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Arsenal manager Mikel Arteta remains optimistic about his team's chances despite mounting injury concerns, particularly with star player Bukayo Saka sidelined with an achilles issue.Arteta insists he has 'zero fear' that Arsenal could end the season without silverware, but admits there are significant doubts over Saka's return. Saka has not played since the Carabao Cup final defeat to Manchester City last month and Arteta is uncertain when he will be back.'Hopefully it's going to be a matter of days and not weeks,' Arteta said. 'But he has to see when he's loading more, how he responds to that kind of progression.'Arsenal are also facing doubts over Jurrien Timber, Riccardo Calafiori and captain Martin Ødegaard for their Champions League match against Sporting. Additionally, Arteta will make a late call on Declan Rice's fitness after the England midfielder missed training on Tuesday.Despite recent setbacks, including a home defeat to Bournemouth in the Premier League, Arteta remains positive. 'Fire. I'm on fire. I'm on fire,' he said. 'Nothing else. I'm dreaming so much. I've done so much to be in this position because I know how this club was. I just see beauty, opportunity, and I want to get it done for all these people that have been in this journey with us.'

George Steinbrenner, the legendary owner of the New York Yankees, left an indelible mark on baseball during his tumultuous reign. Known as 'The Boss,' Steinbrenner purchased the Yankees in 1973 for $8.8 million and went on to build a dynasty that won seven World Series championships under his watch.Steinbrenner's tenure was marked by both remarkable success and controversy. He was suspended from baseball twice - once for illegal campaign contributions to Richard Nixon and again for paying a gambler to discredit Yankees star Dave Winfield. Despite these setbacks, Steinbrenner continued to shape the Yankees into a formidable team, with stars like Reggie Jackson and Derek Jeter leading the charge.The book, which draws from Vaccaro's extensive experience covering the Yankees, offers a nuanced portrayal of Steinbrenner's complex personality and his relationships with key figures like Billy Martin, who served as Yankees manager during five separate stints. Vaccaro also explores the contributions of other influential Yankees executives, including Gabe Paul and Gene 'Stick' Michael, who played crucial roles during Steinbrenner's periods of exile from baseball.Under Steinbrenner's leadership, the Yankees entered into lucrative partnerships, including the creation of the YES Network, and secured a new stadium, which has helped maintain the team's value at an estimated $7 billion to $10 billion. Despite the team's recent struggles, including a championship drought since 2009, Steinbrenner's legacy continues to shape the Yankees' identity and influence.Vaccaro notes that Yankees fans remain passionate and spoiled by the team's past successes, with some expressing concerns about the current leadership under Hal Steinbrenner, George's son, and the team's management, including Brian Cashman and Aaron Boone. However, Vaccaro suggests that the modern baseball landscape is inherently unpredictable, making it challenging for any team to sustain long-term dominance.

The United States military has begun a mine clearance operation in the Strait of Hormuz, a vital waterway for global oil and gas supplies, in response to Iran's alleged laying of sea mines. The operation, led by guided missile destroyers USS Frank E Peterson and USS Michael Murphy, aims to establish a 'safe pathway' for the free flow of global commerce.Iran's Islamic Revolutionary Guard Corps (IRGC) recently released a map of the Strait of Hormuz showing a safe route for ships to follow through the strait, directing vessels farther north towards the Iranian coast and away from the traditional route closer to the coast of Oman. The IRGC stated that all vessels must use the new map for navigation due to 'the likelihood of the presence of various types of anti-ship mines in the main traffic zone.'The stakes are high, with one-fifth of the world's oil and liquefied natural gas (LNG) supplies having been shipped through the Strait of Hormuz before the war. Even a single mine can compel operators to assume a wider threat, effectively invalidating insurance and shutting down their use of the waterway.Iran's stockpile is estimated to number 2,000 to 6,000 mines, a significant portion of which are produced domestically. These mines generally fall into three categories: contact mines, bottom (influence) mines, and 'smart' and rocket mines.The US Navy is facing a 'mine gap,' with experts calling for institutional neglect that led to the retirement of dedicated mine countermeasures (MCM) assets. The current US strategy relies on small combat ships built for coastal operations and fitted with MCM mission modules, but only one of these vessels, the USS Canberra, is currently available in the region.

