A radical Muslim killed a soldier outside Canada's Parliament.
A right-wing extremist opened fire on buildings in Texas' capital and tried to burn down the Mexican Consulate.
An Al-Qaida-inspired assailant hacked an off-duty soldier to death in London.
Police said all three were terrorists and motivated by ideology.
Authorities and family members said they may have been mentally ill.
A growing body of research suggests they might well have been both.
New studies have challenged several decades of thinking that psychological problems are only a minor factor in the making of terrorists.
The research has instead found a significant link between mental problems and "lone wolf" terrorism.
Now academics and law enforcement officials are working to turn that research into tools to prevent deadly attacks.
"It's never an either-or in terms of ideology versus mental illness," said Ramon Spaaij, a sociologist at Australia's Victoria University who conducted a major study, funded by the US Justice Department, of lone wolf extremists.
"It's a dangerous cocktail."
The study preceded Tuesday's ending of a 16-hour siege involving a gunman who took hostages in a cafe in Sydney.
The gunman, Iranian-born Man Haron Monis, was already facing charges including sexual assault and accessory to murder in separate cases, and his former lawyer said the standoff was "not a concerted terrorism event" but the work of "a damaged-goods individual.
