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In general, any measurable function can be pushed forward. The push-forward then becomes a linear operator, known as the transfer operator or Frobenius–Perron operator.In finite spaces this operator typically satisfies the requirements of the Frobenius–Perron theorem, and the maximal eigenvalue of the operator corresponds to the invariant measure.
The notion of pushforward in mathematics is "dual" to the notion of pullback, and can mean a number of different but closely related things.. Pushforward (differential), the differential of a smooth map between manifolds, and the "pushforward" operations it defines
Let : be a smooth map of smooth manifolds. Given , the differential of at is a linear map : from the tangent space of at to the tangent space of at (). The image of a tangent vector under is sometimes called the pushforward of by .
The president’s advisers, under the directive that he’s committed to staying in the race, huddle every day on a 9 a.m. call to discuss his path forward, including whether what the president is ...
Moving forward Making progress on an idea or scheme Move the goal posts Change the criteria for success [1] Pick the low-hanging fruit Go (initially) for the easiest options [1] Power to the elbow Get additional backup information to make your case stronger Pull the plug Close a venture that is losing money or has no prospects of success Punt
Positive feedback is used in digital electronics to force voltages away from intermediate voltages into '0' and '1' states. On the other hand, thermal runaway is a type of positive feedback that can destroy semiconductor junctions. Positive feedback in chemical reactions can increase the rate of reactions, and in some cases can lead to explosions.
A pure feed-forward system is different from a homeostatic control system, which has the function of keeping the body's internal environment 'steady' or in a 'prolonged steady state of readiness.' A homeostatic control system relies mainly on feedback (especially negative), in addition to the feedforward elements of the system.
A popular meme depicts a road diverging. In one direction is a many-towered palace glistening in the sunshine. In the other is a crumbling castle beset by storm clouds and eerie purple lightning.