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.     

Evaluating part designs for automatic feeding in robotic assembly systems: A geometric analysis of the nesting of polyhedral objects

One of the problems encountered by automatic feeding devices, such as vibratory bowl feeders, in robotic assembly systems is nesting which leads to inseparability of parts and jamming. In this paper, we describe a design evaluation procedure to determine whether a part is prone to nesting and to quantify the degree of nesting. The proposed methodology reduces the 3-D protrusion-hole polyhedral containment problem of nesting to a 2-D polygon containment problem by employing a loop-based feature recognition scheme. Subsequently, the 3-D containment configuration is reconstructed from that of the 2-D by using a strategy calleddrop, pull and push. In this context, we introduce the notion of axis as a characteristic direction of a feature that facilitates the analysis of generalized 3-D polyhedral containment. The algorithms are applicable to generic B-Rep CAD data, and their time and space complexities are polynomial.     

Grouped Approach for the Design of H.264/AVC Motion Estimation Architectures

This letter presents a novel approach for organizing computational resources into groups within H.264/AVC motion estimation architectures, leading to reductions of up to 75% in the equivalent gate count with respect to state‐of‐the‐art designs.     

Experience, Context, and the Visual Perception of Human Movement.

Why are human observers particularly sensitive to human movement? Seven experiments examined the roles of visual experience and motor processes in human movement perception by comparing visual sensitivities to point-light displays of familiar, unusual, and impossible gaits across gait-speed and identity discrimination tasks. In both tasks, visual sensitivity to physically possible gaits was superior to visual sensitivity to physically impossible gaits, supporting perception-action coupling theories of human movement perception. Visual experience influenced walker-identity perception but not gait-speed discrimination. Thus, both motor experience and visual experience define visual sensitivity to human movement. An ecological perspective can be used to define the conditions necessary for experience-dependent sensitivity to human movement. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

一种基于bit位的运动补偿方法

本文讨论了等离子体显示屏所特有的在显示运动画面时出现的伪轮廓线现象，对产生的原因进行了分析并给出了软件模拟的结果。在此基础上，提出了一种基于bit位的运动补偿方法来改善运动图像的画面质量，同时根据人眼的视觉特征对补偿方法做了进一步的优化。最后对基于bit位的运动补偿方法进行了比较和验证，结果表明基于bit位的运动补偿方法可以基本消除运动画面的伪轮廓线现象。     

Position synchronization of multiple motion axes with adaptive coupling control

A new control approach to position synchronization of multiple motion axes is developed, by incorporating cross-coupling technology into adaptive control architecture. The control strategy is to stabilize position tracking of each axis while synchronizing its motion with other axes’ motions so that differential position errors amongst axes converge to zero. The proposed adaptive controller and parameter estimator employ coupling control by feeding back position errors and differential position errors, and have been realized to guarantee asymptotic convergence to zero of both position and synchronization errors. Simulations conducted on a multi-axis motion control system demonstrate the effectiveness of the method.     

Simulation model of general human and humanoid motion

In the last decade we have witnessed a rapid growth of Humanoid Robotics, which has already constituted an autonomous research field. Humanoid robots (or simply humanoids) are expected in all situations of humans’ everyday life, “living” and cooperating with us. They will work in services, in homes, and hospitals, and they are even expected to get involved in sports. Hence, they will have to be capable of doing diverse kinds of tasks. This forces the researchers to develop an appropriate mathematical model to support simulation, design, and control of these systems. Another important fact is that today’s, and especially tomorrow’s, humanoid robots will be more and more humanlike in their shape and behavior. A dynamic model developed for an advanced humanoid robot may become a very useful tool for the dynamic analysis of human motion in different tasks (walking, running and jumping, manipulation, various sports, etc.). So, we derive a general model and talk about a human-and-humanoid simulation system. The basic idea is to start from a human/humanoid considered as a free spatial system (“flier”). Particular problems (walking, jumping, etc.) are then considered as different contact tasks – interaction between the flier and various objects (being either single bodies or separate dynamic systems).     

线性八元树表示的三维客体群的连通分量标号和计数

本文提出二种算法分别标号和计数线性八元树表示的三维客体群的连通分量.这些操作典型地需要检查线性八元树中诸八分体在三个主方向上的面邻接对.根据这些邻接对,可以建造在计算机中用关联矩阵表示的邻接图.连通分量标号和计数是在关联矩阵上分别执行相应的操作而完成的.连通分量标号的执行时间是O(n+m·logm),而连通分量计数需要O(n)时间,其中m和n分别是线性八元树中八分体和邻接对的数目.     

Representing temporal knowledge in conceptual graphs

This study was motivated by some difficulties encountered by the authors when trying to express temporal knowledge using Sowa's conceptual graph (CG) approach. An overview of Sowa's approach is given and the difficulties encountered when trying to model temporal knowledge are outlined: the disparity of notations allowed by CG theory for expressing temporal information; the ambiguity and incompleteness of tense sspecification; the difficulty of harmonizing tenses and intergraph temporal relations. Various approaches suggested for representing time both in artificial intelligence and linguistics are presented, and an extension to Sowa's approach is proposed in which temporal and nontemporal knowledge are differentiated. In this model points in time are represented as well as time intervals. A semantic interpretation of verbs is provided based on an extension of Reichenbach's model of temporal markers. The authors show how their approach enables the representation of tenses as well as the aspectual properties of natural language sentences.