An 85-year old woman who was attacked in her own home was stabbed and might have been sexually assaulted.
The woman, who was found with life-threatening injuries at a house in Edinburgh's Morningside area on Friday, is in a critical but stable condition in hospital.
Police have released a description of a man they want to trace in connection with the attack.
Police Scotland's Detective Chief Inspector Keith Hardie said the attack, which is being treated as attempted murder, took place after the woman's husband left the house.
He said: "We are satisfied from the injuries sustained by our victim that she had been stabbed on numerous occasions. They are life-threatening injuries without a doubt.
"Her condition is described as critical but stable. She was possibly the victim of a blunt force trauma.
"She is also displaying injuries which may be consistent with some form of sexual attack.
"As a result of the door-to-door inquiries, we have identified a witness who saw a male standing outside the locus, we believe in the doorway, about 3.30pm on the Friday afternoon.
"That is clearly a crucial time for us because the victim's husband had left the house at that point, leaving our victim on her own."
The man is described as aged 18 to 30, of average build with short dark hair. Police are appealing for anyone who can help identify the man to come forward.
Officers in the area are continuing door-to-door inquiries and CCTV footage in the area is being examined.
Mr Hardie said the possibility of rape was "absolutely" being looked into as part of the inquiry.
The victim remains unconscious in Edinburgh Royal Infirmary and police said they have not been able to speak to her.
She was on her own in the house for around an hour and a half and was discovered in the living room by her husband on his return from the shops.
Her family were "shocked and traumatised" by the incident, Mr Hardie said.
He said: "In my experience within the service, I've never really heard of anything to this extent, of this nature - an attack on an elderly woman in the safety of her own house, a vicious attack, and plainly an attempt to take her life."
Mr Hardie said it was "unlikely" that the woman had been specifically targeted, saying he would not rule out the possibility that the perpetrator saw the husband leaving the house and thought it was empty.
He praised the response from the community, adding: "I would appeal to people if they have been in the area and have seen anything that's been even very, very slightly suspicious to get in touch, because it might be hugely significant to our ongoing inquiry."
Mr Hardie said nothing was being ruled out in the investigation.
He said: "We're dealing with undoubtedly an attempted murder, there's a potential sexual element to it and we can't rule out the possibility of a theft. Perhaps the lady has disturbed somebody carrying out a theft or something similar to that."
Chief Inspector Richard Horan reassured Morningside and Edinburgh residents that extra patrols were being carried out in the area, and said the response from the public had been "excellent".
He said: "People are obviously concerned for the victim, for their neighbour.
"I would say that crimes like this are incredibly rare and we will continue to try and reassure the community using every possible avenue.
"We do have extra police officers out on the street, we are able to attend and respond to any concerns people have, we will continue that as long as it takes as we progress the investigation towards detecting and arresting the perpetrator.
"If anyone has any concerns, if they see any suspicious activity, then feel free to contact us, either using the 101 number or, in an emergency, 999."