Could Ukraine hold a presidential election right now? Will Europe use frozen Russian assets to fund war? How can Ukraine rebuild China ties? 'Ukraine is running out of men, money and time' Putin says Russia believes it will win in Ukraine in New Year's Eve address Russian President Vladimir Putin has said his country believes it will win the war in Ukraine, nearly four years after he launched an invasion of the neighbouring nation, in comments made during his televised annual New Year's Eve address. The Russian leader called on the country on Wednesday to "support our heroes" fighting in Ukraine, where troops have been waging a brutal offensive since February 2022.

Aston Villa boss Unai Emery had an unhappy 18-month spell in charge of Arsenal that ended in 2019, but can he get the better of his old club on Tuesday? After the abuse he took from Arsenal fans, I'd love nothing more than Emery to go back to the Emirates and win, said BBC Sport football expert Chris Sutton. He absolutely didn't deserve that. Some of those fans should take a long, hard look at themselves for the way they mocked him. I hope Villa go there and spank them, just because of that. Sutton is making predictions for all 380 Premier League games this season, against AI, BBC Sport readers and a variety of guests. For week 19 - which includes the final games of 2025 on Tuesday, 30 December and the first matches of 2026 on New Year's Day - he takes on singer-songwriter Tom A Smith, who is a Sunderland fan.

Ramzan Kadyrov vows retaliation against Ukraine following drone attack on Grozny building, while Ukrainian officials say Zelenskyy remains unafraid of threats.

What is in the 28-point US plan for Ukraine? 'Ukraine is running out of men, money and time' Can the US get all sides to end the war? Why is Europe opposing Trump's peace plan? Here's where things stand on Saturday, December 6: A Russian drone attack killed two men, aged 52 and 67, in the Ukrainian city of Izyum as they were unloading firewood from a truck, according to local officials. Russian forces also killed a 12-year-old boy in an attack on the Vasylkivska community in Ukraine's Dnipropetrovsk region, and wounded more than a dozen Ukrainians in attacks on the Kherson, Donetsk and Sumy regions, local officials said.

This paper studies the removal of salt-and-pepper noise from images using median filter (MF) and simple three-layer autoencoder (AE) within recursive threshold algorithm. The performance of denoising is assessed with two metrics: the standard Structural Similarity Index SSIMImg of restored and clean images and a newly applied metric SSIMMap - the SSIM of entropy maps of these images computed via 2D Sample Entropy in sliding windows. We shown that SSIMMap is more sensitive to blur and local intensity transitions and complements SSIMImg. Experiments on low- and high-resolution grayscales images demonstrate that recursive threshold MF robustly restores images even under strong noise (50-60 %), whereas simple AE is only capable of restoring images with low levels of noise (<30 %). We propose two scalable schemes: (i) 2MF, which uses two MFs with different window sizes and a final thresholding step, effective for highlighting sharp local details at low resolution; and (ii) MFs-AE, which aggregates features from multiple MFs via an AE and is beneficial for restoring the overall scene structure at higher resolution. Owing to its simplicity and computational efficiency, MF remains preferable for deployment on resource-constrained platforms (edge/IoT), whereas AE underperforms without prior denoising. The results also validate the practical value of SSIMMap for objective blur assessment and denoising parameter tuning.

We also provide examples where biased estimators outperform their unbiased counterparts or where unbiased versions are simply not available. Finally, we demonstrate the effectiveness of our framework through experimental results that validate our theoretical findings.