The interaction of representation and reasoning

Automated reasoning is an enabling technology for many applications of informatics. These applications include verifying that a computer program meets its specification; enabling a robot to form a plan to achieve a task and answering questions by combining information from diverse sources, e.g. on the Internet, etc. How is automated reasoning possible? Firstly, knowledge of a domain must be stored in a computer, usually in the form of logical formulae. This knowledge might, for instance, have been entered manually, retrieved from the Internet or perceived in the environment via sensors, such as cameras. Secondly, rules of inference are applied to old knowledge to derive new knowledge. Automated reasoning techniques have been adapted from logic, a branch of mathematics that was originally designed to formalize the reasoning of humans, especially mathematicians. My special interest is in the way that representation and reasoning interact. Successful reasoning is dependent on appropriate representation of both knowledge and successful methods of reasoning. Failures of reasoning can suggest changes of representation. This process of representational change can also be automated. We will illustrate the automation of representational change by drawing on recent work in my research group

Dislocation density and graphitization of diamond crystals

Two sets of diamond specimens compressed at 2 GPa at temperatures varying between 1060 K and 1760 K were prepared; one in which graphitization was promoted by the presence of water and another in which graphitization of diamond was practically absent. X-ray diffraction peak profiles of both sets were analyzed for the microstructure by using the modified Williamson-Hall method and by fitting the Fourier coefficients of the measured profiles by theoretical functions for crystallite size and lattice strain. The procedures determined mean size and size distribution of crystallites as well as the density and the character of the dislocations. The same experimental conditions resulted in different microstructures for the two sets of samples. They were explained in terms of hydrostatic conditions present in the graphitized samples

The development of an age structured model for schistosomiasis transmission dynamics and control and its validation for Schistosoma mansoni

Mathematical models are potentially useful tools to aid in the design of control programmes for parasitic diseases. In this paper, a fully age structured epidemiological model of human schistosomiasis is developed and parameterized, and used to predict trends in infection prevalence, intensity and prevalence of heavy infections over age and time during several rounds of mass and age targeted treatment. The model is validated against data from a Schistosoma mansoni control programme in Keny

Pressure-induced metallization in solid boron

Different phases of solid boron under high pressure are studied by first principles calculations. The $\alpha$-B$_{12}$ structure is found to be stable up to 270 GPa. Its semiconductor band gap (1.72 eV) decreases continuously to zero around 160 GPa, where the material transforms to a weak metal. The metallicity, as measured by the density of states at the Fermi level, enhances as the pressure is further increased. The pressure-induced metallization can be attributed to the enhanced boron-boron interactions that cause bands overlap. These results are consist with the recently observed metallization and the associated superconductivity of bulk boron under high pressure (M.I.Eremets et al, Science{\bf 293}, 272(2001)).Comment: 14 pages, 5 figure

Comparison of structural transformations and superconductivity in compressed Sulfur and Selenium

Density-functional calculations are presented for high-pressure structural phases of S and Se. The structural phase diagrams, phonon spectra, electron-phonon coupling, and superconducting properties of the isovalent elements are compared. We find that with increasing pressure, Se adopts a sequence of ever more closely packed structures (beta-Po, bcc, fcc), while S favors more open structures (beta-Po, simple cubic, bcc). These differences are shown to be attributable to differences in the S and Se core states. All the compressed phases of S and Se considered are calculated to have weak to moderate electron-phonon coupling strengths consistent with superconducting transition temperatures in the range of 1 to 20 K. Our results compare well with experimental data on the beta-Po --> bcc transition pressure in Se and on the superconducting transition temperature in beta-Po S. Further experiments are suggested to search for the other structural phases predicted at higher pressures and to test theoretical results on the electron-phonon interaction and superconducting properties

Total energy calculation of high pressure selenium: The origin of incommensurate modulations in Se-IV and the instability of proposed Se-II

We present calculation of the high pressure crystal structures in selenium, including rational approximants to the recently reported incommensurate phases. We show how the incommensurate phases can be intuitively explained in terms of imaginary phonon frequencies arising from Kohn anomalies in the putative undistorted phase. We also find inconsistencies between the calculated and experimental Se-II phase - the calculations show it to be a metastable metal while the experiment finds a stable semiconductor. We propose that the experimentally reported structure is probably in error.Comment: 4 pages 4 figure

Electronic Transport in a Three-dimensional Network of 1-D Bismuth Quantum Wires

The resistance R of a high density network of 6 nm diameter Bi wires in porous Vycor glass is studied in order to observe its expected semiconductor behavior. R increases from 300 K down to 0.3 K. Below 4 K, where R varies approximately as ln(1/T), the order-of-magnitude of the resistance rise, as well as the behavior of the magnetoresistance are consistent with localization and electron-electron interaction theories of a one-dimensional disordered conductor in the presence of strong spin-orbit scattering. We show that this behaviour and the surface-enhanced carrier density may mask the proposed semimetal-to-semiconductor transition for quantum Bi wires.Comment: 19 pages total, 4 figures; accepted for publication in Phys. Rev.

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