The new designs honor the Constitution, Civil War, and more. Breakthroughs, discoveries, and DIY tips sent every weekday. While we've said goodbye to both the year 2025 and the penny, five new United States quarters will be finding their way into your pocket soon enough. The designs of each new quarter will honor the country's 250th anniversary (aka its semiquincentennial). According to a press release from the U.S. Mint, the coins "commemorate 250 years of American Liberty by reflecting our country's founding principles and honoring our Nation's history."

We introduce \textit{basic inequalities} for first-order iterative optimization algorithms, forming a simple and versatile framework that connects implicit and explicit regularization. While related inequalities appear in the literature, we isolate and highlight a specific form and develop it as a well-rounded tool for statistical analysis. Let $f$ denote the objective function to be optimized. Given a first-order iterative algorithm initialized at $θ_0$ with current iterate $θ_T$, the basic inequality upper bounds $f(θ_T)-f(z)$ for any reference point $z$ in terms of the accumulated step sizes and the distances between $θ_0$, $θ_T$, and $z$. The bound translates the number of iterations into an effective regularization coefficient in the loss function. We demonstrate this framework through analyses of training dynamics and prediction risk bounds. In addition to revisiting and refining known results on gradient descent, we provide new results for mirror descent with Bregman divergence projection, for generalized linear models trained by gradient descent and exponentiated gradient descent, and for randomized predictors. We illustrate and supplement these theoretical findings with experiments on generalized linear models.

Russia releases video allegedly showing Ukrainian drone wreckage from a failed attack on President Vladimir Putin's residence, but Ukraine dismisses claims as fabrication.

The U.S. State Department reissued its Russia travel warning as the Ukraine conflict intensifies, telling U.S. citizens to leave immediately due to detention risks and limited embassy help.

'Super' virus spreading uncontrollably... as New York sees most flu cases ever and experts warn'we don't know when it will stop' Behind-the-scenes snaps from Kimberly Guilfoyle's magazine shoot look VERY different than the published photos Trump's HHS halts child care funding to ALL states after viral video sparks Somali daycare scandal in Minnesota She wore the ultimate revenge dress after their brutal break up. But Nashville's hottest couple is'trying again'... and her friends are terrified MARK HALPERIN blows apart the Minnesota scandal... and reveals who will pay the ultimate price Marla Maples' chilling Epstein warning as she feared his growing sway over Trump Megyn Kelly names'meanest' celebrities... and hints NBC's twinkly-eyed TV grandpa is not as nice as he seems Democrat mayor blasted for sneaking through reparations plan'in dark of night' that could see city's black residents handed $5m each Leonardo DiCaprio flaunts weight loss for much-younger girlfriend... but chooses very middle-aged accessory I tried the $12 'miracle' hangover cure... but I made a critical mistake that left me full of regret Snitch reveals all the gossip from inside the New England Patriots after Stefon Diggs allegedly'strangled' his female chef St Barts regulars complain paradise island is'tacky' and overrun with vulgar yachts blocking ocean views as A-Listers and billionaires flock there for annual New Year's Eve celebrations My husband set me a kinky New Year's resolution... DEAR JANE, I'm disgusted. But I'm afraid I can't say no'Work maintained my sense of self': How one woman's cancer journey inspired her company to give back New York City mayor-elect Zohran Mamdani is set to ring in his inauguration with a public block party open to residents on January 1. But alongside the celebration, the Democratic socialist has also released a lengthy list of items barred from the event, some expected, others raising eyebrows. While weapons, explosives, and illegal substances are banned, the list also prohibits strollers, Flipper Zero devices and Raspberry Pis, two pieces of consumer technology that are legal and widely used.

Woman wags her finger at journalist who asks her if she's running a daycare out of stunning Seattle home Marla Maples' chilling Epstein warning as she feared his growing sway over Trump She wore the ultimate revenge dress after their brutal break up. But Nashville's hottest couple is'trying again'... and her friends are terrified MARK HALPERIN blows apart the Minnesota scandal... and reveals who will pay the ultimate price Kellyanne Conway brands lesbian comic Rosie O'Donnell a'slob' and says Trump-hating star needs to get a HUSBAND Daily Mail graphic reveals the bottled waters with the most cancer-causing'forever chemicals' 'Super' virus spreading uncontrollably... as New York sees the most cases ever and experts warn'we don't know when it will stop' Brave little girl jumped out apartment window and begged strangers to save her from abuse... only to be tortured to death after disbelieving cops sent her home Megyn Kelly names'meanest' celebrities... and hints NBC's twinkly-eyed TV grandpa is not as nice as he seems Hollywood's nastiest star: How Chevy Chase's outrageous behavior turned him into a pariah on and off set Children in headscarves seen being brought into notorious Minneapolis daycare hit by fraud allegations as local claims misspelt sign was just a'printing error' I tried the $12 'miracle' hangover cure... but I made a critical mistake that left me full of regret Snitch reveals all the gossip from inside the New England Patriots after Stefon Diggs allegedly'strangled' his female chef Heartbreak after body found in search for teenager as brother's missing weapon link emerges and devastated mom is left repeating four tragic words My husband set me a kinky New Year's resolution... DEAR JANE, I'm disgusted. But I'm afraid I can't say no'Work maintained my sense of self': How one woman's cancer journey inspired her company to give back As 2025 comes to a close, several mysteries that left the world in stunned disbelief still have yet to be fully explained. The past 12 months have read like a science-fiction novel, with thousands of UFOs swarming over the US East Coast, an interstellar visitor invading our solar system, and the potential discovery of giant columns under the Egyptian pyramids. Moreover, scientists and government officials have been unable to disprove all of the wild theories surrounding many of these jaw-dropping events, including one respected scientist's claim that the giant space rock 3I/ATLAS may be an alien craft.

Ukraine peace negotiations falter as Russia claims Kyiv launched drone attacks on a presidential residence, with President Donald Trump investigating the disputed allegations.

The company's shares are worth $1.4tn on the back of hopes for self-driving cars and robotics. The company's shares are worth $1.4tn on the back of hopes for self-driving cars and robotics. Tesla endured tough year in part thanks to some consumers' distaste for Elon Musk's embrace of rightwing politics Tesla has taken the unusual step of publishing sales forecasts that suggest 2025 deliveries will be lower than expected and future years' sales will be well below targets set by its chief executive, Elon Musk . The US electric vehicle maker published figures from analysts suggesting it will announce 423,000 deliveries during the fourth quarter of 2025, in a new "consensus" section on its investor website. That would represent a 16% decline from the final quarter of 2024.

EU's top diplomat rejects Russian claims of Ukrainian attack on government sites The EU's top diplomat has called Moscow's claims that Ukraine targeted Russian government sites a deliberate distraction and an attempt to derail the peace process. Kaja Kallas' comments on social media appear to be a reference to the Kremlin's allegation that Ukraine attempted a drone strike on one of Vladimir Putin's residences. No one should accept unfounded claims from the aggressor who has indiscriminately targeted Ukraine's infrastructure and civilians, Kallas wrote on social media. Earlier this week Moscow accused Ukraine of targeting Putin's private home on Lake Valdai in north-west Russia. Russia would review its position in the ongoing peace negotiations as a result, the Kremlin said.

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.