An adaptive Metropolis-Hastings scheme: sampling and optimization

We propose an adaptive Metropolis-Hastings algorithm in which sampled data are used to update the proposal distribution. We use the samples found by the algorithm at a particular step to form the information-theoretically optimal mean-field approximation to the target distribution, and update the proposal distribution to be that approximatio. We employ our algorithm to sample the energy distribution for several spin-glasses and we demonstrate the superiority of our algorithm to the conventional MH algorithm in sampling and in annealing optimization.Comment: To appear in Europhysics Letter

Thermodynamics of deterministic finite automata operating locally and periodically

Real-world digital computers have operational constraints that cause nonzero entropy production (EP). In particular, almost all real-world computers are "periodic" in that they iteratively undergo the same physical process, and are "local" in that not all physical variables that are statistically coupled are also directly coupled physically. These constraints are so universal because the ability to decompose a complex computation into small, iterative logical updates is what makes digital computers so powerful. Here we first derive expressions for the nonzero EP caused by these two particular constraints in physical implementations of deterministic finite automata (DFA), a foundational system of computer science theory. We then relate this minimal EP to the computational characteristics of the DFA. Specifically, we show that DFA divide into two classes: those with an invertible local update map, which have zero local and periodic EP, and those with a non-invertible local update map, which have high minimal EP. We also demonstrate the thermodynamic advantages of implementing a DFA with a physical process that is agnostic about the inputs that it processes. \end{abstract

The effect of disorder in multi-component covalent organic frameworks

We examined the effect of two different types of linker distribution—random or correlated distribution—on the pore size and shape within single-layers of three multi-component COFs. We reveal a relationship between linker distribution and the porosity of COF solid solutions. The methods presented in this paper are generalisable and could be used in further studies to examine the properties of disordered framework materials

How does the British public understand mental health? A qualitative analysis of open-text responses

BACKGROUND: An individual's understanding of mental health can influence their attitudes towards those experiencing mental health problems, and also impact their response to any mental health problems they experience. However, what the lay public understand about mental health is not well explored in existing research. AIMS: This study aims to gain a deeper insight into what the general public understand by the term 'mental health problem'. METHODS: Data were taken from a large-scale representative sample of adults from Great Britain (n = 2,708). A thematic analysis was carried out on an open-text question which asked people what they understood by the term 'mental health problem'. RESULTS: Six themes were identified in the thematic analysis, which included understanding mental health through thinking about cause and effect, thinking about the location of mental health problems in the body, the universality and variation of mental health problems, reflections on lived experience and identifying a specific mental health problem. CONCLUSION: The analysis suggests that there are many diverse ways the public conceptualises mental health. The themes identified may be useful for future quantitative analyses, and also may suggest how information about mental health can be best communicated to the public

Structure and Connectivity of Depressive Symptom Networks Corresponding to Early Treatment Response.

Background There are suggestions that denser network connectivity (i.e., the strength of associations between individual symptoms) may be a prognostic indicator of poor treatment response in depression. We sought to examine this aspect of depressive symptom networks in the context of early responses to treatment in adolescents. Methods Routine psychiatric data were obtained for child/adolescent service users who underwent at least three treatment sessions in publicly funded services in England between 2011 and 2015 (N = 3017, 78% female; mean age [SD] = 14.43 years [1.75]). Depressive symptoms were assessed using the Revised Children's Anxiety and Depression Scale at presentation, and again after three treatment sessions. Treatment response was determined using the Reliable Change Index. Network analysis was used to compare the depressive symptom structure and connectivity of sub-samples who, after three treatment sessions had: 1) positively responded (n = 566), 2) not reliably changed (n = 2277), and 3) reliably deteriorated (n = 174), using matched samples to control for baseline severity. Findings Overall connectivity (i.e., the summed total of weighted connections) was significantly weaker for the positive treatment response group at baseline (compared with unchanged and deteriorated groups), however, this group saw the largest increase in connectivity over the course of treatment. With regard to the overall importance of specific symptoms within the networks, fatigue was highest in strength for the unchanged and deteriorated groups, whereas low mood was highest in strength for the improved group. Interpretation This study demonstrates that adolescents who respond early to treatment for depression are characterised by symptom networks that are less densely connected initially, yet increase in connectivity over the course of treatment. This may be indicative of ‘positive spirals’ whereby improvement in one symptom triggers improvements in other symptoms, thereby increasing symptom–symptom associations even as severity decreases. Funding The study was supported by the Wellcome Trust grant 204366/Z/16/Z. The funders had no role in the study design, data collection, data analysis, interpretation, or writing of the report

Algebraic-geometrical formulation of two-dimensional quantum gravity

We find a volume form on moduli space of double punctured Riemann surfaces whose integral satisfies the Painlev\'e I recursion relations of the genus expansion of the specific heat of 2D gravity. This allows us to express the asymptotic expansion of the specific heat as an integral on an infinite dimensional moduli space in the spirit of Friedan-Shenker approach. We outline a conjectural derivation of such recursion relations using the Duistermaat-Heckman theorem.Comment: 10 pages, Latex fil