A Coalgebraic View of Infinite Trees and Iteration

AbstractThe algebra of infinite trees is, as proved by C. Elgot, completely iterative, i.e., all ideal recursive equations are uniquely solvable. This is proved here to be a general coalgebraic phenomenon: let H be an endofunctor such that for every object X a final coalgebra, TX, of H(_) + X exists. Then TX is an object-part of a monad which is completely iterative. Moreover, a similar contruction of a “completely iterative monoid” is possible in every monoidal category satisfying mild side conditions

The generalised type-theoretic interpretation of constructive set theory

We present a generalisation of the type-theoretic interpretation of constructive set theory into Martin-Löf type theory. The original interpretation treated logic in Martin-Löf type theory via the propositions-as-types interpretation. The generalisation involves replacing Martin-Löf type theory with a new type theory in which logic is treated as primitive. The primitive treatment of logic in type theories allows us to study reinterpretations of logic, such as the double-negation translation

Anisotropic intrinsic lattice thermal conductivity of phosphorene from first principles

Phosphorene, the single layer counterpart of black phosphorus, is a novel two-dimensional semiconductor with high carrier mobility and a large fundamental direct band gap, which has attracted tremendous interest recently. Its potential applications in nano-electronics and thermoelectrics call for a fundamental study of the phonon transport. Here, we calculate the intrinsic lattice thermal conductivity of phosphorene by solving the phonon Boltzmann transport equation (BTE) based on first-principles calculations. The thermal conductivity of phosphorene at $300\,\mathrm{K}$ is $30.15\,\mathrm{Wm^{-1}K^{-1}}$ (zigzag) and $13.65\,\mathrm{Wm^{-1}K^{-1}}$ (armchair), showing an obvious anisotropy along different directions. The calculated thermal conductivity fits perfectly to the inverse relation with temperature when the temperature is higher than Debye temperature ($\Theta_D = 278.66\,\mathrm{K}$). In comparison to graphene, the minor contribution around $5\%$ of the ZA mode is responsible for the low thermal conductivity of phosphorene. In addition, the representative mean free path (MFP), a critical size for phonon transport, is also obtained.Comment: 5 pages and 6 figures, Supplemental Material available as http://www.rsc.org/suppdata/cp/c4/c4cp04858j/c4cp04858j1.pd

Quantifying Support for the Null Hypothesis in Psychology: An Empirical Investigation

In the traditional statistical framework, nonsignificant results leave researchers in a state of suspended disbelief. In this study, we examined, empirically, the treatment and evidential impact of nonsignificant results. Our specific goals were twofold: to explore how psychologists interpret and communicate nonsignificant results and to assess how much these results constitute evidence in favor of the null hypothesis. First, we examined all nonsignificant findings mentioned in the abstracts of the 2015 volumes of Psychonomic Bulletin & Review, Journal of Experimental Psychology: General, and Psychological Science (N = 137). In 72% of these cases, nonsignificant results were misinterpreted, in that the authors inferred that the effect was absent. Second, a Bayes factor reanalysis revealed that fewer than 5% of the nonsignificant findings provided strong evidence (i.e., BF01 > 10) in favor of the null hypothesis over the alternative hypothesis. We recommend that researchers expand their statistical tool kit in order to correctly interpret nonsignificant results and to be able to evaluate the evidence for and against the null hypothesis

Voluntary exercise does not increase gastrointestinal motility but increases spatial memory, intestinal eNOS, Akt levels, and Bifidobacteria abundance in the microbiome

