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North Korea did not clarify what those measures might be, but it referred to a series of earlier statements in which Mr. Kim's government has threatened to launch more long-range rockets and conduct a third nuclear test to build an ability to "target" the United States.

Mr. Kim threw his weight behind his government's escalating standoff with Washington when he called a meeting of top security and foreign affairs officials and gave an instruction in his name. He inherited the supreme party and military leadership from his father, Kim Jong-il, who died in December 2011.

By calling such a meeting and having it reported in state news media, Mr. Kim seemed to assert his leadership in what his country called an "all-out action" against the United States, as opposed to his father, who tended to remain reclusive during similar confrontations.

"At the consultative meeting, Kim Jong-un expressed the firm resolution to take substantial and high-profile important state measures in view of the prevailing situation," said the North's Korean Central News Agency, or K.C.N.A. "He advanced specific tasks to the officials concerned."

The K.C.N.A. dispatch, which was distributed on Sunday, was dated Saturday, indicating that the meeting in Pyongyang took place then. That was the same day on which the North's main party newspaper, Rodong Sinmun, said that the United Nations Security Council's resolution last Tuesday calling for tightening sanctions against the North left it with "no other option" but a nuclear test.

"A nuclear test is what the people demand," it said in a commentary.

The resolution was adopted unanimously — with the support of the North's traditional protector, China — as punishment for its Dec. 12 rocket launching. The Security Council determined that the launching was a cover for testing intercontinental ballistic missile technology and a violation of its earlier resolutions banning North Korea from such tests.

The North rejected the old resolutions, as well as the latest, insisting that launching rockets to put satellites into orbit was its sovereign right. Its successful rocket launching in December, coming after a failure last April, was the most visible achievement Mr. Kim's government could present for its people, who have suffered decades of poverty and isolation. In North Korean propaganda, defending its rocket program is likened to protecting national pride and independence — even if it has to pay economic prices.

Last Thursday, North Korea said that its drive to rebuild its moribund economy and its rocket program, until now billed as a peaceful space project, would be adjusted into efforts to foil United States hostilities. On Sunday, it said the Security Council's action "has thrown a grave obstacle" to its efforts to focus on "economic construction so that the people may not tighten their belts any longer."

Still, it said it had to "defend its sovereignty by itself" because "different countries concerned" failed to "fairly solve the problem." In the past few days, North Korea, without citing China by name, expressed bitterness and defiance against its long-time Communist ally for endorsing the American-led Security Council resolution. On Saturday, Rodong reaffirmed its dislike of "sadae," or toadying big countries, including China.

China provides all of North Korea's fuel and remains its biggest trade partner, but analysts believe that its influence is limited on the recalcitrant government in Pyongyang. Beijing has been thus far reluctant to use its economic leverage, fearing it could only drive its neighbor into more provocations and harming China's interest in keeping stability in the region.

International attention has focused on the Punggye nuclear test site in northeastern North Korea, where the country conducted its two previous underground nuclear tests, in 2006 and 2009. Enough preparations have been made there recently that a third test could happen on short notice from the Pyongyang leadership, South Korean officials said.

In a report issued on Sunday, the Institute for National Security Strategy, a research organization affiliated with South Korea's main intelligence service, said that North Korea may use provocations this year to tame the incoming government of President-elect Park Geun-hye, who will be sworn in next month.

"It will wait and see until the new government's North Korea policy shapes up," it said. "If the policy is not favorable, the North may lash out with provocations."

So they have been prone to wild swings of inconsistency, such as a seven-game losing streak in mid-January, and on the other end, their performance Saturday against the Nets, who again dug themselves a deep first-half hole. Brooklyn tried but could not recover, falling 119-106 at the Toyota Center.

The Nets went from facing one of the league's staunchest defensive teams, the Memphis Grizzlies, to trying to keep up with its fastest, the Rockets, who led the league in possessions per game (100.4) and were third in scoring average (104.1) entering Saturday's game. The end results were largely the same.

Before the game, Nets Coach P. J. Carlesimo indicated that the Nets' success hinged on its ability to slow the Rockets to a steady, more deliberate pace. Instead, they fell victim to the same early defensive sluggishness that cost them in a blowout loss the night before.

