OPTIMAL CONTROL OF MULTIPLE-USE PRODUCTS: THE CASE OF TIMBER,FORAGE AND WATER PRODUCTION

ABSTRACT. A thorough analysis of the optimal control of multiple-use forest management at the stand level reveals that the results of earlier studies, which seem to contradict each other, are in fact part of a common solution space. We provide an explanation for this result by showing that it is caused by the growth function and the interaction between the timber and forage production functions. We discuss the sensibility of the results using this new knowledge. Most optimal control models focusing on multiple-use forest management have applied production functions that are quadratic in the state variable. This makes explicit solutions easy because the first order derivative is linear. However, in reality, production is often better described by more complex nonlinear functions, but, unfortunately, such functions are difficult to handle in an optimal control framework. We illustrate how the convenience of the quadratic production function can be combined with better approximations to nonlinear production functions.     

Structure preserving simulation of muscle actuated movements

Biomechanical simulation of human locomotion is commonly done via dynamical simulations of multibody systems. The actuation of the system is thereby often represented via muscle models that create a force depending on muscle length and activation level. We show a comparison of such a simulation using a structure preserving integration framework to MATLAB/Simulink results. The conclusion is that structure preservation is important to represent such systems correctly, in particular concerning energy and angular momentum evolutions. We introduce a method for structure preserving simulation of muscle actuated movements. Additionally we show examples of a simple arm movement including only one muscle as well as a finger movement including up to six muscles as an example for more complex biomechanical systems. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Novel method of identifying time series based on network graphs

In this article, we propose a novel method for transforming a time series into a complex network graph. The proposed algorithm is based on the spatial distribution of a time series. The characteristics of geometric parameters of a network represent the dynamic characteristics of a time series. Our algorithm transforms, respectively, a constant series into a fully connected graph, periodic time series into a regular graph, linear divergent time series into a tree, and chaotic time series into an approximately power law distribution network graph. We find that when the dimension of reconstructed phase space increases, the corresponding graph for a random time series quickly turns into a completely unconnected graph, while that for a chaotic time series maintains a certain level of connectivity. The characteristics of the generated network, including the total edges, the degree distribution, and the clustering coefficient, reflect the characteristics of the time series, including diverging speed, level of certainty, and level of randomness. This observation allows a chaotic time series to be easily identified from a random time series. The method may be useful for analysis of complex nonlinear systems such as chaos and random systems, by perceiving the differences in the outcomes of the systems—the time series—in the identification of the systemic levels of certainty or randomness. © 2011 Wiley Periodicals, Inc. Complexity, 2011     

Uniform boundedness of the derivatives of meromorphic inner functions on the real line

Inner functions are an important and popular object of study in the field of complex function theory. We look at meromorphic inner functions with a given spectrum and provide sufficient conditions for them to have uniformly bounded derivative on the real line. This question was first studied by Louis de Branges in 1968 and was later revived by Anton Baranov in 2011.     

The ecology of instructional teacher leadership

Instructional teacher leadership, in which classroom teachers intentionally influence the practice of their colleagues, is a complex social dynamic. In this article, we argue for the use of an analytic framework that acknowledges this complexity, and we apply it to three cases of teacher leaders, all in the context of elementary and middle grades mathematics instruction. In each case, Urie Bronfenbrenner’s ecological systems theory, complemented by social network analysis, proves useful for understanding the unique circumstances and the leadership activities in which the individual is able to engage. This comprehensive framework accounts for factors ranging from those internal to the individual to those inherent in the society at large, viewing the teacher leader as part of a complex social ecosystem of other individuals, institutions, policies and cultural norms. Following a brief overview of the theory, we apply it to the three cases in sequence. We conclude with implications for the field, both those who study instructional teacher leadership and those who train and support teacher leaders.     

Speeding-up structured probabilistic inference using pattern mining

In many domains where experts are the main source of knowledge, e.g., in reliability and risk management, a framework well suited for modeling, maintenance and exploitation of complex probabilistic systems is essential. In these domains, models usually define closed-world systems and result from the aggregation of multiple patterns repeated many times. Object Oriented-based Frameworks such as Probabilistic Relational Models (PRM) thus offer an effective way to represent such systems. They define patterns as classes and substitute large Bayesian networks (BN) by graphs of instances of these classes. In this framework, Structured Inference avoids many computation redundancies by exploiting class knowledge, hence reducing BN inference times by orders of magnitude. However, to keep modeling and maintenance costs low, object oriented-based framework’s classes often encode only generic situations. More complex situations, even those repeated many times, are only represented by combinations of instances. In this paper, we propose to determine online such combination patterns and exploit them as classes to speed-up Structured Inference. We prove that determining an optimal set of patterns is NP-hard. We also provide an efficient algorithm to approximate this set and show numerical experiments that highlight its practical efficiency.     

