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The new map it published at the same time, built through crowdsourcing, provides people who normally visit the site for driving directions with a look, to the street level in some cases, of places they have previously read about only in articles about the North's nuclear program. The map of Pyongyang, the capital, shows everything from landmarks — the tower that celebrates the country's self-reliance doctrine of Juche and the main square where military parades are held — to hotels, schools and hospitals.

Users can zoom in for photos and even to post comments, updating a map that had previously been mostly blank. The site also marks what it says are the locations of some of the police state's notorious gulags.

The popular mapping program is focusing new attention on the North at a time when the country is locked in a tense standoff with the United States and its allies over tightened sanctions and has promised to conduct a third nuclear test.

Google's initiative came three weeks after its executive chairman, Eric E. Schmidt, visited Pyongyang in a highly publicized yet contentious trip organized by Bill Richardson, the former governor of New Mexico. Mr. Schmidt, a proponent of Internet connectivity who likes to describe the Web as the enemy of despots, said he urged North Korean officials he met in Pyongyang to let more North Koreans use the Internet.

The map is still not very detailed in much of the country, though it does include four enormous prison camps, highlighting them in gray shading. Google Maps is unlikely to provide important new information to policy makers and others who already have satellite maps, and Google Earth views, to depend on. But the crowdsourcing project provides a tool for Internet users anywhere in the world to help identify at least some features in the isolated country that the regime in Pyongyang doesn't want the world to know. (The regime cherishes secrecy to such an extent that its propagandists liked to boast: "When our enemies try to peek into our republic, they only see a fog.")

At the moment, the map released Tuesday is far less detailed than North Korean maps available in South Korean bookstores, or the one on Google Earth.

In recent years, Internet bloggers and activists have relied on Google Earth, and defectors from North Korea, to locate several places believed to be prison camps. In each of the gulags, international human rights groups have said, thousands of political prisoners have been forced into hard labor for crimes like criticizing the ruling Kim dynasty in Pyongyang.

The Washington-based Web site 38 North, also using Google Earth, has created a digital atlas of North Korea far more detailed than what exists on Google Maps.

"So far, Google's efforts are largely symbolic," said Kim Yong-hyun, a North Korea specialist at Dongguk University in Seoul. "It won't be easy to make a Google map of North Korea of the kind you see of other countries."

Google Maps' basic premise — Internet users filling in information about their neighborhood to help update and perfect a map — is severely limited for North Korea. The country is cut off from the Internet, except for its tiny elite, and even that group's access is controlled.

Google can try to enlist the more than 24,000 North Korean defectors who live in South Korea, one of the world's most wired countries. But most of them come from the north of the country and, given the tight control on people's movements, their knowledge of other parts of North Korea before their defection is limited.

There was no immediate North Korean reaction to Google's announcement on Tuesday.

Google said that although its map of North Korea is incomplete, it could be important to some South Koreans who originated from the North and who could now identify their old home villages.

Its $650 million rebuilding project called for a new 11-acre plaza over the Potomac Freeway — offering better access between the center and the National Mall in Washington — and buildings for a new education center and rehearsal space designed by the architect Rafael Viñoly.

But in 2005 Congress balked, omitting from a transportation bill some $400 million earmarked for the project.

Now, eight years later, the center has unveiled a more modest $100 million plan, designed by Steven Holl, that will give the institution the rehearsal and education space. The money is being raised privately, and half has been donated by the center's chairman, David M. Rubenstein.

"When you're the chairman of something, you have the obligation to be a leader," Mr. Rubenstein said. "I am very much interested in promoting the idea that the federal government can't do all of the things that it used to be able to do."

The center plans to break ground in 2016 and complete the project in 2018.

Although the Kennedy Center has 1.5 million square feet of space, it opened to the public in 1971 without rehearsal or classroom space and with only one office. "We educate 11 million children a year and we don't have a classroom," said Michael M. Kaiser, the center's president.

The Kennedy Center also needs work space for its training of arts managers (Mr. Kaiser founded its DeVos Institute of Arts Management in 2001) and it needs large rehearsal space for opera and ballet.

