两类Chemotaxis模型解的性质

本文讨论了抛物-双曲和抛物-常微两个Chemotaxis模型初边值问题解的性质.利用形式级数展开的方法，得到全局解在微小扰动下，导致解在有限时间内爆破，并对爆破时间进行了估计.因此说明了这种模型空间齐性解的不稳定性。     

A contracting model for flexible distributed scheduling

We are interested in building systems of autonomous agents that can automate routine information processing activities in human organizations. Computational infrastructures for cooperative work should contain embedded agents for handling many routine tasks [9], but as the number of agents increases and the agents become geographically and/or conceptually dispersed, supervision of the agents will become increasingly problematic. We argue that agents should be provided with deep domain knowledge that allows them to make quantitatively justifiable decisions, rather than shallow models of users to mimic. In this paper, we use the application domain of distributed meeting scheduling to investigate how agents embodying deeper domain knowledge can choose among alternative strategies for searching their calendars in order to create flexible schedules within reasonable cost.     

Nonparametric Bayesian topic modelling with the hierarchical Pitman–Yor processes

The Dirichlet process and its extension, the Pitman–Yor process, are stochastic processes that take probability distributions as a parameter. These processes can be stacked up to form a hierarchical nonparametric Bayesian model. In this article, we present efficient methods for the use of these processes in this hierarchical context, and apply them to latent variable models for text analytics. In particular, we propose a general framework for designing these Bayesian models, which are called topic models in the computer science community. We then propose a specific nonparametric Bayesian topic model for modelling text from social media. We focus on tweets (posts on Twitter) in this article due to their ease of access. We find that our nonparametric model performs better than existing parametric models in both goodness of fit and real world applications.     

Children with mathematical difficulties cope with modelling tasks: what develops?

This study investigates the participation and knowledge growth of children with mathematical difficulties as they work in groups with their classmates on a year-long sequence of modelling tasks. It involves observations of a class of 23 fifth graders, 9 of whom were identified as having difficulties in mathematics. All the students worked for 8 months on a sequence of 12 modelling task in heterogeneous groups. The findings show a gradual growth in modelling competencies and mathematical knowledge of the students with mathematical difficulties together with an increase in their contribution to the group. The growth in modelling competencies involved their ability to analyse situations and the growth of mathematical knowledge was evident in offering mathematical ideas during group work and in a better posttest performance. Student reflections indicated their awareness of these changes and of the appreciation of their ideas by their peers.     

Three kinds of normative behaviour: minimal requirements for feedback models

We present an analysis for modelling social norms. In social psychology three different normative behaviours have been identified: obedience, conformity and compliance. We show that this triad is a useful conceptualisation of normative behaviour and that current models only ever deal with conformity and obedience two, neglecting compliance. We argue that this is a result from modelling having so far focussed too much on agent behaviour rather than agent knowledge and that cognitive models of normative behaviour are needed to capture this third and arguably most interesting normative behaviour.     

Metamodels for role-driven agent-based modelling

A major challenge in agent-based modelling is the management of the process to generate executable simulations from the initial conceptual models. This process is complex and usually involves several roles, which may raise communication problems due to the diverse backgrounds and perspectives of participants and the use of non-explicit knowledge. This situation demands a clear separation and precise definition of the multiple aspects of the process, in order to facilitate their understanding, grasp their relationships and develop them. This paper addresses this goal with a fine-step refinement process for information based on the use of domain-specific languages. It considers analysis contexts that include a particular theoretical framework, domain, type of problem and target platform. For a given context, the process formally defines modelling languages conceptually close to the different aspects relevant to it. It also defines mappings between concepts in those languages. Researchers develop simulations by specifying models with the languages, and share and refine information by using mappings between these models. This infrastructure provides guidance throughout the process and makes the information involved explicit. A case study of continuous double auctions illustrates the approach.     

