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Tokyo ( ˈtoʊkioʊ , Japanese : toːkʲoː ) , officially Tokyo Metropolis , is the capital city of Japan and one of its 47 prefectures .
Tokyo ( ˈtoʊkioʊ , Japanese : toːkʲoː ) , officially Tokyo Metropolis , is the capital city of Japan .
Tokyo ( ˈtoʊkioʊ , Japanese : toːkʲoː ) , officially Tokyo Metropolis , is one of its 47 prefectures .

The Greater Tokyo Area is the most populous metropolitan area in the world .

It is the seat of the Emperor of Japan and the Japanese government .
It is the seat of the Emperor of Japan .
It is the seat of the Japanese government .

Tokyo is in the Kantō region on the southeastern side of the main island Honshu and includes the Izu Islands and Ogasawara Islands .
Tokyo is in the Kantō region on the southeastern side of the main island Honshu .
Tokyo includes the Izu Islands .
Tokyo includes Ogasawara Islands .

Formerly known as Edo , it has been the de facto seat of government since 1603 when Shogun Tokugawa Ieyasu made the city his headquarters .

It officially became the capital after Emperor Meiji moved his seat to the city from the old capital of Kyoto in 1868 ; at that time Edo was renamed Tokyo .

Tokyo Metropolis was formed in 1943 from the merger of the former Tokyo Prefecture ( 東京府 Tōkyō - fu ) and the city of Tokyo ( 東京市 Tōkyō - shi ) .
Tokyo Metropolis was formed in 1943 from the merger of the former Tokyo Prefecture ( 東京府 Tōkyō - fu ) .
Tokyo Metropolis was formed in 1943 from the merger of the city of Tokyo ( 東京市 Tōkyō - shi ) .

Tokyo is often referred to as a city , but is officially known and governed as a " metropolitan prefecture " , which differs from and combines elements of a city and a prefecture , a characteristic unique to Tokyo .
Tokyo is often referred to as a city .
Tokyo is officially known as a " metropolitan prefecture " , which differs from of a city , a characteristic unique to Tokyo .
Tokyo is officially known as a " metropolitan prefecture " , which differs from of a prefecture , a characteristic unique to Tokyo .
Tokyo is officially known as a " metropolitan prefecture " , which combines elements of a city , a characteristic unique to Tokyo .
Tokyo is officially known as a " metropolitan prefecture " , which combines elements of a prefecture , a characteristic unique to Tokyo .
Tokyo is officially governed as a " metropolitan prefecture " , which differs from of a city , a characteristic unique to Tokyo .
Tokyo is officially governed as a " metropolitan prefecture " , which differs from of a prefecture , a characteristic unique to Tokyo .
Tokyo is officially governed as a " metropolitan prefecture " , which combines elements of a city , a characteristic unique to Tokyo .
Tokyo is officially governed as a " metropolitan prefecture " , which combines elements of a prefecture , a characteristic unique to Tokyo .

The Tokyo metropolitan government administers the 23 Special Wards of Tokyo ( each governed as an individual city ) , which cover the area that was the City of Tokyo before it merged and became the metropolitan prefecture in 1943 .
The Tokyo metropolitan government administers the 23 Special Wards of Tokyo ( each governed as an individual city ) , which cover the area that was the City of Tokyo before it merged .
The Tokyo metropolitan government administers the 23 Special Wards of Tokyo ( each governed as an individual city ) , which cover the area that was the City of Tokyo before it became the metropolitan prefecture in 1943 .

The metropolitan government also administers 39 municipalities in the western part of the prefecture and the two outlying island chains .
The metropolitan government also administers 39 municipalities in the western part of the prefecture .
The metropolitan government also administers 39 municipalities in the two outlying island chains .

The population of the special wards is over 9 million people , with the total population of the prefecture exceeding 13 million .