Just as Lincoln Center's redevelopment opened its campus with new, inviting public areas, the Kennedy Center hopes to lure audiences with an outdoor stage and gardens where people can see a free performance, eat at a new restaurant or picnic by the Potomac. Mr. Holl and Chris McVoy, a senior partner at Steven Holl Architects, were unanimously selected by the Kennedy Center board after a search that started with 21 architects. The search was led by a 10-member architect selection committee, directed by Mr. Rubenstein and Fred Eychaner, a Chicago financier. Jean Kennedy Smith and Victoria Reggie Kennedy were committee members.

"We wanted to make an artistic statement," Mr. Kaiser said. "We weren't just looking for a mini version of what we had."

Mr. Holl's initial concept — a formal design will be created in the coming months — features three connected pavilions south of the existing building, amounting to 60,000 square feet.

The board was particularly taken by the design's orientation to the Potomac, since President Kennedy had expressed a strong affinity for water. Mr. Holl said this was deliberate. "My first sketch was to make a connection to the river," he said. "The original Edward Durrell Stone design was connected to the river."

One pavilion will float on the Potomac and include an outdoor stage. The exteriors will use translucent Okalux, an insulating glass that diffuses light. "It glows like a Japanese lantern," Mr. Holl said of the material. He also used the same Italian Carrara marble that cloaks the original building.

To avoid interrupting the current center's silhouette, the new structure will connect to it underground and via the main plaza.

"The idea was to fuse the addition with the landscape, rather than try to add an object on," Mr. Holl said.

Mr. Rubenstein's gift — among the largest ever given to a federally supported nonprofit organization — begins the Kennedy Center's $125 million fund-raising campaign. The institution plans to raise $50 million more for the expansion and an additional $25 million for future major programming.

Mr. Rubenstein has given more than $75 million to the center to date, making him the most generous benefactor in its history. He has also donated major gifts to the National Archives, the Washington Monument, Lincoln Center and the Smithsonian Institution.

Last June a bill that authorized the center to construct an expansion at the south end of its grounds was approved by both houses of Congress and signed into law by President Obama.

The expansion will be part of Mr. Kaiser's legacy to the center; he steps down at the end of 2014 after what will have been nearly 14 years in the job. He then will stay on for three more years running the DeVos Institute.

Mr. Holl said he felt inspired adding to a complex that honors President Kennedy. "Kennedy was so important for me," Mr. Holl said. "I was 13 years old when he was inaugurated, and they brought a television into my junior high."

Because the center is known as "a living memorial," and Kennedy's statements about the arts are carved into its facade, Mr. Holl did the same with his new buildings, using Kennedy's statements about water.

"We are tied to the ocean," Kennedy said in one of them. "And when we go back to the sea — whether it is to sail or to watch it — we are going back from whence we came."

He cited the improving national economy, the recovery on Wall Street and the city's increasingly diversified economy as reasons the city was in decent financial shape.

In his final budget proposal after 11 years in office, Mr. Bloomberg said that New York schools could be hit the hardest, mainly as a result of the failure to reach an agreement with the teachers' union over an evaluation system.

"We expect our schools to take a $250 million hit in the current fiscal year," Mr. Bloomberg said. That would mean that there would be hundreds of fewer teachers, mainly through attrition.

While noting the many challenges the city faces, he said the city's $70.1 billion budget would protect all vital services even as individual agencies worked to keep their spending in check.

"The financial plan presented today continues to protect critical services and foster economic growth, while also taking the responsible, budget-minded actions that have resulted in a more efficient city government," Mr. Bloomberg said.

Hurricane Sandy has cost the city $4.5 billion in emergency services and damage to public infrastructure, he said.

"We do expect that all of those costs will be covered by federal funding," he said.

The mayor's budget outline marks the starting point for what will most likely be months of negotiations with city lawmakers before the official start of the fiscal year on July 1.

By law, the mayor and the City Council must agree on a balanced budget each fiscal year.

Mr. Bloomberg said that the loss of education money would have an impact on schools across the city.

