Ditto for Dylann Roof, the racist who murdered nine African-American churchgoers in South Carolina in 2015, and Christopher Harper-Mercer, the angry young man who killed nine people at a community college in Oregon the same year.
Nor does anything in these criminals’ history — including domestic violence, like Mr. Kelley’s — serve to reliably predict their spectacularly cruel acts. Even if spree killers have committed domestic violence disproportionately more often — and this assertion is in dispute — the vast majority of men who are guilty of that crime never proceed to mass murder.
Most mass murderers instead belong to a rogue’s gallery of the disgruntled and aggrieved, whose anger and intentions wax and wane over time, eventually curdling into violence in the wake of some perceived humiliation.
“In almost all high-end mass killings, the perpetrator’s thinking evolves,” said Kevin Cameron, executive director of the Canadian Center for Threat Assessment and Trauma Response.
“They have a passing thought. They think about it more, they fantasize, they slowly build a justification. They prepare, and then when the right set of circumstances comes along, it unleashes the rage.”
This evolution proceeds rationally and logically, at least in the murderer’s mind. The unthinkable becomes thinkable, then inevitable.
Researchers define mass killings as an event leaving four or more dead at the same place and time. These incidents occur at an average of about one a day across the United States; few make national headlines.
At least half of the perpetrators die in the act, either by committing suicide (Mr. Kelley is said to have shot himself in the head) or being felled by police.
Analyzing his database, Dr. Stone has concluded that about 65 percent of mass killers exhibited no evidence of a severe mental disorder; 22 percent likely had psychosis, the delusional thinking and hallucinations that characterize schizophrenia, or sometimes accompany mania and severe depression. (The remainder likely had depressive or antisocial traits.)
Among the psychotic, he counts Jared Loughner, the Arizona man who shot Rep. Gabrielle Giffords, Democrat of Arizona, and 18 others in 2011. By most accounts, including his own, Mr. Loughner was becoming increasingly delusional.
Adam Lanza, who in 2012 killed 26 people at Sandy Hook Elementary in Newtown, Conn., exhibited extreme paranoia in the months leading up to his crime, isolating himself in his room.
But what to make of John Robert Neumann Jr., who in June shot and killed five former co-workers at a warehouse in Orlando before turning the gun on himself? Mr. Neumann was not overtly psychotic, as far as anyone knows, and this is far more typical of the men who commit mass killings generally.
“The majority of the killers were disgruntled workers or jilted lovers who were acting on a deep sense of injustice,” and not mentally ill, Dr. Stone said of his research.
In a 2016 analysis of 71 lone-actor terrorists and 115 mass killers, researchers convened by the Department of Justice found the rate of psychotic disorders to be about what Dr. Stone had discovered: roughly 20 percent.
The overall rate of any psychiatric history among mass killers — including such probable diagnoses as depression, learning disabilities or A.D.H.D. — was 48 percent.
About two-thirds of this group had faced “long-term stress,” like trouble at school or keeping a job, failure in business, or disabling physical injuries from, say, a car accident.
Substance abuse was also common: More than 40 percent had problems with alcohol, marijuana or other drugs.
Looking at both studies, and using data from his own work, J. Reid Meloy, a forensic psychologist who consults with the F.B.I., has identified what he believes is a common thread: a “paranoid spectrum,” he calls it.
At the extreme end is full-on psychosis of the Loughner variety. But the majority of people on this spectrum are not deeply ill; rather, they are injustice collectors. They are prone to perceive insults and failures as cumulative, and often to blame them on one person or one group.
“If you have this paranoid streak, this vigilance, this sense that others have been persecuting you for years, there’s an accumulation of maltreatment and an intense urge to stop that persecution,” Dr. Meloy said.
“That may never happen. The person may never act on the urge. But when they do, typically there’s a triggering event. It’s a loss in love or work — something that starts a clock ticking, that starts the planning.”
Mental health treatment might make a difference for the one in five murderers who have severe mental disorders, experts say. Prevention is also possible in a few other cases — for instance, if the perpetrators make overt threats and those threats are reported.
But other factors must be weighed.
