Leading Terms of SL3 Web Invariants

We use Khovanov and Kuperberg’s web growth rules to identify the leading term in the invariant associated to an $\textrm{SL}_3$ web diagram, with respect to a particular term order.

Can a simple, short-term memory task help to screen dyslexia?

Funding to support students with dyslexia in post-compulsory education is under pressure and more efficient assessments may offset some of this shortfall. We tested potential tasks for screening dyslexia: recall of adjective-noun, compared to noun-adjective, pairings (syntax) and recall of high versus low frequency letter pairings (bigrams). Students who reported themselves as dyslexic failed to show a normal syntax effect (greater recall of adjective-noun compared to noun-adjective pairings) and no significant difference in recall between the two types of bigrams whereas students who were not dyslexic showed the syntax effect and a bias towards recalling high frequency bigrams. Findings are consistent with recent explanations of dyslexia suggesting that those affected find it difficult to learn and utilise sequential long-term order information (Szmalec et al. Journal of Experimental Psychology: Learning, Memory & Cognition, 37(5) ,1270-1279, 2011). Further, ROC curve analyses revealed both tasks showed acceptable diagnostic properties as they were able to discriminate between the two groups of participants.

Improving Legal Information Retrieval by Distributional Composition with Term Order Probabilities

Legal professionals worldwide are currently trying to get up-to-pace with the explosive growth in legal document availability through digital means. This drives a need for high efficiency Legal Information Retrieval (IR) and Question Answering (QA) methods. The IR task in particular has a set of unique challenges that invite the use of semantic motivated NLP techniques. In this work, a two-stage method for Legal Information Retrieval is proposed, combining lexical statistics and distributional sentence representations in the context of Competition on Legal Information Extraction/Entailment (COLIEE). The combination is done with the use of disambiguation rules, applied over the rankings obtained through n-gram statistics. After the ranking is done, its results are evaluated for ambiguity, and disambiguation is done if a result is decided to be unreliable for a given query. Competition and experimental results indicate small gains in overall retrieval performance using the proposed approach. Additionally, an analysis of error and improvement cases is presented for a better understanding of the contributions.

Algebraic Cryptanalysis Scheme of AES-256 Using Gröbner Basis

The zero-dimensional Gröbner basis construction is a crucial step in Gröbner basis cryptanalysis on AES-256. In this paper, after performing an in-depth study on the linear transformation and the system of multivariate polynomial equations of AES-256, the zero-dimensional Gröbner basis construction method is proposed by choosing suitable term order and variable order. After giving a detailed construction process of the zero-dimensional Gröbner basis, the necessary theoretical proof is presented. Based on this, an algebraic cryptanalysis scheme of AES-256 using Gröbner basis is proposed. Analysis shows that the complexity of our scheme is lower than that of the exhaustive attack.

Improving quantum algorithms for quantum chemistry

We present several improvements to the standard Trotter-Suzuki based algorithms used in the simulation of quantum chemistry on a quantum computer. First, we modify how Jordan-Wigner transformations are implemented to reduce their cost from linear or logarithmic in the number of orbitals to a constant. Our modification does not require additional ancilla qubits. Then, we demonstrate how many operations can be parallelized, leading to a further linear decrease in the parallel depth of the circuit, at the cost of a small constant factor increase in number of qubits required. Thirdly, we modify the term order in the Trotter-Suzuki decomposition, significantly reducing the error at given Trotter-Suzuki timestep. A final improvement modifies the Hamiltonian to reduce errors introduced by the non-zero Trotter-Suzuki timestep. All of these techniques are validated using numerical simulation and detailed gate counts are given for realistic molecules.

Decomposition of Reflexive Differential-Difference Polynomial Systems

This paper presents a zero decomposition algorithm for reflexive difference and differential polynomial systems. The problem of negative exponent of difference operators in DD-polynomials is solved by means of generalized term order. Our algorithm would be used to decompose the zero set of a finitely generated reflexive DD-polynomial set into the union of zero sets of coherent chains.