This paper develops a structural, operator‑geometric framework for classifying dynamical systems under coarse‑grained evolution. The central proposal is that many physically and conceptually distinct systems—ranging from stochastic processes and dissipative flows to causal mechanisms and transport semigroups—exhibit recurrent large‑scale geometric behaviors that can be captured through a finite f…

basic constructions: strong axioms further Predicative mathematics is a way of doing mathematics without allowing impredicative definitions. Informally, a definition is impredicative if it refers to a totality which includes the thing being defined. For example, the definition of a particular real number as the least upper bound of a given set is impredicative, because it characterizes as a parti…

A California fire district’s experience highlights a growing challenge for public safety drone programs: turning flight data into operational intelligence. As public safety agencies expand their use of drones, the challenge is no longer simply getting aircraft into the air. Increasingly, agencies must manage growing fleets, larger volumes of data, and more complex operations while […] The post As…

Nature Communications, Published online: 29 May 2026; doi:10.1038/s41467-026-73881-9 Antisense oligonucleotides targeting the glycine transporter SLC6A20 restore NMDA -receptor function and rescue behavioral and synaptic phospho-proteomic deficits in Shank2- and Shank3-mutant mice and in human SHANK2/SHANK3 cortical organoids.

Nature, Published online: 29 May 2026; doi:10.1038/d41586-026-01708-0 Organs from genetically modified pigs are being used in trials in China and the US.

Nature, Published online: 29 May 2026; doi:10.1038/d41586-026-01669-4 Traces on tweezers and surgical scissors suggest liquid medication was applied to the skin of patients.

Nature, Published online: 29 May 2026; doi:10.1038/d41586-026-01630-5 The deadly disease was identified half a century ago in the Democratic Republic of the Congo. It is unacceptable that it continues to take lives.

Nature, Published online: 29 May 2026; doi:10.1038/d41586-026-01736-w Nature staff discuss memory in the legal system plus the benefits of Registered Reports.

Scientific Reports, Published online: 29 May 2026; doi:10.1038/s41598-026-54163-2 Variability of cassava ( Manihot esculenta [Cranz]) genotypes for nutritional composition in Southwestern Ethiopia

The perception of teachers and nurses as boundlessly, selflessly resilient is a classic example of survivorship bias, says Dr Jenny Andrew Gaby Hinsliff’s article about the Green MP Carla Denyer refers to “angry men on radio phone-ins asking why politicians can’t handle ‘a few emails’ without needing a lie-down when nurses and teachers just have to soldier on regardless” ( The curse of burnout Br…

Readers respond to Jonathan Freedland’s article on Arsenal and one of its most famous fans Congratulations to Arsenal on winning the Premier League. However, I fear that Jonathan Freedland’s allegiances have led him to a flawed attempted analogy ( Arsenal’s title win should be studied by politicians everywhere – and especially Keir Starmer. Here’s why, 22 May ). Keir Starmer has already achieved …

International student belonging is a critical aspect of higher education research. This article advances the conceptualisations of international student belonging that further our understanding of researching student experience. Through in-depth explorations of stories obtained through narrative interviewing with Chinese postgraduate international students at a UK university, this study presents …

Mathematical reasoning has long been emphasised as a central component of mathematics education and research. Nevertheless, few studies have synthesised how this concept has been treated both theoretically and methodologically in previous research. Reviewing the status of this treatment is crucial for understanding how the concept can be operationalised in classroom contexts. This review synthesi…

Given a positive odd number \$n\$, return two primes \$p\$ and \$q\$ such that \$p\$ bitwise-and \$q\$ equals \$n\$. \$n\$ \$p\$ \$q\$ \$p\$ & \$q\$ 1 3 5 1 3 3 3 3 9 11 13 9 Shortest code in each ...

Let $A$ be a countably infinite graph, and $B$ a countably infinite graph which contains $A$ as an induced subgraph; let $\alpha$ be an automorphism of $A$; is there an embedding of $B$ in the Rado ...

I have a Windows 11 PC with 32 GB of RAM, and I usually have about 10 GB to 15 GB of free, unused memory during my daily workflow. However, when monitoring performance in Resource Monitor, I noticed ...

I have a mathematical physics question. I'm taking a physics class (at the Master's level) called "topology and new kinds of order in condensed matter systems" but I'm very confused about ...

How 100 AI agents evolved a shared symbolic vocabulary through trade — with no pre-programmed definitions, no mock data, and no shortcuts. The Core Idea Most emergent communication demos cheat. They hardcode symbol meanings, or use mock LLM responses, or simulate the entire thing with random number generators. The result is a demo that looks impressive but teaches you nothing about how actual lan…

A few weeks ago I watched my AI coding agent successfully fix a bug. The tests passed. The patch looked clean. The agent reported success. I shipped it. Three hours later I noticed the agent had also "improved" four unrelated files in the same session. One of those improvements quietly removed a guard clause that I had spent a full evening writing two months earlier. There was no test covering th…