• Minute-by-minute coverage of Sunday’s clash at Anfield

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This is a good read.

Arne Slot, Liverpool manager, is next to speak to Sky Sports. He reiterates that the biggest recent improvement that his side have made is their work rate out of possession.

We have made a lot of steps forward mainly off the ball, mainly with players better able to play this schedule we are playing. The biggest improvement I see is players are more ready for the combination of the Premier League and Champions League at the intensity we need.

We have both shown we are good in ball possession and can create chances. Both teams want the ball as much as possible and both have shown from a high press they are a threat as well. A good and proper counter attack can be dangerous at both ends as well.

Valeria Chomsky says Epstein had deceived them and they were ‘careless’ not to thoroughly research his background

Noam Chomsky and his wife, Valeria, made a “grave mistake” and were “careless” not to thoroughly research the background of Jeffrey Epstein, Valeria Chomsky said in a lengthy statement on Saturday, adding also that Epstein had deceived them.

The relationship between Noam Chomsky, the 97-year-old linguist and philosopher, and Epstein has been under scrutiny after documents released by the justice department shed light on their friendship. As Epstein came under scrutiny for sex trafficking allegations in 2019, he asked Chomsky for advice on how to respond. “I’ve watched the horrible way you are being treated in the press and public. It’s painful to say, but I think the best way to proceed is to ignore it,” Chomsky wrote in a message signed “Noam” that Epstein shared in email with an associate.

While AI is having an impact on the workplace, experts suggest tariffs, overhiring during the pandemic and simply maximising profits may be bigger factors

Over the last year, US corporate leaders have often explained layoffs by saying the positions were no longer needed because artificial intelligence had made their companies more efficient, replacing humans with computers.

But some economists and technology analysts have expressed skepticism about such justifications and instead think that such workforce cuts are driven by factors like the impact of tariffs, overhiring during the Covid-19 pandemic and perhaps simple maximising of profits.

This 1-0 defeat of Manchester City at the Emirates Stadium was never going to be a statement of ­Arsenal’s title intentions – City’s lead at the top is just too big – but a result against the likely champions still had huge value, mentally and in terms of the race for Champions League football.

It would take the most almighty of collapses for City to lose their grip on a second league title, 10 years after their first. They are still eight points clear of ­Manchester United and 10 ahead of Arsenal, who have a game in hand over those around them.

Longtime aide has said he takes ‘full responsibility’ for advising PM to appoint Peter Mandelson as US ambassador

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Morgan McSweeney, Keir Starmer’s chief of staff, has quit his role as the prime minister’s closest aide amid anger over his role in the appointment of Peter Mandelson as US ambassador.

His position had grown increasingly untenable as pressure on Starmer mounted over the scandal, which followed the release of emails underlining the extent of Mandelson’s relationship with the convicted child sex offender Jeffrey Epstein.

Several men appear in photos on the nearly 10,000-acre Zorro ranch, which included a 26,700 sq ft mansion

For years, Jeffrey Epstein took respite at a sprawling ranch in the desert scrub outside Santa Fe, New Mexico. Epstein’s nearly 10,000-acre (4,000-hectare) property – known as Zorro ranch – was dotted with cholla cactus and Angus cattle, and came to include a 26,700 sq ft mansion, as well as a private runway and hangar.

For years, Epstein abused teenage girls and young women on this ranch with impunity, according to testimony from several women. In court proceedings, survivors detailed horror after horror they say unfolded on this isolated expanse of land.

The series in which readers answer other readers’ questions explores the sounds and music that play on repeat mentally – and how to escape their aural clutches

• This week’s question: can you acquire courage?

I know a song that’ll get on your nerves, get on your nerves, get on your nerves. I know a so … you get the gist! Why does a song sometimes get stuck in our heads? (And good luck stopping this one now!) Laura Ashton, Haslemere, Surrey

Send new questions to nq@theguardian.com.

Since a presidential post on Truth Social the Washington DC arts hub has lost its leadership, had its name changed and will now be closed for years

The Brentano String Quartet had finished their performance when a special guest dropped in backstage: the US supreme court justice Ruth Bader Ginsburg. “We thanked her for everything she had done for our country,” recalls violinist Mark Steinberg. “It was a nice moment.”

The year was 2016 and the place was the John F Kennedy Center for the Performing Arts in Washington. Fast forward a decade and old certainties have been shaken: Ginsburg is dead, Donald Trump is president and the Kennedy Center has become a case study in how a seemingly solid American institution can quickly unravel.

The Bucks star has become a shareholder in one of the world’s largest prediction markets. It only ushers the NBA further into the fetid swamp of sports betting

Couldn’t he have just started a podcast? “The Internet is full of opinions. I decided it was time to make some of my own,” Giannis Antetokounmpo, one of the four best basketball players in the world, posted in a statement announcing that he was joining the prediction market Kalshi as a shareholder. “We all on Kalshi now.”

