The human story behind Everettian quantum mechanics

Hugh Everett III was an unappealing character with a remarkable mind. His Princeton doctoral thesis on the foundations of physics transformed our understanding of quantum-mechanical reality, and he made original contributions to military operations research and to game theory. His domestic life was less inspiring; he died young after a lifetime of over-indulgence in food, alcohol, tobacco and sex, leaving behind a somewhat dysfunctional family with which he had little emotional connection

Everett and the Born Rule

During the last ten years or so, derivations of the Born rule based on decision theory have been proposed and developed, and it is claimed that these are valid in the context of the Everett interpretation. This claim is critically assessed and it is shown that one of its key assumptions, although natural in the context of the Copenhagen interpretation, is not consistent with that of Everett. It is further argued that any interpretation that relates outcome likelihood to the expansion coefficients connecting the wavefunction with the eigenfunctions of the measurement operator must be inconsistent with the Everett interpretation.Comment: 22 pages 1 figur

State Transfer and Spin Measurement

We present a Hamiltonian that can be used for amplifying the signal from a quantum state, enabling the measurement of a macroscopic observable to determine the state of a single spin. We prove a general mapping between this Hamiltonian and an exchange Hamiltonian for arbitrary coupling strengths and local magnetic fields. This facilitates the use of existing schemes for perfect state transfer to give perfect amplification. We further prove a link between the evolution of this fixed Hamiltonian and classical Cellular Automata, thereby unifying previous approaches to this amplification task. Finally, we show how to use the new Hamiltonian for perfect state transfer in the, to date, unique scenario where total spin is not conserved during the evolution, and demonstrate that this yields a significantly different response in the presence of decoherence.Comment: 4 pages, 2 figure

Nutrition and the gastrointestinal tract

In this year’s issue, we again have a high-calibre collection of topical reviews. Gracie and Ford commence with an assessment of the role of symbiotics (i.e. probiotics and prebiotics given together) in patients with irritable bowel syndrome. They first review the many randomized trials of probiotics and the significant and persistent reductions in symptoms that (on balance) these yield – that may persist after the end of treatment. Pain, bloating and flatulence are all better than with placebo with a range of different regimens. However, although symbiotics appear promising, their current conclusion is that the evidence for superiority over probiotics alone is lacking. Jin and Vos then consider the pathophysiology of nonalcoholic fatty liver disease and specifically the role of fructose. Their synthesis of the literature includes the conclusion that unregulated lipogenesis is key to nonalcoholic fatty liver disease, linked to generalized increases in visceral adiposity – in turn probably secondary to changes in the intestinal microbiota. Dietary fructose seems an important determinant of these phenomena, and early-in-life exposure appears of most significance. Although dogmatic advice is not justified, continuing to argue for limitation of dietary fructose seems wise. Barrett et al. consider the immune response in patients on artificial nutrition in the current context wherein we aim for enteral nutrition whenever possible – thus recognizing that patients who need parenteral nutrition are then an especially high-risk group. They conclude from AQ3 a wide consideration of animal and human data that the intestinal epithelial barrier is significantly compromised and to a clinically relevant extent in patients on exclusive parenteral nutrition. They encourage targeted new work to exploit the mechanisms that have now been unearthed, such that future parenteral nutrition could be used with fewer adverse immunological consequences. Plank and Russell look at nutrition in liver transplantation incorporating new data from patients with concomitantmorbid obesity. It is of course clear that obesity is a perioperative risk factor but we lack proof that pretransplant weight loss would change this. The main issue here is probably the sarcopenic element, and weight loss without muscle preservation (or growth) would be unlikely to help. As obese patients are AQ4 being transplanted, better data are clearly needed to guide optimal nutritional strategies. After a comprehensive review on the state of the art on gluten sensitivity in the absence of coeliac disease by David Sanders, the issue finishes with a intriguing article by Murphy et al. in which they consider the evidence that chronic disease is made more likely by changes in the gut microbiota driven by a high-fat diet. Although dysbiosis is present and linked to obesity, on present evidence, this falls short of a direct causal relationship. We feel confident that readers will find plenty to provoke thought and hopefully to stimulate research in the many loci where data are sparse or inconclusive