Match details: Atletico Madrid will meet Barcelona on Tuesday at 21:00 CET (19:00 GMT) in the Metropolitano Stadium for the Champions League quarter‑final second leg. The fixture decides which side advances to the semi‑finals. After a 2‑0 first‑leg triumph at Camp Nou, Atletico enter the tie as favourites despite trailing Barcelona in the La Liga table. Their advantage stems from goals by Julian Alvarez and Alexander Sörloth, who capitalised on a red card for Barcelona defender Pau Cubarsi. Barcelona, the reigning Spanish champions, are desperate to overturn the deficit. They bolstered their domestic campaign with a 4‑1 win over Espanyol, extending their lead over Real Madrid to nine points. Ferran Torres netted a brace, assisted by teenage prodigy Lamine Yamal, while Marcus Rashford added the fourth. Atletico’s weekend league performance was less convincing, suffering a 2‑1 loss to Sevilla after heavy rotation by Diego Simeone. The loss left them fourth in La Liga with 57 points, four behind Villarreal. Historical context: The two clubs have met 251 times, with Barcelona winning 115 matches, Atletico 79 and 57 draws. Their recent knockout encounters include Atletico’s victories in the 2014 and 2016 quarter‑finals, both decided over two legs. Team news: Atletico will miss Marc Pubill (suspension) and have Jose Giménez, Pablo Barrios and David Hancko listed as doubtful. Barcelona’s defender Pau Cubarsi is suspended, replaced by Ronald Araujo. Injuries rule out Marc Bernal, Raphinha and Andreas Christensen. Predicted line‑ups: Atletico – Musso; Molina, Le Normand, Lenglet, Ruggeri; Llorente, Koke; Simeone, Griezmann, Lookman; Alvarez.Barcelona – Joan Garcia; Koundé, Araujo, Martín, Cancelo; Eric Garcia, Pedri; Yamal, Fermin, Rashford; Lewandowski. Managerial insights: Simeone stressed the need to stay focused on the objective of advancing, while Barcelona coach Hansi Flick highlighted the quality of his squad and the importance of collective effort. With a slim margin separating the sides, the second leg promises a tactical battle that could see either club secure a coveted place in the Champions League semi‑finals.

Dominic Frimpong, a 20‑year‑old midfielder for Berekum Chelsea, was killed in an armed robbery targeting the club’s team bus on Sunday. The attack occurred on the road between Goaso and Bibiani as the squad travelled back from a Ghana Premier League match against Samartex in Samreboi. The club’s statement described how "masked men wielding guns and assault rifles" blocked the road, opened fire, and forced the driver to reverse. Players and staff fled into nearby bushes for cover while the assailants continued shooting. The Ghana Football Association (GFA) confirmed Frimpong’s death, expressing "profound shock and deep sorrow" and noting that the loss affects not only Berekum Chelsea but Ghanaian football as a whole. The GFA pledged to strengthen security arrangements for clubs travelling for domestic competitions. This tragic event follows a similar, non‑lethal bus attack on Legon Cities in 2023 after a match at Samartex, underscoring a growing security concern for teams traveling across the country. Key takeaway: The fatal shooting of Frimpong highlights urgent gaps in travel safety for Ghana Premier League clubs, prompting calls for immediate security reforms.

The National Gallery of Art's latest exhibition, 'Dear America: Artists Explore the American Experience', is a thought-provoking collection of over 100 works by 95 artists. This 'open letter to the nation' offers a multifaceted exploration of the American experience, delving into themes of land, community, and freedom.Upon entering the exhibition, visitors are immediately struck by the unconventional representations of iconic American symbols. The Statue of Liberty, for instance, is reimagined through the lens of South African photographer Zanele Muholi and a geometric screenprint by Roy Lichtenstein.The exhibition's curatorial approach is to create 'provocative conversations across centuries, disciplines and demographics.' E Carmen Ramos, the gallery's chief curatorial and conservation officer, notes that the show was 'years in the making' and showcases an 'embarrassment of riches' from the gallery's permanent collection of over 160,000 works.Structured around three core themes – land, community, and freedom – the exhibition presents a diverse array of works. These include Thomas Moran's idyllic watercolours of the American West juxtaposed with Thomas Hart Johnson's photographs of a landscape ravaged by coal mining and railroads. The exhibition also features poignant pieces such as Carrie Mae Weems's haunting silhouette and Gordon Parks's indelible 'American Gothic.'The show's second section, 'Community,' features Richard Avedon's massive 1976 commission 'The Family,' which comprises 69 stark, uniform portraits of the bicentennial era's political, media, and corporate elite. This is contrasted with John Wilson's tender sketches of his teenage children and their friends.The final act of the exhibition turns its lens to 'Freedom,' showcasing historical portraits of figures such as Frederick Douglass, Sojourner Truth, and George Washington, alongside powerful works by Kara Walker, Martha Rosler, and Faith Ringgold. As visitors exit, they are met with Robert Indiana's boldly coloured screenprint 'Liberty '76,' created for the 1976 bicentennial.Ramos reflects on the exhibition's significance, stating that it 'explores how artists in the United States have explored the American experience across different moments in time.' The exhibition will be on view in the National Gallery's West Building until 20 September.