Decision development in facilitated modelling workshops

While the facilitated modelling literature recognises the importance of the group process within facilitated modelling workshops, published empirical research rarely examines their dynamic nature. In this paper, we address this gap in the literature in two ways. First, we propose to locate facilitated modelling workshops as the main focus of investigation, and adopt decision development as the analytical lens. Second, we provide guidance regarding how to implement a research strategy that is informed by such a focus. We start by mapping the different conceptualisations of decision development that seem embedded within the facilitated modelling tradition, and contrast them with theoretical models from the group communication field. Our analysis identifies a number of potentially useful areas for the study of facilitated modelling workshops from a decision development perspective, and articulates a number tentative research questions and testable propositions amenable to empirical research. Central to our proposal are research methods for the study of dynamic group processes. We thus discuss the steps required to extract group process data from facilitated modelling workshops that are usable and open to analysis. This includes a review of issues regarding research design, coding scheme development, data coding and choice of analytical techniques. Finally, we offer conclusions and briefly discuss some feasibility issues related to the implementation of our proposal.     

Accept & reject statement-based uncertainty models

We develop a framework for modelling and reasoning with uncertainty based on accept and reject statements about gambles. It generalises the frameworks found in the literature based on statements of acceptability, desirability, or favourability and clarifies their relative position. Next to the statement-based formulation, we also provide a translation in terms of preference relations, discuss—as a bridge to existing frameworks—a number of simplified variants, and show the relationship with prevision-based uncertainty models. We furthermore provide an application to modelling symmetry judgements.     

An architecture for knowledge evolution in organisations

Methodology for Knowledge System Management (MKSM) is a methodology, based on modelling techniques, to support knowledge capitalisation and management. This kind of approach faces a new challenge: knowledge evolution. Indeed, as knowledge of the organisation evolves, it seems necessary to have models and supporting tools to represent this evolution. Biologic evolution theories can offer the basis of a dynamic theory of Knowledge System evolution. We especially propose to adapt Lamarckism's principles and the Cladistic classification to support such a modelling and propose a conceptual architecture for managing knowledge evolution.     

Supervision of teachers based on adjusted arithmetic learning in special education

This article reports on 20 children's learning in arithmetic after teaching was adjusted to their conceptual development. The report covers periods from three months up to three terms in an ongoing intervention study of teachers and children in schools for the intellectually disabled and of remedial teaching in regular schools. The researcher classified each child's current counting scheme before and after each term. Recurrent supervision, aiming to facilitate the teachers’ modelling of their children's various conceptual levels and needs of learning, was conducted by the researcher. The teaching content in harmony with each child's ability was discussed with the teachers. This approach gives the teachers the opportunity to experience the children's own operational ways of solving problems. At the supervision meetings, the teachers theorized their practice together with the researcher, ending up with consistent models of the arithmetic of the child. So far, the children's and the teachers’ learning patterns are promising.     

Domain knowledge integration in data mining using decision tables: case studies in churn prediction

Companies' interest in customer relationship modelling and key issues such as customer lifetime value and churn has substantially increased over the years. However, the complexity of building, interpreting and applying these models creates obstacles for their implementation. The main contribution of this paper is to show how domain knowledge can be incorporated in the data mining process for churn prediction, viz. through the evaluation of coefficient signs in a logistic regression model, and secondly, by analysing a decision table (DT) extracted from a decision tree or rule-based classifier. An algorithm to check DTs for violations of monotonicity constraints is presented, which involves the repeated application of condition reordering and table contraction to detect counter-intuitive patterns. Both approaches are applied to two telecom data sets to empirically demonstrate how domain knowledge can be used to ensure the interpretability of the resulting models.     

Bilateral gamma distributions and processes in financial mathematics

We present a class of Lévy processes for modelling financial market fluctuations: bilateral Gamma processes. Our starting point is to explore the properties of bilateral Gamma distributions, and then we turn to their associated Lévy processes. We treat exponential Lévy stock models with an underlying bilateral Gamma process as well as term structure models driven by bilateral Gamma processes, and apply our results to a set of real financial data (DAX 1996–1998).     

Measuring and investigating strategic knowledge about drawing to solve geometry modelling problems

We report on the construction, validation, and implementation of an instrument for measuring students’ strategic knowledge about drawing for geometry modelling problems, namely, the strategic knowledge about drawing scale. We conducted a qualitative study and a quantitative study to validate the proposed construction and interpretation of the scale and to obtain initial findings on students’ strategic knowledge about drawing. Results showed that ninth-grade students in the intermediate achievement track had less elaborated strategic knowledge about drawing than their peers in the high achievement track. Further, strategic knowledge about drawing was found to be related to drawing accuracy and modelling performance even when cognitive abilities and interest were controlled for. The current study suggests that promoting strategic knowledge about drawing might be a means to increase drawing and modelling performance—especially among non-high-achieving students.     