Nets' guard Deron Williams did his best early to try to avoid another letdown. He scored 20 points in the first quarter and scored or assisted on the Nets' first 22 points. But he got little support. Brook Lopez missed six of his first seven shots and Joe Johnson scored only 5 points in the first half. Meanwhile, the Rockets took off, starting the second quarter on a 25-6 run.

The Rockets outrebounded the Nets, 27-15, in the first half and assisted on 17 of their first 20 field goals. They scored 20 points in the paint to the Nets' 2 in the second quarter to take a 62-49 lead at halftime.

The Nets cut the deficit to 9 with a stronger showing in the third quarter, making five 3-pointers and not committing a turnover. But the Rockets managed to pull away again in the fourth. Jeremy Lin finished with 14 points and 9 assists, and the center Omer Asik had 20 points and 16 rebounds.

Williams was embarrassed by Lin the first time they faced each other, last Feb. 4, when Lin scored 25 points on 10 of 19 shooting off the bench for the Knicks, the performance that gave birth to Linsanity. The next time they matched up, less than a month later, Williams scored 38 points in an obvious save-face performance. After his first-quarter outburst Saturday, Williams was held to 7 more points and was ejected with 1 minute 7 seconds left in the game after arguing with the referees.

Houston is still fighting its way out of a lengthy mid-month funk, following a stretch in which they had won 10 of 12. McHale acknowledged the team was still fumbling its grasp on a new system.

"We like the style we play when the ball moves," McHale said before the game. "And we're not very good when it doesn't."

When that style is working fluidly, as it did at times Saturday, it can be a majestic thing to behold. On Dec. 17, at Madison Square Garden, the Rockets flattened the Knicks, 109-96, shooting 51.3 percent from the field, with 25 fast-break points and 21 points off turnovers.

The backcourt combination of James Harden, named an All-Star last week, and Lin have shown signs of devastating effectiveness but also maddening lapses. Lin, who is third on the team averaging 12 points per game, is shooting just 28 percent from 3-point range, down from 32 percent last season.

Behind them, Houston leads the N.B.A. in points in transition and turnovers per game. Against the Nets, the Rockets turned the ball over 11 times, but shot 50 percent from the field, had 31 assists and a third win in four games. McHale will take it.

"Everybody wants to believe in a microwave society, where everything works in three days," McHale said. "But it takes time."

The ball looked attached to Holiday's hand, the way he crossed over, hit jumpers and glided for layups. Holiday's dribble drives were so mesmerizing, his jump shot so smooth, that even the Knicks stopped to watch. He scored 35 points as the 76ers beat the Knicks, 97-80, but both Holiday's total and the margin felt like much more.

The Knicks would say the 76ers beat them with two simple plays — isolations for Holiday, and high pick-and-rolls to Holiday — yet they did not adjust.

"He dominated the whole game, in terms of where he wanted to go with the basketball, and a lot of it was at the rim," Coach Mike Woodson said. "We just didn't sit down and defend."

Felton played for the first time since breaking his right pinkie on Christmas Day, and he looked rusty. Shumpert, in his fifth game back from an injury, missed all six of his shots. Kidd, who played with a sore lower back, appeared to grimace with each miss.

Not every Knick had an excuse. Smith missed all eight shots he took. Anthony wrestled with Thaddeus Young and jostled with Evan Turner, sometimes on the same possession. Philadelphia's 24-year-old forwards should have been overmatched against Anthony, one of the league's most prolific scorers, but he struggled with their quickness and energy.

Anthony stayed on the court for 39 minutes and scored 25 points, but he shot 9 of 28 from the field. Every shot Anthony took looked as difficult as every one of Holiday's looked easy.

"I couldn't throw a rock in the ocean today," Anthony said. "It happens."

The 76ers (18-25) looked younger and hungrier. They dove for loose balls and high-fived on their way back on defense. Young jumped so high for one dunk, he appeared to throw it through the net. Nick Young chirped after each successful possession, up and down the court.

On one drive, Holiday found himself guarded by Stoudemire. Before Stoudemire took one step, Holiday yo-yoed the ball and ran past him. All Stoudemire could do was grab him. The 76ers ran circles around the Knicks (26-15).

