The Experts below are selected from a list of 300 Experts worldwide ranked by ideXlab platform
Simon Colton - One of the best experts on this subject based on the ideXlab platform.
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using analogical representations for mathematical concept Formation
Model-Based Reasoning in Science and Technology: Abduction Logic and Computational Discovery, 2010Co-Authors: Alison Pease, Simon Colton, Ramin Ramezani, Alan Smaill, Markus GuheAbstract:We argue that visual, analogical representations of mathematical concepts can be used by automated Theory Formation systems to develop further concepts and conjectures in mathematics. We consider the role of visual reasoning in human development of mathematics, and consider some aspects of the relationship between mathematics and the visual, including artists using mathematics as inspiration for their art (which may then feed back into mathematical development), the idea of using visual beauty to evaluate mathematics, mathematics which is visually pleasing, and ways of using the visual to develop mathematical concepts. We motivate an analogical representation of number types with examples of “visual” concepts and conjectures, and present an automated case study in which we enable an automated Theory Formation program to read this type of visual, analogical representation.
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computational discovery in pure mathematics
Discovery Science, 2007Co-Authors: Simon ColtonAbstract:We discuss what constitutes knowledge in pure mathematics and how new advances are made and communicated. We describe the impact of computer algebra systems, automated theorem provers, programs designed to generate examples, mathematical databases, and Theory Formation programs on the body of knowledge in pure mathematics. We discuss to what extent the output from certain programs can be considered a discovery in pure mathematics. This enables us to assess the state of the art with respect to Newell and Simon's prediction that a computer would discover and prove an important mathematical theorem.
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CADE - The Homer System
Automated Deduction – CADE-19, 2003Co-Authors: Simon Colton, Sophie HuczynskaAbstract:The Homer system combines the HR automated Theory Formation program [2], the Otter theorem prover [6], and the Maple computer algebra package [1] to make intelligent conjectures about number Theory functions supplied by the user. The integration is as follows: given Maple code for some functions the user is interested in, Maple is used to calculate values for those functions. HR then forms a Theory using the functions as background knowledge, calling Maple whenever necessary to perform additional calculations. The Theory Formation process makes conjectures empirically and the user is initially asked to prove or disprove each conjecture. As the Theory Formation progresses, however, Homer uses the theorems it has found (namely those proved by the user) as axioms in attempts to prove the conjectures itself using Otter. Any conjectures proved in this way are likely to follow easily from the theorems already known to the user, so Homer does not present them, in order to keep the quality of the output high. Using Otter in this extreme way is not meant to indicate that Otter can only prove trivial theorems, nor that HR produces too many dull conjectures. Rather, we wish to emphasise the power of the combined system (Homer) at discovering interesting conjectures by generate (HR) and quick test (Otter).
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Agent Based Cooperative Theory Formation in Pure Mathematics
2000Co-Authors: Simon Colton, Alan Bundy, Toby WalshAbstract:The HR program, Colton et al. (1999), performs Theory Formation in domains of pure mathematics. Given only minimal inFormation about a domain, it invents concepts, make conjectures, proves theorems and finds counterexamples to false conjectures. We present here a multi-agent version of HR which may provide a model for how individual mathematicians perform separate investigations but communicate their results to the mathematical community, learning from others as they do. We detail the exhaustive categorisation problem to which we have applied a multi-agent approach.
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Computational Discovery of Scientific Knowledge - Computational Discovery in Pure Mathematics
Lecture Notes in Computer Science, 1Co-Authors: Simon ColtonAbstract:We discuss what constitutes knowledge in pure mathematics and how new advances are made and communicated. We describe the impact of computer algebra systems, automated theorem provers, programs designed to generate examples, mathematical databases, and Theory Formation programs on the body of knowledge in pure mathematics. We discuss to what extent the output from certain programs can be considered a discovery in pure mathematics. This enables us to assess the state of the art with respect to Newell and Simon's prediction that a computer would discover and prove an important mathematical theorem.
Zhang Shaomin - One of the best experts on this subject based on the ideXlab platform.
