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The wedge sum of k unit circles = is a (,), where is the free group on k generators. The complement to any connected knot or graph in a 3-dimensional sphere S 3 {\displaystyle S^{3}} is of type K ( G , 1 ) {\displaystyle K(G,1)} ; this is called the " asphericity of knots", and is a 1957 theorem of Christos Papakyriakopoulos .
The Barzilai-Borwein method [1] is an iterative gradient descent method for unconstrained optimization using either of two step sizes derived from the linear trend of the most recent two iterates. This method, and modifications, are globally convergent under mild conditions, [ 2 ] [ 3 ] and perform competitively with conjugate gradient methods ...
Limited-memory BFGS (L-BFGS or LM-BFGS) is an optimization algorithm in the family of quasi-Newton methods that approximates the Broyden–Fletcher–Goldfarb–Shanno algorithm (BFGS) using a limited amount of computer memory. [1] It is a popular algorithm for parameter estimation in machine learning.
WASHINGTON − Less than three days ago, House Republicans were well past their self-imposed deadline to come up with a blueprint to pass President Donald Trump's agenda through Congress. Now ...
Upon first approach, Republic Airways Flight 4514 diverts from course, circles around, and lands during a second attempt at Reagan National Airport.
Nvidia stock tanked on Monday, falling more than 17% and losing nearly $600 billion off its market cap as investors digested the growing popularity of a new cost-effective artificial intelligence ...
For a nilpotent group, the smallest n such that G has a central series of length n is called the nilpotency class of G; and G is said to be nilpotent of class n. (By definition, the length is n if there are + different subgroups in the series, including the trivial subgroup and the whole group.)
The presence of neurofibrillary tangles in the brain is one of the key hallmarks of Alzheimer’s disease. These irregular clumps of protein are closely associated with disease progression.