We are not, but doesn’t the tone sum it up? The universe’s ineffable forces have clearly decided that the ubiquity of sports betting companies is insufficient. There must be new companies, with which you can bet on any outcome – Kalshi competitor Polymarket has hosted markets tied to geopolitical outcomes, including scenarios related to Israel and Gaza, for instance – that incentivize people to treat life’s most important avenues as trivially as a sports game. Kalshi and Polymarket are prediction platforms rather than traditional betting companies. Users effectively bet (or “trade”) against others on the platform about the outcome of events, from familiar wagers such as the result of a sporting event, to the obscure, such as the color of a politician’s suit at an election appearance. Kalshi has enjoyed plenty of freedom under the second Donald Trump administration, and Donald Trump Jr is a “strategic advisor” for them and Polymarket. A Kalshi outcome taking bets until recently was “Giannis Antetokounmpo’s next team?” as rumors swirled that the two-time NBA MVP was about to leave the Milwaukee Bucks. Antetokounmpo will be involved in marketing and publicity for Kalshi, and is forbidden from trading on markets related to the NBA. The move is also in step with the NBA’s rules – players are allowed to endorse betting companies as long as they don’t gamble on the league itself. But that hasn’t prevented scores of fans across Instagram and Reddit, and media members on Twitter, from expressing their displeasure at the move and insisting there is a conflict of interest.

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I’ll probably end up looking silly, but I quite fancy Palace here. Brighton lack a reliable scorer – though Katsoulas’ brilliant goal against Bournemouth tells us he knows where the goal is – and I think Palace have the speed of foot and of pass to cause them problems.

So where is the game? Brighton will expect – and probably allowed – to have more of the ball, with Mitoma and Rutter staying narrow and Kadioglu and De Cuyper keeping width outside them – especially useful when facing a three-at-the-back system. The space will be in behind the wing-backs and down the sides of the centre-backs, though I’d also expect Katsoulas to target the space in behind.

Arrests follow discovery on Friday of magistrate and her mother in a garage in south-east of country

French authorities have arrested five suspects after a magistrate and her mother were held captive last week for about 30 hours in a cryptocurrency ransom plot.

Four men and one woman were detained, three overnight and two on Sunday morning, the Lyon prosecutor Thierry Dran told Agence France-Presse.

Olivia Smith’s strike ends the WSL leader’s wining run

3 min: Caitlin Foord turns Kerstin Casparij inside out on the left. She drives towards the byline before crossing the ball across the box. Nobody’s there to tap the ball in though.

1 min: Former Arsenal player Vivianne Miedema has an early opportunity. Manchester City win the ball off Arsenal shortly after kick off and Miedema strikes from about 25 yards out. It travels comfortably past the post.

• England, 184-7, bt Nepal, 180-6, by four runs

• Sam Curran bowls final over to deny minnows

On a raucous early evening in front of a hugely one-sided crowd, Nepal so nearly provided the upset this World Cup needed and England were so desperate to avoid, as they seek to buff a tarnished winter into some kind of shine. As their captain, Rohit Paudel, had pointed out before the tournament began, the Nepalese are used to climbing mountains. Even on an awkward surface a target of 185 was pretty trivial by Himalayan standards.

A brave and sometimes brutal batting performance, capped by a ­thrilling and so nearly decisive contribution from the aptly named Lokesh Bam, hauled them to within ­touching distance of the summit. In the end they needed 10 off the last over, having plundered 46 off the previous three. But Sam Curran held his nerve where so many of his teammates had wobbled and England won, in the end, by just four runs.

With the end of the New Start treaty, we face a potentially catastrophic arms race. It can still be prevented

The risk of nuclear war is greater now than in decades – and rising. The Bulletin of Atomic Scientists recently set its famous Doomsday Clock closer to midnight, indicating a level of risk equivalent to the 1980s, when US and Soviet nuclear stockpiles were increasing rapidly. In those years, massive waves of disarmament protest arose in Europe and the United States. Political leaders responded, the cold war ended, and many people stopped worrying about the bomb.

Today, the bomb is back. Political tensions are rising, and nuclear weapons have spread to other countries, including Israel, India, Pakistan and North Korea. China is rapidly increasing its nuclear arsenal. The US-Russia arms competition may accelerate soon with the expiration on 5 February of the last remaining arms control agreement, the New Start treaty. To prevent the growing nuclear threat, we need a new global peace movement.

David Cortright, a visiting scholar at Cornell University’s Reppy Institute for Peace and Conflict Studies, was the executive director of Sane, the Committee for a Sane Nuclear Policy, during the 1980s

This unofficial diagnosis describes the anxiety-driven, compulsive obsession with living as long as possible. While it might seem healthy to monitor your diet, exercise and biomarkers, it can come at a huge emotional cost

It was a pitta bread that finally broke Jason Wood. It arrived with hummus instead of the vegetable crudites he had preordered in a restaurant that he had painstakingly researched, as he always did, weeks before he and his husband visited. “In that moment, I just snapped,” he recalls. “I hit rock bottom, I got angry … I started crying, I started shaking. I just felt like I couldn’t do it any more, like I had been crushed by all this pressure I put on myself.”