From the start the 76ers followed the lead established by Holiday, who began the game with three quick layups and a smooth 17-foot jumper. His penetration meant that 18 of Philadelphia's 24 first-quarter points came within two feet of the basket. He fit a whole night's worth of production into the first half — 19 points, 4 rebounds and 3 assists — and the Knicks trailed, 53-41.

"We just didn't have any effort tonight and it started right from the beginning," Woodson said. "I mean, layup after layup, we just didn't come to compete tonight. That's kind of disappointing."

He added, "Across the board, we were awful."

If anything positive came from the first half for the Knicks, it was that Stoudemire again validated Woodson's decision to bring him off the bench. In the second quarter, Stoudemire made four layups and re-established the Knicks inside. In 27 minutes, Stoudemire scored 20 points.

The Knicks' starting lineup Saturday — Felton, Shumpert, Kidd, Anthony and Chandler — could be the team's starting lineup in the playoffs. Woodson has said he prefers having Stoudemire, Smith and Steve Novak come off the bench, so Stoudemire's success in that role has been an encouraging development.

But on Saturday, the 76ers seemed to go faster and harder as their lead grew. It swelled to 29 points in the third quarter, when Nick Young added 14 points. Turner found his stroke at midrange and finished with 20 points.

The 76ers led by more than 20, and Holiday kept going. He knocked down a 13-foot jumper, and then a 16-footer, eventually setting a career high only days after being chosen by the coaches as a reserve on the All-Star team.

As he left NewYork-Presbyterian/Columbia hospital on a cold and bright day, Mr. Koch, 88, said he was feeling much better and planned to be back in his law office on Monday, according to the spokesman, Fred Winters.

It was the third time that the former mayor had been hospitalized in recent months.

Mr. Koch, who led New York for 12 years beginning in 1978 after serving in Congress and the City Council, was told to limit the amount of salt in his diet, something of a challenge for a man who said that the two staples of his diet were garlic and salt.

Nevertheless, he seemed in good spirits.

At a lunch with former aides on Jan. 19, Mr. Koch complained of swollen ankles and breathing problems. That night, a physician friend told the former mayor that he should get medical attention, and Mr. Koch headed uptown to the hospital. Tests showed he had fluid on the lungs.

Mr. Koch was last hospitalized in December, when he was treated for a lung infection. In September, he was admitted for treatment of anemia.

But this time his shot missed — though by less than an inch. Andy Murray, Djokovic's opponent, staggered to his left, past where the ball had landed just behind the baseline, and then dropped his racket and covered his face with disbelief. That narrow miss by Djokovic had sealed Murray's first Grand Slam title, forever changing his career and reputation all in one swing, all by a mere inch. The two will meet Sunday in Rod Laver Arena with the 2013 Australian Open title on the line, and the margins are likely to be just as small.

In the past several years, the gap in men's tennis between the so called Big 4 of Djokovic, Murray, Federer and Rafael Nadal versus everyone else has been massive. Witness, for example, Djokovic's 6-2, 6-2, 6-1 dismantling of David Ferrer in the semifinals here Thursday, which was the rare best-of-five match to last less than 90 minutes.

But when the Big 4 square off against one another, it has been difficult to know who will prevail.

Djokovic is on top of the heap at the moment, having beaten Murray and Federer in their most recent meetings at the ATP World Tour Finals in London in November. But last summer, he lost five straight matches against other members of the Big 4, including defeats to Murray at the Olympics and United States Open.

But Djokovic changed his fortunes at the October ATP Masters 1000 tournament in Shanghai, when he played within himself and saved some five match points in the final against Murray to prevail, 5-7, 7-6 (11), 6-3. That victory helped turn the tide of the top of the tour, and Djokovic reclaimed the No. 1 ranking from Federer within weeks.

Going into Sunday, Djokovic has the advantage of an extra day of rest (a scheduling quirk of the Australian Open putting the men's semifinals on separate nights), but on paper there is little else separating him and Murray.

They are both 25, although Murray is seven days older. Murray, ranked No. 3, is an inch taller, standing 6-foot-3. But Djokovic has more experience winning on big stages, with five Grand Slam titles to Murray's one. Djokovic has slightly more speed and flexibility, and can change directions better than anyone on the tour. But the sturdiness of Murray's movement, propped up by his increasingly sequoia-like leg muscles, led to a steadiness in his ball-striking that gave Federer fits in their semifinal.

