Some Empirical Criteria for Attributing Creativity to a Computer Program

Peer reviewedPostprin

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

Improving the Efficiency of Reasoning Through Structure-Based Reformulation

Abstract. We investigate the possibility of improving the efficiency of reasoning through structure-based partitioning of logical theories, combined with partitionbased logical reasoning strategies. To this end, we provide algorithms for reasoning with partitions of axioms in first-order and propositional logic. We analyze the computational benefit of our algorithms and detect those parameters of a partitioning that influence the efficiency of computation. These parameters are the number of symbols shared by a pair of partitions, the size of each partition, and the topology of the partitioning. Finally, we provide a greedy algorithm that automatically reformulates a given theory into partitions, exploiting the parameters that influence the efficiency of computation.

The algebra of lexical semantics

Abstract. The current generative theory of the lexicon relies primar-ily on tools from formal language theory and mathematical logic. Here we describe how a different formal apparatus, taken from algebra and automata theory, resolves many of the known problems with the gener-ative lexicon. We develop a finite state theory of word meaning based on machines in the sense of Eilenberg [11], a formalism capable of de-scribing discrepancies between syntactic type (lexical category) and se-mantic type (number of arguments). This mechanism is compared both to the standard linguistic approaches and to the formalisms developed in AI/KR. 1 Problem Statement In developing a formal theory of lexicography our starting point will be the informal practice of lexicography, rather than the more immediately related for-mal theories of Artificial Intelligence (AI) and Knowledge Representation (KR). Lexicography is a relatively mature field, with centuries of work experience an

Cumulants and the moment algebra: tools for analysing weak measurements

Recently it has been shown that cumulants significantly simplify the analysis of multipartite weak measurements. Here we consider the mathematical structure that underlies this, and find that it can be formulated in terms of what we call the moment algebra. Apart from resulting in simpler proofs, the flexibility of this structure allows generalizations of the original results to a number of weak measurement scenarios, including one where the weakly interacting pointers reach thermal equilibrium with the probed system.Comment: Journal reference added, minor correction

Knowledge discovery in an agents environment

Presented at European Semantic Web Symposium 2004<br/

A DNA Barcode Library for North American Ephemeroptera: Progress and Prospects

DNA barcoding of aquatic macroinvertebrates holds much promise as a tool for taxonomic research and for providing the reliable identifications needed for water quality assessment programs. A prerequisite for identification using barcodes is a reliable reference library. We gathered 4165 sequences from the barcode region of the mitochondrial cytochrome c oxidase subunit I gene representing 264 nominal and 90 provisional species of mayflies (Insecta: Ephemeroptera) from Canada, Mexico, and the United States. No species shared barcode sequences and all can be identified with barcodes with the possible exception of some Caenis. Minimum interspecific distances ranged from 0.3–24.7% (mean: 12.5%), while the average intraspecific divergence was 1.97%. The latter value was inflated by the presence of very high divergences in some taxa. In fact, nearly 20% of the species included two or three haplotype clusters showing greater than 5.0% sequence divergence and some values are as high as 26.7%. Many of the species with high divergences are polyphyletic and likely represent species complexes. Indeed, many of these polyphyletic species have numerous synonyms and individuals in some barcode clusters show morphological attributes characteristic of the synonymized species. In light of our findings, it is imperative that type or topotype specimens be sequenced to correctly associate barcode clusters with morphological species concepts and to determine the status of currently synonymized species

Submarine Fernandina : magmatism at the leading edge of the Galapagos hot spot

Author Posting. © American Geophysical Union, 2006. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geochemistry Geophysics Geosystems 7 (2006): Q12007, doi:10.1029/2006GC001290.New multibeam and side-scan sonar surveys of Fernandina volcano and the geochemistry of lavas provide clues to the structural and magmatic development of Galápagos volcanoes. Submarine Fernandina has three well-developed rift zones, whereas the subaerial edifice has circumferential fissures associated with a large summit caldera and diffuse radial fissures on the lower slopes. Rift zone development is controlled by changes in deviatoric stresses with increasing distance from the caldera. Large lava flows are present on the gently sloping and deep seafloor west of Fernandina. Fernandina's submarine lavas are petrographically more diverse than the subaerial suite and include picrites. Most submarine glasses are similar in composition to aphyric subaerially erupted lavas, however. These rocks are termed the “normal” series and are believed to result from cooling and crystallization in the subcaldera magma system, which buffers the magmas both thermally and chemically. These normal-series magmas are extruded laterally through the flanks of the volcano, where they scavenge and disaggregate olivine-gabbro mush to produce picritic lavas. A suite of lavas recovered from the terminus of the SW submarine rift and terraces to the south comprises evolved basalts and icelandites with MgO = 3.1 to 5.0 wt.%. This “evolved series” is believed to form by fractional crystallization at 3 to 5 kb, involving extensive crystallization of clinopyroxene and titanomagnetite in addition to plagioclase. “High-K” lavas were recovered from the southwest rift and are attributed to hybridization between normal-series basalt and evolved-series magma. The geochemical and structural findings are used to develop an evolutionary model for the construction of the Galápagos Platform and better understand the petrogenesis of the erupted lavas. The earliest stage is represented by the deep-water lava flows, which over time construct a broad submarine platform. The deep-water lavas originate from the subcaldera plumbing system of the adjacent volcano. After construction of the platform, eruptions focus to a point source, building an island with rift zones extending away from the adjacent, buttressing volcanoes. Most rift zone magmas intrude laterally from the subcaldera magma chamber, although a few evolve by crystallization in the upper mantle and deep crust.This work was supported by the National Science Foundation grants OCE0002818 and EAR0207605 (D.G.), OCE0002461 (D.J.F. and M.K.), OCE9811504 (D.J.F. and M.R.P.), and EAR0207425 (K.H.) and WHOI postdoctoral support for Soule

Challenges Using Extrapolated Family-level Macroinvertebrate Metrics in Moderately Disturbed Tropical Streams: a Case-study From Belize

Family-level biotic metrics were originally designed to rapidly assess gross organic pollution effects, but came to be regarded as general measures of stream degradation. Improvements in water quality in developed countries have reignited debate about the limitations of family-level taxonomy to detect subtle change, and is resulting in a shift back towards generic and species-level analysis to assess smaller effects. Although the scale of pollution characterizing past condition of streams in developed countries persists in many developing regions, some areas are still considered to be only moderately disturbed. We sampled streams in Belize to investigate the ability of family-level macroinvertebrate metrics to detect change in stream catchments where less than 30% of forest had been cleared. Where disturbance did not co-vary with natural gradients of change, and in areas characterized by low intensity activities, none of the metrics tested detected significant change, despite evidence of environmental impacts. We highlight the need for further research to clarify the response of metrics to disturbance over a broader study area that allows replication for confounding sources of natural variation. We also recommend research to develop more detailed understanding of the taxonomy and ecology of Neotropical macroinvertebrates to improve the robustness of metric use