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.
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The research has instead found a significant link between mental problems and "lone wolf" terrorism.
"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.
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