Extending the process of comparison in soft systems methodology

Soft systems methodology (SSM) is a leading interpretive approach to real-world problem management and the idea of comparison is one of its core concepts. However, it is argued in this paper that the concept of comparison could be usefully enriched and made easier to operationalise since it has received very little attention in the research literature. The paper explores comparison as a problem area and proposes a framework consisting of expectation, desirability and importance as a basis for extending and clarifying the notion of comparison.     

Global convergence of SSM for minimizing a quadratic over a sphere

In an earlier paper [Minimizing a quadratic over a sphere, SIAM J. Optim., 12 (2001), 188-208], we presented the sequential subspace method (SSM) for minimizing a quadratic over a sphere. This method generates approximations to a minimizer by carrying out the minimization over a sequence of subspaces that are adjusted after each iterate is computed. We showed in this earlier paper that when the subspace contains a vector obtained by applying one step of Newton's method to the first-order optimality system, SSM is locally, quadratically convergent, even when the original problem is degenerate with multiple solutions and with a singular Jacobian in the optimality system. In this paper, we prove (nonlocal) convergence of SSM to a global minimizer whenever each SSM subspace contains the following three vectors: (i) the current iterate, (ii) the gradient of the cost function evaluated at the current iterate, and (iii) an eigenvector associated with the smallest eigenvalue of the cost function Hessian. For nondegenerate problems, the convergence rate is at least linear when vectors (i)-(iii) are included in the SSM subspace.

     

An acquisition policy for a single item multi-supplier system with real-world constraints

This paper proposes an exact acquisition policy for solving the single-item multi-supplier problem with real-world constraints. Compared with the model of Rosenblatt et al. [Note. An acquisition policy for a single item multi-supplier system, Manage. Sci. 44 (1998) S96–S100], the proposed method has contributions in that the global optimal solutions can be obtained to indicate the best acquisition policy, and real-world constraints can easily be added as appropriate for real-world situations. In addition, the benefits of price-quantity discount (PQD) under conditions of the single item muti-supplier system are also considered in the paper.     

Learning from conflicts in propositional satisfiability

Learning is a general concept, playing an important role in many Artificial intelligence domains. In this paper, we address the learning paradigm used to explain failures or conflicts encountered during search. This explanation, derived by conflict analysis, and generally expressed as a new constraint, is usually used to dynamically avoid future occurrences of similar situations. Before focusing on clause learning in Boolean satisfiability (SAT), we first overview some important works on this powerful reasoning tool in other domains such as constraint satisfaction and truth maintenance systems. Then, we present a comprehensive survey of the most important works having led to what is called today—conflict driven clause learning (CDCL)—which is one of the key components of modern SAT solvers. In theory, current SAT solvers with clause learning are as powerful as general resolution proof systems. In practice, real-world SAT instances with millions of variables and clauses are now in the scope of this solving paradigm.     

An application of Soft Systems Dynamics Methodology (SSDM)

The paper argues that by combining some of systems dynamics (SD) and soft systems methodology (SSM) stages, within the intellectual framework proposed by soft systems dynamics methodology (SSDM), a systemic methodology developed by Rodriguez-Ulloa, much can be gained in a systemic intervention when tackling complex social problematic situations. A framework for comparing the ontological, epistemological and methodological principles of SD, SSM and SSDM is proposed and the synthesizing role of SSDM is advanced. SSDM ten stages are briefly outlined and a full account of an application on a small Peruvian enterprise is presented. A reflection on SSDM as a systemic intellectual tool is proposed and conclusions together with points for further research are suggested.     

Where There's a Model, There's a Metaphor: Metaphorical Thinking in Students' Understanding of a Mathematical Model

The central question addressed in this article concerns the ways in which applied problem situations provide distinctive conditions to support the production of meaning and the understanding of mathematical topics. In theoretical terms, a first approach is rooted in C. S. Peirce's perspective on semiotic mediation, and it represents a standpoint from which the notion of interpretation is taken as essential to learning. A second route explores metaphorical thinking and undertakes the position according to which human understanding is metaphorical in its own nature. The connection between the two perspectives becomes a fundamental issue, and it entails the conception of some hybrid constructs. Finally, the analysis of empirical data suggests that the activity on applied situations, as it fosters metaphorical thinking, offer students' reasoning a double anchoring (or a duplication of references) for mathematical concepts.     

Where There's a Model,There's a Metaphor: Metaphorical Thinking in Students' Understanding of a Mathematical Model

The central question addressed in this article concerns the ways in which applied problem situations provide distinctive conditions to support the production of meaning and the understanding of mathematical topics. In theoretical terms, a first approach is rooted in C. S. Peirce's perspective on semiotic mediation, and it represents a standpoint from which the notion of interpretation is taken as essential to learning. A second route explores metaphorical thinking and undertakes the position according to which human understanding is metaphorical in its own nature. The connection between the two perspectives becomes a fundamental issue, and it entails the conception of some hybrid constructs. Finally, the analysis of empirical data suggests that the activity on applied situations, as it fosters metaphorical thinking, offer students' reasoning a double anchoring (or a duplication of references) for mathematical concepts.     

