The Laplace-Jaynes approach to induction

An approach to induction is presented, based on the idea of analysing the context of a given problem into `circumstances'. This approach, fully Bayesian in form and meaning, provides a complement or in some cases an alternative to that based on de Finetti's representation theorem and on the notion of infinite exchangeability. In particular, it gives an alternative interpretation of those formulae that apparently involve `unknown probabilities' or `propensities'. Various advantages and applications of the presented approach are discussed, especially in comparison to that based on exchangeability. Generalisations are also discussed.Comment: 38 pages, 1 figure. V2: altered discussion on some points, corrected typos, added reference

Numerical Bayesian quantum-state assignment for a three-level quantum system. II. Average-value data with a constant, a Gaussian-like, and a Slater prior

This paper offers examples of concrete numerical applications of Bayesian quantum-state assignment methods to a three-level quantum system. The statistical operator assigned on the evidence of various measurement data and kinds of prior knowledge is computed partly analytically, partly through numerical integration (in eight dimensions) on a computer. The measurement data consist in the average of outcome values of N identical von Neumann projective measurements performed on N identically prepared three-level systems. In particular the large-N limit will be considered. Three kinds of prior knowledge are used: one represented by a plausibility distribution constant in respect of the convex structure of the set of statistical operators; another one represented by a prior studied by Slater, which has been proposed as the natural measure on the set of statistical operators; the last prior is represented by a Gaussian-like distribution centred on a pure statistical operator, and thus reflecting a situation in which one has useful prior knowledge about the likely preparation of the system. The assigned statistical operators obtained with the first two kinds of priors are compared with the one obtained by Jaynes' maximum entropy method for the same measurement situation. In the companion paper the case of measurement data consisting in absolute frequencies is considered.Comment: 10 pages, 4 figures. V2: added "Post scriptum" under Conclusions, slightly changed Acknowledgements, and corrected some spelling error

Numerical Bayesian state assignment for a three-level quantum system. I. Absolute-frequency data; constant and Gaussian-like priors

This paper offers examples of concrete numerical applications of Bayesian quantum-state-assignment methods to a three-level quantum system. The statistical operator assigned on the evidence of various measurement data and kinds of prior knowledge is computed partly analytically, partly through numerical integration (in eight dimensions) on a computer. The measurement data consist in absolute frequencies of the outcomes of N identical von Neumann projective measurements performed on N identically prepared three-level systems. Various small values of N as well as the large-N limit are considered. Two kinds of prior knowledge are used: one represented by a plausibility distribution constant in respect of the convex structure of the set of statistical operators; the other represented by a Gaussian-like distribution centred on a pure statistical operator, and thus reflecting a situation in which one has useful prior knowledge about the likely preparation of the system. In a companion paper the case of measurement data consisting in average values, and an additional prior studied by Slater, are considered.Comment: 23 pages, 14 figures. V2: Added an important note concerning cylindrical algebraic decomposition and thanks to P B Slater, corrected some typos, added reference

Asymmetric Thermal Lineshape Broadening in a Gapped 3-Dimensional Antiferromagnet - Evidence for Strong Correlations at Finite Temperature

It is widely believed that magnetic excitations become increasingly incoherent as temperature is raised due to random collisions which limit their lifetime. This picture is based on spin-wave calculations for gapless magnets in 2 and 3 dimensions and is observed experimentally as a symmetric Lorentzian broadening in energy. Here, we investigate a three-dimensional dimer antiferromagnet and find unexpectedly that the broadening is asymmetric - indicating that far from thermal decoherence, the excitations behave collectively like a strongly correlated gas. This result suggests that a temperature activated coherent state of quasi-particles is not confined to special cases like the highly dimerized spin-1/2 chain but is found generally in dimerized antiferromagnets of all dimensionalities and perhaps gapped magnets in general

What makes it work? Exploring experiences of patient research partners and researchers involved in a long-term co-creative research collaboration

Background: Exchanging experiences of patient and public involvement (PPI) can bring insights into why, how and when PPI is most effective. The aim of this study was to explore the experiences of patient research partners (PRPs) and researchers engaged in a co-creative long-term collaboration in cancer research. Methods: The aim and procedures of this study were jointly decided upon by PRPs and researchers. The PRPs included former patients treated for cancer and significant others of the same target group. The participants (11 PRPs, 6 researchers) took part in semi-structured telephone interviews. The interviews were analysed using qualitative content analysis by a researcher who had no prior relationships with the participants. Results: Five overarching categories were identified: Reasons for investing in a long-term collaboration, Benefits of participating, Improving the research, Elements of success and Challenges and ways to improve. Reasons for investing in the collaboration included the desire to improve cancer care and to make use of own negative experiences. Benefits of participating included a positive impact on the PRPs' psychosocial adjustment to the illness. Moreover, the researchers highlighted that working together with the PRPs made the research feel more meaningful. The participants reported that the collaboration improved the relevance and acceptability of the research. Having a shared goal, a clear but yet accommodating structure, as well as an open and trustful working atmosphere were recognised as elements of success. The PRPs furthermore emphasized the importance of seeing that their input mattered. Among the few challenges raised were the distance to the meeting venues for some PRPs and a limited diversity among participants. Conclusions: This study identified factors essential to researchers and clinicians attempting to engage the public in research. Our results suggest that for successful patient involvement, the purpose and format of the collaboration should be clear to both PRPs and researchers. A clear but yet accommodating structure and keen leadership emerged as key factors to create a sense of stability and a trustful atmosphere. Furthermore, providing regular feedback on how PRPs input is implemented is important for PRPs to stay committed over time

The coherent {\it d}-wave superconducting gap in underdoped La2−x_{2-x}Srx_{x}CuO4_4 as studied by angle-resolved photoemission

We present angle-resolved photoemission spectroscopy (ARPES) data on moderately underdoped La$_{1.855}$Sr$_{0.145}$CuO$_4$ at temperatures below and above the superconducting transition temperature. Unlike previous studies of this material, we observe sharp spectral peaks along the entire underlying Fermi surface in the superconducting state. These peaks trace out an energy gap that follows a simple {\it d}-wave form, with a maximum superconducting gap of 14 meV. Our results are consistent with a single gap picture for the cuprates. Furthermore our data on the even more underdoped sample La$_{1.895}$Sr$_{0.105}$CuO$_4$ also show sharp spectral peaks, even at the antinode, with a maximum superconducting gap of 26 meV.Comment: Accepted by Phys. Rev. Let