Some observations on the logical foundations of inductive theorem proving

In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a goal. Based on this model, we then analyze the following aspects: the choice of a proof shape, the choice of an induction rule and the language of the induction formula. In particular, using model-theoretic techniques, we clarify the relationship between notions of inductiveness that have been considered in the literature on automated inductive theorem proving. This is a corrected version of the paper arXiv:1704.01930v5 published originally on Nov.~16, 2017

Initial segments and end-extensions of models of arithmetic

This thesis is organized into two independent parts. In the first part, we extend the recent work on generic cuts by Kaye and the author. The focus here is the properties of the pairs (M, I) where I is a generic cut of a model M. Amongst other results, we characterize the theory of such pairs, and prove that they are existentially closed in a natural category. In the second part, we construct end-extensions of models of arithmetic that are at least as strong as ATR$_0$. Two new constructions are presented. The first one uses a variant of Fodor’s Lemma in ATR$_0$ to build an internally rather classless model. The second one uses some weak versions of the Galvin–Prikry Theorem in adjoining an ideal set to a model of second-order arithmetic

The Role of the Lateral Habenula in inhibitory-driven action selection

In order to behave adaptively, animals are required to use cues that predicts the presence or the absence of the desired outcome to guide their selection of actions. Previous studies of how cue influences on choice, using the Specific Pavlovian Instrumental Transfer (S-PIT) paradigm, have yielded considerable progress in our understanding of the underlying mechanism. However, most of them focused on the influence from the excitatory association, where the cue is signalling the presence of outcome. While some pioneering studies have demonstrated the possibility of a cue predicting the absence of outcome affecting the animal's choice behaviour, the neural mechanism that specific to this effect is still largely unexplored. Therefore, the aim of the current thesis was to investigate the role of the Lateral Habenula (LHb) in this type of inhibitory-driven action selection process, as there is reasonable evidences suggesting that this region involved heavily in processing cue that signal the absence of outcome. Our result has shown that the LHb lesion i) weakened the effect of conditioned inhibition, ii) abolished the reversed S-PIT effect that caused by the negative predicting cue, but iii) not affected the normal S-PIT that elicited by the positive predicting cue nor the choice bias that based on the value of the outcomes. Overall speaking, it suggested that the LHb is essential for stimulus-based, and not value-based, choice in situations where the stimuli have been trained as negative, but not positive, predictors of their associated outcomes

Where pigeonhole principles meet Koenig lemmas

We study the pigeonhole principle for Σ2-definable injections with domain twice as large as the codomain, and the weak König lemma for Δ02-definable trees in which every level has at least half of the possible nodes. We show that the latter implies the existence of 2-random reals, and is conservative over the former. We also show that the former is strictly weaker than the usual pigeonhole principle for Σ2-definable injections

Where Pigeonhole Principles meet K\"onig Lemmas

We study the pigeonhole principle for $\Sigma_2$-definable injections with domain twice as large as the codomain, and the weak K\"onig lemma for $\Delta^0_2$-definable trees in which every level has at least half of the possible nodes. We show that the latter implies the existence of $2$-random reals, and is conservative over the former. We also show that the former is strictly weaker than the usual pigeonhole principle for $\Sigma_2$-definable injections.Comment: 33 page

Distribution, Risk Factors, and Temporal Trends for Lung Cancer Incidence and Mortality: A Global Analysis

BACKGROUND: Lung cancer ranks second for cancer incidence and first for cancer mortality. Investigation into its risk factors and epidemiologic trends could help describe geographical distribution and identify high-risk population groups. RESEARCH QUESTION: What is the global incidence, mortality, associated risk factors, and temporal trends of lung cancer by sex, age, and country? STUDY DESIGN AND METHODS: Data on incidence and mortality were retrieved from the Global Cancer Observatory (GLOBOCAN), Cancer Incidence in Five Continents series I-X, World Health Organization (WHO) mortality database, the Nordic Cancer Registries (NORDCAN), and the Surveillance, Epidemiology, and End Results Program (SEER). We searched the WHO Global Health Observatory data repository for age-adjusted prevalence of current smoking. The Average Annual Percentage Change (AAPC) of the trends were obtained by Joinpoint Regression. RESULTS: The age-standardized rate of incidence and mortality were 22.4 and 18.0 per 100,000 globally. The lung cancer incidence and mortality were associated with Human Development Index (HDI), Gross Domestic Products (GDP), and prevalence of smoking. For incidence, more countries had increasing trends in females but decreasing trends in males (AAPC, 1.06 to 6.43 for female; -3.53 to -0.64 for male). A similar pattern was found in those 50 years or older, whereas those aged younger than 50 years had declining incidence trends in both sexes in most countries. For mortality, similar to incidence, 17 of 48 countries showed decreasing trends in males and increasing trends in females (AAPC, -3.28 to -1.32 for male, 0.63 to 3.96 for female). INTERPRETATION: Most countries had increasing trends in females but decreasing trends in males and in lung cancer incidence and mortality. Tobacco related measures and early cancer detection should be implemented to control the increasing trends of lung cancer in females, and in regions identified as having these trends. Future studies may explore the reasons behind these epidemiological transitions

Towards a global partnership model in interprofessional education for cross-sector problem-solving

Objectives A partnership model in interprofessional education (IPE) is important in promoting a sense of global citizenship while preparing students for cross-sector problem-solving. However, the literature remains scant in providing useful guidance for the development of an IPE programme co-implemented by external partners. In this pioneering study, we describe the processes of forging global partnerships in co-implementing IPE and evaluate the programme in light of the preliminary data available. Methods This study is generally quantitative. We collected data from a total of 747 health and social care students from four higher education institutions. We utilized a descriptive narrative format and a quantitative design to present our experiences of running IPE with external partners and performed independent t-tests and analysis of variance to examine pretest and posttest mean differences in students’ data. Results We identified factors in establishing a cross-institutional IPE programme. These factors include complementarity of expertise, mutual benefits, internet connectivity, interactivity of design, and time difference. We found significant pretest–posttest differences in students’ readiness for interprofessional learning (teamwork and collaboration, positive professional identity, roles, and responsibilities). We also found a significant decrease in students’ social interaction anxiety after the IPE simulation. Conclusions The narrative of our experiences described in this manuscript could be considered by higher education institutions seeking to forge meaningful external partnerships in their effort to establish interprofessional global health education

A reference-grade wild soybean genome

Wild relatives of crop plants are invaluable germplasm for genetic improvement. Here, Xie et al. report a reference-grade wild soybean genome and show that it can be used to identify structural variation and refine quantitative trait loci

A reference-grade wild soybean genome

Efficient crop improvement depends on the application of accurate genetic information contained in diverse germplasm resources. Here we report a reference-grade genome of wild soybean accession W05, with a final assembled genome size of 1013.2 Mb and a contig N50 of 3.3 Mb. The analytical power of the W05 genome is demonstrated by several examples. First, we identify an inversion at the locus determining seed coat color during domestication. Second, a translocation event between chromosomes 11 and 13 of some genotypes is shown to interfere with the assignment of QTLs. Third, we find a region containing copy number variations of the Kunitz trypsin inhibitor (KTI) genes. Such findings illustrate the power of this assembly in the analysis of large structural variations in soybean germplasm collections. The wild soybean genome assembly has wide applications in comparative genomic and evolutionary studies, as well as in crop breeding and improvement programs