Derived Category Automorphisms from Mirror Symmetry

Inspired by the homological mirror symmetry conjecture of Kontsevich, we construct new classes of automorphisms of the bounded derived category of coherent sheaves on a smooth Calabi-Yau variety.Comment: LaTeX, 27 pages, no figures; substantially revised; the erroneous lemma 2.6 has been removed; to appear in the Duke Mathematical Journa

Reducing or Eliminating Curl on Wax Parts Produced in the SinterstationTM 2000 System

Mechanical Engineerin

A Skyrme lattice with hexagonal symmetry

Recently it has been found that the structure of Skyrmions has a close analogy to that of fullerene shells in carbon chemistry. In this letter we show that this analogy continues further, by presenting a Skyrme field that describes a lattice of Skyrmions with hexagonal symmetry. This configuration, a novel `domain wall' in the Skyrme model, has low energy per baryon (about 6% above the Faddeev-Bogomolny bound) and in many ways is analogous to graphite. By comparison to the energy per baryon of other known Skyrmions and also the Skyrme crystal, we discuss the possibility of finding Skyrmion shells of higher charge.Comment: 12 pages, 1 figure. To appear in Phys. Lett.

A Multi-level Blocking Distinct Degree Factorization Algorithm

We give a new algorithm for performing the distinct-degree factorization of a polynomial P(x) over GF(2), using a multi-level blocking strategy. The coarsest level of blocking replaces GCD computations by multiplications, as suggested by Pollard (1975), von zur Gathen and Shoup (1992), and others. The novelty of our approach is that a finer level of blocking replaces multiplications by squarings, which speeds up the computation in GF(2)[x]/P(x) of certain interval polynomials when P(x) is sparse. As an application we give a fast algorithm to search for all irreducible trinomials x^r + x^s + 1 of degree r over GF(2), while producing a certificate that can be checked in less time than the full search. Naive algorithms cost O(r^2) per trinomial, thus O(r^3) to search over all trinomials of given degree r. Under a plausible assumption about the distribution of factors of trinomials, the new algorithm has complexity O(r^2 (log r)^{3/2}(log log r)^{1/2}) for the search over all trinomials of degree r. Our implementation achieves a speedup of greater than a factor of 560 over the naive algorithm in the case r = 24036583 (a Mersenne exponent). Using our program, we have found two new primitive trinomials of degree 24036583 over GF(2) (the previous record degree was 6972593)

Dissertation by portfolio : an alternative to the traditional thesis

Both the absolute numbers and proportion of international students in the student cohorts of postgradute computing and engineering courses rose dramatically between 2005 and 2009. One of the hardest tasks these students have to perform is the production of a dissertation in English. This paper will concentrate on experiences with students studying computing masters level courses. This paper asks the question whether we are assessing a student's skills with academic English or their ability to meet the learning outcomes of the dissertation module. It will present an alternative to the traditional written dissertation in the form of a portfolio model which is applicable in highly technical research projects. The lessons learned from a pilot project which introduced portfolio dissertations to the Department of Computing at Sheffield Hallam University will be presented along with plans for the next stage of implementation

Congruences in ordered pairs of partitions

Dyson defined the rank of a partition (as the first part minus the number of parts) whilst investigating certain congruences in the sequence p−1(n). The rank has been widely studied as have been other statistics, such as the crank. In this paper a “birank” is defined which relates to ordered pairs of partitions, and is used in an elementary proof of a congruence in p−2(n

A model of suspense for narrative generation

Most work on automatic generation of narratives, and more specifically suspenseful narrative, has focused on detailed domain-specific modelling of character psychology and plot structure. Recent work on the automatic learning of narrative schemas suggests an alternative approach that exploits such schemas for modelling and measuring suspense. We propose a domain-independent model for tracking suspense in a story which can be used to predict the audience’s suspense response on a sentence-by-sentence basis at the content determination stage of narrative generation. The model lends itself as the theoretical foundation for a suspense module that is compatible with alternative narrative generation theories. The proposal is evaluated by human judges’ normalised average scores correlate strongly with predicted values

Monocrystalline silicon gradiometer for gravity experiments in space

A very important research effort has been made in the last decade in the field of high precision measurement with laser instrumentation. The development of a space borne gradiometer operating at a high sensitivity level using laser measurement of the distance between proof mass over a short base line of order one meter is discussed. Two aspects of laser technology make it a promising tool for gradiometry measurements: quantum limited accuracy and absolute distance measurements. The quantum limit associated with laser instrumentation was formulated. The relevant quantum and classical sources of errors in laser measurements were reviewed and corresponding laser performance requirements for gradient measurements were evaluated. Some mechanical quality factor measurements were made on simple resonant monocrystalline silicon suspensions. It was discovered that the use of zero derivative restoring forces to position the gradiometer test masses will dramatically reduce the gradiometer temperature control requirements. A laser beam side injection scheme was discovered which permits rejection of common mode accelerations. These concepts are briefly discussed