Such steep distributions on lower-dimensional manifolds pose problems to many other methods: Methods based on the estimation of mean and co-variance fail to describe the true shape of the distribution.
America has caused manifold problems while proving unable to solve any of them.
None of this worked especially well, and the Army has had to confront the manifold problems of the radicalized groups it helped to create, but which now question the legitimacy of Pakistan's own government and military.
I notice the air of apathy all the more, having been away for a couple of years as Guardian correspondent in West Africa, enjoying life in a region where, despite manifold problems, breaking the race barrier to the highest political office is not one.
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In recent years, foreign reporting of the country has often gone too far the other way, lauding India's economic growth with only occasional easy-to-spot regard to the country's manifold problems.Mr French is a fine reporter, with an appealing fascination for all things Indian, as his book makes clear.
In this formulation, the European central government is reduced, perhaps not unfairly, to little more than an instrument of global capital; in touch only with the managerial class and unable to provide a unified response to any of the manifold problems assailing Europe in 2016.
It is a comprehensive plan meant to provide solutions for Egypt's manifold problems: from an overhaul of the economy and security services to dealing with the sanitation problem of rubbish in the streets.
Its fragile coalition government is struggling to take the necessary decisions to tackle the country's manifold problems.
The pro-government camp itself is also potentially a source of unrest, divided as it is among a variety of personalities, ambitions and different opinions on how to tackle Ukraine's manifold problems.