Today, Wood, 40, speaks calmly. Neat and groomed, he seems orderly by nature. But at that time, his attempts to control every aspect of his life had spiralled. He painstakingly monitored what he ate (sometimes only organic, sometimes raw or unprocessed; calories painstakingly counted), his exercise regime (twice a day, seven days a week), and tracked every bodily function from his heart rate to his blood pressure, body fat and sleep “schedule”. He even monitored his glucose levels repeatedly throughout the day. “I was living by those numbers,” he says.

Tens of thousands of artefacts were unearthed not by careful excavation but by the 2011 floods. Now, students are piecing together Queensland’s history

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In a white and sterile office that could belong to any one of the warehouses that dot this industrial strip between Brisbane’s airport and horse-racing precinct, a young woman is engrossed in a puzzle.

Only this puzzle comprises, perhaps, three different sets, each almost (but not quite) identical to the other – and none likely to be completed.

Blaze probably caused by candles at makeshift tribute near Le Constellation bar in Crans-Montana, say police

A memorial for the victims of a deadly fire at a new year party in Switzerland caught fire early on Sunday, probably sparked by candles left burning inside, police have said.

The memorial was a makeshift tribute to the 41 people killed and the 115 injured in the fire that erupted in the early hours of 1 January at Le Constellation bar in the ski resort town of Crans-Montana, which was packed with mainly teenagers and young adults.

Whoever succeeds Keir Starmer will still have an almost impossible task: convincing voters that politicians will serve the people, not themselves

So, there goes Morgan McSweeney, leaving Keir Starmer even more exposed, and the British side of the vast Jeffrey Epstein scandal still unfolding. The resignation note penned by the prime minister’s former chief of staff is as clear as it had to be, and acknowledges that McSweeney advised Starmer to make the most fateful choice of his time as Labour leader. “The decision to appoint Peter Mandelson was wrong,” it says. “He has damaged our party, our country and trust in politics itself.” The vetting process for such decisions, it goes on, “must now be fundamentally overhauled”. But the key question festers on, and it has always been political rather than procedural: between late 2024 and early 2025, despite knowing that Mandelson had maintained his friendship with Epstein after the latter’s conviction for what US law calls soliciting prostitution from a minor, why did McSweeney, Starmer and their inner circle still conclude that he was the right man to be the UK’s ambassador in Washington DC?

There is a very important contextual element of the story, which began to surface at the end of last week, about the absence of alarm – in both politics and the media – at the appointment at the time it was made, suggestive of an amazing collective amnesia about details of the Mandelson/Epstein relationship that had been made public. But even so, that doesn’t detract from the awfulness of what the prime minister and his people did, which sits at the heart of the story like an incurable headache. They surely know it, and so does everyone else: presented with a due diligence report based on a vivid account of what Mandelson had been up to (much of which was well known anyway), they apparently took his denials at face value. Despite warnings to the contrary – from, we now hear, the-then foreign secretary David Lammy and Starmer’s then-deputy Angela Rayner – they gave Mandelson exactly what he wanted.

John Harris is a Guardian columnist

Northern leaders urge government to support proposal as Manchester mayor says a London bid ‘wouldn’t be right’

The north of England is seeking to host the Olympic and Paralympic Games to boost a region “left out of the national story”.

Northern leaders have written to the culture secretary, Lisa Nandy, urging the government to back a multi-city games spanning an area with a population of 15 million people.

Murdoch tabloid leads charge as big freeze persists – could the mayor please do something about the weather?

It snowed two weeks ago in New York. Since then, the temperature has barely risen above freezing – a temperature science naturally dictates is necessary to melt snow and ice.

But science isn’t enough for some US political critics, however, who have instead blamed Zohran Mamdani, New York’s new socialist mayor, for the snow not having melted and still clogging up some of the city’s streets.

These chocolatey Brazilian treats are endlessly customisable to fit your sweet tooth preferences – and they’re quick and easy for those in a last-minute romantic rush

If you’re not au fait with these soft, chocolatey treats, you clearly haven’t spent much time in Brazil, where, in the words of blogger Olivia Mesquita, they’re national treasures, “a must-have at special celebrations, from kids’ parties to weddings”. As content creator Camila Hurst puts it, “It’s basically not a party without them.” Quick and simple to make from everyday ingredients, they’re also an ideal last-minute gift for someone you love.

The Guardian’s picture editors select photographs from around the world

Relatives shut out of €200m fortune reportedly receive letters from executor saying will could be overturned

The late German-born Chanel designer Karl Lagerfeld was famously precise, exacting and known to hold a grudge, but his final wishes concerning the beneficiaries of his vast fortune could now be overturned beyond the grave in a looming court battle.

Seven years after Lagerfeld’s death from cancer, an unnamed plaintiff has come forward to challenge the haute couture titan’s last will and testament.

Providers report rise in demand as companies seek mental health benefits and increased sense of community

In a growing number of workplaces, the soundtrack of the lunch break is no longer the rustle of sandwiches at a desk, but the quiet hum of bees – housed just outside the office window.

Employers from Manchester to Milton Keynes are working with professional beekeepers to install hives on rooftops, in courtyards and car parks – positioning beekeeping not as a novelty but as a way to ease stress, build community and reconnect workers with nature in an era of hybrid work and burnout.