Two full moons in one month occurs about once every 2.5 years. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. The Eta Aquariids meteor shower appears in the night sky in Kandalama, Sri Lanka, on May 5, 2024. Unlike most major annual meteor showers, there is no sharp peak for this shower, but rather a broad maximum with good rates that last approximately one week. Breakthroughs, discoveries, and DIY tips sent six days a week.

Science Space Deep Space Fastest comet ever recorded spewed 70 Olympic pools' worth of water daily More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. A new study of the interstellar comet 3I/ATLAS led by the University of Michigan shows that its water has a remarkably high content of deuterium. This form of hydrogen is comparatively less abundant in our solar system, enabling researchers to glean new insights about other planetary processes at work in our galaxy. Breakthroughs, discoveries, and DIY tips sent six days a week. Astronomers knew 3I/ATLAS wasn't a local comet not long after first spotting it in July 2025 .

Benchmarking the performance of complex systems such as rail networks, renewable generation assets and national economies is central to transport planning, regulation and macroeconomic analysis. Classical frontier methods, notably Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA), estimate an efficient frontier in the observed input-output space and define efficiency as distance to this frontier, but rely on restrictive assumptions on the production set and only indirectly address heterogeneity and scale effects. We propose Geometric Manifold Analysis (GeMA), a latent manifold frontier framework implemented via a productivity-manifold variational autoencoder (ProMan-VAE). Instead of specifying a frontier function in the observed space, GeMA represents the production set as the boundary of a low-dimensional manifold embedded in the joint input-output space. A split-head encoder learns latent variables that capture technological structure and operational inefficiency. Efficiency is evaluated with respect to the learned manifold, endogenous peer groups arise as clusters in latent technology space, a quotient construction supports scale-invariant benchmarking, and a local certification radius, derived from the decoder Jacobian and a Lipschitz bound, quantifies the geometric robustness of efficiency scores. We validate GeMA on synthetic data with non-convex frontiers, heterogeneous technologies and scale bias, and on four real-world case studies: global urban rail systems (COMET), British rail operators (ORR), national economies (Penn World Table) and a high-frequency wind-farm dataset. Across these domains GeMA behaves comparably to established methods when classical assumptions hold, and provides additional insight in settings with pronounced heterogeneity, non-convexity or size-related bias.

An artist's impression of 3I/ATLAS is shown as it passes near the Sun, illuminating one side of the comet. On the side of the comet closer to the sun, the methanol gas is shown in blue, with icy dust grains still present in the gas. On the dark side of the comet, the hydrogen cyanide is shown in orange. Breakthroughs, discoveries, and DIY tips sent six days a week. The comet 3I/ATLAS is well on its way back into deep space, but the famous cosmic visitor continues to fascinate astronomers.

However, existing contrastive learning methods primarily focus on one single data level, which fails to fully exploit the intricate nature of medical time series.

The interstellar space rock shows off the illuminating effects of its brush with the sun. Breakthroughs, discoveries, and DIY tips sent six days a week. After months of unprecedented observations, astronomers are bidding goodbye to the beloved comet 3I/ATLAS . First spotted in July 2025, the frigid, dusty space rock is only the third known interstellar object to pass through the solar system, offering researchers the rare opportunity to examine a visitor from deep space. Among other discoveries, scientists have since confirmed that the interstellar comet is the fastest ever recorded as well as covered in ice volcanoes --and definitely not extraterrestrial tourists .

However,inpractice, we did not find both effects inthe training. The last term in the loss function of COMET does not need the information from the dataset. This section contains the experiment details for cases tested in section 4. In section 4, there are 6 simple experiments performed todemonstrate the capability ofCOMET:(1) mass-spring, (2) 2D Case5: 2Dnonlinear spring.Weconsider acaseofamotion ofanobjectofmassm=1in2D where it is connected to the origin with a nonlinear spring with forceF = |r|2r where r is the position of the object in 2D coordinate. The constants of motion of this systems are the energy and the angular momentum,whichmakesnc=2. Case 6: Lotka-Volterraequation isanordinary differential equation modelling thepopulation of predatorandprey. The training loss in this case was composed of the reconstruction loss and the dynamics loss.

Inthis paper,we present a neural network that cansimultaneously learn the dynamics of the system and the constants of motion from data.