It is impossible to guess which minute detail will make the difference this time.

In the often wrenching world of foster care, the plight of American Indian children is especially fraught. Under the Indian Child Welfare Act of 1978, local agencies must try to place Indian children with Indian families whenever possible, and tribes may intervene in certain custody proceedings.

Congress passed the law after generations of Indian children were wrested from their homes and placed in non-Indian foster facilities and boarding schools. The law's supporters say it has worked in many instances — allowing Indian children to remain connected to their heritage, even when families fall apart.

But a chronic shortage of licensed Indian foster families in states like New Mexico, coupled with the poverty and substance abuse endemic to American Indian communities, has also made it challenging to apply.

In Bernalillo County, for instance, there are 65 Indian children in state custody but only 5 Indian foster homes, prompting Gov. Susana Martinez to publicly appeal for more families last March.

"Having enough families to meet the intent of the Indian Child Welfare Act is a big problem," said Jared Rounsville, the protective services director for New Mexico's Children, Youth and Families Department. "Which ends up resulting in Native children at times being placed with non-Native families. And then often times they are adopted by non-Native families."

Recently, the law's interpretation has been tested in a case that will be heard by the United States Supreme Court this year and is being watched closely by child welfare experts.

In that case, a family court judge ordered a white South Carolina couple to turn over a 27-month-old girl they had raised since birth to her Indian biological father.

The father, a member of the Cherokee tribe, was estranged from the mother and had relinquished rights to the child. He said he was unaware his daughter would be put up for adoption and sought custody when he found out, four months after she was born.

Lawyers for the couple said the child, known as Baby Veronica, forged a deep bond with her adoptive parents, who were present at her birth.

The South Carolina Supreme Court upheld the decision after the couple appealed. The court ruled that the birth mother made some efforts to conceal the father's Cherokee identity during the adoption and that federal law required Veronica to remain with her father, whom the court found had created a safe, loving home.

In a 3-to-2 ruling, the court said it had reached its decision "with a heavy heart," conceding that the adoptive couple, Matt and Melanie Capobianco, were ideal, loving parents.

Last year, supporters of the Capobiancos delivered a petition signed by more than 20,000 people to South Carolina lawmakers, urging them to revisit the law.

But its proponents say the case illustrates, with heartbreaking consequences, what happens when information about a child's tribal status is withheld.

"What is at stake is whether or not we not we go back to the days where deception and coercion are the norm in adoptions," said Terry L. Cross, the executive director of the National Indian Child Welfare Association.

According to the child welfare group, Indian children are still overrepresented in foster care at twice their rate in the general population — evidence, Mr. Cross said, that child welfare agencies are still too quick to pull Indian children from their homes.

The prize: 31 guns, with a new winner drawn each day of the month.

The fund-raiser, sponsored by the association in partnership with two New Hampshire gun makers, Sig Sauer and Sturm, Ruger & Company, has prompted a chorus of protests from lawmakers and gun-control advocates questioning why the police are giving away guns, even in the name of a good cause.

Some in law enforcement have also raised questions. When Chief Nicholas J. Giaccone Jr. of Hanover pulled up information about the raffle on the Internet, he said, he was flabbergasted.

"I looked at the first weapon and Googled that one," said Chief Giaccone, who recalled using an expletive when he pulled up information about the Ruger SR-556C, a semiautomatic weapon. "It's an assault rifle."

In a letter to the editor of The Eagle-Tribune, which covers southern New Hampshire, Richard J. O'Shaughnessy of Salem wrote, "People who should know better are adding to the glorification of the gun culture in this state."

And referring to the shootings last month at Sandy Hook Elementary School in Connecticut, State Representative Sharon L. Nordgren, a Hanover Democrat, said, "They're just the same kind that were used in Newtown."

The Ruger that caught Chief Giaccone's attention is an AR-15-style rifle, which is the most popular style of gun in America, according to dealers, and was the type used by Adam Lanza to kill 20 children and six adults at the elementary school. Another gun in the raffle, the Sig Sauer P226 handgun, was also carried by Mr. Lanza, according to the Connecticut State Police.

