Knowledge graphs have become a common approach for knowledge representation. Yet, the application of graph methodology is elusive due to the sheer number and complexity of knowledge sources. In addition, semantic incompatibilities hinder efforts to harmonize and integrate across these diverse sources. As part of The Biomedical Translator Consortium, we have developed a knowledge graph–based question-answering system designed to augment human reasoning and accelerate translational scientific discovery: the Translator system. We have applied the Translator system to answer biomedical questions in the context of a broad array of diseases and syndromes, including Fanconi anemia, primary ciliary dyskinesia, multiple sclerosis, and others. A variety of collaborative approaches have been used to research and develop the Translator system. One recent approach involved the establishment of a monthly “Question-of-the-Month (QotM) Challenge” series. Herein, we describe the structure of the QotM Challenge; the six challenges that have been conducted to date on drug-induced liver injury, cannabidiol toxicity, coronavirus infection, diabetes, psoriatic arthritis, and ATP1A3-related phenotypes; the scientific insights that have been gleaned during the challenges; and the technical issues that were identified over the course of the challenges and that can now be addressed to foster further development of the prototype Translator system. We close with a discussion on Large Language Models such as ChatGPT and highlight differences between those models and the Translator system.

The stable core, an inner model of the form $\langle L[S],\in , S\rangle $ for a simply definable predicate S, was introduced by the first author in [8], where he showed that V is a class forcing extension of its stable core. We study the structural properties of the stable core and its interactions with large cardinals. We show that the $\operatorname {GCH} $ can fail at all regular cardinals in the stable core, that the stable core can have a discrete proper class of measurable cardinals, but that measurable cardinals need not be downward absolute to the stable core. Moreover, we show that, if large cardinals exist in V, then the stable core has inner models with a proper class of measurable limits of measurables, with a proper class of measurable limits of measurable limits of measurables, and so forth. We show this by providing a characterization of natural inner models $L[C_1, \dots , C_n]$ for specially nested class clubs $C_1, \dots , C_n$, like those arising in the stable core, generalizing recent results of Welch [29].

Precision medicine has the potential to transform healthcare by moving from one-size-fits-all to personalised treatment and care. This transition has been greatly facilitated through new high-throughput sequencing technologies that can provide the unique molecular profile of each individual patient, along with the rapid development of targeted therapies directed to the Achilles heels of each disease. To implement precision medicine approaches in healthcare, many countries have adopted national strategies and initiated genomic/precision medicine initiatives to provide equal access to all citizens. In other countries, such as Sweden, this has proven more difficult due to regionally organised healthcare. Using a bottom-up approach, key stakeholders from academia, healthcare, industry and patient organisations joined forces and formed Genomic Medicine Sweden (GMS), a national infrastructure for the implementation of precision medicine across the country. To achieve this, Genomic Medicine Centres have been established to provide regionally distributed genomic services, and a national informatics infrastructure has been built to allow secure data handling and sharing. GMS has a broad scope focusing on rare diseases, cancer, pharmacogenomics, infectious diseases and complex diseases, while also providing expertise in informatics, ethical and legal issues, health economy, industry collaboration and education. In this review, we summarise our experience in building a national infrastructure for precision medicine. We also provide key examples how precision medicine already has been successfully implemented within our focus areas. Finally, we bring up challenges and opportunities associated with precision medicine implementation, the importance of international collaboration, as well as the future perspective in the field of precision medicine.

We explore the possibilities for elementary embeddings $j : M \to N$ , where M and N are models of ZFC with the same ordinals, $M \subseteq N$ , and N has access to large pieces of j. We construct commuting systems of such maps between countable transitive models that are isomorphic to various canonical linear and partial orders, including the real line ${\mathbb R}$ .

We show that if M is a countable transitive model of $\text {ZF}$ and if $a,b$ are reals not in M, then there is a G generic over M such that $b \in L[a,G]$ . We then present several applications such as the following: if J is any countable transitive model of $\text {ZFC}$ and $M \not \subseteq J$ is another countable transitive model of $\text {ZFC}$ of the same ordinal height $\alpha $ , then there is a forcing extension N of J such that $M \cup N$ is not included in any transitive model of $\text {ZFC}$ of height $\alpha $ . Also, assuming $0^{\#}$ exists, letting S be the set of reals generic over L, although S is disjoint from the Turing cone above $0^{\#}$ , we have that for any non-constructible real a, $\{ a \oplus s : s \in S \}$ is cofinal in the Turing degrees.

A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often model-theoretic constructions that add sets to models are cited as evidence in favor of the latter. This paper informs this debate by developing a way for a Universist to interpret talk that seems to necessitate the addition of sets to V. We argue that, despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We present a method of interpreting extension-talk (V-logic), and show how it captures satisfaction in ‘ideal’ outer models and relates to impredicative class theories. We provide some reasons to regard the technique as philosophically virtuous, and argue that it opens new doors to philosophical and mathematical discussions for the Universist.