NEW YORK » In Canada and Australia, young men inspired by the bloody, apocalyptic vision of the Islamic State were thwarted in their efforts to join the battle in Syria, so they took up arms in their homelands, staging small attacks that drew widespread attention.

In London, Mohammed Emwazi was known for years to be sympathetic to the message of Islamic extremists, and by 2013 he had joined the militants on the Islamic State in Syria. Now he is better known as "Jihadi John," the black-masked figure who has appeared in numerous beheading videos.

In stark contrast, two young men in New York who were similarly enthralled by the Islamic State’s vision and who the government claims wanted nothing more than to join the fight, were arrested before they could make it to the desert.

In all of these cases, the suspects were known to the authorities. But only in New York were the suspects arrested, accused of pledging support for the Islamic State and trying to leave the country.

As officials around the world grapple with the emerging security concerns posed by the Islamic State and its sympathizers, the New York case provides one of the first public examples of how officials in the United States are approaching the threat.

The decision to arrest the men highlights the evolving challenges confronting law enforcement as officials calculate whether and when to intervene in instances of what some have begun calling "known wolves."

There are "lone wolves and known wolves," said a law enforcement official, who spoke on the condition of anonymity because of the continuing investigation. "A lone wolf is someone who comes out of the woodwork; a known wolf is on your radar."

The challenge posed by recruits for the Islamic State, also known as ISIS, is different in significant ways from what law enforcement previously confronted, and it potentially shifts the equation when it comes to dealing with people the authorities are already monitoring.

Dating back to the bombing of the World Trade Center in 1993, the focus of much of the counterterrorism apparatus in New York was on finding and breaking up secretive cells.

Terrorism plots that have been thwarted have included plans to blow up the Brooklyn Bridge, destroy bridges and tunnels and kill scores of people in Times Square.

Now, officials said, it is not that large-scale, al-Qaida-style attacks are no longer a concern, but that the more diffuse threats posed by Islamic State recruits mean their intelligence-gathering and counterterrorism methods must adapt accordingly.

When the Islamic State issued an edict for Westerners to join the fight, it explicitly told those who could not travel to Syria to kill wherever and however they could.

"Do not ask for anyone’s advice and do not seek anyone’s verdict," an Islamic State representative, Abu Muhammad Adnani, said in a 42-minute video posted online in September.

It would not be hard for anyone heeding those words to act with little warning. For the New York Police Department, what might have been seen as simply the ravings of an unstable individual might now require closer scrutiny.

When a man attacked police officers with a hatchet in Queens in October, the police said he had spent time online looking at the videos of killings done in the name of the Islamic State, and they may have helped push him to act.

Similarly, the radicalization of the two men in Brooklyn and their willingness to act on their desires expressed online, officials said, show how quickly aspirations can turn to reality.

What is also clear is that some of the most sophisticated recruitment efforts by the Islamic State, particularly online, are geared toward Westerners, featuring speakers who are fluent in English.

For instance, in a video available on YouTube and Facebook, the Islamic State has manipulated the video game Grand Theft Auto, making the game’s officers look like New York police officers and showing how a militant could attack them.

That has forced law enforcement officials to shift their strategies, resources and use of time.

"You have to focus much more broadly on, ‘Where is ISIS going to put the message out?’ And look into those places to see who seems to be looking to act on that message," the law enforcement official said. "You’ve got a lot more people looking at social media."

The case against the Brooklyn suspects, in fact, focuses heavily on their online activities.

Abdurasul Hasanovich Juraboev, 24, worked in a gyro shop, chopping lettuce and tomatoes 10 hours a day, six days a week. Akhror Saidakhmetov, 19, worked at cellphone repair kiosks. The men shared an apartment, according to the authorities, as well as a desire to fight for the Islamic State.

In August, Juraboev posted a message on a website sympathetic to the Islamic State, pledging his allegiance and saying he would attack President Barack Obama if ordered to do so, according to court documents.

But if he had not invoked the name of the president, officials said, he may never have been on their radar.

"If you didn’t pick up the phone, if you didn’t go on the Internet, you didn’t use technology, you’re virtually undetectable," a second law enforcement official said, speaking anonymously in order to discuss the investigation.

Although it is unclear exactly how the authorities discovered Juraboev’s posting, they took it seriously enough to visit him twice.

Then they had a decision to make.

"We could have arrested the guy the day he threatened the president," the first law enforcement official said. "But then, they would have learned nothing else about any possible network. How people and money moved and what else might be unearthed."

Ideally, the official said, "we would have let that case go potentially for a longer period if it helped us develop a better understanding."

When one of the men went to Kennedy International Airport to board a plane, the authorities decided they "could not let him go. He might get overseas, receive training, become hardened or proficient, and possibly do harm there or come back," the first official said.

That many of the recent attacks against Western targets have involved "known wolves" may reflect the fact that, in some ways, the number of people considered of concern nowadays is overwhelming.

There are reportedly from 700,000 to 1 million names on the U.S. terrorism watch list alone. The sheer number inevitably affects law enforcement’s new calculus as well. To track all of these potential threats, here or abroad, while taking time to gain additional intelligence, is unrealistic, said Rep. Adam Schiff, D-Calif., a member of the House Intelligence Committee.

"I suppose if you were completely confident in your ability to interdict people around the world, then you might let the plot mature a little further," Schiff said. "But I don’t think we can have that confidence."

In the end, officials said, deciding when to act is a judgment call.

On the surface, someone might not seem to have the means, methods or skills to pull off an attack. But if the goal is to attack a soft target to simply sow fear, the calculations by officials can change quickly.

"Nobody who ever got killed by a terrorist got killed by a terrorist who was not aspirational first," the first official said. "Ask the dead guys."

Marc Santora and Al Baker, New York Times

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