"It's just ironic that that would be their choice of the kind of gun that they're raffling," Ms. Nordgren said.

Organizers of the raffle are standing firm. In a statement released this month, Chief Paul T. Donovan of Salem, the president of the association, defended the fund-raiser, saying that all winners would be required to meet all applicable rules for gun ownership.

"While this raffle falls on the heels of the recent tragedy in Newtown, Conn., the New Hampshire Association of Chiefs of Police extends their deepest sympathies to the families and first responders," Chief Donovan wrote. "New Hampshire Chiefs of Police feel the issues with these tragic shootings are ones that are contrary to lawful and responsible gun ownership."

The proceeds from the raffle go toward a cadet program involving participants ages 14 to 20 who are given instructions in various kinds of police skills and procedures. Some of them go on to pursue careers in law enforcement.

The guns will be distributed through another raffle partner, Rody's Gun Shop, a windowless outpost here in Newport, a town that comes to life when employees of Ruger, which is one of its main employers, leave work for the day.

"Around here, most people are into guns," said Michael Gaffney, an employee of a nearby hardware store who won a rifle in a raffle years ago. "You get a chance to win a free gun! It's like any raffle, very much akin to trailer raffles, snowmobile raffles or turkey raffles."

On a recent weeknight, the Rody's parking lot was filled with idling cars, their occupants waiting for the store to open at 6 o'clock. The store filled up immediately. Customers, some with their children in tow, browsed the shotguns and rifles on the walls and discussed the possibility of gun bans. While the shop's owner would not comment on the raffle, his customers were nonchalant.

"Honestly, I don't see what the big deal is — they're just talking about it because of Sandy Hook," said Lorraine Peterson of Litchfield. "I don't mean to sound insensitive. This is New Hampshire. This is a sport."

Gun raffles are business as usual here and in many other parts of the country — frequently used by hunting clubs and sometimes by athletics booster clubs to raise money and anchor galas.

"We host raffles like this all the time," said Richard Olson Jr., the president of the New Hampshire Wildlife Federation and the Londonderry Fish and Game Club. "Anybody that's speaking up is using the Newtown massacre as a pretext to poke at the issue negatively."

Mr. Olson said that he once planned a gun raffle to raise money for a fishing derby and that he was considering using one to raise money for the wildlife federation's conservation efforts on New England cottontail rabbits.

Shifting economic and political conditions have spread gun raffles to other spheres, too. Josh Harms, a Republican state representative in Illinois, intends to raffle three guns in March to raise money for his campaign treasury.

Greg Hay, a firefighter from Quincy, Ill., said his union decided last January to hold a gun raffle to replenish its accounts after a drawn-out arbitration. He said the sluggish economy had limited fund-raising from the union's annual country music concert.

"We didn't really want to have any more assessments, so we needed to start looking at better moneymakers," said Mr. Hay, who expects the union, Quincy Firefighters Local 63, to take home about $25,000 from the raffle, which started last June and awards one gun per week for a year.

The fund-raiser has been so successful that the union had planned to sponsor a second one until a recent increase in gun prices — fueled by increased demand amid fears of gun bans in the wake of the Newtown shooting — made the effort less promising.

"Maybe we'll hold off until gun prices go down and start to go back to a decent level," Mr. Hay said.

Opponents of the raffle in New Hampshire are quick to say it is not the guns they oppose, but the fact that the police are conducting it.

"I think in some respects it shows the wrong message," said State Representative Stephen Shurtleff, Democrat of Merrimack. "For law enforcement, normally they're dealing with firearms in a negative way. For that reason, it's just not an appropriate thing. We're trying to get guns off the street."

He emphatically added that Mr. Chávez would return to Venezuela take charge of the government again.

Mr. Maduro spoke on his return from Cuba, where Mr. Chávez had surgery on Dec. 11.

"The commander is in the best moment that we have seen him in all these days of struggle and battle," Mr. Maduro said. "He is smiling, he has a look full of light, he has a special illumination in his thought."

Mr. Maduro said that Mr. Chávez had asked him to deliver a brief message to Venezuelans.

"He said tell the people that he is optimistic and has lots of faith in what we're doing," Mr. Maduro said, adding that Mr. Chávez was referring to his medical treatment. He said the president was "holding tight to Christ and to life."

