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Author(s):  
Véronique Bazier-Matte ◽  
Guillaume Douville ◽  
Alexander Garver ◽  
Rebecca Patrias ◽  
Hugh Thomas ◽  
...  
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Abstract 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.


Author(s):  
Nick Perham ◽  
Toni Howell ◽  
Andy Watt

AbstractFunding 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.


10.29007/2xzw ◽  
2018 ◽  
Author(s):  
Danilo S. Carvalho ◽  
Vu Tran ◽  
Khanh Van Tran ◽  
Nguyen Le Minh

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.


2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Kaixin Zhao ◽  
Jie Cui ◽  
Zhiqiang Xie

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.


2015 ◽  
Vol 15 (1&2) ◽  
pp. 1-21 ◽  
Author(s):  
Matthew B. Hastings ◽  
Dave Wecker ◽  
Bela Bauer ◽  
Matthias Troyer

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.


2013 ◽  
Vol 380-384 ◽  
pp. 1645-1648 ◽  
Author(s):  
Zhi Wang Gan ◽  
Meng Zhou

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.


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