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Status and Trends in Research on Deep-Water Gravity Flow Deposits
Acta Geologica Sinica-english Edition, 2015Co-Authors: Yang Tian, Cao Yingchang, Wang Yanzhong, Li Ya, Zhang ShaominAbstract:Deep-water gravity flows are one of the most important sediment transport mechanisms on Earth. After 60 years of study, significant achievements have been made in terms of classification schemes, genetic mechanisms, and depositional models of deep-water gravity flows. The research history of deep-water gravity flows can be divided into five stages: incipience of turbidity current Theory; Formation of turbidity current Theory; development of deep-water gravity flow Theory; improvement and perfection of deep-water gravity flow Theory; and comprehensive development of deep-water gravity flow Theory. Currently, three primary classification schemes based on the sediment support mechanism, the rheology and transportation process, and the integration of sediment support mechanisms, rheology, sedimentary characteristics, and flow state are commonly used. Different types of deep-water gravity flow events form different types of gravity flow deposits. Sediment slump retransportation mainly forms muddy debris flows, sandy debris flows, and surge-like turbidity currents. Resuspension of deposits by storms leads to quasi-steady hyperpycnal turbidity currents (hyperpycnal flows). Sustainable sediment supplies mainly generate muddy debris flows, sandy debris flows, and hyperpycnal flows. Deep-water fans, which are commonly controlled by debris flows and hyperpycnal flows, are triggered by sustainable sediment supply; in contrast, deep-water slope sedimentary deposits consist mainly of debris flows that are triggered by the retransportation of sediment slumps and deep-water fine-grained sedimentary deposits are derived primarily from fine-grained hyperpycnal flows that are triggered by the resuspension of storm deposits. Harmonization of classification schemes, transFormation between different types of gravity flow deposit, and monitoring and reproduction of the sedimentary processes of deep-water gravity flows as well as a source-to-sink approach to document the evolution and deposition of deep-water gravity flows are the most important research aspects for future studies of deep-water gravity flows study in the future.
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Status and Trends in Research on Deep‐Water Gravity Flow Deposits
Acta Geologica Sinica-english Edition, 2015Co-Authors: Yang Tian, Cao Yingchang, Wang Yanzhong, Li Ya, Zhang ShaominAbstract:Deep-water gravity flows are one of the most important sediment transport mechanisms on Earth. After 60 years of study, significant achievements have been made in terms of classification schemes, genetic mechanisms, and depositional models of deep-water gravity flows. The research history of deep-water gravity flows can be divided into five stages: incipience of turbidity current Theory; Formation of turbidity current Theory; development of deep-water gravity flow Theory; improvement and perfection of deep-water gravity flow Theory; and comprehensive development of deep-water gravity flow Theory. Currently, three primary classification schemes based on the sediment support mechanism, the rheology and transportation process, and the integration of sediment support mechanisms, rheology, sedimentary characteristics, and flow state are commonly used. Different types of deep-water gravity flow events form different types of gravity flow deposits. Sediment slump retransportation mainly forms muddy debris flows, sandy debris flows, and surge-like turbidity currents. Resuspension of deposits by storms leads to quasi-steady hyperpycnal turbidity currents (hyperpycnal flows). Sustainable sediment supplies mainly generate muddy debris flows, sandy debris flows, and hyperpycnal flows. Deep-water fans, which are commonly controlled by debris flows and hyperpycnal flows, are triggered by sustainable sediment supply; in contrast, deep-water slope sedimentary deposits consist mainly of debris flows that are triggered by the retransportation of sediment slumps and deep-water fine-grained sedimentary deposits are derived primarily from fine-grained hyperpycnal flows that are triggered by the resuspension of storm deposits. Harmonization of classification schemes, transFormation between different types of gravity flow deposit, and monitoring and reproduction of the sedimentary processes of deep-water gravity flows as well as a source-to-sink approach to document the evolution and deposition of deep-water gravity flows are the most important research aspects for future studies of deep-water gravity flows study in the future.
Yang Tian - One of the best experts on this subject based on the ideXlab platform.
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Status and Trends in Research on Deep-Water Gravity Flow Deposits
Acta Geologica Sinica-english Edition, 2015Co-Authors: Yang Tian, Cao Yingchang, Wang Yanzhong, Li Ya, Zhang ShaominAbstract:Deep-water gravity flows are one of the most important sediment transport mechanisms on Earth. After 60 years of study, significant achievements have been made in terms of classification schemes, genetic mechanisms, and depositional models of deep-water gravity flows. The research history of deep-water gravity flows can be divided into five stages: incipience of turbidity current Theory; Formation of turbidity current Theory; development of deep-water gravity flow Theory; improvement and perfection of deep-water gravity flow Theory; and comprehensive development of deep-water gravity flow Theory. Currently, three primary classification schemes based on the sediment support mechanism, the rheology and transportation process, and the integration of sediment support mechanisms, rheology, sedimentary characteristics, and flow state are commonly used. Different types of deep-water gravity flow events form different types of gravity flow deposits. Sediment slump retransportation mainly forms muddy debris flows, sandy debris flows, and surge-like turbidity currents. Resuspension of deposits by storms leads to quasi-steady hyperpycnal turbidity currents (hyperpycnal flows). Sustainable sediment supplies mainly generate muddy debris flows, sandy debris flows, and hyperpycnal flows. Deep-water fans, which are commonly controlled by debris flows and hyperpycnal flows, are triggered by sustainable sediment supply; in contrast, deep-water slope sedimentary deposits consist mainly of debris flows that are triggered by the retransportation of sediment slumps and deep-water fine-grained sedimentary deposits are derived primarily from fine-grained hyperpycnal flows that are triggered by the resuspension of storm deposits. Harmonization of classification schemes, transFormation between different types of gravity flow deposit, and monitoring and reproduction of the sedimentary processes of deep-water gravity flows as well as a source-to-sink approach to document the evolution and deposition of deep-water gravity flows are the most important research aspects for future studies of deep-water gravity flows study in the future.