He went on to predict Mr. Chávez's return, but did not say when that might occur.

"This blessed land of the Liberator will see our commander president, it will see him, in his time, in his time it will see him here," Mr. Maduro said. "We're going to have him, as he should be, as president, in charge of our country."

Mr. Chávez has not been seen since his surgery last month. Unlike the president's previous trips to Cuba for treatment, this time there have been no photographs or videos or television appearances, and Mr. Chávez has not called in to government run television programs to make his voice heard.

The political opposition has demanded more information about his condition and has asked for a team of medical experts to travel to Cuba to get an update on his health, but the government has rebuffed those requests.

Mr. Chávez has refused to say what kind of cancer he has or exactly where it was found in his body. Government officials have not offered details about his most recent cancer surgery, his fourth since June 2011. But on Saturday, Information Minister Ernesto Villegas said that the purpose of the surgery was "to remove a malignant lesion in the pelvis." He added that Mr. Chávez had recovered from a severe lung infection that occurred after surgery.

Mr. Chávez, who was re-elected in October, was unable to return to Venezuela for the inauguration for his new term, which began Jan. 10. The long absence has plunged the country into uncertainty and has led many to question whether he will be able to regain his health and continue as president.

But by the time Michael R. Bloomberg left Johns Hopkins University, with a smattering of A's and a lust for leadership, he was a social and political star — the president of his fraternity, his senior class and the council overseeing Greek life. "An all-around big man on campus," as he puts it.

His gratitude toward the university, starting with a $5 donation the year after he graduated, has since taken on a supersize, Bloombergian scale.

On Sunday, as he makes a $350 million gift to his alma mater — by far the largest in its history — the New York City mayor, along with the president of the university, will disclose the staggering sum of his donations to Johns Hopkins over the past four decades: $1.1 billion.

That figure, kept quiet even as it transformed every corner of the university, makes Mr. Bloomberg the most generous living donor to any education institution in the United States, according to university officials and philanthropic tallies.

The timing of his latest donation, as the mayor's third term draws to a close, offers a glimpse of the sky-is-the-limit philanthropy that he and his aides say is likely to dominate his life after City Hall. The mayor, who is 70, has pledged to give away all of his $25 billion fortune before he dies, and he has built up a foundation on the Upper East Side of Manhattan to carry out the task.

At the same time, the donations highlight the unusually close relationship between Mr. Bloomberg and Johns Hopkins, which, interviews show, has played an unseen role in several of his biggest undertakings as mayor.

In an interview here, Mr. Bloomberg said he was making his donations public to encourage greater charitable giving toward education. He lamented, "In our society, we are defunding education."

The mayor, a member of the class of 1964, explained his fidelity to the university in deeply personal terms. Johns Hopkins, he said, was where he escaped the crushing boredom of Medford High and discovered an urban campus of stately Georgian buildings brimming with new people and ideas.

"I just thought I'd died and gone to heaven," he said.

"If I had been the son of academics," he added, "maybe I would have been on campuses and would never have been as impressed as I was when I was here, because it's the first time I really was walking among people who were world leaders, who were creating, inventing."

Johns Hopkins as it exists today is inconceivable without Mr. Bloomberg, whose giving has fueled major improvements in the university's reputation and rankings, its competitiveness for faculty and students, and the appearance of its campus.

His wealth — not to mention a small army of his favored architects, art consultants and landscape designers — has bankrolled and molded the handsome brick-and-marble walkways, lamps and benches that dot the campus; has constructed a physics building, a school of public health, a children's hospital, a stem-cell research institute, a malaria institute and a library wing; has commissioned giant art installations by Kendall Buster, Mark Dion and Robert Israel; and has financed 20 percent of all need-based financial aid grants to undergraduates over the past few years. (Even his ex-wife and in-laws make a campus cameo, on the dedication plaque for a science building he financed.)

"The modern story of Hopkins is inextricably linked to him," said Ronald J. Daniels, the university's president, as he walked around the campus recently. "When you look at these great investments that have transformed American higher education, it's Rockefeller, it's Carnegie, it's Mellon, it's Stanford — and it's Bloomberg."