The prefecture is part of the world 's most populous metropolitan area with upwards of 37.8 million people and the world 's largest urban agglomeration economy .
The prefecture is part of the world 's most populous metropolitan area with upwards of 37.8 million people .
The prefecture is part of the world 's most populous metropolitan area with the world 's largest urban agglomeration economy .

In 2011 , the city hosted 51 of the Fortune Global 500 companies , the highest number of any city in the world , at that time .

Tokyo ranked third ( twice ) in the International Financial Centres Development IndexEdit .

The city is also home to various television networks such as Fuji TV , Tokyo MX , TV Tokyo , TV Asahi , Nippon Television , NHK and the Tokyo Broadcasting System .
The city is also home to various television networks such as Fuji TV .
The city is also home to various television networks such as Tokyo MX .
The city is also home to various television networks such as TV Tokyo .
The city is also home to various television networks such as TV Asahi .
The city is also home to various television networks such as Nippon Television .
The city is also home to various television networks such as NHK .
The city is also home to various television networks such as the Tokyo Broadcasting System .

Finnish police reprimanded a man for traveling in a car boot to hide his meeting with Prime Minister Juha Sipila during a government crisis last summer , saying this was breach of the traffic code .

A police statement did not name the man in the boot , but in effect indicated the traveler was State Secretary Samuli Virtanen , who is also the deputy to Foreign Minister Timo Soini .
A police statement did not name the man in the boot .
A police statement in effect indicated the traveler was State Secretary Samuli Virtanen , who is also the deputy to Foreign Minister Timo Soini .

The meeting took place in June , a day after Virtanen 's co-ruling Finns party had elected anti-immigration hardliners as its new leaders .

The government was close to collapse until a group of politicians , including Virtanen and Soini , in the following week walked out of the Finns party and announced they would form a new group .
The government was close to collapse until a group of politicians , including Virtanen , in the following week walked out of the Finns party .
The government was close to collapse until a group of politicians , including Virtanen , in the following week announced they would form a new group .
The government was close to collapse until a group of politicians , including Soini , in the following week walked out of the Finns party .
The government was close to collapse until a group of politicians , including Soini , in the following week announced they would form a new group .

The Finns party was thrown out of the government and the new '' Blue Reform '' group kept its cabinet seat .
The Finns party was thrown out of the government .
the new '' Blue Reform '' group kept its cabinet seat .

Virtanen has not commented on the case , but lawmaker Tiina Elovaara from Blue Reform said in a blog that Virtanen climbed into the boot to keep the meeting secret at a critical moment .
Virtanen has not commented on the case .
lawmaker Tiina Elovaara from Blue Reform said in a blog that Virtanen climbed into the boot to keep the meeting secret at a critical moment .

'' He avoided media attention when the situation was most serious , and the risk of leakage about the parliamentarians ' transition was too big , '' Elovaara said .
'' He avoided media attention when the situation was most serious , '' Elovaara said .
'' He avoided media attention when the risk of leakage about the parliamentarians ' transition was too big , '' Elovaara said .

Chilly Gonzales ( born Jason Charles Beck ; 20 March 1972 ) is a Grammy - winning Canadian musician who resided in Paris , France for several years , and now lives in Cologne , Germany .
Chilly Gonzales ( born Jason Charles Beck ; 20 March 1972 ) is a Grammy - winning Canadian musician who resided in Paris , France for several years .
Chilly Gonzales ( born Jason Charles Beck ; 20 March 1972 ) is a Grammy - winning Canadian musician who now lives in Cologne , Germany .

