Enumerative properties of Ferrers graphs

We define a class of bipartite graphs that correspond naturally with Ferrers diagrams. We give expressions for the number of spanning trees, the number of Hamiltonian paths when applicable, the chromatic polynomial, and the chromatic symmetric function. We show that the linear coefficient of the chromatic polynomial is given by the excedance set statistic.Comment: 12 page

Global information technology infrastructure for a global non-profit organisation : a thesis presented in partial fulfilment of the requirements for the degree of Master of Technology at Massey University

Page 103 missing from vault and scanned copyWith the recent worldwide growth of the Internet, computers are becoming interconnected in a global communications network. Most people view the Internet as a universal communications medium that can replace telephone, television, and radio. Historically, for organisations and enterprises that could afford to do so, expensive telecommunication lines and Wide Area Network technologies were used for global communications, which allowed computers to communicate using proprietary protocols. For non-profit organisations in particular, the Internet has made it possible to connect offices and individuals, using open standard protocols, at a fraction of the cost of other alternatives. This study focuses on the investigation and development of a global communication system and information technology (IT) infrastructure that uses the Internet as its communication platform for a particular non-profit organisation, OMF International. Without a clear understanding of the limitations of the technologies involved, the development of an IT project is likely to be flawed or fail. (Standish Group, 1995) The findings from this investigation revealed that a global communication system and IT infrastructure, suitable for OMF International, needed to overcome limitations in the use and access of the Internet, the unreliability of different email systems to deliver email messages, and financial and human resource constraints. The study found that methods used in 'for-profit' organisations for the development of an IT infrastructure, were applicable to this non-profit organisation, resulting in the successful implementation of a global communication system and IT infrastructure. The choice of IT solutions and technologies within OMF was often based on functionality rather than feasibility, and its global IT infrastructure requirements were overlooked. The study found that by comparison Lotus Notes' client/server IT infrastructure requirements were considerably less than that of Microsoft Exchange client/server, however, alternative low-cost open standard messaging options were more affordable. Conclusively, open standard IT solutions for global communications are better suited that for this non-profit organisation, than proprietary solutions. The study also highlighted the need for an IT architecture, that would provide a plan and strategic context for future IT development within OMF International, which would overcome problems with concurrent IT projects using different technologies

Development of non-equilibrium Green's functions for use with full interaction in complex systems

We present an ongoing development of an existing code for calculating ground-state, steady-state, and transient properties of many-particle systems. The development involves the addition of the full four-index two electron integrals, which allows for the calculation of transport systems, as well as the extension to multi-level electronic systems, such as atomic and molecular systems and other applications. The necessary derivations are shown, along with some preliminary results and a summary of future plans for the code

Types are weak omega-groupoids

We define a notion of weak omega-category internal to a model of Martin-L\"of type theory, and prove that each type bears a canonical weak omega-category structure obtained from the tower of iterated identity types over that type. We show that the omega-categories arising in this way are in fact omega-groupoids.Comment: 28 pages; v2: final journal versio

Classical simulation complexity of extended Clifford circuits

Clifford gates are a winsome class of quantum operations combining mathematical elegance with physical significance. The Gottesman-Knill theorem asserts that Clifford computations can be classically efficiently simulated but this is true only in a suitably restricted setting. Here we consider Clifford computations with a variety of additional ingredients: (a) strong vs. weak simulation, (b) inputs being computational basis states vs. general product states, (c) adaptive vs. non-adaptive choices of gates for circuits involving intermediate measurements, (d) single line outputs vs. multi-line outputs. We consider the classical simulation complexity of all combinations of these ingredients and show that many are not classically efficiently simulatable (subject to common complexity assumptions such as P not equal to NP). Our results reveal a surprising proximity of classical to quantum computing power viz. a class of classically simulatable quantum circuits which yields universal quantum computation if extended by a purely classical additional ingredient that does not extend the class of quantum processes occurring.Comment: 17 pages, 1 figur