To make up for the lost money, the city would keep 700 fewer teachers on the payroll, with staff reductions coming mainly through attrition, "as well as the reduction of funds for extracurricular activities and after-school programming," according to a budget summary provided by the administration.

"The cuts would have a direct and dire impact on classrooms across the city and will be borne by the students who need and deserve high-quality education," according to the statement.

In outlining his budget, Mr. Bloomberg noted the city's continued commitment to education, saying that the $13.9 billion budget for education he proposed on Tuesday was $8 billion more than when he took office.

Mr. Bloomberg said that while there would be no tax increases, he expected tax revenues to be $222 million greater than initial projections.

"I am reasonably optimistic that we will have a small increase in our tax revenues," he said.

But the budget also relies heavily on the cost-cutting measures put in place by city agencies, which he said will result in $6.5 billion in savings in 2014.

Administration officials had already warned city agencies about the likelihood of deep cuts, projecting a steep budget shortfall.

Mr. Bloomberg reiterated his warnings of coming fiscal pain during testimony in Albany on Monday, when he urged the State Legislature to intervene so that the city did not lose hundreds of millions of dollars because it missed a deadline this month to finish negotiating a teacher evaluation system.

He had also hinted, more broadly, of belt-tightening in November, when he unveiled a plan to cope with a budget shortfall for the rest of the current fiscal year, which ends on June 30.

He noted that because his plan to sell 2,000 new yellow-taxi medallions was still tied up in the courts, and up in the air, and because any additional costs related to Hurricane Sandy had not yet been determined, he felt that he had to slash a slew of programs.

While there was talk in the administration about an increase in school-lunch fees to $2.50 from $1.50 — which would have netted the city an extra $4.4 million — the plan was not included in Tuesday's budget address.

The idea was shut down by Christine C. Quinn, the City Council speaker, according to city officials.

The mayor's proposed budget could change significantly after wrangling with lawmakers.

Last year, for instance, additional money that poured into the city's coffers enabled the city to avoid cutting child-care and after-school programs, and to keep open firehouses.

But this year's budget "sidesteps some crucial issues," according to the city's Independent Budget Office, like uncertain education funding, Medicaid reimbursements, taxi revenues and expired labor contracts.

"While projected budget gaps may currently appear modest — certainly when compared with gaps faced in some recent years — the next mayor and City Council are likely to face significant budget challenges," the budget office concluded.

When Mr. Bloomberg took office, he inherited a $4.8 billion deficit in a $42.3 billion budget.

Mr. Bloomberg vowed that he would not pass along a similar debt to his successor, making a habit of stashing away extra revenue in years when the city ran a budget surplus.

"I'm determined that when I leave the city, we won't have, my successor, the first year in office, won't have enormous deficits to deal with," Mr. Bloomberg said in 2007.

Despite the challenges the city faces, Mr. Bloomberg said he was determined to keep the budget balanced while not cutting essential services.

When asked to reflect on how he felt presenting his final preliminary budget proposal, Mr. Bloomberg sounded wistful and hardly ready to move on.

"I would be hard pressed to come up with anything that I have had to do in the last 11 years and almost one month that I did not enjoy and look at as a challenge," he said. He said that there were still 336 days left in his term and that he planned to make the most of them.

"The best days for this city are yet to come," he said.

The full Senate is expected to vote on Mr. Kerry's confirmation Tuesday afternoon.

Mr. Kerry, 69, a Massachusetts Democrat, has strong support on both sides of the aisle, making his confirmation all but assured.

Hillary Rodham Clinton, who was participating in a global forum at the State Department during her final week as secretary of state, expressed her hope that Mr. Kerry could make headway on the Middle East.

Taking note of the recent Israeli parliamentary elections, in which a centrist coalition made significant gains, Mrs. Clinton said that the shifting political landscape might facilitate progress.

"I actually think that this election opens doors, not nails them shut," she said. "I know that President Obama, my successor, soon to be Secretary of State John Kerry, will pursue this."

