Here\u2019s what you need to know at the end of the day.<\/b>
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Good evening. Here\u2019s the latest.
1. President Trump lobbed familiar accusations about Robert Mueller\u2019s Russia investigation the day after prosecutors asserted that Paul Manafort, the former Trump campaign chairman, had violated his plea agreement by repeatedly lying to them.
In a court filing, prosecutors said that Mr. Manafort\u2019s \u201ccrimes and lies\u201d had nullified the promises made to him in the deal. Defense lawyers denied that Mr. Manafort had broken the agreement.
Mr. Manafort, above, was convicted in August of eight counts of financial fraud stemming from his work as a political consultant in Ukraine. The Times examined his rise and fall.
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2. The number of undocumented immigrants in the U. S. has dropped significantl y \u2014 even as the national debate around immigration has become much more divisive.
A new study, published by the Pew Research Center, put the number of undocumented immigrants at 10.7 million in 2016, down from a peak of 12.2 million in 2007. And it noted a sharp decrease in \u201crecent arrivals.\u201d Above, at the border near Laredo, Tex.
Separately, our reporters looked at deaths at the U. S.-Mexico frontier. Here\u2019s the story of a woman who was injured trying to scale a border wall last week, and the tragic history of a boy shot at the border by a Marine two decades ago.
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3. China\u2019s richest man and the founder of the country\u2019s biggest e-commerce company, Alibaba, was listed as a member of the Chinese Communist Party in its official newspaper.
It might seem paradoxical that an entrepreneur who amassed wealth in the private sector belongs to an organization that propagates the ideals of Karl Marx.
But Jack Ma\u2019s membership didn\u2019t surprise many in China \u2014 and it \u201creveals a party that is eager to prove its legitimacy by affiliating itself with capitalist success stories,\u201d our Asia tech columnist writes.
Separately, in the second part of our China Rules special series, we look at how the country unleashed upward economic mobility and embraced free enterprise while still maintaining state control .
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4. Juul Labs, the leading manufacturer of e-cigarettes in the U. S., is looking to duplicate that success in markets overseas .
The company, which has come under scrutiny for producing flavored vaping products popular with children and teenagers, is creating a potent e-cigarette pod that it hopes will appeal to adult smokers and sidestep stricter nicotine regulations in Europe.
The new pods contain less nicotine than their U. S. counterparts, but they create an intense vapor, potentially making them even more addictive, experts told us. One researcher said the approach could amount to a workaround, saying, \u201cIt\u2019s more like cheating the test.\u201d
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5. The final Senate race of the year is almost over.
Mississippi voters are deciding between Senator Cindy Hyde-Smith, a Republican, and her Democratic challenger, Mike Espy, in a runoff election. Ms. Hyde-Smith is white, Mr. Espy is black, and the campaign has seen policy debates mixed with tense racial politics. Above, in Jackson, Miss.
Republicans are believed to have an edge today, but Mr. Espy has mounted one of the strongest Democratic campaigns in Mississippi in recent decades.
Polls close at 8 p.m. Eastern and we\u2019ll have an update. Here\u2019s what to watch for tonight.
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6. The creator of SpongeBob SquarePants, Stephen Hillenburg, died Monday at his home in California. He was 57.
Inspiration for the cartoon show\u2019s main character grew from Mr. Hillenburg\u2019s background as a marine biology teacher, sort of. At first he drew blob-like sea sponges. \u201cThen I drew a square sponge, and it looked so funny,\u201d he said in a 2001 interview. \u201cHe seemed to fit the character type I was looking for \u2014 a somewhat nerdy, squeaky-clean oddball.\u201d
The television cartoon spawned two movies and a Broadway musical that was nominated for nine Tony Awards (and won one, for scenic design).
Mr. Hillenburg announced last year that he had Lou Gehrig\u2019s disease.
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7. A fatal tug-of-war.
The two pilots on the doomed Lion Air flight that nose-dived into the Java Sea off Indonesia last month struggled with the Boeing 737 almost from takeoff, our reporters learned .
The flight data recorder, above, shows the plane plunged dangerously downward more than two dozen times during the 11-minute flight, consistent with investigators\u2019 theory that a new computerized system malfunctioned. The pilots repeatedly pulled the nose back up but finally lost control, investigators said, leaving the plane to crash, killing all 189 people on board.
And our journalists, who interviewed dozens of employees, officials and aviation analysts, found that Lion Air was cutting corners long before the crash.
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8. Three U. S. soldiers were killed in Afghanistan.
Witnesses said a roadside bomb detonated as an American convoy passed near Ghazni City, in the southeast. It was the worst loss of life for U. S. troops in the country this year.
The Taliban, which now controls more territory than at any time since the start of the war, claimed responsibility for the attack. The group has been pressing the fight for Ghazni City, pictured above, since August.
Meanwhile, the military is investigating whether an Afghan soldier who killed a Czech soldier last month in the western province of Herat was beaten or tortured to death while in custody. The U. S. Green Beret unit at the scene has been sent home, officials said.
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9. Roz Chast\u2019s jittery cartoons capture the essence of the anxiously obsessive New Yorker.
A retrospective of her work, now on display at a Manhattan gallery, includes drawings, childhood sketchbooks, hand-decorated Ukrainian-style eggs and a life-size \u201cM. R. I. of Love,\u201d based on one of her cartoons.
She talked with our reporter about getting started as a cartoonist, why she loves crafts and the one thing she hates to draw. (Hint: You won\u2019t find it in the city.)
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10. Finally, a reason to celebrate.
The N.F.L. last year relaxed its strict rules about on-field jubilation after big plays. Before long, high fives evolved into elaborate routines: drum lines, a phone call, famous moments in other sports, even a pantomime birth with a football baby. Above, Vikings move to a limbo beat.
Our sports reporter has assembled a video sampler of this year\u2019s best celebrations, most of which would have once drawn a flag.
Have a winning evening.
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