ON THIS WEEKEND

first_imgSaturday7:45 a.m.: TOTTENHAM VS SUNDERLAND10 a.m.: CHELSEA VS EVERTON12:30 p.m.: ASTON VILLA VS LEICESTER7 p.m.: NEWCASTLE VS WEST HAMSunday9:05 a.m.: LIVERPOOL VS MAN UNITED11:15 a.m.: STOKE VS ARSENAL11:15 a.m: BOURNEMOUTH VS NORWICH Sunday4:30 p.m.: SOUTHAMPTON VS WEST BROMSPORTSMAX2 SPORTSMAXlast_img

Trump accuses Obama of tapping his phone

first_imgDonald TrumpUS president Donald Trump on Saturday accused Barack Obama of “tapping” his phone during last year’s White House campaign, without providing evidence of the explosive charge, in his most virulent attack yet on his predecessor.“I’d bet a good lawyer could make a great case out of the fact that President Obama was tapping my phones in October, just prior to Election!” Trump wrote on Twitter.“How low has President Obama gone to tapp (sic) my phones during the very sacred election process. This is Nixon/Watergate. Bad (or sick) guy!” he wrote in another tweet, referring to the political scandal that toppled president Richard Nixon in 1974.Top Obama advisor Ben Rhodes issued a searing response on Twitter.“No President can order a wiretap. Those restrictions were put in place to protect citizens from people like you,” Rhodes wrote.A spokesman for Obama did not immediately respond to an email seeking comment.Trump leveled the charges in a flurry of tweets shortly after dawn, as his administration remains mired in controversy over communications between Russian officials and some of his senior aides, including Attorney General Jeff Sessions.Trump and Obama frequently traded barbs on the campaign trail, and the Republican real estate magnate was a driving force behind the so-called “birther” movement that questioned whether Obama was born on US soil and eligible to be president.The two men initially adopted a cordial tone as Trump took office, though the president has stepped up accusations against Obama in recent weeks, blaming his predecessor for being behind damaging leaks to journalists.‘Witch hunt’ -Since US intelligence took the unprecedented step of publicly accusing Russia of trying to swing the November election in Trump’s favor, questions have swirled about whether some in Trump’s campaign colluded with Moscow.A slew of associates, including Sessions and already fired national security advisor Michael Flynn met Russian Ambassador Sergey Kislyak before Trump took office.The businessman-turned-politician, who has accused his political foes of conducting “a total witch hunt,” on Saturday directed his Twitter tirade at his Democratic predecessor.“Terrible! Just found out that Obama had my ‘wires tapped’ in Trump Tower just before the victory. Nothing found,” Trump wrote a day after departing Washington for a weekend getaway at his Mar-a-Lago Florida resort for the fourth time in five weeks.The president compared the alleged action to Senator Joe McCarthy’s campaign in the 1950s to root out alleged Communists and sympathizers, which was marked by improper investigative techniques.“Is it legal for a sitting President to be ‘wire tapping’ a race for president prior to an election? Turned down by court earlier. A NEW LOW!” Trump said, again providing no proof of Obama’s efforts to seek a court order to spy on the then-candidate.Leaks -Trump delivered a well-received address to Congress late Wednesday, but the White House was plunged back into turmoil the following morning after it confirmed a news report that Sessions failed to disclose two meetings with ambassador Kislyak during last year’s election campaign.Trump has repeatedly denied having any personal ties to the Kremlin, and his aides have denied or downplayed contacts with Russian officials.But the accusations have continued amid almost daily leaks revealing new details about connections between Moscow and senior Trump officials.One such revelation in the Washington Post about a meeting between Sessions and Kislyak prompted the Republican former US senator to recuse himself from any investigations into the presidential election campaign.Sessions had told a Senate committee under oath that he “did not have communications with the Russians,” but reporters found that he had actually met the Russian ambassador twice in the months before taking up his post as attorney general, the top US law enforcement officer.Trump has expressed his displeasure over the charges and the leaks that led to them. On Friday he lashed out in tweets directed at the top Democrats in the Republican-led Congress, Senator Chuck Schumer and Representative Nancy Pelosi.last_img read more

Team announces construction of a formal computerverified proof of the Kepler conjecture

first_img More information: code.google.com/p/flyspeck/wik … AnnouncingCompletionvia Newscientist This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission. The content is provided for information purposes only. Computer generated math proof is too large for humans to check It was back in 1611 that Johannes Kepler first suggested in a paper he’d written (after corresponding with Thomas Harriot) that if you want to stack cannon balls on a ship’s deck in the most efficient way possible (a question originally posed by Sir Walter Raleigh), the best way to do it is in a pyramid shape. Cut to 1998 when Hales completed work on his written proof (which included portions that could only be verified by computer). But it was huge, as many mathematical proofs tend to be—300 pages in all that took 12 reviewers four years to verify. A 99 percent certainty rating wasn’t enough for Hales, however, so he launched the Flyspeck Project to create a means for proving the proof correct using a computer.Hales and his team used two software tools that have been created for the sole purpose of verifying proofs—HOL Light and Isabelle—they work by checking the logic of statements made in the proof. Now after eleven years of work, the team has announced that they’ve succeeded in their endeavor. Hales’ original proof has been converted to code the computer can work with and the software checkers found no discrepancies, which means the proof of the conjecture has been verified.The success by the team highlights a growing movement of using computers to verify proofs that human beings have created giving the results more credence. Computers have also been used to construct original proofs for some basic problems, which suggests that someday in the not-too-distant future, computers will be doing all the heavy work, leaving mathematicians to ponder the deeper questions regarding what the proofs represent and how they can be used in real world applications. Citation: Team announces construction of a formal computer-verified proof of the Kepler conjecture (2014, August 13) retrieved 18 August 2019 from https://phys.org/news/2014-08-team-formal-computer-verified-proof-kepler.html (Phys.org) —A team of researchers led by the man, Thomas Hales, who came up with written proof of the Kepler conjecture is now reporting that they have constructed a formal proof of the conjecture, which implies the use of a computer. The announcement was made on The Flyspeck Project page, and puts to rest any doubts about the correctness of the proof done by Hales in 1998. Explore further © 2014 Phys.org One of the diagrams from Strena Seu de Nive Sexangula, illustrating the Kepler conjecturelast_img read more