Opportunities to Learn: Inverse Relations in U.S. and Chinese Textbooks

This study, focusing on inverse relations, examines how representative U.S. and Chinese elementary textbooks may provide opportunities to learn fundamental mathematical ideas. Findings from this study indicate that both of the U.S. textbook series (grades K-6) in comparison to the Chinese textbook samples (grades 1–6), presented more instances of inverse relations, while also containing more unique types of problems; yet, the Chinese textbooks provided more opportunities supporting meaningful and explicit learning. In particular, before presenting corresponding practice problems, Chinese textbooks contextualized worked examples of inverse relations in real-world situations to aid in sense making of computational or checking procedures. The Chinese worked examples also differed in representation uses especially through concreteness fading. Finally, the Chinese textbooks spaced learning over time, systematically stressing structural relations including the inverse quantities relationships. These findings shed light on ways to support students’ meaningful and explicit learning of fundamental mathematical ideas in elementary school.     

Integrating memetic search into the BioHEL evolutionary learning system for large-scale datasets

Local search methods are widely used to improve the performance of evolutionary computation algorithms in all kinds of domains. Employing advanced and efficient exploration mechanisms becomes crucial in complex and very large (in terms of search space) problems, such as when employing evolutionary algorithms to large-scale data mining tasks. Recently, the GAssist Pittsburgh evolutionary learning system was extended with memetic operators for discrete representations that use information from the supervised learning process to heuristically edit classification rules and rule sets. In this paper we first adapt some of these operators to BioHEL, a different evolutionary learning system applying the iterative learning approach, and afterwards propose versions of these operators designed for continuous attributes and for dealing with noise. The performance of all these operators and their combination is extensively evaluated on a broad range of synthetic large-scale datasets to identify the settings that present the best balance between efficiency and accuracy. Finally, the identified best configurations are compared with other classes of machine learning methods on both synthetic and real-world large-scale datasets and show very competent performance.     

Exact observability,square functions and spectral theory

In the first part of this article we introduce the notion of a backward–forward conditioning (BFC) system that generalises the notion of zero-class admissibility introduced in Xu et al. (2008) [30]. We can show that unless the spectrum contains a half-plane, the BFC property occurs only in situations where the underlying semigroup extends to a group. In a second part we present a sufficient condition for exact and final state observability in Banach spaces that is designed for infinite-dimensional output spaces and general strongly continuous semigroups. To obtain this we make use of certain weighted square function estimates. Specialising to the Hilbert space situation we obtain a result for contraction semigroups without an analyticity condition on the semigroup.     

增量式Huber-支持向量回归机算法研究

传统的面向支持向量回归的一次性建模算法中样本增加时,均需从头开始学习,而增量式算法可以充分利用上一阶段的学习成果。SVR的增量算法通常基于ε-不敏感损失函数,该损失函数对大的异常值比较敏感,而Huber损失函数对异常值敏感度低。所以在有噪声的情况下,Huber损失函数是比ε-不敏感损失函数更好的选择,在现实情况当中。基于此,本文提出了一种基于Huber损失函数的增量式Huber-SVR算法,该算法能够持续地将新样本信息集成到已经构建好的模型中,而不是重新建模。与增量式ε-SVR算法和增量式RBF算法相比,在对真实数据进行预测建模时,增量式Huber-SVR算法具有更高的预测精度。     

The greater whole: Towards a synthesis of system dynamics and soft systems methodology

This paper makes a theoretical case for using these two systems approaches together. The theoretical and methodological assumptions of system dynamics (SD) and soft system methodology (SSM) are briefly described and a partial critique is presented. SSM generates and represents diverse perspectives on a problem situation and addresses the socio-political elements of an intervention. However, it is weak in ensuring `dynamic coherence'. consistency between the intuitive behaviour resulting from proposed changes and behaviour deduced from ideas on causal structure. Conversely, SD examines causal structures and dynamic behaviours. However, whilst emphasising the need for a clear issue focus, it has little theory for generating and representing diverse issues. Also, there is no theory for facilitating sensitivity to socio-political elements. A synthesis of the two called ‘Holon Dynamics' is proposed. After an SSM intervention, a second stage continues the socio-political analysis and also operates within a new perspective which values dynamic coherence of the mental construct - the holon - which is capable of expressing the proposed changes. A model of this holon is constructed using SD and the changes are thus rendered `systemically desirable' in the additional sense that dynamic consistency has been confirmed. The paper closes with reflections on the proposal and the need for theoretical consistency when mixing tools is emphasised.     

Multiple criteria districting problems

Districting problems are of high importance in many different fields. Multiple criteria models seem a more adequate representation of districting problems in real-world situations. Real-life decision situations are by their very nature multidimensional. This paper deals with the problem of partitioning a territory into “homogeneous” zones. Each zone is composed of a set of elementary territorial units. A district map is formed by partitioning the set of elementary units into connected zones without inclusions. When multiple criteria are considered, the problem of enumerating all the efficient solutions for such a model is known as being NP-hard, which is why we decided to avoid using exact methods to solve large-size instances. In this paper, we propose a new method to approximate the Pareto front based on an evolutionary algorithm with local search. The algorithm presents a new solution representation and the crossover/mutation operators. Its main features are the following: it deals with multiple criteria; it allows to solve large-size instances in a reasonable CPU time and generates high quality solutions. The algorithm was applied to a real-world problem, that of the Paris region public transportation. Results will be used for a discussion about the reform of its current pricing system.     

