Natural Halting Probabilities, Partial Randomness, and Zeta Functions

We introduce the zeta number, natural halting probability and natural complexity of a Turing machine and we relate them to Chaitin's Omega number, halting probability, and program-size complexity. A classification of Turing machines according to their zeta numbers is proposed: divergent, convergent and tuatara. We prove the existence of universal convergent and tuatara machines. Various results on (algorithmic) randomness and partial randomness are proved. For example, we show that the zeta number of a universal tuatara machine is c.e. and random. A new type of partial randomness, asymptotic randomness, is introduced. Finally we show that in contrast to classical (algorithmic) randomness--which cannot be naturally characterised in terms of plain complexity--asymptotic randomness admits such a characterisation.Comment: Accepted for publication in Information and Computin

Positive and negative well-being and objectively measured sedentary behaviour in older adults: evidence from three cohorts

Background: Sedentary behaviour is related to poorer health independently of time spent in moderate to vigorous physical activity. The aim of this study was to investigate whether wellbeing or symptoms of anxiety or depression predict sedentary behaviour in older adults. Method: Participants were drawn from the Lothian Birth Cohort 1936 (LBC1936) (n = 271), and the West of Scotland Twenty-07 1950s (n = 309) and 1930s (n = 118) cohorts. Sedentary outcomes, sedentary time, and number of sit-to-stand transitions, were measured with a three-dimensional accelerometer (activPAL activity monitor) worn for 7 days. In the Twenty-07 cohorts, symptoms of anxiety and depression were assessed in 2008 and sedentary outcomes were assessed ~ 8 years later in 2015 and 2016. In the LBC1936 cohort, wellbeing and symptoms of anxiety and depression were assessed concurrently with sedentary behaviour in 2015 and 2016. We tested for an association between wellbeing, anxiety or depression and the sedentary outcomes using multivariate regression analysis. Results: We observed no association between wellbeing or symptoms of anxiety and the sedentary outcomes. Symptoms of depression were positively associated with sedentary time in the LBC1936 and Twenty-07 1950s cohort, and negatively associated with number of sit-to-stand transitions in the LBC1936. Meta-analytic estimates of the association between depressive symptoms and sedentary time or number of sit-to-stand transitions, adjusted for age, sex, BMI, long-standing illness, and education, were β = 0.11 (95% CI = 0.03, 0.18) and β = − 0.11 (95% CI = − 0.19, −0.03) respectively. Conclusion: Our findings indicate that depressive symptoms are positively associated with sedentary behavior. Future studies should investigate the causal direction of this association

Children’s sedentary behaviour: descriptive epidemiology and associations with objectively-measured sedentary time

Background: Little is known regarding the patterning and socio-demographic distribution of multiple sedentary behaviours in children. The aims of this study were to: 1) describe the leisure-time sedentary behaviour of 9-10 year old British children, and 2) establish associations with objectively-measured sedentary time. Methods: Cross-sectional analysis in the SPEEDY study (Sport, Physical activity and Eating behaviour: Environmental Determinants in Young people) (N=1513, 44.3% boys). Twelve leisure-time sedentary behaviours were assessed by questionnaire. Objectively-measured leisure-time sedentary time (Actigraph GT1M, <100 counts/minute) was assessed over 7 days. Differences by sex and socioeconomic status (SES) in self-reported sedentary behaviours were tested using Kruskal-Wallis tests. The association between objectively-measured sedentary time and the separate sedentary behaviours (continuous (minutes) and categorised into 'none' 'low' or 'high' participation) was assessed using multi-level linear regression. Results: Sex differences were observed for time spent in most sedentary behaviours (all p ≤ 0.02), except computer use. Girls spent more time in combined non-screen sedentary behaviour (median, interquartile range: girls: 770.0 minutes, 390.0-1230.0; boys: 725.0, 365.0 - 1182.5; p = 0.003), whereas boys spent more time in screen-based behaviours (girls: 540.0, 273.0 - 1050.0; boys: 885.0, 502.5 - 1665.0; p < 0.001). Time spent in five non-screen behaviours differed by SES, with higher values in those of higher SES (all p ≤ 0.001). Regression analyses with continuous exposures indicated that reading (β = 0.1, p < 0.001) and watching television (β = 0.04, p < 0.01) were positively associated with objectively-measured sedentary time, whilst playing board games (β = -0.12, p < 0.05) was negatively associated. Analysed in categorical form, sitting and talking (vs. none: 'low' β = 26.1,ns; 'high' 30.9, p < 0.05), playing video games (vs. none: 'low' β = 49.1, p < 0.01; 'high' 60.2, p < 0.01) and watching television (vs. lowest tertile: middle β = 22.2,ns; highest β = 31.9, p < 0.05) were positively associated with objectively-measured sedentary time whereas talking on the phone (vs. none: 'low' β = -38.5, p < 0.01; 'high' -60.2, p < 0.01) and using a computer/internet (vs. none: 'low' β = -30.7, p < 0.05; 'high' -4.2,ns) were negatively associated. Conclusions: Boys and girls and children of different socioeconomic backgrounds engage in different leisure-time sedentary behaviours. Whilst a number of behaviours may be predictive of total sedentary time, collectively they explain little overall variance. Future studies should consider a wide range of sedentary behaviours and incorporate objective measures to quantify sedentary time where possible

Unravelling the evolution of the Allatostatin-Type A, KISS and Galanin Peptide-Receptor gene families in Bilaterians: insights from Anopheles Mosquitoes