Polynomial Processes for Power Prices

ABSTRACT

Polynomial processes have the property that expectations of polynomial functions (of degree n, say) of the future state of the process conditional on the current state are given by polynomials (of degree ≤ n) of the current state. Here we explore the potential of polynomial maps of polynomial processes for modelling energy prices. We focus on the example of Alberta power prices, derive one- and two-factor models for spot prices. We examine their performance in numerical experiments, and demonstrate that the richness of the dynamics they are able to generate makes them well suited for modelling even extreme examples of energy price behaviour.     

On the modelling of nested risk-neutral stochastic processes with applications in insurance

We propose a modelling framework for risk-neutral stochastic processes nested in a real-world stochastic process. The framework is important for insurers that deal with the valuation of embedded options and in particular at future points in time. We make use of the class of State Space Hidden Markov models for modelling the joint behaviour of the parameters of a risk-neutral model and the dynamics of option market instruments. This modelling concept enables us to perform non-linear estimation, forecasting and robust calibration. The proposed method is applied to the Heston model for which we find highly satisfactory results. We use the estimated Heston model to compute the required capital of an insurance company under Solvency II and we find large differences compared to a basic calibration method.     

Exploring communication networks to understand organizational crisis using exponential random graph models

In recent social network studies, exponential random graph (ERG) models have been used comprehensively to model global social network structure as a function of their local features. In this study, we describe the ERG models and demonstrate its use in modelling the changing communication network structure at Enron Corporation during the period of its disintegration. We illustrate the modelling on communication networks, and provide a new way of classifying networks and their performance based on the occurrence of their local features. Among several micro-level structures of ERG models, we find significant variation in the appearance of A2P (Alternating k-two-paths) network structure in the communication network during crisis period and non-crisis period. We also notice that the attribute of hierarchical positions of actors (i.e., high rank versus low rank staff) have impact on the evolution process of networks during crisis. These findings could be used in analyzing communication networks of dynamic project groups and their adaptation process during crisis which could lead to an improved understanding how communications network evolve and adapt during crisis.     

Research on the reasoning, teaching and learning of probability and uncertainty

In this editorial, we set out the aims in the call to publish papers on informal statistical inference, randomness, modelling and risk. We discuss how the papers published in this issue have responded to those aims. In particular, we note how the nine papers contribute to some of the major debates in mathematics and statistics education, often taking contrasting positions. Such debates range across: (1) whether knowledge is fractured or takes the form of mental models; (2) heuristic or intuitive thinking versus operational thinking as for example in dual process theory; (3) the role of different epistemic resources, such as perceptions, modelling, imagery, in the development of probabilistic reasoning; (4) how design and situation impact upon probabilistic learning.     

Decision support models in climate policy

Climate change is considered among the most critical risks that global society faces in this century. So far, climate policy strategies have been evaluated by means of a variety of climate-economy models, or Integrated Assessment Models (IAMs), in the aim of supporting climate-related decision making. However, their inherent complexity, the number and nature of driving assumptions, and usual exclusion of stakeholders from the modelling process raise the issue of the extent to which they can provide fruitful insights for policy makers. Moreover, as with all modelling frameworks, IAMs inevitably fail to incorporate all relevant types of uncertainty and risk when used as stand-alone tools. This exclusion can have a significant impact on the model outcomes, but can be mitigated if experts’ knowledge is elicited in a structured manner and effectively taken into account, towards identifying such factors or reducing respective knowledge gaps. At the same time, a growing number of research publications have been suggesting decision support frameworks for assessing specific aspects in climate policy, based on “bottom-up” approaches and participatory processes. The objective of this paper is to provide a critical review of such frameworks—namely Portfolio Analysis, Multiple Criteria Decision Making and Fuzzy Cognitive Maps—in order to explore their strengths and weaknesses in this area, and propose a new integrative approach, appropriately exploiting blends of these frameworks, to productively complement IAMs, towards enhancing climate policy support.