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Their bills projected plummet in Medicaid spending isnt helping matters for G.O.P. leaders. Even a proposal for $45 billion to fight opioid abuse is under fire, as addiction specialists say its simply not enough to counter the cuts.

Dean Heller, above, the Republican senator from Nevada who denounced his partys bill, is facing the wrath of Las Vegas titans and the states rank and file.

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3. Newly unfettered by the Supreme Court, the Trump administration swiftly enacted portions of its travel ban, which bars entry to the U.S. by refugees and visitors from six predominantly Muslim countries. Heres who can get in, and who cant.

The court will hear arguments on the travel ban in October.

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4. In a meeting on Miami Beach, where fighting rising seas is now routine, American mayors called on President Trump and Congress to rejoin the Paris climate accord, and they doubled down on their own efforts to combat climate change and commit to renewable energy.

According to a new study, Southern states will be hardest hit by global warming.

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5. Combating climate change and bolstering international institutions are priorities as Chancellor Angela Merkel of Germany, above, prepares to host a G-20 summit meeting beginning Friday. She has her sights set on President Trump, predicting very difficult talks.

Mr. Trump will meet with Vladimir V. Putin on the sidelines. The White House wouldnt say whether Mr. Trump would press him on Russias meddling in last years election.

There was, however, some action on the election: A White House commission set up to examine unsubstantiated claims of voter fraud set off bipartisan furor with a sweeping request for the personal and public data of the nations 200 million voters. Many states said no.

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6. Questions about President Trumps priorities grew pointed after a particularly crude explosion on Twitter.

Rebukes abounded, even in media usually friendly to Mr. Trump, after he lashed out at the often critical co-hosts of MSNBCs Morning Joe, above, bashing Mika Brzezinskis appearance and intellect and calling Joe Scarborough psycho. The co-hosts then said the White House had told them that The National Enquirer would quash a story about their romantic relationship if they apologized to the president for criticizing him.

Our media columnist took the fracas as proof of TVs iron grip on the president.

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7. Doctors and hospital staff moved quickly and worked furiously to help those shot during a rampage at a New York hospital on Friday. Had the injured not been treated where they fell, they might not have lived.

Six people were wounded and one doctor was killed before the gunman, a disgruntled doctor, committed suicide.

And a shooting at a nightclub in Little Rock, Ark., early Saturday left at least 25 people with gunshot wounds; all are expected to survive. The police said it appeared to be the result of a dispute.

Above, the scene in New York.

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8. Disclosures that a venture capitalist, Justin Caldbeck, had preyed on female entrepreneurs prompted more than two dozen women to speak to our tech reporter about being sexually harassed by investors and mentors.

Ten named the investors involved, often providing corroborating messages and emails.

For instance, this Facebook message: I was getting confused figuring out whether to hire you or hit on you.

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9. Turning our attention upward, a new initiative to beam messages into space may be our best shot yet at learning whether were alone in the universe.

But if were not, theres an important consideration. As Stephen Hawking once said, If aliens visit us, the outcome would be much as when Columbus landed in America.

Above, the astronomer Frank Drake at the Green Bank observatory in West Virginia in the 1960s.

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10. Back down on Earth, Hong Kong also observed a major anniversary: the 20th of the territorys return from British rule.

President Xi Jinpings speech underscored Chinas tightening grip, and it came as mainland authorities refused to allow the democracy advocate Liu Xiaobo, a Nobel Peace laureate paroled from prison for cancer treatment, to go abroad for care, despite appeals to Mr. Xi, above, from dozens of prominent writers.

And China reacted with fury over the U.S. decision to sell $1.4 billion in arms to Taiwan, which one Chinese official said contradicted President Trumps agreements with Mr. Xi.

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11. Bankers and economists are increasingly discussing whether artificial intelligence could permanently eliminate huge numbers of jobs.

The U.S. jobs numbers for June come out Friday. In the previous report, unemployment was at a 16-year low, but with stubborn weak spots, like lagging wage growth and a shrinking labor force.

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12. Finally, welcome to Broadways biggest night for teenagers.

More than 70 of the countrys most talented theatrical hopefuls took the stage last week for the Jimmy Awards, the Tonys for teens. They warbled, kicked and smiled until their faces hurt, vying for scholarships, cash prizes, and maybe even the eye of a Broadway casting director.

We also went behind the scenes at the Met Opera just before a show, a wondrous maze. Here are the 12 rooms youll probably never see otherwise, featuring Misty Copeland, Toscaninis head, wigs, harps and a snow yak.

Have a great week.

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Photographs may appear out of order for some readers. Viewing this version of the briefing should help.

Your Weekend Briefing is published Sundays at 6 a.m. Eastern.

And dont miss Your Morning Briefing, weekdays at 6 a.m. Eastern, and Your Evening Briefing, weeknights at 6 p.m. Eastern.

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Republicans, Mika Brzezinski, Trump: Your Weekend Briefing - New York Times