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On the Navier–Stokes Millennium Prize Problem

We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. We’re sharing both a writeup of the proof and a formalization in Lean.

The Millennium Prize Problems ⁠ (opens in a new window) represent some of the deepest questions at the frontier of mathematics. The question of whether smooth three-dimensional fluid motion can break down has remained unresolved for roughly 90 years.

World’s most endangered tigers born in Greece as zoos build a safety net

SPATA, Greece (AP) — The world’s most endangered tigers have started a family in Greece, offering hope for a predator rapidly vanishing from the wild.

Three 2-month-old Sumatran tiger cubs received identification microchips and their first vaccinations Tuesday at a zoo near Athens, as part of a global effort to build a backup population.

The Sumatran tiger, classified as critically endangered, is found only on the Indonesian island of Sumatra, which is slightly larger than Sweden.

Researchers traced Leonardo da Vinci’s family through 21 generations and found matching Ychromosome markers in six living men from a Renaissance family tomb could connect that genetic trail directly to his time

A genetic thread stretches across five centuries, connecting living descendants to the Renaissance master through his prolific father—and newly excavated remains could prove it.

Scientists observe Einstein’s gravity in the quantum world for the first time

Physicists have directly observed a long-predicted quantum effect of gravity, putting one of Einstein’s foundational ideas to a striking new test. Using ultracold atoms, researchers split an atom’s quantum wave so that one part was held in place while the other fell freely under gravity, then reunited the two to measure the tiny difference that emerged.

Around 2000, a Florida tropicalfish collector hung rescued coral fragments from underwater “trees”; the small nursery grew into a reefrestoration network

Both the deterioration of the Florida Keys reef and the response to it took time. Staghorn and elkhorn corals grew so numerous throughout the Florida Reef Tract for decades that divers reported swimming through underwater thickets.

Plasmalogens Eliminate AgingAssociated Synaptic Defects and MicrogliaMediated Neuroinflammation in Mice

Neurodegeneration is a pathological condition in which nervous system or neuron losses its structure, function, or both leading to progressive neural degeneration. Growing evidence strongly suggests that reduction of plasmalogens (Pls), one of the key brain lipids, might be associated with multiple neurodegenerative diseases, including Alzheimer’s disease (AD). Plasmalogens are abundant members of ether-phospholipids. Approximately 1 in 5 phospholipids are plasmalogens in human tissue where they are particularly enriched in brain, heart and immune cells. In this study, we employed a scheme of 2-months Pls intragastric administration to aged female C57BL/6J mice, starting at the age of 16 months old. Noticeably, the aged Pls-fed mice exhibited a better cognitive performance, thicker and glossier body hair in appearance than that of aged control mice. The transmission electron microscopic (TEM) data showed that 2-months Pls supplementations surprisingly alleviate age-associated hippocampal synaptic loss and also promote synaptogenesis and synaptic vesicles formation in aged murine brain. Further RNA-sequencing, immunoblotting and immunofluorescence analyses confirmed that plasmalogens remarkably enhanced both the synaptic plasticity and neurogenesis in aged murine hippocampus. In addition, we have demonstrated that Pls treatment inhibited the age-related microglia activation and attenuated the neuroinflammation in the murine brain. These findings suggest for the first time that Pls administration might be a potential intervention strategy for halting neurodegeneration and promoting neuroregeneration.

Plasmalogens (Pls) are a special type of vinyl ether-bonded phospholipids actively participating in structure and function of biological membranes. Approximately 20% of phospholipids are plasmalogens in human tissue, where they are particularly rich in the brain, heart, and immune cells (Lessig and Fuchs 2009; Braverman and Moser 2012). In brain, ethanolamine plasmalogens (PlsEtns) constitute approximately 60 and 80% of the total ethanolamine phospholipids in gray and white matter, respectively (Macala et al., 1983). Pls are also concentrated in specialized membranes, such as sarcolemma, myelin, and synaptic vesicles (Post et al., 1988; Takamori et al., 2006; Poitelon et al., 2020). Reduced levels of PlsEtns have been found to be associated with aging (Pradas et al., 2019) and several neurodegenerative diseases, including Alzheimer’s disease (AD) (Guan et al., 1999; Han et al., 2001; Goodenowe et al., 2007; Wood 2010; Wood et al., 2015; Yamashita et al.

Folding Giant AI Brains Into Your Pocket

A team of researchers proved a simple mathematical law — the “linearity theorem” — that lets engineers predict, in advance and with precision, exactly how compressing an AI model will affect its intelligence. No more guess-and-check. No more crossing your fingers and hoping a 70-billion-parameter model doesn’t collapse into gibberish after compression.

A global research team just proved a simple mathematical law that lets engineers shrink massive AI models onto ordinary laptops and phones — without guessing, and without dumbing them down.

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