Computation in generalised probabilistic theories

From the existence of an efficient quantum algorithm for factoring, it is likely that quantum computation is intrinsically more powerful than classical computation. At present, the best upper bound known for the power of quantum computation is that BQP is in AWPP. This work investigates limits on computational power that are imposed by physical principles. To this end, we define a circuit-based model of computation in a class of operationally-defined theories more general than quantum theory, and ask: what is the minimal set of physical assumptions under which the above inclusion still holds? We show that given only an assumption of tomographic locality (roughly, that multipartite states can be characterised by local measurements), efficient computations are contained in AWPP. This inclusion still holds even without assuming a basic notion of causality (where the notion is, roughly, that probabilities for outcomes cannot depend on future measurement choices). Following Aaronson, we extend the computational model by allowing post-selection on measurement outcomes. Aaronson showed that the corresponding quantum complexity class is equal to PP. Given only the assumption of tomographic locality, the inclusion in PP still holds for post-selected computation in general theories. Thus in a world with post-selection, quantum theory is optimal for computation in the space of all general theories. We then consider if relativised complexity results can be obtained for general theories. It is not clear how to define a sensible notion of an oracle in the general framework that reduces to the standard notion in the quantum case. Nevertheless, it is possible to define computation relative to a `classical oracle'. Then, we show there exists a classical oracle relative to which efficient computation in any theory satisfying the causality assumption and tomographic locality does not include NP.Comment: 14+9 pages. Comments welcom

Minimizing Effective Many-Body Interactions

A simple two-level model is developed and used to test the properties of effective interactions for performing nuclear structure calculations in truncated model spaces. It is shown that the effective many-body interactions sensitively depend on the choice of the single-particle basis and they appear to be minimized when a self- consistent Hartree-Fock basis is used.Comment: (15 pages of text and 1 postscript figure (Figure available upon request), Preprint Number not assigned ye

Interview with Lee Michael Barrett, Eco-Logistics, 2009 (audio)

Interview of Lee Michael Barrett by Angie Cirello in Portland, Oregon on November 20th, 2009. The interview index is available for download

PTO Perspective on Recent Developments in Patent Protection for Computer Hardware and Software

This Article explores the area of patent protection for computer related inventions, The author examines the problem of determining whether a mathematical algorithm qualifies as patentable subject matter under 35 U.S.C. § 101 and the interpretation of means-plus-function limitations under 35 U.S.C. § 112 6. In his examination, the author explains the perspective of the United States Patent and Trademark Office, as well as the position taken by the Federal Circuit Court of Appeals in the recent cases of In re Alappat and In re Donaldson Co

Investigation of the molecular basis of virulence of Streptococcus equi

Equine strangles is a purulent lymphadenitis of the head and neck and is caused by Streptococcus equi ssp equi remaining a worldwide, endemic infection that represents around 30% of all annually recorded incidents of equine disease. Despite much effort, current vaccination strategies have proved largely ineffective towards S. equi, ssp equi, with the current focus based on ‘reverse vaccinology’, using genome sequence data of S. equi ssp equi to identify surface exposed and secreted proteins. Streptococcus equi shares much of its genome with the genetically closely related, S. equi ssp zooepidemicus. Despite this close genetic association, S. equi ssp zooepidemicus exhibits very distinct pathogenicity variations. S. equi ssp zooepidemicus can infect a wide variety of vertebrate hosts showing a high degree of antigenic variability and a large amount of strain variability whereas S. equi is largely equine specific and processes a limited number of strain types. Understanding the molecular basis of virulence of these contrasting organisms therefore remains a key requirement if a suitable vaccination. Identification of potential virulence factors has been greatly aided by the availability of the full genome sequence of S. equi ssp equi (4047) and S. equi ssp zooepidemicus (H70). In this study, we identified and investigated a range of putative virulence factors including the covalently attached surface protein SEQ2190, the secreted phospholipase enzymes SlaA (SEQ0849) and SlaB (SEQ2155) and finally the lipoprotein, acid phosphatase SeLppC (SEQ0346) and its orthologue SzLppC (SZO16870). In all cases, using molecular biology techniques the coding region representative for each of these proteins was cloning into expression constructs, expressed and purified and further investigations carried out. Although efforts to obtain a 3-dimensional structure of SEQ2190 were unsuccessful, bioinformatic investigations have identified SEQ2190 as a unique protein in S. equi ssp equi with a putative structure suggesting a role in bacteria-host interaction. SlaA was demonstrated to be an active sPLA2 enzyme, active against a 1, 2-dithio analog of diheptanoyl phosphatidylcholine but not 2-deoxy-2-thio- Arachidonoyl phosphatidylcholine. It was also demonstrated to have a specific requirement for the divalent ion, Ca2+ for activity, an optimum temperature higher than expected (40°C), a Km of 14.40 ± 7.866 mM and a specific activity of 5.06x10-2 ± 3.01x10-3 μmol/min/mg. SlaA was also shown to react to equine post-infection convalescent serum. Although some characterisation had been previously undertaken regarding whole cell SeLppC extracts, in this study we produced expression constructs of SeLppC and its orthologous pseudogene (SzLppC) found in the genome strain of S. equi ssp zooepidemicus. We used purified SeLppC and SzLppC to demonstrate activity against pNPP and two biologically significant substrates (5’AMP and 5’UMP) and recorded the Km values for each. We also identified SeLppC to not possess a specific activity for the divalent ion Cu2+, a lower than expected pH optimum and a higher than expected temperature range. Furthermore we also demonstrated that SzLppC is not a pseudogene, indicating an error within the S. equi spp zooepidemicus genome strain

Exact Solutions of Model Hamiltonian Problems with Effective Interactions

We demonstrate with soluble models how to employ the effective Hamiltonian approach of Lee and Suzuki to obtain all the exact eigenvalues of the full Hamiltonian. We propose a new iteration scheme to obtain the effective Hamiltonian and demonstrate its convergence properties.Comment: 12 pages and 1 figur

No-core shell model in an effective-field-theory framework

We present a new approach to the construction of effective interactions suitable for many-body calculations by means of the no-core shell model (NCSM). We consider an effective field theory (EFT) with only nucleon fields directly in the NCSM model spaces. In leading order, we obtain the strengths of the three contact terms from the condition that in each model space the experimental ground-state energies of 2H, 3H and 4He be exactly reproduced. The first (0^+;0) excited state of 4He and the ground state of 6Li are then obtained by means of NCSM calculations in several spaces and frequencies. After we remove the harmonic-oscillator frequency dependence, we predict for 4He an energy level for the first (0^+;0) excited state in remarkable agreement with the experimental value. The corresponding 6Li binding energy is about 70% of the experimental value, consistent with the expansion parameter of the EFT.Comment: 4 pages, 3 figures, revtex