Talks with other devolved leaders were held at Downing Street.
Queen Opens Fifth Session Of Scottish Parliament
The Queen has stressed the need for political leaders to make ''room for quiet thinking and contemplation'' to deal with developments in a ''fast-moving world''.
The monarch used her address at the opening of the fifth session of the Scottish Parliament to refer to ''increasingly complex and demanding'' times.
The opening ceremony was held just over a week after the UK voted to leave the EU - but Scotland's vote to stay prompted fresh fears over the future of the Union, with a second independence referendum now a real possibility.
The Queen said: ''Of course we all live and work in an increasingly complex and demanding world where events and developments can and do take place with remarkable speed, and retaining the ability to stay calm and collected can at times be hard.
''As this Parliament has successfully demonstrated over the years, one hallmark of leadership in such a fast-moving world is allowing sufficient room for quiet thinking and contemplation which can enable deeper consideration of how challenges and opportunities can be best addressed.''
Scotland's First Minister Nicola Sturgeon used her address to celebrate the country's diversity, highlighting the role of immigrants in Scotland past and present.
She also stressed Scotland's determination to ''play our part in a stronger Europe''.
At the ceremony, held to mark the new parliamentary session that is beginning after May's Holyrood election, she said that while MSPs come from ''a diverse variety of backgrounds all of us have been given the precious opportunity to contribute to building a better country and build it we will''.
Ms Sturgeon added: ''To do so we must be bold and ambitious, we must show courage and determination. Our collective commitment to the people of Scotland today is that we will not shy away from any challenge we face, no matter how difficult or deep rooted.''
She recalled that at the opening of the first Scottish Parliament in 1999, the late first minister Donald Dewar said the Holyrood institution ''is about more than our politics and our laws, this is about who we are, how we carry ourselves''.
The First Minister continued: ''So allow me to reflect on who we are in Scotland today. We are more than five million men and women, adults, young people and children, each with our own life story and family history, and our own hopes and dreams.
''We are the grandchildren and the great grandchildren of the thousands who came from Ireland to work in our shipyards and in our factories
''We are the 80,000 Polish people, the 8,000 Lithuanians, the 7,000 each from France, Spain, Germany, Italy and Latvia. We are among the many from countries beyound our shores that we are so privileged to have living here amongst us.
''We are the more than half a million people born in England, Wales and Northern Ireland who have chosen to live here in Scotland. We are the thousands of European students studying at our universities and our colleges. We are the doctors and nurses from all across our continent and beyond who care for us daily in our National Health Service.
''Whether we have lived here for generations or are new Scots, from Europe, India, Pakistan, Africa and countries across the globe we are all of this and more. We are so much stronger for the diversity that shapes us.
''We are one Scotland and we are simply home to all of those who have chosen to live here, that is who and what we are.''
As a nation Ms Sturgeon said ``we carry ourselves with dignity, we treat others with respect, we celebrate our differences''.
The First Minister added: ''We are not perfect, far from it, and we do make mistakes. But every day, especially in adversity or sadness, we should seek to offer a hand to our neighbour.''
She went on to stress the ``open and inclusive nation that we are, the open and inclusive nation we are determined to remain''.
Stefano Brizzi is accused of murdering the Scottish police officer.
It happened in the Govanhill area at lunchtime.
It's being treated as attempted murder.
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