“In my large file of mass murders, if you look decade by decade, the numbers of victims are fairly small up until the 1960s,” said Dr. Stone. “That’s when the deaths start going way up. When the AK-47s and the Kalashnikovs and the Uzis — all these semiautomatic weapons, when they became so easily accessible.”
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The blaze ripped through part of the secret service facility in Yasenevo, Moscow.
Local media reported 15 fire crews had been sent to battle the flames.
Workers were evacuated as the fire raged.

It is thought the fire affected a two-storey building in the complex, situated on the outskirts of Moscow.
Colonel Sergei Ivanov, a spokesman for the spy agency, later said the fire happened at one of the service’s “technical installations.
He later said the fire had been extinguished, and there were no casualties.
Russian media, quoting unnamed sources in the emergency services, said that the fire broke out in a cable gallery under the spy service’s headquarters.

The job was made more complex by the fact that mobile communication is blocked at the centre.
The country’s Foreign Intelligence Service, a successor to the KGB, is the centre for the regime’s spy network, directing espionage activities outside the country.
Its building complex has doubled in size in recent years.
The service is led by Mikhail Fradkov, an ex-diplomat who is thought to have served with the KGB.

More than a decade before he became Donald Trump’s campaign chairman, Paul Manafort started advising another future president, Viktor Yanukovych of Ukraine. That relationship would lead him into a network of Russian and pro-Russian business and political interests, netting him millions of dollars.
On Monday, it led to his surrender to the FBI to face criminal charges in the widening investigation into the Trump campaign’s connections to Russian meddling in the 2016 election.
While the White House said that the indictment of Manafort and his longtime business partner had nothing to do with President Trump or his campaign, Manafort’s Ukrainian connections put him near the center of a political drama that experts say became a prelude to Russia’s eventual determination to interfere in the presidential election.
In interviews for the film Putin’s Revenge, FRONTLINE’s months-long investigation into the origins of Russia’s electoral meddling, former U.S. diplomats, intelligence officials, historians, and Russian and American journalists singled out protests in 2014 to oust Yanukovych as a pivotal moment for Russian President Vladimir Putin, who blamed the Obama administration for the unrest.
It  was in Ukraine, that Putin would test out a new type of “hybrid” warfare, a strategy combining diplomatic and military deception along with cyber attacks and efforts to sow confusion through propaganda and “fake news” – foreshadowing what would eventually transpire in the U.S. elections two years later.
As demonstrators marched on the Ukrainian capital, hackers intercepted a phone call between Assistant U.S. Secretary of State Victoria Nuland and the U.S. ambassador to Ukraine. On the call, Nuland appeared to signal a preference for a new government in Ukraine and uttered a profanity about the European Union, a key American ally during negotiations over the crisis.
Intercepting diplomatic communications was nothing new. But the subsequent leak of the conversation, experts said, was designed to create division between U.S. negotiators and the EU.
“Clearly they were looking to discredit me personally as the main negotiator at that time to thereby reduce U.S. influence,” Nuland told FRONTLINE.
“In retrospect, some people think we should have taken this a lot more seriously than we did … Because it was the first demonstration that Russia was willing and able to use techniques against the United States that it had previously not dared to attempt,”  Evan Osnos of The New Yorker said in an interview with FRONTLINE.
Ukraine would also become a testing ground for using disinformation as a weapon, most notably, in Putin’s denials after Russian forces moved into the Ukrainian territory of Crimea. The forces numbered in the thousands, and although they wore Russian-style combat uniforms, the uniforms lacked Russian insignia, providing the Kremlin a measure of deniability.
“This is a classic example of [Russia] using asymmetric tactics,” said Antony Blinken, who served as deputy secretary of state from 2015 to 2017. “It sent in small numbers of special forces who allied themselves with local separatists, gave them instruction, gave them equipment, gave them money, gave them direction, and then Putin denied their presence.”
“It was striking,” added Blinken. “We would be in the Oval Office, and the president would be on the phone with Putin, and Putin would be denying, and in fact, flat-out lying, about Russia’s presence in Ukraine. Obama would say to him, ‘Vladimir, we’re not blind. We have eyes. We can see.’ And Putin would just move on as if nothing had happened.”
