Knowledge representation for mathematical discovery: Three experiments in graph theory

This paper describes the nature of mathematical discovery (including concept definition and exploration, example generation, and theorem conjecture and proof), and considers how such an intelligent process can be simulated by a machine. Although the material is drawn primarily from graph theory, the results are immediately relevant to research in mathematical discovery and learning.The thought experiment, a protocol paradigm for the empirical study of mathematical discovery, highlights behavioral objectives for machine simulation. This thought experiment provides an insightful account of the discovery process, motivates a framework for describing mathematical knowledge in terms of object classes, and is a rich source of advice on the design of a system to perform discovery in graph theory. The evaluation criteria for a discovery system, it is argued, must include both a set of behavior to display (behavioral objectives) and a target set of facts to be discovered (factual knowledge).Cues from the thought experiment are used to formulate two hierarchies of representational languages for graphy theory. The first hierarchy is based on the superficial terminology and knowledge of the thought experiment. Generated by formal grammars with set-theoretic semantics, this eminently reasonable approach ultimately fails to meet the factual knowledge criteria. The second hierarchy uses declarative expressions, each of which has a semantic interpretation as a stylized, recursive algorithm that defines a class by generating it correctly and completely. A simple version of one such representation is validated by a successful, implemented system called Graph Theorist (GT) for mathematical research in graph theory. GT generates correct examples, defines and explores new graph theory properties, and conjectures and proves theorems.Several themes run through this paper. The first is the dual goals, behavioral objectives and factural knowledge to be discovered, and the multiplicity of their demands on a discovery system. The second theme is the central role of object classes to knowledge representation. The third is the increased power and flexibility of a constructive (generator) definition over the more traditional predicate (tester) definition. The final theme is the importance of examples and recursion in mathematical knowledge. The results provide important guidance for further research in the simulation of mathematical discovery.     

The social consequences of expressive suppression.

At times, people keep their emotions from showing during social interactions. The authors' analysis suggests that such expressive suppression should disrupt communication and increase stress levels. To test this hypothesis, the authors conducted 2 studies in which unacquainted pairs of women discussed an upsetting topic. In Study 1, one member of each pair was randomly assigned to (a) suppress her emotional behavior, (b) respond naturally, or (c) cognitively reappraise in a way that reduced emotional responding. Suppression alone disrupted communication and magnified blood pressure responses in the suppressors' partners. In Study 2, suppression had a negative impact on the regulators' emotional experience and increased blood pressure in both regulators and their partners. Suppression also reduced rapport and inhibited relationship formation. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Effect of sampling density on the measurement of stream condition indicators in two lowland Australian streams

There is widespread application of indicators to the assessment of environmental condition of streams. These indicators are intended for use by managers in making various comparative and absolute assessments and often have a role in resource allocation and performance assessment. Therefore, the problem of formally defining confidence in the results is important but difficult because the sampling strategies used are commonly based on a compromise between the requirements of statistical rigour and the pragmatic issues of access and resources. It is rare to see this compromise explicitly considered and consequently there is seldom quantification of the uncertainty that could affect the confidence a manager has in an indicator. In this paper, we present a method for quantitatively assessing the tradeoffs between sampling density and uncertainty in meeting various monitoring objectives. Assessments using judgement‐based representative reaches are shown to be unreliable; instead a sampling approach is recommended based on the random selection of measuring sites. A detailed dataset was collected along two streams in Victoria, Australia, and the effect of sampling density was assessed by subsampling from this dataset with precision related to the number of sites assessed per reach length and the intensity of the sampling at each site. The sampling scheme to achieve a given precision is shown to depend on the monitoring objective. In particular, three objectives were considered: (1) making a baseline assessment of current condition; (2) change detection; and (3) detection of a critical threshold in condition. Change detection is shown to be more demanding than assessing baseline condition with additional sampling effort required to achieve the same precision. Sampling to detect a critical threshold depends on nominating acceptable values of Type I and II error and the size of the effect to be detected. Copyright © 2006 John Wiley & Sons, Ltd.     

Mathematical model of an industrial robot with articulated configuration and six degrees of freedom

This paper analyses the load influence on a d.c. drive motor servo system for all six degrees of freedom of industrial robots with an articulated configuration. Through the analyses, the analytical equations of total inertia and gravitation moments of an industrial robot servo system for external coordinate function were obtained. A mathematical model of an electro-mechanical industrial robot system was also developed.     

On the geometrical material structure of anelasticity

Summary G-structures are the geometric backbone of the theory of material uniformity in continuum mechanics. Within this geometric framework, anelasticity is seen as a result of evolving distributions of inhomogeneity reflected as material nonintegrability. Constitutive principles governing thetime evolution of the G-structure underlying the finite-strain theory of anelasticity (e.g., plasticity) are proposed. The material Eshelby stress tensor is shown to be thedriving force behind this evolution. This should allow for a thermodynamically admissible formulation of anelasticity viewed as a G-structure evolution.     

The bone marrow stromal environment is a major factor in myeloma cell resistance to dexamethasone

The expression of several markers of epithelial cell proliferation was analyzed to establish baseline data for future chemoprevention studies of oral premalignant lesions. Punch biopsies (n = 60) from three different sites of oral mucosa (bucca, lateral tongue, and the floor of the mouth) were obtained from 20 normal donors of both sexes. After formaldehyde fixation and paraffin embedding, immunohistochemistry was used to detect the proliferation markers Mib-1, cyclin D1, and centromere-associated protein CENP-F. Analysis of sections stained for the three markers showed similar patterns, i.e., a low labeling index (LI) in the basal layer and a high LI in the parabasal layer at all three intraoral sites. No proliferative activity was seen above the parabasal layer (superficial layer). All sites showed similar Mib-1 LI values for the proliferative markers. The tongue epithelium exhibited higher parabasal LIs of cyclin D1 and CENP-F than did the other two sites. No significant differences were detected between smokers and nonsmokers. The data from normal mucosa were compared with those from low (n = 30)- and high (n = 17)-grade dysplastic leukoplakias. The Mib-1 LI showed a very significant change, with a 9-fold increase in the basal layer LI in dysplastic leukoplakias. Cyclin D1 and CENP-F showed similar trends with increments of up to 7-fold in the basal layer of high-grade dysplasia. Although the proliferative activity of the parabasal layer was similar in normal and leukoplakic epithelia, the superficial layer showed a significant increment in proliferative activity mainly in high-grade leukoplakia. These studies suggest that proliferation markers in the basal and superficial cells of premalignant lesions may serve as surrogate end point biomarkers for chemoprevention trials.     

On the modification of reprints.

Defends the practice of modifying reprints of journal articles to amend typographical and other errors that can affect meaning. A standard should be developed for dealing with such errors by hand writing corrections, including a list of errata, or issuing professionally corrected reprints with the notation that corrections have been made. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

联合式电路保护有助于防止损坏DVB网络设备

随着广播、电信和IT业的融合，未来的电话和数字电视都将成为互联网上的应用，这样就需要采用新型的客户端设备（CPE）和网络基础设施，以适应更高数据传输速率的要求，并满足新出现的DVB—T／S／C标准以及符合当前和提议中的通讯要求。