Local and global existence of mild solution to an impulsive fractional functional integro-differential equation with nonlocal condition

This paper is concerned with the local and global existence of mild solution for an impulsive fractional functional integro differential equations with nonlocal condition. We establish a general framework to find the mild solutions for impulsive fractional integro-differential equations, which will provide an effective way to deal with such problems. The results are obtained by using the fixed point technique and solution operator on a complex Banach space.     

Evolving systems: Adaptive key component control and inheritance of passivity and dissipativity

We propose a new framework called Evolving Systems to describe the self-assembly, or autonomous assembly, of actively controlled dynamical subsystems into an Evolved System with a higher purpose. Autonomous assembly of large, complex flexible structures in space is a target application for Evolving Systems. A critical requirement for autonomous assembling structures is that they remain stable during and after assembly. The fundamental topic of inheritance of stability, dissipativity, and passivity in Evolving Systems is the primary focus of this research. In this paper, we develop an adaptive key component controller to restore stability in Nonlinear Evolving Systems that would otherwise fail to inherit the stability traits of their components. We provide sufficient conditions for the use of this novel control method and demonstrate its use on an illustrative example.     

A neural network approach to efficient valuation of large portfolios of variable annuities

Managing and hedging the risks associated with Variable Annuity (VA) products require intraday valuation of key risk metrics for these products. The complex structure of VA products and computational complexity of their accurate evaluation have compelled insurance companies to adopt Monte Carlo (MC) simulations to value their large portfolios of VA products. Because the MC simulations are computationally demanding, especially for intraday valuations, insurance companies need more efficient valuation techniques. Recently, a framework based on traditional spatial interpolation techniques has been proposed that can significantly decrease the computational complexity of MC simulation (Gan and Lin, 2015). However, traditional interpolation techniques require the definition of a distance function that can significantly impact their accuracy. Moreover, none of the traditional spatial interpolation techniques provide all of the key properties of accuracy, efficiency, and granularity (Hejazi et al., 2015). In this paper, we present a neural network approach for the spatial interpolation framework that affords an efficient way to find an effective distance function. The proposed approach is accurate, efficient, and provides an accurate granular view of the input portfolio. Our numerical experiments illustrate the superiority of the performance of the proposed neural network approach compared to the traditional spatial interpolation schemes.     

Nash equilibrium based fairness

There are several approaches of sharing resources among users. There is a noncooperative approach wherein each user strives to maximize its own utility. The most common optimality notion is then the Nash equilibrium. Nash equilibria are generally Pareto inefficient. On the other hand, we consider a Nash equilibrium to be fair as it is defined in a context of fair competition without coalitions (such as cartels and syndicates). We show a general framework of systems wherein there exists a Pareto optimal allocation that is Pareto superior to an inefficient Nash equilibrium. We consider this Pareto optimum to be ??Nash equilibrium based fair.?? We further define a ??Nash proportionately fair?? Pareto optimum. We then provide conditions for the existence of a Pareto-optimal allocation that is, truly or most closely, proportional to a Nash equilibrium. As examples that fit in the above framework, we consider noncooperative flow-control problems in communication networks, for which we show the conditions on the existence of Nash-proportionately fair Pareto optimal allocations.     

Modeling the complexity of genetic networks: Understanding multigenic and pleiotropic regulation

Molecular genetics presents an increasingly complex picture of the genome and biological function. Evidence is mounting for distributed function, redundancy, and combinatorial coding in the regulation of genes. Satisfactory explanation will require the concept of a parallel processing signaling network. Here we provide an introduction to Boolean networks and their relevance to present-day experimental research. Boolean network models exhibit global complex behavior, self-organization, stability, redundancy and periodicity, properties that deeply characterize biological systems. While the life sciences must inevitably face the issue of complexity, we may well look to cybernetics for a modeling language such as Boolean networks which can manageably describe parallel processing biological systems and provide a framework for the growing accumulation of data. We finally discuss experimental strategies and database systems that will enable mapping of genetic networks. The synthesis of these approaches holds an immense potential for new discoveries on the intimate nature of genetic networks, bringing us closer to an understanding of complex molecular physiological processes like brain development, and intractable medical problems of immediate importance, such as neurodegenerative disorders, cancer, and a variety of genetic diseases.     

