The attack occurred at about 9:50 pm, soon after the Tokaido Shinkansen line train left Tokyo Station.
The suspected attacker told police that he had attacked the passengers, according to Odawara police official Satoshi Oiye.
Police said two female passengers in their 20s were injured in the neck and other parts of their bodies, though their conditions were not life-threatening.
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Kudlow, who is a wry and upbeat speaker, has adopted some of Trump's hard-line rhetoric while working inside the West Wing. His recovery was a great source of pride for him and for his friends, contributing to his upbeat manner.
Kojima told police that he is unemployed and from Okazaki, Aichi Prefecture.
Kojima was holding a knife when police seized him at the station. At least two knives were found at the scene of the crime.
Under questioning, Kojima admitted to the allegations, saying he attacked the people because he was feeling frustrated and that the victims were chosen at random, according to the Kanagawa police.
Afterward, witnesses said some of the passengers were crying as they fled to the other coaches, shouting "Just keep going ahead", and "He has a knife!"
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Kudlow, an unabashed supporter of free trade, joined the Trump administration earlier this year. It was not immediately known when Kudlow suffered the heart attack or what his condition was.
"I have always been anxious about him", the woman said in a telephone interview with Kyodo News early Sunday. The Nozomi train was heading to Osaka from Tokyo.
He talked about suicidal thoughts before running away, she said.
The incident took place on a bullet train travelling west in the south of Tokyo, which was carrying 880 passengers. The train was carrying more than 800 passengers at the time of the incident.
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But Sessions recently called into question whether such cases merited protection under U.S. asylum laws. Asylum-seekers must also demonstrate that their home government is unwilling or unable to protect them.