Based on the success of his efforts in Ukraine, by the start of the 2016 election, Putin saw a ripe opportunity for intervention in the U.S. election, according to interviews for Putin’s Revenge.
One reason was Trump’s public praise of Putin and the involvement in the Trump campaign of officials with ties to Russia. These included Manafort, a longtime Republican political operative who had worked as a political consultant to Yanukovych and his pro-Russia Party of Regions.
Manafort was brought onto the Trump campaign in 2016 to help keep GOP delegates from breaking with Trump. Just three months later, he was promoted to the role of chief strategist and campaign manager. In August, Manafort was fired following reports about his business dealings in Ukraine, but not before raising Russia’s profile within the candidate’s team.
“Manafort has these connections to Putin-friendly forces in Eastern Europe, so the campaign suddenly started to reflect more of Manafort’s instincts than the disorienting Trump instincts on foreign policy that we saw earlier in the campaign,” said Robert Costa, a national political reporter for The Washington Post. “There wasn’t really a Russia view from Trump or his campaign team until the summer of 2016, the spring of 2016, when Manafort comes on.”
Manafort not only “spent years in Ukrainian politics,” he also “became close to Russian oligarchs,” according to Ryan Lizza, the Washington correspondent for The New Yorker. 
“If you’re Putin, you’re saying: ‘Huh, OK. This is a whole new team. This is not Hillary Clinton and her circle of anti-Putin hawks. This is a group of people that knows that region, is skeptical of NATO, and is probably willing to reach out to Moscow,’” said Lizza.
President Trump is now trying to distance himself from Manafort, saying in a tweet on Monday, “Sorry, but this is years ago, before Paul Manafort was part of the Trump campaign.” But the 31-page indictment alleges that for nearly a decade — including while he running the Trump campaign — Manafort and his longtime business partner, Rick Gates, used overseas shell companies to launder millions of dollars earned while lobbying on behalf of pro-Russian officials in the Ukrainian government. The two men were also charged with making false statements and other counts. Both have pleaded not guilty.
Putin and the Kremlin have denied any involvement in the U.S. election. But the case against Manafort and Gates is just part of the intensifying Russia probe, which now also includes the cooperation of a former foreign policy adviser to the Trump campaign, George Papadopoulos, who admitted lying to the F.B.I. about how he sought to meet with Russians offering “dirt” on Hillary Clinton.
Of particular interest to investigators will be what Trump officials knew about Papadopoulos’s contacts with Russians ahead of a June meeting at Trump Tower between Russians who were promising damaging information on Clinton and senior members of the Trump campaign, including the candidate’s eldest son and Manafort.
Court documents released Monday show that Papadopoulos informed members of the Trump campaign about his conversations with the Russians. What the documents leave out, however, is whether Papadopoulos informed campaign officials about a conversation in which he was told by that Moscow had “dirt” on Clinton in the form of “thousands of emails.”
Adam Schiff, the top Democrat on the House Intelligence Committee, told FRONTLINE that the Trump Tower meeting suggested that its members had previous knowledge about what the Russian government wanted to achieve.
“It’s significant because a whole context of the meeting was set up under the premise, ‘We have some dirt to give you on Hillary Clinton as a part of our effort to help elect Donald Trump,’” he said. “It was part of the Russian government’s effort to help Donald Trump. That suggests a prior relationship, prior work, prior communication about what the Russian government hopes an effort was designed to accomplish.”
In their initial response to the meeting, Trump officials did not say whether the presidential campaign was discussed, but maintained that the conversation focused “primarily” on the issue of Russian adoptions. The New York Times later reported that Trump officials attended the meeting after a trusted intermediary told Trump’s eldest son that a senior Russian government official was offering documents that “would incriminate Hillary … and would be very useful to your father.”
Donald Trump Jr. responded, “If it’s what you say I love it especially later in the summer.” Trump Jr. agreed to the meeting and said he would bring colleagues, including “Paul Manafort (campaign boss).