Mathematical practice, crowdsourcing, and social machines

The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically extending the power and limits of individuals. Crowdsourcing pulls together diverse experts to solve problems; symbolic computation tackles huge routine calculations; and computers check proofs too long and complicated for humans to comprehend. Mathematical practice is an emerging interdisciplinary field which draws on philosophy and social science to understand how mathematics is produced. Online mathematical activity provides a novel and rich source of data for empirical investigation of mathematical practice - for example the community question answering system {\it mathoverflow} contains around 40,000 mathematical conversations, and {\it polymath} collaborations provide transcripts of the process of discovering proofs. Our preliminary investigations have demonstrated the importance of "soft" aspects such as analogy and creativity, alongside deduction and proof, in the production of mathematics, and have given us new ways to think about the roles of people and machines in creating new mathematical knowledge. We discuss further investigation of these resources and what it might reveal. Crowdsourced mathematical activity is an example of a "social machine", a new paradigm, identified by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity, and the subject of major international research endeavours. We outline a future research agenda for mathematics social machines, a combination of people, computers, and mathematical archives to create and apply mathematics, with the potential to change the way people do mathematics, and to transform the reach, pace, and impact of mathematics research.Comment: To appear, Springer LNCS, Proceedings of Conferences on Intelligent Computer Mathematics, CICM 2013, July 2013 Bath, U

Predicting Network Attacks Using Ontology-Driven Inference

Graph knowledge models and ontologies are very powerful modeling and re asoning tools. We propose an effective approach to model network attacks and attack prediction which plays important roles in security management. The goals of this study are: First we model network attacks, their prerequisites and consequences using knowledge representation methods in order to provide description logic reasoning and inference over attack domain concepts. And secondly, we propose an ontology-based system which predicts potential attacks using inference and observing information which provided by sensory inputs. We generate our ontology and evaluate corresponding methods using CAPEC, CWE, and CVE hierarchical datasets. Results from experiments show significant capability improvements comparing to traditional hierarchical and relational models. Proposed method also reduces false alarms and improves intrusion detection effectiveness.Comment: 9 page

Universal Intelligence: A Definition of Machine Intelligence

A fundamental problem in artificial intelligence is that nobody really knows what intelligence is. The problem is especially acute when we need to consider artificial systems which are significantly different to humans. In this paper we approach this problem in the following way: We take a number of well known informal definitions of human intelligence that have been given by experts, and extract their essential features. These are then mathematically formalised to produce a general measure of intelligence for arbitrary machines. We believe that this equation formally captures the concept of machine intelligence in the broadest reasonable sense. We then show how this formal definition is related to the theory of universal optimal learning agents. Finally, we survey the many other tests and definitions of intelligence that have been proposed for machines.Comment: 50 gentle page

Utilization of The Thrasher and Rice Mill Machines in Composition Function Learning: A Hypothetical Learning Trajectory Design

The study aims to design mathematics learning in composite function concepts with farm tools, which are thrasher and rice mill machines; this farm’s tool is used as to starting point in the learning process. The research method used is design research with a  preliminary design, design experiment, and analysis retrospective stages. This study describes the design of the thrasher and rice mill machine to facilitate a real contribution for student understanding of the composite function concept. The participant of this research is 10 eleventh-grade students from one of the senior high school in East Java. The results of this study reveal that students are able to make associations from the thrasher and rice mill machine through the determination of the input and output of the machines to the formula of the composite function concept. So, the stages in the learning trajectory have an important role in understanding the composition function concept from informal level to formal level and also make the study of mathematics more easy, simple, fun, and comfortable

Formal specification techniques in object-oriented analysis: a comparative view.

During the last decade, object orientation has been advanced as a promising paradigm for software construction. In addition several authors have advocated the use of formal specification techniques during software development. Formal methods enable reasoning (in a mathematical sense) about properties of programs and systems. It is clear that also object oriented software development can benefit from the use of formal techniques.But although the object oriented analysis (OOA) methods claim to provide the necessary concepts and tools to improve the quality of software development, they are in general informal. This is surprising as the modeling techniques used in OOA have a high potential for formalization. The purpose of this study is to compare the specification techniques used in current OOA-methods. In particular, the degree of formality provided by most of the methods is discussed and evaluated from a quality control perspective.Software; Methods; Programs; Systems; Studies; Quality control;