Asymptotically this method takes approximately two read operations and one write operation per item.Counting sort is an integer sorting algorithm that uses the prefix sum of a histogram of key frequencies to calculate the position of each key in the sorted output array.…

A scale-free network is a network whose degree distribution follows a power law, at least asymptotically.

Then that subtree is traversed depth first and the path labels of each of its nodes is updated.As described above, this asymptotically takes no longer than the usual rebuilding operation.…

The ambient construction is canonical in the sense that it is performed only using the conformal class of the metric: it is conformally invariant.However, the construction only works asymptotically, up to a certain order of approximation.There is, in general, an obstruction to continuing this extension past the critical order.…

If a system containing gravitational sources is surrounded by an infinite vacuum region, the geometry of the space-time will tend to approach the flat Minkowski geometry of special relativity at infinity.Such space-times are known as "asymptotically flat" space-times.For systems in which space-time is asymptotically flat, the ADM and Bondi energy, momentum, and mass can be defined.…

The escape time has been the subject of a number of studies using the small gate as an asymptotically small parameter.

A common life analog is standing in a line or queue waiting for the checkout in a grocery store.If the line asymptotically grows longer and longer without bound, the checkout process is not real-time.If the length of the line is bounded, customers are being "processed" and output as rapidly, on average, as they are being inputted and that process is real-time.…

In some models the distribution of t-statistic is different from normal, even asymptotically.For example, when a time series with unit root is regressed in the augmented Dickey-Fuller test, the test t-statistic will asymptotically have one of the Dickey-Fuller distributions (depending on the test setting).…

This is the technical meaning of "external universe".These points are only defined in an asymptotically flat universe.An absolute horizon is defined as the boundary of a region from which null rays cannot escape to future null infinity.…

For asymptotically faster operations, a different data structure is needed.

Scale-free networks: A scale-free network is a network whose degree distribution follows a power law, at least asymptotically.In network theory a scale-free ideal network is a random network with a degree distribution that unravels the size distribution of social groups.…

In a continuous linear time-invariant system, this is the case if and only if the real part of every pole in the system's transfer-function is non-positive, and all poles with zero real value are simple roots (i.e. the poles on the imaginary axis are all distinct from one another).If all the poles have strictly negative real parts, the system is instead asymptotically stable.If one or more poles have positive real parts, the system is unstable.…

If this function is negative, the theory is asymptotically free.

If there is an ideal money which can be stable in a very long period, we do not really need to worry about lots of problems in the longrun.Asymptotically ideal money is the currency close to but still not ideal money.…

The condition of asymptotic flatness is analogous to similar conditions in mathematics and in other physical theories.Such conditions say that some physical field or mathematical function is asymptotically vanishing in a suitable sense.In general relativity, an asymptotically flat vacuum solution models the exterior gravitational field of an isolated massive object.…

The following table is taken from Schrijver (2004).A green background indicates an asymptotically best bound in the table.The all-pairs shortest path problem finds the shortest paths between every pair of vertices, in the graph.…

Key-independent optimality has been proved to be asymptotically equivalent to the working set theorem.Splay trees are known to have key-independent optimality.…

Thus, if the mean is intended as a measure of the location of the center of the data, it is, in a sense, biased when outliers are present.Also, the distribution of the mean is known to be asymptotically normal due to the central limit theorem.However, outliers can make the distribution of the mean non-normal even for fairly large data sets.…

Blum's speedup theorem shows that there exist artificially constructed problems with speedup.However, it is an open problem whether many of the most well-known algorithms today are asymptotically optimal or not.…

In the simple picture of stellar collapse leading to formation of a black hole, an event horizon forms before an apparent horizon.As the black hole settles down, the two horizons approach each other, and asymptotically become the same surface.If the AH exists, it is necessarily inside of the EH.…