An Analysis of Tennenbaum's Theorem in Constructive Type Theory

Tennenbaum's theorem states that the only countable model of Peano arithmetic (PA) with computable arithmetical operations is the standard model of natural numbers. In this paper, we use constructive type theory as a framework to revisit, analyze and generalize this result. The chosen framework allows for a synthetic approach to computability theory, exploiting that, externally, all functions definable in constructive type theory can be shown computable. We then build on this viewpoint and furthermore internalize it by assuming a version of Church's thesis, which expresses that any function on natural numbers is representable by a formula in PA. This assumption provides for a conveniently abstract setup to carry out rigorous computability arguments, even in the theorem's mechanization. Concretely, we constructivize several classical proofs and present one inherently constructive rendering of Tennenbaum's theorem, all following arguments from the literature. Concerning the classical proofs in particular, the constructive setting allows us to highlight differences in their assumptions and conclusions which are not visible classically. All versions are accompanied by a unified mechanization in the Coq proof assistant.Comment: 23 pages, extension of conference paper published at FSCD 202

Synthetic Undecidability and Incompleteness of First-Order Axiom Systems in Coq

We mechanise the undecidability of various frst-order axiom systems in Coq, employing the synthetic approach to computability underlying the growing Coq Library of Undecidability Proofs. Concretely, we cover both semantic and deductive entailment in fragments of Peano arithmetic (PA) as well as ZF and related fnitary set theories, with their undecidability established by many-one reductions from solvability of Diophantine equations, i.e. Hilbert’s tenth problem (H10), and the Post correspondence problem (PCP), respectively. In the synthetic setting based on the computability of all functions defnable in a constructive foundation, such as Coq’s type theory, it sufces to defne these reductions as metalevel functions with no need for further encoding in a formalised model of computation. The concrete cases of PA and the considered set theories are supplemented by a general synthetic theory of undecidable axiomatisations, focusing on well-known connections to consistency and incompleteness. Specifcally, our reductions rely on the existence of standard models, necessitating additional assumptions in the case of full ZF, and all axiomatic extensions still justifed by such standard models are shown incomplete. As a by-product of the undecidability of set theories formulated using only membership and no equality symbol, we obtain the undecidability of frst-order logic with a single binary relation

Generalized parton correlation functions for a spin-1/2 hadron

The fully unintegrated, off-diagonal quark-quark correlator for a spin-1/2 hadron is parameterized in terms of so-called generalized parton correlation functions. Such objects, in particular, can be considered as mother distributions of generalized parton distributions on the one hand and transverse momentum dependent parton distributions on the other. Therefore, our study provides new, model-independent insights into the recently proposed nontrivial relations between generalized and transverse momentum dependent parton distributions. We find that none of these relations can be promoted to a model-independent status. As a by-product we obtain the first complete classification of generalized parton distributions beyond leading twist. The present paper is a natural extension of our previous corresponding analysis for spin-0 hadrons.Comment: 41 pages, 3 figures; v2: added referenc

The Multi-Period Settlement Dali in Southeastern Kazakhstan: Bronze Age Institutional Dynamics along the Inner Asian Mountain Corridor`

Archaeological excavations at the Dali site complex located in southeastern Kazakhstan provide a rich picture of Bronze Age life spanning from the early third to late second millennia B.C. Nearly ten years of research at the site have produced an abundant assemblage of architectural remains, ritual and burial contexts, human and animal ancient DNA, and evidence for related economic practices and other material forms (ceramics, metallurgy). A systematic radiocarbon dating program provides detailed chronological context for the numerous stratigraphically documented phases of occupation, burial, and economy at the site. The settlement contexts at Dali provide some of the most varied and well-dated material assemblages known in the region and help illustrate how local pastoralist societies developed traditions of architecture, ceramic production, herd management, and ritual in the Early Bronze Age, while innovating and incorporating novel craft techniques, economic strategies, burial styles, and settlement construction in the Middle and Late Bronze Age. Taken together, the archaeological data from Dali allow for a detailed reconstruction of the local practices and regional interactions that engaged agro-pastoralist communities within diverse, shared institutional domains across the Inner Asian Mountain Corridor and beyond over a span of more than 2000 years

COVID-19 Follow-App. Mobile App-Based Monitoring of COVID-19 Patients after Hospital Discharge: A Single-Center, Open-Label, Randomized Clinical Trial