A Combination Theorem for Metric Bundles

We introduce the notion of metric (graph) bundles which provide a coarse-geometric generalization of the notion of trees of metric spaces a la Bestvina?CFeighn in the special case that the inclusions of the edge spaces into the vertex spaces are uniform coarsely surjective quasi-isometries. We prove the existence of quasi-isometric sections in this generality. Then we prove a combination theorem for metric (graph) bundles that establishes sufficient conditions, particularly flaring, under which the metric bundles are hyperbolic. We use this to give examples of surface bundles over hyperbolic disks, whose universal cover is Gromov-hyperbolic. We also show that in typical situations, flaring is also a necessary condition.     

Expanding context and domain: A cross-curricular activity in mathematics and physics

This article is based on my 15 years of experience as a teacher of mathematics and physics in the Danish Gymnasium (high school), and it gives an example of an interdisciplinary course between mathematics and physics. The course is centered around the concept of exponential functions. The starting point is that concepts are rooted in practice and gain their meaning through application, and the concept of a function is regarded as a tool for modelling real-world situations. It is the intention to teach a course that emphasizes factors that promote transfer of the concept and use of the various representations of the concept, to make it more practical and meaningful for the students. It is concluded that a coordinated cross-curricular activity between mathematics and physics, by offering a great variety of domain relations and context settings, has a great potential for creating a learning environment where the students, through applicational and modelling activities, are engaged actively in constructing and using knowledge.     

A constraint programming-based approach to the crew scheduling problem of the Taipei mass rapid transit system

This paper addresses the crew scheduling problem for a mass rapid transit (MRT) system. The problem is to find a minimum number of duties to cover all tasks while satisfying all the hard and soft scheduling rules. Such rules are complicated in real-world operations and difficult to follow through optimization methods alone. In this paper, we propose a constraint programming (CP)-based approach to solve the problem. The approach involves a CP model for duty generation, a set covering problem model for duty optimization, and alternative ways to identify the final solution in different situations. We applied the proposed CP-based approach to solve a case problem for the Taipei MRT. Case application results using real-world data showed that our approach is capable of reducing the number of daily duties from 58 to 55 and achieving a 5.2 % savings in labor costs. We also incorporated the soft rule considerations into the CP model in order to generate alternative optimum solutions that would improve the workload balance. The coefficient of variation of the work time distribution improves significantly, falling from 21 % to approximately 5 %. Given the CP model’s comprehensive coverage of various scheduling rules, our proposed approach and models would also be applicable to other MRT systems.     

Generalization bounds of ERM algorithm with Markov chain samples

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.     

Arguing About the Effectiveness of Assessments for the Classroom

Approaches to test score use and test purpose lack the well-developed methodological guidelines and established sources of evidence available for intended score interpretation. We argue in this paper that this lack fails to reflect the ultimate purpose of a test score—to help solve an important problem faced by intended test users. We explore the treatment of intended test purpose and test score use under the chain of assumption/inferences perspective identified within an argument-based approach to validity. Next, we revisit the notion of test score use and argue that, at least for classroom assessments based on complex constructs, such as learning progressions in math and science, test score use can be more effectively conceptualized as part of a potential solution to solving a problem, or “job-to-be-done.”. We argue for shifting from the definition of validity to the concept of effectiveness. Finally, we illustrate an argument- based approach to test score effectiveness by contrasting effectiveness arguments for interim assessments based on a conventional test blueprint or a test blueprint augmented with learning progressions.     

Generalized Assignment Type Goal Programming Problem: Application to Nurse Scheduling

The notion of the Generalized Assignment Type Goal Programming Problem is introduced to consider the additional side constraints of an Assignment Type problem as goal functions. A short term Tabu Search method together with diversification strategies are used to deal with this model. The methods are tested on real-world Nurse Scheduling Problems.     

On the nature of discontinuities in system dynamics modelling of disrupted projects

When complex projects result in large-cost over-runs, managers want to understand why this happened. There may be the possibility of making a claim against another party, or managers may simply wish to learn from any mistakes made. When using system dynamics (SD) models to analyse the reasons for project over-runs as a part of a litigation or organizational learning process, there is a strong focus on explaining historical aspects precisely. This leads to a need for the inclusion of discontinuous variables. This paper discusses the nature of discontinuities in SD models of project over-runs. Examples are given to demonstrate that the modelling of such discontinuities needs to be an integral part of the continuous simulation modelling process. Their inclusion helps to improve model validity and also, by forcing validity, uncover the important drivers of project behaviour. The examples given in this paper are significant drivers and suggest important learning about the behaviour of disrupted complex projects.