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Status and Trends in Research on Deep‐Water Gravity Flow Deposits
Acta Geologica Sinica-english Edition, 2015Co-Authors: Yang Tian, Cao Yingchang, Wang Yanzhong, Li Ya, Zhang ShaominAbstract:Deep-water gravity flows are one of the most important sediment transport mechanisms on Earth. After 60 years of study, significant achievements have been made in terms of classification schemes, genetic mechanisms, and depositional models of deep-water gravity flows. The research history of deep-water gravity flows can be divided into five stages: incipience of turbidity current Theory; Formation of turbidity current Theory; development of deep-water gravity flow Theory; improvement and perfection of deep-water gravity flow Theory; and comprehensive development of deep-water gravity flow Theory. Currently, three primary classification schemes based on the sediment support mechanism, the rheology and transportation process, and the integration of sediment support mechanisms, rheology, sedimentary characteristics, and flow state are commonly used. Different types of deep-water gravity flow events form different types of gravity flow deposits. Sediment slump retransportation mainly forms muddy debris flows, sandy debris flows, and surge-like turbidity currents. Resuspension of deposits by storms leads to quasi-steady hyperpycnal turbidity currents (hyperpycnal flows). Sustainable sediment supplies mainly generate muddy debris flows, sandy debris flows, and hyperpycnal flows. Deep-water fans, which are commonly controlled by debris flows and hyperpycnal flows, are triggered by sustainable sediment supply; in contrast, deep-water slope sedimentary deposits consist mainly of debris flows that are triggered by the retransportation of sediment slumps and deep-water fine-grained sedimentary deposits are derived primarily from fine-grained hyperpycnal flows that are triggered by the resuspension of storm deposits. Harmonization of classification schemes, transFormation between different types of gravity flow deposit, and monitoring and reproduction of the sedimentary processes of deep-water gravity flows as well as a source-to-sink approach to document the evolution and deposition of deep-water gravity flows are the most important research aspects for future studies of deep-water gravity flows study in the future.
M W Finnis - One of the best experts on this subject based on the ideXlab platform.
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supercell size scaling of density functional Theory Formation energies of charged defects
Physical Review B, 2009Co-Authors: Nicholas D M Hine, K Frensch, W M C Foulkes, M W FinnisAbstract:18.09.12 KB. Published pdf uploaded, ok to add to spiral. APS states that pdf ok to post on institutional repository.
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supercell size scaling of density functional Theory Formation energies of charged defects
Physical Review B, 2009Co-Authors: Nicholas D M Hine, K Frensch, W M C Foulkes, M W FinnisAbstract:We address the calculation within density functional Theory (DFT) of defect Formation energies in alumina, a ceramic oxide often considered an archetype for a wide variety of other similar oxides. We examine the conditions under which calculated defect Formation energies, especially those of charged defects, are independent of the principal approximations of the plane-wave DFT formalism, most significant of which is the finite-sized supercell in which the calculation must be performed. We introduce a variation on existing methods of extrapolation to infinite system size to reduce dependence of the result on finite-size errors in the electrostatic and elastic energies of a periodic supercell containing a defect. We also show how the results can be made relatively insensitive to the choice of exchange-correlation functional and pseudopotential by a suitable treatment of the chemical potentials of the atomic species. Our results for Formation energies of charged defects are less sensitive than traditional approaches to supercell size and choices of exchange-correlation functional and pseudopotential, and differ notably from previous results.
Krzysztof Wnuk - One of the best experts on this subject based on the ideXlab platform.
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A Theory of openness for software engineering tools in software organizations
Information & Software Technology, 2017Co-Authors: Hussan Munir, Per Runeson, Krzysztof WnukAbstract:Abstract Context The increased use of Open Source Software (OSS) affects how software-intensive product development organizations (SIPDO) innovate and compete, moving them towards Open Innovation (OI). Specifically, software engineering tools have the potential for OI, but require better understanding regarding what to develop internally and what to acquire from outside the organization, and how to cooperate with potential competitors. Aim This paper aims at synthesizing a Theory of openness for software engineering tools in SIPDOs, that can be utilized by managers in defining more efficient strategies towards OSS communities. Method We synthesize empirical evidence from a systematic mapping study, a case study, and a survey, using a narrative method. The synthesis method entails four steps: (1) Developing a preliminary synthesis, (2) Exploring the relationship between studies, (3) Assessing the validity of the synthesis, and (4) Theory Formation. Result We present a Theory of openness for OSS tools in software engineering in relation to four constructs: (1) Strategy, (2) Triggers, (3) Outcomes, and (4) Level of openness. Conclusion The Theory reasons that openness provides opportunities to reduce the development cost and development time. Furthermore, OI positively impacts on the process and product innovation, but it requires investment by organizations in OSS communities. By betting on openness, organizations may be able to significantly increase their competitiveness.