Spotify, which began streaming music in Sweden in 2008, lets users choose from millions of songs over the Internet free or by subscription, and is increasingly seen as representing the future of music consumption. Mr. Broe, a 26-year-old from Brooklyn, said that having all that music at his fingertips helped him trim his monthly music budget from $30 to the $10 fee he pays for Spotify's premium service.

"The only time I download anything on iTunes is in the rare case that I can't find it on Spotify," he said.

A decade after Apple revolutionized the music world with its iTunes store, the music industry is undergoing another, even more radical, digital transformation as listeners begin to move from CDs and downloads to streaming services like Spotify, Pandora and YouTube.

As purveyors of legally licensed music, they have been largely welcomed by an industry still buffeted by piracy. But as the companies behind these digital services swell into multibillion-dollar enterprises, the relative trickle of money that has made its way to artists is causing anxiety at every level of the business.

Late last year, Zoe Keating, an independent musician from Northern California, provided an unusually detailed case in point. In voluminous spreadsheets posted to her Tumblr blog, she revealed the royalties she gets from various services, down to the ten-thousandth of a cent.

Even for an under-the-radar artist like Ms. Keating, who describes her style as "avant cello," the numbers painted a stark picture of what it is like to be a working musician these days. After her songs had been played more than 1.5 million times on Pandora over six months, she earned $1,652.74. On Spotify, 131,000 plays last year netted just $547.71, or an average of 0.42 cent a play.

"In certain types of music, like classical or jazz, we are condemning them to poverty if this is going to be the only way people consume music," Ms. Keating said.

The way streaming services pay royalties represents a major shift in the economic gears that have been underlying the industry for decades.

From 78 r.p.m. records to the age of iTunes, artists' record royalties have been counted as a percentage of a sale price. On a 99-cent download, a typical artist may earn 7 to 10 cents after deductions for the retailer, the record company and the songwriter, music executives say. One industry joke calls the flow of these royalties a "river of nickels."

In the new economics of streaming music, however, the river of nickels looks more like a torrent of micropennies.

Spotify, Pandora and others like them pay fractions of a cent to record companies and publishers each time a song is played, some portion of which goes to performers and songwriters as royalties. Unlike the royalties from a sale, these payments accrue every time a listener clicks on a song, year after year.

The question dogging the music industry is whether these micropayments can add up to anything substantial.

"No artist will be able to survive to be professionals except those who have a significant live business, and that's very few," said Hartwig Masuch, chief executive of BMG Rights Management.

Spotify has 20 million users in 17 countries, with five million of them paying $5 to $10 a month to eliminate the ads seen by freeloaders.

In a recent interview, Sean Parker, a board member, said he believed Spotify would eventually attract enough subscribers to help return the music industry to its former glory — that is, to the days before Mr. Parker's first major enterprise, Napster, came along.

"I believe that Spotify is the company that will make it succeed," said Mr. Parker, who is also a former president of Facebook. "It's the right model if you want to build the pot of money back up to where it was in the late '90s, when the industry was at its peak. This is the only model that's going to get you there."

The former security official, Gen. Oleksei Pukach, who once headed a surveillance department for Ukraine's Interior Ministry, testified that he had not intended to kill Mr. Gongadze, but strangled him with a belt accidentally in the course of an interrogation. He is the highest-ranking official to be convicted in Mr. Gongadze's death.

Mr. Gongadze went missing in September 2000 and his body was found two months later, beheaded, in a forest 75 miles from Kiev, the capital. He had infuriated the president, Mr. Kuchma, with muckraking publications in Ukrainskaya Pravda, an Internet newspaper he had founded.

Suspicions of official involvement grew with the release of covert recordings made by one of Mr. Kuchma's bodyguards, in which the a man who sounded like the president spoke of Mr. Gongadze, telling a subordinate to "throw him out, give him to the Chechens."

The killing came to epitomize the role that crime had come to play in Ukrainian politics and provoked a wave of demonstrations that some describe as the first manifestation of the 2004 Orange Revolution.

Three former police officers who stood trial over Mr. Gongadze's death said that he had climbed into what he believed to be a taxi and was taken to a location outside Kiev, where he was beaten and strangled, doused with gasoline and burned.