Resonance bifurcations of robust heteroclinic networks

Robust heteroclinic cycles are known to change stability in resonance bifurcations, which occur when an algebraic condition on the eigenvalues of the system is satisfied and which typically result in the creation or destruction of a long-period periodic orbit. Resonance bifurcations for heteroclinic networks are more complicated because different subcycles in the network can undergo resonance at different parameter values, but have, until now, not been systematically studied. In this article we present the first investigation of resonance bifurcations in heteroclinic networks. Specifically, we study two heteroclinic networks in $\R^4$ and consider the dynamics that occurs as various subcycles in each network change stability. The two cases are distinguished by whether or not one of the equilibria in the network has real or complex contracting eigenvalues. We construct two-dimensional Poincare return maps and use these to investigate the dynamics of trajectories near the network. At least one equilibrium solution in each network has a two-dimensional unstable manifold, and we use the technique developed in [18] to keep track of all trajectories within these manifolds. In the case with real eigenvalues, we show that the asymptotically stable network loses stability first when one of two distinguished cycles in the network goes through resonance and two or six periodic orbits appear. In the complex case, we show that an infinite number of stable and unstable periodic orbits are created at resonance, and these may coexist with a chaotic attractor. There is a further resonance, for which the eigenvalue combination is a property of the entire network, after which the periodic orbits which originated from the individual resonances may interact. We illustrate some of our results with a numerical example.Comment: 46 pages, 20 figures. Supplementary material (two animated gifs) can be found on http://www.maths.leeds.ac.uk/~alastair/papers/KPR_res_net_abs.htm

Using multiple criteria decision analysis to aid the selection of enterprise resource planning software : a case study

BHC Ltd is a family owned SME which specialises in steel fabrication for the construction industry. Due to rapid growth over the past decade the company’s current business software has evolved from a collection of semi-integrated individual packages and Excel spreadsheets. To help the company become more efficient during the current financial downturn and to ensure they are capable of future growth, BHC Ltd initiated a project with the University of Strathclyde to select and implement an Enterprise Resource Planning (ERP) solution. This paper will provide a case study of BHC’s ERP selection process. In particular it will discuss how steel specific business requirements and organisational culture led us to use multiple criteria decision analysis (MCDA) when making a final software selection. The MCDA process that was followed is further discussed and includes the success that was achieved by using this approach

INFORMATION CRITERIA FOR IMPULSE RESPONSE FUNCTION MATCHING ESTIMATION OF DSGE MODELS

We propose new information criteria for impulse response function matching estimators (IRFMEs). These estimators yield sampling distributions of the structural parameters of dynamic sto- chastic general equilibrium (DSGE) models by minimizing the distance between sample and theoretical impulse responses. First, we propose an information criterion to select only the responses that produce consistent estimates of the true but unknown structural parameters: the Valid Impulse Response Selection Criterion (VIRSC). The criterion is especially useful for mis-speci?ed models. Second, we propose a criterion to select the impulse responses that are most informative about DSGE model parameters: the Relevant Im- pulse Response Selection Criterion (RIRSC). These criteria can be used in combination to select the subset of valid impulse response functions with minimal dimension that yields asymptotically e¢ cient estimators. The criteria are general enough to apply to impulse responses estimated by VARs, local projections, and simulation methods. We show that the use of our criteria signi?cantly a§ects estimates and inference about key parameters of two well-known new Keynesian DSGE models. Monte Carlo evidence indicates that the criteria yield gains in terms of ?nite sample bias as well as o§ering tests statistics whose behavior is better approximated by ?rst order asymptotic theory. Thus, our criteria improve on existing methods used to implement IRFMEs.Output Growth Forecasts, Inflation Forecasts, Model Selection, Structural Change, Forecast Evaluation, Real-time data. Evaluation

Perfect State Transfer: Beyond Nearest-Neighbor Couplings

In this paper we build on the ideas presented in previous works for perfectly transferring a quantum state between opposite ends of a spin chain using a fixed Hamiltonian. While all previous studies have concentrated on nearest-neighbor couplings, we demonstrate how to incorporate additional terms in the Hamiltonian by solving an Inverse Eigenvalue Problem. We also explore issues relating to the choice of the eigenvalue spectrum of the Hamiltonian, such as the tolerance to errors and the rate of information transfer.Comment: 8 pages, 2 figures. Reorganised, more detailed derivations provided and section on rate of information transfer adde