COVID-19; App; PneumoniaCOVID-19; App; PneumòniaCOVID-19; App; NeumoníaIntroduction: In the midst of a pandemic, apps can be used to provide close follow-up, ensure that patients are monitored at home, avoid excessive pressure on medical facilities, prevent the movement of people (both patients and health professionals), and reduce the risk of infection. Objective: To adapt and validate the use of a smartphone application for outpatient follow-up of COVID-19 patients after hospital discharge. Methods: We conducted an open-label clinical trial at Hospital Universitari Vall d’Hebron in Barcelona, Spain. Patients were randomly assigned in a 1:1 ratio to be followed by the Farmalarm app or by their primary care center. The primary endpoint was the reduction in the need for in-person return visits. Results: From 31 March to 4 May 2020, 150 patients were enrolled in the study at hospital discharge: 74 patients were randomized to the experimental group, and 76 to the control group. All patients in the control group and all except for six in the experimental group completed the study. During hospitalization, before study inclusion, all but 4 (97.3%) had viral pneumonia, 91 (60.7%) required supplemental oxygen, and 16 (10.7%) required intensive care unit (ICU) admission. COVID-19–related return visits to the emergency department were significantly higher in the control group (7.9% vs. 0%; p = 0.028) in the per-protocol analysis. Telephone consultations with the emergency department were performed by 12 (15.8%) patients in the control group and 0 (0%) in the experimental group (p < 0.001). Satisfaction with outpatient monitoring was rated higher by the experimental group (5 vs. 4 points; p < 0.001). Conclusions: Following COVID-19 hospital discharge, home follow-up via a mobile app was effective in reducing in-person return visits without undermining patient satisfaction or perception of health, compared with standard follow-up

The multi‐scale architecture of mammalian sperm flagella and implications for ciliary motility

Motile cilia are molecular machines used by a myriad of eukaryotic cells to swim through fluid environments. However, available molecular structures represent only a handful of cell types, limiting our understanding of how cilia are modified to support motility in diverse media. Here, we use cryo-focused ion beam milling-enabled cryo-electron tomography to image sperm flagella from three mammalian species. We resolve in-cell structures of centrioles, axonemal doublets, central pair apparatus, and endpiece singlets, revealing novel protofilament-bridging microtubule inner proteins throughout the flagellum. We present native structures of the flagellar base, which is crucial for shaping the flagellar beat. We show that outer dense fibers are directly coupled to microtubule doublets in the principal piece but not in the midpiece. Thus, mammalian sperm flagella are ornamented across scales, from protofilament-bracing structures reinforcing microtubules at the nano-scale to accessory structures that impose micron-scale asymmetries on the entire assembly. Our structures provide vital foundations for linking molecular structure to ciliary motility and evolution

SEAmester – South Africa’s first class afloat

publisher versionFrom Introduction: Marine science is a highly competitive environment. The need to improve the cohort of South African postgraduates, who would be recognised both nationally and internationally for their scientific excellence, is crucial. It is possible to attract students early on in their careers to this discipline via cutting-edge science, technology and unique field experiences. Through the engagement of students with real-life experiences such as SEAmester, universities supporting marine science postgraduate degree programmes can attract a sustainable throughput of numerically proficient students. By achieving a more quantitative and experienced input into our postgraduate degree programmes, we will, as a scientific community, greatly improve our long-term capabilities to accurately measure, model and predict the impacts of current climate change scenarios. The short-term goal is to attract and establish a cohort of proficient marine and atmospheric science graduates who will contribute to filling the capacity needs of South African marine science as a whole. The SEAmester programme, by involving researchers from across all the relevant disciplines and tertiary institutions, provides an opportunity to build a network of collaborative teaching within the marine field. In doing so, these researchers will foster and strengthen new and current collaborations between historically white and black universities (Figure 1). The long-term objective of SEAmester is to build critical mass within the marine sciences to ensure sustained growth of human capacity in marine science in South Africa – aligning closely with the current DST Research and Development strategies and the Operation Phakisa Oceans Economy initiative

Pan-Cancer Analysis of lncRNA Regulation Supports Their Targeting of Cancer Genes in Each Tumor Context

Long noncoding RNAs (lncRNAs) are commonly dys-regulated in tumors, but only a handful are known toplay pathophysiological roles in cancer. We inferredlncRNAs that dysregulate cancer pathways, onco-genes, and tumor suppressors (cancer genes) bymodeling their effects on the activity of transcriptionfactors, RNA-binding proteins, and microRNAs in5,185 TCGA tumors and 1,019 ENCODE assays.Our predictions included hundreds of candidateonco- and tumor-suppressor lncRNAs (cancerlncRNAs) whose somatic alterations account for thedysregulation of dozens of cancer genes and path-ways in each of 14 tumor contexts. To demonstrateproof of concept, we showed that perturbations tar-geting OIP5-AS1 (an inferred tumor suppressor) andTUG1 and WT1-AS (inferred onco-lncRNAs) dysre-gulated cancer genes and altered proliferation ofbreast and gynecologic cancer cells. Our analysis in-dicates that, although most lncRNAs are dysregu-lated in a tumor-specific manner, some, includingOIP5-AS1, TUG1, NEAT1, MEG3, and TSIX, synergis-tically dysregulate cancer pathways in multiple tumorcontexts