Ideal multiplication and reduction are fundamental operations on ideals and are used extensively in class group and infrastructure computations; hence, the efficiency of these operations is extremely important. In this thesis we focus on reduction in real quadratic fields and examine all of the known reduction algorithms, converting them whenever required to work with ideals of positive discrim...

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Despite persistent effort, there is no known technique for obtaining super-linear lower bounds for the computational complexity of the problems in P. Vassilevska Williams and Williams [38] introduce a fruitful approach to advance a better understanding of the computational complexity of the problems in P. In particular, they consider All Pairs Shortest Paths (APSP) and other fundamental problem...

This paper describes a study of a large design and manufacture engineering project, undertaken as part of a Delay and Disruption litigation. Design changes and delays in design approval would have caused delay to the project; in order to fulfil a tight time-constraint, management had to increase parallel development in the network logic, reducing delay but setting up feed-back loops that marked...

where χ is a non-trivial additive character of the finite field Fq, q = p odd, and a ∈ Fq . In my dissertation [5], in particular in [4], I considered more generally the sums S(a,N) for all factors N of p+1. The aim of the present note is to evaluate S(a,N) in a short way, following [4]. We note that our result is also valid for even q, and the technique used in our proof can also be used to ev...

Efforts to study consciousness using computational models over the last two decades have received a decidedly mixed reception. Investigators in mainstream AI have largely ignored this work, and some members of the philosophy community have argued that the whole endeavor is futile. Here we suggest that very substantial progress has been made, to the point where the use of computational simulatio...