‐EVT outperforms traditional methods, both in‐ and out‐of‐sample, by capturing the observed nonlinearities in prices and demand spikes. Finally, we conclude with directions for future research.     

Preservice Teachers of High School Mathematics: Success,Failure, and Persistence in the Face of Mathematical Challenges

The goal of this study was to identify variables related to success and resilience in an undergraduate, high school mathematics teacher education program. Over a five‐year period, we tracked the academic performance and achievement motivation goals of multiple cohorts of students. Students who successfully completed their degrees had higher grade point average (GPAs) upon entering the program, earned higher grades in their first college mathematics course, and failed fewer courses than students who left the program or university. Learning and performance motivational goals did not predict success in the program. Performance goals decreased over time. Nearly half the successful students repeated one or more mathematics courses. Ten students completed their degrees, obtained a teaching license, and are teaching despite the need for multiple repetitions of the same mathematics courses. These persistent students did not differ from their peers in motivational goals. Our results suggest that although students with higher GPAs and initial mathematics grades were more likely to complete the program, students who experienced challenges in mathematics courses were able to succeed. We discuss the implications of these results for recruiting, advising, and retention of students in mathematics education programs.     

Fluctuations of interface statistical physics models applied to a stock market model

In this paper, applying the theory of fluctuations of the interfaces for statistical physics lattice models, we construct a financial model and use this financial model to describe the behavior or fluctuations of a stock price process in a stock market. By using the methods of statistical physics and under some conditions, we show that the finite dimensional distribution of a normalized random process for this financial model converges to the corresponding distribution of the Black–Scholes model.     

Dynamical Behavior of a Stochastic Nutrient-Plankton Food Chain Model with L\''{e}vy Jumps

In aquatic ecosystem, plankton populations are easily affected by environmental fluctuations due to the unpredictability of many physical factors. To better understand how environmental fluctuations influence plankton populations, in this paper, we propose and investigate a stochastic nutrient-plankton food chain model with L$\acute{\rm e}$vy jumps. Firstly, by constructing a suitable Lyapunov function, we prove that the stochastic model has a unique global positive solution for any given positive initial value. Then, we establish sufficient conditions for the persistence and extinction of plankton. Finally, we provide some numerical simulations to illustrate the analytical results.     

Influence of hydrodynamic fluctuations on the phase transition in the E and F models of critical dynamics

We use the renormalization group method to study the E model of critical dynamics in the presence of velocity fluctuations arising in accordance with the stochastic Navier-Stokes equation. Using the Martin-Siggia-Rose theorem, we obtain a field theory model that allows a perturbative renormalization group analysis. By direct power counting and an analysis of ultraviolet divergences, we show that the model is multiplicatively renormalizable, and we use a two-parameter expansion in ∈ and δ to calculate the renormalization constants. Here, ∈ is the deviation from the critical dimension four, and δ is the deviation from the Kolmogorov regime. We present the results of the one-loop approximation and part of the fixedpoint structure. We briefly discuss the possible effect of velocity fluctuations on the arge-scale behavior of the model.     

Combining latent learning with dynamic programming in the modular anticipatory classifier system

Learning Classifier Systems (LCS) are rule based Reinforcement Learning (RL) systems which use a generalization capability. In this paper, we highlight the differences between two kinds of LCSs. Some are used to directly perform RL while others latently learn a model of the interactions between the agent and its environment. Such a model can be used to speed up the core RL process. Thus, these two kinds of learning processes are complementary. We show here how the notion of generalization differs depending on whether the system anticipates (like Anticipatory Classifier System (ACS) and Yet Another Classifier System (YACS)) or not (like XCS). Moreover, we show some limitations of the formalism common to ACS and YACS, and propose a new system, called Modular Anticipatory Classifier System (MACS), which allows the latent learning process to take advantage of new regularities. We describe how the model can be used to perform active exploration and how this exploration may be aggregated with the policy resulting from the reinforcement learning process. The different algorithms are validated experimentally and some limitations in presence of uncertainties are highlighted.     

Second order freeness and fluctuations of random matrices: I. Gaussian and Wishart matrices and cyclic Fock spaces

We extend the relation between random matrices and free probability theory from the level of expectations to the level of fluctuations. We introduce the concept of “second order freeness” and interpret the global fluctuations of Gaussian and Wishart random matrices by a general limit theorem for second order freeness. By introducing cyclic Fock space, we also give an operator algebraic model for the fluctuations of our random matrices in terms of the usual creation, annihilation, and preservation operators. We show that orthogonal families of Gaussian and Wishart random matrices are asymptotically free of second order.     

Learning objects and objectives towards automatic learning construction

This paper presents a method that creates instructionally sound learning experiences by means of learning objects. The method uses a mathematical model, distinguishes two kinds of Learning Objects Properties and proceeds in two major steps: first, the Course Creation is transformed into Set Covering under specific requirements derived from Learning Theories and practice; second, the Alternative Learning Sources are selected by using a similarity measure specially defined for this purpose.     

Learning multicriteria classification models from examples: Decision rules in continuous space

The classification problem statement of multicriteria decision analysis is to model the classification of the alternatives/actions according to the decision maker's preferences. These models are based on outranking relations, utility functions or (linear) discriminant functions. Model parameters can be given explicitly or learnt from a preclassified set of alternatives/actions.In this paper we propose a novel approach, the Continuous Decision (CD) method, to learn parameters of a discriminant function, and we also introduce its extension, the Continuous Decision Tree (CDT) method, which describes the classification more accurately.The proposed methods are results of integration of Machine Learning methods in Decision Analysis. From a Machine Learning point of view, the CDT method can be considered as an extension of the C4.5 decision tree building algorithm that handles only numeric criteria but applies more complex tests in the inner nodes of the tree. For the sake of easier interpretation, the decision trees are transformed to rules.