The interaction between the gut and brain is a great puzzle since it is mediated by very complex mechanisms. Therefore, the possible interactions of the brain–exercise–intestine–microbiome axis were investigated in a control (C, N = 6) and voluntarily exercised (VE, N = 8) middle-aged rats. The endurance capacity was assessed by VO2max on the treadmill, spatial memory by the Morris maze test, gastrointestinal motility by EMG, the microbiome by 16S RNA gene amplicon sequencing, caveolae by electron microscopy, and biochemical assays were used to measure protein levels and production of reactive oxygen species (ROS). Eight weeks of voluntary running increased VO2max, and spatial memory was assessed by the Morris maze test but did not significantly change the motility of the gastrointestinal tract or production of ROS in the intestine. The protein kinase B (Akt) and endothelial nitric oxide synthase (eNOS) protein levels significantly increased in the intestine, while peroxisome proliferator–activated receptor gamma coactivator 1 alpha (PGC-1α), mitochondrial transcription factor A (TFAM), nuclear respiratory factor 1 (NFR1), SIRT1, SIRT3, nicotinamide phosphoribosyl transferase (NAMPT), and nuclear factor κB (NF-κB) did not change. On the other hand, voluntary exercise increased the number of caveolae in the smooth muscles of the intestine and relative abundance of Bifidobacteria in the microbiome, which correlated with the Akt levels in the intestine. Voluntary exercise has systemic effects and the relationship between intestinal Akt and the microbiome of the gastrointestinal tract could be an important adaptive response

Indexed induction–recursion

AbstractAn indexed inductive definition (IID) is a simultaneous inductive definition of an indexed family of sets. An inductive–recursive definition (IRD) is a simultaneous inductive definition of a set and a recursive definition of a function on that set. An indexed inductive–recursive definition (IIRD) is a combination of both.We present a closed theory which allows us to introduce all IIRD in a natural way without much encoding. By specialising it we also get a closed theory of IID. Our theory of IIRD includes essentially all definitions of sets which occur in Martin–Löf type theory. We show in particular that Martin–Löf’s computability predicates for dependent types and Palmgren’s higher order universes are special kinds of IIRD and thereby clarify why they are constructively acceptable notions.We give two axiomatisations. The first formalises a principle for introducing meaningful IIRD by using the data-construct in the original version of the proof assistant Agda for Martin–Löf type theory. The second one admits a more general form of introduction rule, including the introduction rule for the intensional identity relation, which is not covered by the first axiomatisation. If we add an extensional identity relation to our logical framework, we show that the theories of restricted and general IIRD are equivalent by interpreting them in each other.Finally, we show the consistency of our theories by constructing a model in classical set theory extended by a Mahlo cardinal

A many-analysts approach to the relation between religiosity and well-being

The relation between religiosity and well-being is one of the most researched topics in the psychology of religion, yet the directionality and robustness of the effect remains debated. Here, we adopted a many-analysts approach to assess the robustness of this relation based on a new cross-cultural dataset (N = 10, 535 participants from 24 countries). We recruited 120 analysis teams to investigate (1) whether religious people self-report higher well-being, and (2) whether the relation between religiosity and self-reported well-being depends on perceived cultural norms of religion (i.e., whether it is considered normal and desirable to be religious in a given country). In a two-stage procedure, the teams first created an analysis plan and then executed their planned analysis on the data. For the first research question, all but 3 teams reported positive effect sizes with credible/confidence intervals excluding zero (median reported beta = 0.120). For the second research question, this was the case for 65% of the teams (median reported beta = 0.039). While most teams applied (multilevel) linear regression models, there was considerable variability in the choice of items used to construct the independent variables, the dependent variable, and the included covariates.</p

Bindings as bounded natural functors

We present a general framework for specifying and reasoning about syntax with bindings. Abstract binder types are modeled using a universe of functors on sets, subject to a number of operations that can be used to construct complex binding patterns and binding-aware datatypes, including non-well-founded and infinitely branching types, in a modular fashion. Despite not committing to any syntactic format, the framework is “concrete” enough to provide definitions of the fundamental operators on terms (free variables, alpha-equivalence, and capture-avoiding substitution) and reasoning and definition principles. This work is compatible with classical higher-order logic and has been formalized in the proof assistant Isabelle/HOL