Authorities are cracking down on a spate of threats against schools following Friday's attack at an elementary school in Newtown, Conn., where a gunman killed 20 children and six adults before killing himself.

In Indiana, police have responded to threats against three separate schools, making arrests in each case. They included a Bloomington South High School student who allegedly threatened a "copycat" school shooting; police removed six guns from his home, The AP reported. Two other teens, one in California, the other in Tennessee, who posted online that they would like to commit similar shootings were promptly arrested, CNN reported. Another teen in Tennessee was arrested after making phone calls to a local elementary school with a bomb threat.

Connecticut State Police Lt. J. Paul Vance said last week than anyone making threats would be investigated and prosecuted.

It's common for threats against schools to spike after a much-publicized shooting, and research has suggested there may be a link between how much attention an incident gets in the media and how many copycat threats follow.

In the 50 days after the Columbine High School shooting in 1999, more than 350 threats were reported at Pennsylvania schools, skyrocketing from the one or two threats reported in the same period a year earlier. A study, published in the Archives of Pediatrics & Adolescent Medicine in 1999, determined that the publicity Columbine received led to a spike in bomb and other threats on schools. A similar shooting a year earlier in Jonesboro, Ark., received a fraction of the media attention that Columbine did, and attracted many fewer copycat threats in the days following.

Based on this finding, the authors of the study urged the media to downplay coverage of shootings, not to portray the killers as "countercultural heroes," and not to describe in detail how the crime was committed.

Though a rise in threats following shootings has been documented, it's much less clear whether mass killings that attract intense media coverage lead people to attempt actual copycat attacks.

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In a paper published in 1999, Christopher Cantor and other researchers examined seven mass killings in Australia, the U.K. and New Zealand. They said they found a "ripple effect" linking some of the mass killings, where some murderers were inspired by coverage of other crimes to commit their own.

But criminology expert Ray Surette cautioned in his own study on copycat crime that "too few copycat criminals have been identified to allow for scientifically adequate research."

Surette's study of juvenile offenders in Florida, published in Crime & Delinquency in 2002, found that about a third of young prisoners had considered committing a crime that they had seen in the media—defined as TV, movies, news and music—and that a quarter of them had actually attempted to commit such a crime. But Surette had no way of knowing whether removing the media would have prevented those prisoners from committing their crimes in the first place.

In a 1984 study of prisoners in Butner, N.C., the researchers Susan Pease and Craig Love found that about 20 percent of prisoners said they had been influenced by either newspaper reports, TV news, TV shows or movies before committing a crime. TV news and newspaper reports ranked far lower than programs and movies as influencers, and almost all of the self-identified "copycat criminals" said they had the intent to commit a crime before they were influenced by media. (Some prisoners said they would watch TV crime programs and literally take notes in order to pick up on new techniques.) The lone exception was mentally ill patients, however, who did not necessarily have criminal intent before they said they were influenced by media before committing a crime.