Leeds United delivered a seismic upset at Old Trafford, beating Manchester United 2‑0 and moving six points clear of Tottenham in the Premier League table. The victory marked United’s first league loss at the stadium since February 1981, ending a 45‑year unbeaten home run.Michael Carrick recorded his first home defeat as United’s interim manager. The team never found rhythm, a situation worsened when defender Lisandro Martínez was shown a red card in the 56th minute for yanking Dominic Calvert‑Lewin’s ponytail. Martínez now faces a three‑match ban, with United considering an appeal.Noah Okafor proved decisive, netting a brace. His first goal arrived five minutes after the red card when a Jayden Bogle cross was flicked on by Leny Yoro and finished by Okafor. The Swiss striker celebrated with a calm, hands‑folded pose as the crowd chanted “Yorkshire, Yorkshire”. He added a second, long‑range strike later in the half, sealing the win.Leeds dominated the early exchanges, creating several chances through wing‑back Gabriel Gudmundsson and forward Jayden Bogle. United’s response was limited to a consolation header from Casemiro, but they could not threaten Leeds’ lead.The result has major implications: Leeds now sit comfortably in the Champions League race, while United’s relegation worries intensify. A win against Wolves on Saturday could further distance Leeds from the drop zone, especially if Tottenham falters against Brighton.Post‑match, Leeds manager Daniel Farke and his players celebrated exuberantly, kneeling on the pitch and shouting “We are Leeds”. The three points are described as “vital” for the club’s season ambitions.

Manchester United's recent loss to Leeds United has exposed the team's shortcomings, particularly in terms of squad depth. The absence of Kobbie Mainoo and Harry Maguire was keenly felt, as their replacements struggled to make an impact.The midfield, in particular, was affected by Mainoo's absence, with Manuel Ugarte failing to live up to expectations. Ugarte, who cost £50m from Paris Saint-Germain almost two years ago, has never justified his price tag, and his performance against Leeds only added to the concerns.The team's defense was also vulnerable, with Lisandro Martínez struggling to cope with the physical threat of Leeds' Dominic Calvert-Lewin. Martínez's frustration ultimately led to his dismissal, which further compounded United's problems.The loss has highlighted the need for United to strengthen their squad, particularly in central midfield. With Casemiro's departure already confirmed and Ugarte's dependability in question, it is little wonder that United are focusing on this area. Elliot Anderson is a key target, while Carlos Baleba, Adam Wharton, and Sandro Tonali are also highly regarded at Old Trafford.Despite the setback, Michael Carrick will take comfort from seeing his team's mental resilience in tough circumstances. However, to compete on all fronts, United will require a busy summer of recruitment to address their squad shortcomings.

Tanya Khovanova has long been a leading voice in the world of recreational mathematics, authoring a popular blog and running the Number Gossip site where enthusiasts can inquire about any number.She now debuts her first book, Mathematical Puzzles and Curiosities, co‑written with fellow puzzle‑enthusiasts Ivo David and Yogev Shpilman. Published by World Scientific, the volume offers fresh challenges and inventive twists on classic problems.To give readers a taste, Khovanova selected three puzzles for the Guardian column:1. Battleships – As a naval admiral you must choose between sending a single vessel with a success probability of P % or two vessels each with a P/2 % chance, where the mission succeeds if at least one ship does. Which strategy maximises the odds?2. The Two Oracles – You face two respondents, Randie, who answers randomly, and Rando, who randomly decides to tell the truth or lie before each answer. Is there a method to distinguish them?3. Bad Maths – A student computes 5548 − 5489 as 59, claiming the “548” cancels out. He then experiments with a subtraction of the form XXYZ − XYZW (distinct digits) and observes the result is XW. How many digits in the new expression match those in the original calculation?Solutions to the trio were later posted online (update), but readers were urged to avoid spoilers until the scheduled reveal.Khovanova also reminds fans that she has been curating puzzles for the Guardian every other Monday since 2015 and welcomes new submissions via email.