Comment on: “Topology identification and adaptive synchronization of uncertain complex networks with adaptive double scaling functions” [Commun Nonlinear Sci Numer Simul 2011;16:3337-43]

In this comment letter we point out that the main result of the recent paper [Xu Y, Zhou W, Fang J, Sun W. Topology identification and adaptive synchronization of uncertain complex networks with adaptive double scaling functions. Commun Nonlinear Sci Numer Simul 2011;16(18):3337-43] has certain errors. The mistakes are corrected and a correct version is presented in this letter. We further indicate that a sufficient condition has been neglected in a series of articles discussing the same topic of network topology identification; hence we hope this letter can help clarify some unclear concepts about this topic.     

Disjointness in hypercyclicity

We introduce a notion of disjointness for finitely many hypercyclic operators acting on a common space, notion that is weaker than Furstenberg's disjointness of fluid flows. We provide a criterion to construct disjoint hypercyclic operators, that generalizes some well-known connections between the Hypercyclicity Criterion, hereditary hypercyclicity and topological mixing to the setting of disjointness in hypercyclicity. We provide examples of disjoint hypercyclic operators for powers of weighted shifts on a Hilbert space and for differentiation operators on the space of entire functions on the complex plane.     

Cyber Swarm Algorithms – Improving particle swarm optimization using adaptive memory strategies

Particle swarm optimization (PSO) has emerged as an acclaimed approach for solving complex optimization problems. The nature metaphors of flocking birds or schooling fish that originally motivated PSO have made the algorithm easy to describe but have also occluded the view of valuable strategies based on other foundations. From a complementary perspective, scatter search (SS) and path relinking (PR) provide an optimization framework based on the assumption that useful information about the global solution is typically contained in solutions that lie on paths from good solutions to other good solutions. Shared and contrasting principles underlying the PSO and the SS/PR methods provide a fertile basis for combining them. Drawing especially on the adaptive memory and responsive strategy elements of SS and PR, we create a combination to produce a Cyber Swarm Algorithm that proves more effective than the Standard PSO 2007 recently established as a leading form of PSO. Applied to the challenge of finding global minima for continuous nonlinear functions, the Cyber Swarm Algorithm not only is able to obtain better solutions to a well known set of benchmark functions, but also proves more robust under a wide range of experimental conditions.     

Boundary controllability of parabolic coupled equations

This paper is concerned with the boundary controllability of non-scalar linear parabolic systems. More precisely, two coupled one-dimensional parabolic equations are considered. We show that, in this framework, boundary controllability is not equivalent and is more complex than distributed controllability. In our main result, we provide necessary and sufficient conditions for the null controllability.     

Network structure,perception level,and participants' welfares

Based on a market consisting of one monopoly and several customers who are embedded in an economic network, we study how the different perception levels about the network structure affect the two kinds of participants' welfares, and then provide some good strategies for the monopoly to mine the information of the network structure. The above question is the embodiment of the “complex structure and its corresponding functions” question often mentioned in the field of complexity science. We apply a two‐stage game to solve for the optimal pricing and consumption at different perception levels of the monopoly and further utilize simulation analysis to explore the influence patterns. We also discuss how this theoretic model can be applied to a real world problem by introducing the statistical exponential random graph model and its estimation method. Further, the main findings have specific policy implications on uncovering network information and demonstrate that it is possible for the policy‐maker to design some win–win mechanisms for uplifting both the monopoly's profit and the whole customers' welfare at the same time. © 2014 Wiley Periodicals, Inc. Complexity 21: 349–362, 2015     

A complex adaptive systems perspective of innovation diffusion: an integrated theory and validated virtual laboratory

In this paper we integrate the rich yet fragmented insights from the extensive literature on the diffusion of innovation into an elegant, coherent model. Using complex adaptive systems theory as the overarching framework, we integrate prior literature around three constructs: agents, interactions, and an environment. The integrated model is presented in both natural language and as an agent-based simulation model. A series of validation experiments instill confidence that our agent-based model (and similar others) can be used as a virtual research laboratory. We provide theoretical and methodological directions for future research.