General Pukach said he had been trying to force Mr. Gongadze to confess to espionage, something Mr. Gongadze refused to do, though he did admit accepting $400,000 from Western diplomats for passing on information.

Volodymyr Shilov, a prosecutor, said that General Pukach had testified that he was carrying out an order, but would not say what the order was or who issued it, according to the Interfax news agency. But just before guards took him away on Tuesday, General Pukach gave a revealing response to journalists who asked him to comment on the verdict, telling them to direct their questions to Mr. Kuchma and his chief of staff, Volodymyr Lytvyn.

"Ask Kuchma and Lytvyn, they'll tell you everything," he said, according to Interfax. "I told everything during the investigation and trial. So ask Lytvyn and Kuchma about their motives and intentions."

The trial was mostly closed to journalists, who were allowed to be present only for the verdict and sentencing. But a lawyer representing Mr. Gongadze's widow complained that the investigation and trial were flawed and inconsistent, overlooking evidence that General Pukach had intended to kill Mr. Gongadze.

"He spoke clearly about receiving an order to kill burn and bury him, and he was prepared for this," said the lawyer, Valentyna Telychenko, in comments broadcast on television. "He brought a shovel and a canister of gasoline, meaning his actions were directed toward murder, and nothing else."

General Pukach testified that he had been ordered to conduct surveillance by Ukraine's interior minister — a man who was found dead in 2005, hours before he was to be questioned by prosecutors in the matter. Officials called it a suicide, though Ukrainian news agencies said he had suffered two gunshot wounds.

Miami New Times, in a report released Tuesday, said that a former employee of the clinic, which is now closed, had provided it with medical records from the facility that tie Rodriguez, Melky Cabrera, Gio Gonzalez, Bartolo Colon, Nelson Cruz and Yasmani Grandal to the use of performance-enhancers.

Cabrera, Colon and Grandal were suspended in the past year by baseball for positive drug tests. Gonzalez and Cruz have not previously been linked to the use of performance-enhancers. Rodriguez, who is now recovering from hip surgery, has admitted to using performance-enhancers from 2001 to 2003, when he was a member of the Texas Rangers.

Rodriguez made that admission in the spring of 2009. Since then, he has been questioned by investigators for Major League Baseball in several instances about possible drug links. In those interviews, he always maintained that he did not use performance-enhancers after 2003.

Now, according to two people in baseball, the investigators plan to question Roidriguez again, along with the others cited in the Miami New Times report, which even cites the actual shorthand notations the clinic made in distributing drugs to its baseball clients.

Until now, Major League Baseball did not have any documents that linked players using the clinic to performance-enhancers. The investigators, the two people said, will now seek to obtain the records cited by Miami New Times and authenticate them in the hopes of using them as evidence to discipline the players.

Baseball first became aware of the clinic in 2009 when its investigators uncovered evidence that the slugger Manny Ramirez had received a banned drug from the facility. Ramirez was ultimately suspended 50 games for that infraction.

Last summer the investigators began to take another look at the clinic as they investigated Cabrera after he tested positive. In the course of that investigation they uncovered evidence that an employee for Cabrera's agents, Sam and Seth Levinson, had hatched a cover-up scheme to deceive a baseball arbitrator and have the suspension for the positive drug test thrown out.

Baseball officials were angered by the attempt to subvert their drug-testing program and began their own investigation of the employee, Juan Nunez, and the Levinsons. In doing so, the two people said, they uncovered the links between players and the clinic. The officials did not believe that Nunez acted alone and asked the players union, which certifies player agents, to conduct their own investigation.

According to one baseball official, six of the players the commissioner's office believes were treated by the clinic are clients of the Levinsons.

Rodriguez is not, but the 37-year-old third baseman will undoubtedly become the focal point of the case. He is not expected to return to action from his surgery until July, when he will turn 38. He has become increasingly brittle just midway through a 10-year, $275 million contract that has become a burden to the Yankees and his link to the medical records will only raise more questions about his future.