Hopkins, in return, has become something of a brain trust for Mr. Bloomberg, shaping his approach to issues like cigarette smoking, gun violence and obesity.

It was faculty members at Hopkins who introduced Mr. Bloomberg, as a donor and as a trustee, to a growing body of science linking behavior and disease.

"That is when he discovered public health," said Alfred Sommer, the dean of the Johns Hopkins Bloomberg School of Public Health from 1990 until 2005.

At times, Mr. Bloomberg, then a high-flying entrepreneur, was resistant to paying for such research, arguing that some of the most intractable health problems were best left to government. "That's policy; that's politics," Mr. Sommer recalled him saying.

But the underlying ideas stuck, and, as mayor, Mr. Bloomberg pressed the City Council to ban smoking in city parks, and the Board of Health to require fast-food chains to post calorie counts and restaurants to stop selling oversize sodas.

"He was in a position to act on things he had once told us we really shouldn't be bothered with," Mr. Sommer said. "He has been the public health mayor ever since."

Years before he would banish cars from parts of Times Square, Mr. Bloomberg removed them from the quads of Johns Hopkins as chairman of the board of trustees, arguing they were unsightly and impeded socializing. (To hide them, he paid for an underground parking garage.)

The relationship between Mr. Bloomberg and Hopkins is, much like the college admissions process, the product of happenstance.

In high school, Mr. Bloomberg worked at an electronics company whose owner happened to have a doctorate from the university. She urged him to apply, despite his mediocre transcript.

"Let's be serious — they took a chance on me," Mr. Bloomberg said.

At Hopkins, the boyish-looking Mr. Bloomberg, whose high school classmates branded him "argumentative" in a class book, blossomed into a charismatic figure, eager to organize those around him. An engineering major, he persuaded his fraternity brothers to pay for a chef to replace a chaotic dinnertime routine, and he doled out assignments to lab mates. "He was like the project manager, at 19 years old," Jim Kelly, a classmate, said.

On campus, Mr. Bloomberg discovered the addictive power of the limelight. When a local judge, tired of hearing cases involving misbehaving Hopkins fraternity brothers, called for an end to Greek life at the college, Mr. Bloomberg challenged him to an hourlong public debate. A healthy crowd showed up for the occasion.

"Mike not only held his own," Mr. Kelly recalled, "he beat him."

Mr. Bloomberg still relishes his star turn in campus governance. "It's the first time that I ever headed something," he said. "The first time I got a chance to pull people together."

These days, his status as the university's top donor has given him mayorlike sway at Hopkins: deans routinely travel to New York to pitch him new programs and research.

His latest passion: genetically engineering mosquitoes to prevent the transmission of malaria. "He always asks about the mosquitoes," said Dr. Peter Agre, a Nobel Prize-winning professor at the university, where Mr. Bloomberg has paid for a temperature-controlled center to cultivate the bugs. The mayor of New York City now speaks of "building a better mosquito."

Mr. Bloomberg tends to finance ideas that appeal to his contrarian style and corporate ethos. For years he has rotated top executives around his media company to encourage collaboration. In the hope of replicating that experience, most of his latest donation, about $250 million, will be used to hire 50 new faculty members who will hold appointments in two departments as they pursue research in areas like the global water supply and the future of American cities. (The remaining $100 million will be devoted to financial aid.)

His approach to philanthropy at the university is remarkablyhands-on. A trusted mayoral architectural adviser, Allen Kolkowitz, and an art guru, Nancy Rosen, guided the construction of the new Charlotte R. Bloomberg children's hospital, named for the mayor's mother. The building's colorful exterior is a whimsical take on Monet's paintings at Giverny. "He got very involved in the design," said Dr. Edward D. Miller, the former chief executive of Hopkins Medicine.

Of course, certain courtesies are extended to a donor at Mr. Bloomberg's level. When Dr. Miller realized that the Charlotte R. Bloomberg Children's Center would be connected to a new tower named for Sheik Zayed bin Sultan al-Nahayan, the former president of the United Arab Emirates, he nervously called the mayor.

"Will you have a problem with this?" he asked Mr. Bloomberg.

The mayor thanked him for the call, but made clear he had no objection. "A Jew on one side, an Arab on the other," he told Dr. Miller. "That's what we should do in this world."