Known for his albums of classical piano compositions with a pop music sensibility , Solo Piano I and Solo Piano II , as well as his MC and electro albums , he is also a producer and songwriter .
Known for his albums of classical piano compositions with a pop music sensibility , Solo Piano I , as well as his MC albums , he is also a producer .
Known for his albums of classical piano compositions with a pop music sensibility , Solo Piano I , as well as his MC albums , he is also a songwriter .
Known for his albums of classical piano compositions with a pop music sensibility , Solo Piano I , as well as his electro albums , he is also a producer .
Known for his albums of classical piano compositions with a pop music sensibility , Solo Piano I , as well as his electro albums , he is also a songwriter .
Known for his albums of classical piano compositions with a pop music sensibility , Solo Piano II , as well as his MC albums , he is also a producer .
Known for his albums of classical piano compositions with a pop music sensibility , Solo Piano II , as well as his MC albums , he is also a songwriter .
Known for his albums of classical piano compositions with a pop music sensibility , Solo Piano II , as well as his electro albums , he is also a producer .
Known for his albums of classical piano compositions with a pop music sensibility , Solo Piano II , as well as his electro albums , he is also a songwriter .

Gonzales broadcasts a web series Pop Music Masterclass on WDR , the documentary Classical Connections on BBC Radio 1 , The History of Music on Arte , and Music 's Cool with Chilly Gonzales on Apple Music 's Beats 1 radio show .
Gonzales broadcasts a web series Pop Music Masterclass on WDR .
Gonzales broadcasts the documentary Classical Connections on BBC Radio 1 .
Gonzales broadcasts The History of Music on Arte .
Gonzales broadcasts Music 's Cool with Chilly Gonzales on Apple Music 's Beats 1 radio show .

He has written several newspaper and magazine opinion pieces in The Guardian , Vice , Billboard , and others .
He has written several newspaper opinion pieces in The Guardian .
He has written several newspaper opinion pieces in Vice .
He has written several newspaper opinion pieces in Billboard .
He has written several newspaper opinion pieces in others .
He has written several magazine opinion pieces in The Guardian .
He has written several magazine opinion pieces in Vice .
He has written several magazine opinion pieces in Billboard .
He has written several magazine opinion pieces in others .

He is the younger brother of the prolific film composer Christophe Beck .

Gonzales was born on 20 March 1972 .

His parents are Ashkenazi Jews who had to flee from Hungary during World War II .

Gonzales began teaching himself piano at age three , when his older brother Chris began taking lessons .

Gonzales graduated from Crescent School in Toronto , Ontario , Canada .

He was classically trained as a pianist at McGill University , where he began both his composing career , co-authoring several musicals with his brother , and his performing career , as a jazz virtuoso .
He was classically trained as a pianist at McGill University , where he began both his composing career , co-authoring several musicals with his brother .
He was classically trained as a pianist at McGill University , where he began both his performing career , as a jazz virtuoso .

In statistics , an expectation – maximization ( EM ) algorithm is an iterative method to find maximum likelihood or maximum a posteriori ( MAP ) estimates of parameters in statistical models , where the model depends on unobserved latent variables .
In statistics , an expectation – maximization ( EM ) algorithm is an iterative method to find maximum likelihood ) estimates of parameters in statistical models , where the model depends on unobserved latent variables .
In statistics , an expectation – maximization ( EM ) algorithm is an iterative method to find maximum a posteriori ( MAP ) estimates of parameters in statistical models , where the model depends on unobserved latent variables .

The EM iteration alternates between performing an expectation ( E ) step , which creates a function for the expectation of the log -likelihood evaluated using the current estimate for the parameters , and a maximization ( M ) step , which computes parameters maximizing the expected log - likelihood found on the E step .

These parameter - estimates are then used to determine the distribution of the latent variables in the next E step .

The EM algorithm was explained and given its name in a classic 1977 paper by Arthur Dempster , Nan Laird , and Donald Rubin .
The EM algorithm was explained in a classic 1977 paper by Arthur Dempster .
The EM algorithm was explained in a classic 1977 paper by Nan Laird .
The EM algorithm was explained in a classic 1977 paper by Donald Rubin .
The EM algorithm was given its name in a classic 1977 paper by Arthur Dempster .
The EM algorithm was given its name in a classic 1977 paper by Nan Laird .
The EM algorithm was given its name in a classic 1977 paper by Donald Rubin .