Allatostatin type A receptors (AST-ARs) are a group of G-protein coupled receptors activated by members of the FGL-amide (AST-A) peptide family that inhibit food intake and development in arthropods. Despite their physiological importance the evolution of the AST-A system is poorly described and relatively few receptors have been isolated and functionally characterised in insects. The present study provides a comprehensive analysis of the origin and comparative evolution of the AST-A system. To determine how evolution and feeding modified the function of AST-AR the duplicate receptors in Anopheles mosquitoes, were characterised. Phylogeny and gene synteny suggested that invertebrate AST-A receptors and peptide genes shared a common evolutionary origin with KISS/GAL receptors and ligands. AST-ARs and KISSR emerged from a common gene ancestor after the divergence of GALRs in the bilaterian genome. In arthropods, the AST-A system evolved through lineage-specific events and the maintenance of two receptors in the flies and mosquitoes (Diptera) was the result of a gene duplication event. Speciation of Anophelesmosquitoes affected receptor gene organisation and characterisation of AST-AR duplicates (GPRALS1 and 2) revealed that in common with other insects, the mosquito receptors were activated by insect AST-A peptides and the iCa(2+)-signalling pathway was stimulated. GPRALS1 and 2 were expressed mainly in mosquito midgut and ovaries and transcript abundance of both receptors was modified by feeding. A blood meal strongly up-regulated expression of both GPRALS in the midgut (p < 0.05) compared to glucose fed females. Based on the results we hypothesise that the AST-A system in insects shared a common origin with the vertebrate KISS system and may also share a common function as an integrator of metabolism and reproduction. Highlights: AST-A and KISS/GAL receptors and ligands shared common ancestry prior to the protostome-deuterostome divergence. Phylogeny and gene synteny revealed that AST-AR and KISSR emerged after GALR gene divergence. AST-AR genes were present in the hemichordates but were lost from the chordates. In protostomes, AST-ARs persisted and evolved through lineage-specific events and duplicated in the arthropod radiation. Diptera acquired and maintained functionally divergent duplicate AST-AR genes.Foundation for Science and Technology, Portugal (FCT) [PTDC/BIA-BCM/114395/2009]; European Regional Development Fund (ERDF) COMPETE - Operational Competitiveness Programme; Portuguese funds through FCT Foundation for Science and Technology [PEst-C/MAR/LA0015/2013, UID/Multi/04326/2013, PEst-OE/SAU/LA0018/2013]; FCT [SFRH/BPD/89811/2012, SFRH/BPD/80447/2011, SFRH/BPD/66742/2009]; auxiliary research contract FCT Pluriannual funds [PEst-C/MAR/LA0015/2013, UID/Multi/04326/2013]info:eu-repo/semantics/publishedVersio

Walk with Me: a protocol for a pilot RCT of a peer-led walking programme to increase physical activity in inactive older adults

Background: Levels of physical activity decline with age. Some of the most disadvantaged individuals in society, such as those from lower socio-economic position, are also the most inactive. Increasing physical activity levels, particularly among those most inactive, is a public health priority. Peer-led physical activity interventions may offer a model to increase physical activity in the older adult population. This study aims to test the feasibility of a peer-led, multicomponent physical activity intervention in socio-economically disadvantaged community dwelling older adults. Methods: The Medical Research Council framework for developing and evaluating complex interventions will be used to design and test the feasibility of a randomised controlled trial (RCT) of a multicomponent peer-led physical activity intervention. Data will be collected at baseline, immediately after the intervention (12 weeks) and 6 months after baseline measures. The pilot RCT will provide information on recruitment of peer mentors and participants and attrition rates, intervention fidelity, and data on the variability of the primary outcome (minutes of moderate to vigorous physical activity measured with an accelerometer). The pilot trail will also assess the acceptability of the intervention and identify potential resources needed to undertake a definitive study. Data analyses will be descriptive and include an evaluation of eligibility, recruitment, and retention rates. The findings will be used to estimate the sample size required for a definitive trial. A detailed process evaluation using qualitative and quantitative methods will be conducted with a variety of stakeholders to identify areas of success and necessary improvements. Discussion: This paper describes the protocol for the ‘Walk with Me’ pilot RCT which will provide the information necessary to inform the design and delivery of a fully powered trial should the Walk with Me intervention prove feasible

Mapping Peptidergic Cells in Drosophila: Where DIMM Fits In

The bHLH transcription factor DIMMED has been associated with the differentiation of peptidergic cells in Drosophila. However, whether all Drosophila peptidergic cells express DIMM, and the extent to which all DIMM cells are peptidergic, have not been determined. To address these issues, we have mapped DIMM expression in the central nervous system (CNS) and periphery in the late larval stage Drosophila. At 100 hr after egg-laying, DIMM immunosignals are largely congruent with a dimm-promoter reporter (c929-GAL4) and they present a stereotyped pattern of 306 CNS cells and 52 peripheral cells. We assigned positional values for all DIMM CNS cells with respect to reference gene expression patterns, or to patterns of secondary neuroblast lineages. We could assign provisional peptide identities to 68% of DIMM-expressing CNS cells (207/306) and to 73% of DIMM-expressing peripheral cells (38/52) using a panel of 24 markers for Drosophila neuropeptide genes. Furthermore, we found that DIMM co-expression was a prevalent feature within single neuropeptide marker expression patterns. Of the 24 CNS neuropeptide gene patterns we studied, six patterns are >90% DIMM-positive, while 16 of 22 patterns are >40% DIMM-positive. Thus most or all DIMM cells in Drosophila appear to be peptidergic, and many but not all peptidergic cells express DIMM. The co-incidence of DIMM-expression among peptidergic cells is best explained by a hypothesis that DIMM promotes a specific neurosecretory phenotype we term LEAP. LEAP denotes Large cells that display Episodic release of Amidated Peptides