Mon 1 Jun 2026
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Erd\H{o}s Rado Sunflower Theorem for Shifted Families
Combinatorics [Submitted on 1 Jun 2026 (v1), last revised 8 Jun 2026 (this version, v2)] Title:Erdős Rado Sunflower Theorem for Shifted Families View PDF HTML (experimental)Abstract:Let $f(k,s)$ denote the minimum integer $m$ such that any family $\mathcal{F}$ consisting of $k$-sized sets of cardinality at least $m$ always contain a sunflower of size $s$. The Erdős-Rado Sunflower Conjecture states that for every $s >2$, there is an constant $C=C(s)$ such that $f(k,s) \leq C^k$.
Thousands of green sea turtle hatchlings swim to sea in a conservation win
Thousands of baby green sea turtles head to sea after successful egg relocation Mon 1 Jun 2026 at 1:25pm In short: An 82 per cent of the northern Great Barrier Reef green sea turtle eggs relocated between two islands have hatched. The species has faced increasing threats nesting on Raine Island, its main rookery. Researchers say future testing will be needed to determine if the successful hatchlings are also the same fitness More than 9,100 northern Great Barrier Reef green sea turtle...
Eerie footage and DNA: What we know four months since Nancy Guthrie vanished
Nancy Guthrie's disappearance remains mystery four months after she vanished Mon 1 Jun 2026 at 1:36pm For more than a decade, Savannah Guthrie has beamed into living rooms of Americans as the co-anchor of NBC's TODAY show, one of the highest-rating morning television programs in the country. So when her mother Nancy Guthrie went missing in January, her fame sparked a national obsession with the case and grabbed headlines around the world. Despite the publicity and hundreds of sheriff's...
Police scour mine shafts, drain dam in search for missing outback woman
Police to search 1,000 mine shafts, drain dam in renewed search for Trisha Graf Mon 1 Jun 2026 at 3:17pm In short: Police have returned to Andamooka and will scour about 1,000 mine shafts and drain a dam in the search for missing woman Trisha Graf. Ms Graf vanished in December 2025 and her disappearance was declared a major crime in January. Police will provide an update on the searches as they progress.
A Nesting-Free Normal Form for Nested Conditions in Finite Lattices of Subgraphs
[Submitted on 26 Jan 2026 (v1), last revised 1 Jun 2026 (this version, v3)] Title:A Nesting-Free Normal Form for Nested Conditions in Finite Lattices of Subgraphs View PDF HTML (experimental)Abstract:We present a nesting-free normal form for the formalism of nested conditions and constraints in the context of finite lattices of subgraphs. Submission history From: Jens Kosiol [view email][v1]
Live: Joyce warns against 'hubris' as One Nation pulls ahead of Labor in poll
live Federal politics live: Joyce warns against 'hubris' as One Nation pulls ahead of Labor in poll One Nation recruit Barnaby Joyce says politics in Australia has changed as he welcomes the results of an opinion poll that suggests his party now has more support than Labor. Follow all the updates in our live blog.
If LLMs Have Human-Like Attributes, Then So Does Age of Empires II
Computer Science > Computation and Language [Submitted on 29 May 2026 (v1), last revised 1 Jun 2026 (this version, v2)] Title:If LLMs Have Human-Like Attributes, Then So Does Age of Empires II View PDFAbstract:Much research has been carried out on large language models (LLMs) and LLM-powered agentic workflows. However, many works within the field state emergence of, ascribe to, or assume, generalised anthropomorphic attributes to them (e.g., morality or understanding of natural language).
Australian housing market stalls in May
National home values flatline in May for the first time since January 2025 Mon 1 Jun 2026 at 4:57am In short: Australia's housing market stalled in May, with national home values flat after months of slowing growth. The weakness was led by Sydney and Melbourne, where values fell 0.9 per cent and 0.8 per cent respectively, according to Cotality data. While the Reserve Bank is widely expected to hold interest rates steady at its June 15-16 meeting, buyers remain highly sensitive to any signs...
Greens stalwart Bob Brown joins fight against small South West sand mine
Greens stalwart Bob Brown joins fight against small South West sand mine Mon 1 Jun 2026 at 10:33am In short: Founding Greens party leader Bob Brown has joined the fight against a proposed sand mine in Yallingup in WA's South West.
Influencer's chat with Sydney nurses recorded for 'protection', court told
Influencer recorded chat with Bankstown nurses for 'protection', court told Mon 1 Jun 2026 at 6:19pm In short: Israeli content creator, Max Veifer, told a Sydney court he recorded his chat with two Sydney nurses for protection and published it because he was "worried about their statements". Mr Veifer also told the court he posted the video because he wanted to "warn our people", denying he did it to get the nurses fired. The case has been adjourned to Thursday.