They pointed out that the method had been " proposed many times in special circumstances " by earlier authors .

A very detailed treatment of the EM method for exponential families was published by Rolf Sundberg in his thesis and several papers following his collaboration with Per Martin - Löf and Anders Martin - Löf .
A very detailed treatment of the EM method for exponential families was published by Rolf Sundberg in his thesis .
A very detailed treatment of the EM method for exponential families was published by Rolf Sundberg in several papers following his collaboration with Per Martin - Löf .
A very detailed treatment of the EM method for exponential families was published by Rolf Sundberg in several papers following his collaboration with Anders Martin - Löf .

The Dempster – Laird–Rubin paper in 1977 generalized the method and sketched a convergence analysis for a wider class of problems .
The Dempster – Laird–Rubin paper in 1977 generalized the method .
The Dempster – Laird–Rubin paper in 1977 sketched a convergence analysis for a wider class of problems .

Regardless of earlier inventions , the innovative Dempster – Laird – Rubin paper in the Journal of the Royal Statistical Society received an enthusiastic discussion at the Royal Statistical Society meeting with Sundberg calling the paper " brilliant " .

The Dempster – Laird –Rubin paper established the EM method as an important tool of statistical analysis .

After a year of relatively healthy global economic growth , economists are predicting pretty much the same for 2018 -- a neither too - hot nor too - cold Goldilocks scenario , but with little sight of the three bears .

The idea is that all is pretty much on track for growth that will be stronger than in 2017 .

Part of this may come from the fact that forecasters generally got it wrong last year , underclubbing this year 's economic performance , particularly for the euro zone and Japan .
Part of this may come from the fact that forecasters generally got it wrong last year , underclubbing this year 's economic performance , particularly for the euro zone .
Part of this may come from the fact that forecasters generally got it wrong last year , underclubbing this year 's economic performance , particularly for Japan .

The International Monetary Fund , for example , saw 2017 global growth at 3.4 percent with advanced economies advancing 1.8 percent .

It now reckons them at 3.6 percent and 2.2 percent .
It now reckons them at 3.6 percent .
It now reckons them at 2.2 percent .

It had the euro zone and Japan growing 1.5 percent and 0.6 percent , respectively .
It had the euro zone growing 1.5 percent , respectively .
It had the euro zone growing 0.6 percent , respectively .
It had Japan growing 1.5 percent , respectively .
It had Japan growing 0.6 percent , respectively .

It now has them at 2.1 percent and 1.5 percent .
It now has them at 2.1 percent .
It now has them at 1.5 percent .

'' Faster growth is reaching roughly two - thirds of the world 's population , '' the IMF said in a December blog post .

This performance has made some economists optimistic .

Nomura is among the more bullish : '' Global growth has far more self - reinforcing characteristics at present than at any time over the last 20 - 30 years . ''

There are huge numbers of potential political and economic risks to the status quo .
There are huge numbers of potential political risks to the status quo .
There are huge numbers of potential economic risks to the status quo .

But as in the fairy tale , let 's go with just three : central banks , trade , and bubbles .
But as in the fairy tale , let 's go with just three : central banks .
But as in the fairy tale , let 's go with just three : trade .
But as in the fairy tale , let 's go with just three : bubbles .

In the first case , the danger is that there will be a policy mistake , squeezing debtors .

The second relates to renewed U.S. protectionism or anger over Chinese exports triggering tit - for - tat , growth - stifling trade barriers .
The second relates to renewed U.S. protectionism triggering tit - for - tat , growth - stifling trade barriers .
The second relates to anger over Chinese exports triggering tit - for - tat , growth - stifling trade barriers .

The third is about sudden market losses that dry up spending and demand .
The third is about sudden market losses that dry up spending .
The third is about sudden market losses that dry up demand .