Republican presidential candidate Ted Cruz's calls to "patrol and secure Muslim neighborhoods" attracted harsh criticism from New York Police Commissioner Bill Bratton on Tuesday, as he and Mayor Bill de Blasio discussed safety at a news conference after the terror attacks in Brussels, Belgium.

Senator Cruz had suggested that more communities should implement programs like New York's now-defunct "Demographics Unit," which used plainclothes officers to closely observe Muslim communities. The program ended in April 2014 under harsh criticism, and was the subject of a federal lawsuit.

"Our European allies are now seeing what comes of a toxic mix of migrants who have been infiltrated by terrorists and isolated, radical Muslim neighborhoods," the candidate said, suggesting that the NYPD closed the unit for the sake of political correctness.

Commissioner Bratton condemned Cruz's remarks as un-American and disrespectful. "We don’t need a president that doesn’t respect the values that form the foundation of this country," he said, noting the presence of 900 Muslim officers in the NYPD. "Before he starts denigrating any population, he should take a close look at who he’s denigrating."

Politicians on both sides of the Atlantic have debated the best approach to reducing homegrown terrorist threats. Critics of hardline policing note both the logistical challenges and how such programs leave Muslim communities feeling isolated and discriminated against, possibly radicalizing frustrated young people.

"Ordering special patrols of Muslim neighborhoods will almost certainly create an adversarial relationship between law enforcement and the communities they have sworn to protect, making those communities more vulnerable, more frightened, and often less willing to help," said Jonathan Greenblatt, CEO of the Anti-Defamation League, to the Washington Post.

Focusing on prevention and outreach isn't being "politically correct," those critics say; it's shaping a long-term solution.

The federal Countering Violent Extremism strategy, or CVE, focuses on community buy-in, reaching out to influential neighborhood figures – including religious leaders, counselors, and family elders – to focus on finding and preventing radicalization.

"We begin with the premise that well-informed and well-equipped families, communities, and local institutions represent the best defense against violent extremist ideologies," says the Department of Homeland Security on the CVE homepage.

CVE "has to be local," said Humera Khan, who designs CVE programs and directed a review of the State Department's CVE plans, in a 2012 interview with Wired. "You have to live there, know the community, know the context. If you’re coming from the outside and you tell them what they ought to do – it doesn’t work."

Pilot community policing programs in cities like Minneapolis, Boston, and Los Angeles have been testing the model.

One major challenge to such programs the lingering suspicion on the part of many Muslim Americans that "community policing" and "outreach" are just surveillance by another name.

But another problem undercuts both traditional suspect "tracking" and long-term prevention efforts: it's hard to predict who will become radicalized, or why.

"There is no standard recruit profile," concluded researchers in a December 2015 study of American ISIS sympathizers and related arrests. "There is also no silver bullet that will blunt ISIS’s allure."

And federal counterterrorism efforts that rely on inaccurate, oversimplified ideas of who presents a threat, say experts, turn commonplace Muslim behavior like mosque attendance, traditional clothing, or facial hair into suspicious "indicators."

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Although analysts struggle to determine what makes someone vulnerable to terrorist propaganda's appeals, many believe it is rooted in a search for community or meaning.

The goal of an intervention is to "harness the power of their significance quest," said Jocelyn Bélanger, a psychology professor at the University of Quebec who helped design the city's Center for the Prevention of Radicalization Leading to Violence, in a December interview with the Christian Science Monitor. "[Y]ou channel it into something positive."