Therefore, given any positive integer n, it produces a string with Kolmogorov complexity at least as great as n. The program itself has a fixed length U. The input to the program GenerateComplexString is an integer n. Here, the size of n is measured by the number of bits required to represent n, which is log < sub > 2 </ sub >( n ).

For example, if the sorted list to which we apply binary search has n elements, and we can guarantee that each lookup of an element in the list can be done in unit time, then at most log < sub > 2 </ sub > n + 1 time units are needed to return an answer.

Berkeley DB's evolution has sometimes led to minor API changes or log format changes, but very rarely have database formats changed.

It has a log structured storage architecture, which gives it different performance and concurrency characteristics.

Conversely, if the data are sparse — that is, if only K out of N Fourier coefficients are nonzero — then the complexity can be reduced to O ( K log N log ( N / K )), and this has been demonstrated to lead to practical speedups compared to an ordinary FFT for N / K > 32 in a large-N example ( N = 2 < sup > 22 </ sup >) using a probabilistic approximate algorithm ( which estimates the largest K coefficients to several decimal places ).

The " Destroyed " log should only be used if there is evidence that the mark has been permanently destroyed.

Although somewhat slower in practice on most machines than a well-implemented quicksort, it has the advantage of a more favorable worst-case O ( n log n ) runtime.

The complexity penalty has a Bayesian interpretation as the negative log prior probability of,, in which case is the posterior probabability of.

The term " log " is used to measure the distance a vessel has moved through the water.

The expression Yule log has also come to refer to log-shaped Christmas cakes, also known as chocolate logs or Bûche de Noël.

The Yule log has frequently been associated with having its origins in the historical Germanic paganism which was practiced across northern Europe prior to Christianization.

The traditions of the Yule log died out in Britain in the latter 19th and early 20th century because of, according to historian Ronald Hutton, " the reduction in farm labour and the disappearance of the old-fashioned open hearths ", however the Bûche de Noël dessert has become a Christmas tradition in the UK, as in many French speaking places.

This popular sorting algorithm has an average-case performance of O ( n log n ), which contributes to making it a very fast algorithm in practice.

Similarly, Barry Hendy of Kodak Australia has plotted the " pixels per dollar " as a basic measure of value for a digital camera, demonstrating the historical linearity ( on a log scale ) of this market and the opportunity to predict the future trend of digital camera price, LCD and LED screens and resolution.

In telecommunication, a log-periodic antenna ( LP, also known as a log-periodic array or log periodic beam antenna / aerial ) is a broadband, multi-element, directional, narrow-beam antenna that has impedance and radiation characteristics that are regularly repetitive as a logarithmic function of the excitation frequency.

There has been a long tradition of decorating an iced cake at Christmas time ; other cakes associated with Christmas include chocolate log and mince pies.

Once a kit car has been correctly registered, a V5C, or log book, will be assigned and then a kit car is treated in exactly the same way as a production car, from any larger manufacturer.

However, a user might be able to circumvent the password by restarting the computer if the computer's owner has set their account to automatically log in upon startup.

It has two reconstructed log cabins, both from the local area being built c. 1790.

If X is a random variable with a normal distribution, then Y = exp ( X ) has a log-normal distribution ; likewise, if Y is log-normally distributed, then X = log ( Y ) has a normal distribution.

Altheimer has many pioneer-era log cabins, Victorian era homes and museums.

By contrast, IGBT has a diode like voltage drop ( typically of the order of 2V ) increasing only with the log of the current.

Herrick claimed that the fire used to burn the log was always started with a remnant from the log that had been burned in the previous year's festivities.

In the Batman: The Animated Series episode " Catwalk ", Catwoman throws a stuffed Tasmanian Tiger onto a log about to burn, and asks Batman, " The lady or the tiger, darling.

The operation log book, 4 May 1948, states " blow up the houses and burn all the bedouin tents ".

ALL BOATERS are encouraged to log on with VSRGs and TO REMEMBER TO LOG OFF ( Real people burn real fuel and leave real jobs to come look for you in their own time )-And if they do not wish to log on with VSRG ( e. g. they want to keep a fishing site private ) they may log on by phone privately OR are encouraged to log on / off with a relative or friend, so that at least someone knows their whereabouts.

Brown knows what he's looking for but took the liberty to burn the ship's log since he now owns 100 % of the antique store's inventory.

Eleazar, pausing on the Hanover plain, found its great forests and remoteness good and with his own hands built the first College Hall, a log hut dedicated `` for the education & instruction of Youth of the Indian Tribes in this Land in reading, writing & all parts of learning which shall appear necessary and expedient for civilizing & christianizing Children of Pagans as well as in all liberal Arts and Sciences ; ;

Lookup, insertion, and deletion all take O ( log n ) time in both the average and worst cases, where n is the number of nodes in the tree prior to the operation.

Some products log all sites that a user accesses and rates them based on content type for reporting to an " accountability partner " of the person's choosing, and the term accountability software is used.

Over all vertices, then, this takes O ( n log n ) time.

The best-known FFT algorithms depend upon the factorization of N, but there are FFTs with O ( N log N ) complexity for all N, even for prime N. Many FFT algorithms only depend on the fact that is an th primitive root of unity, and thus can be applied to analogous transforms over any finite field, such as number-theoretic transforms.

More precisely, all known FFT algorithms require Θ ( N log N ) operations ( technically, O only denotes an upper bound ), although there is no known proof that better complexity is impossible.

The single round log achieves this by being careful that the center of gravity remains well below the center of buoyancy at all times.

Sometimes k is presented as a constant, which would make radix sort better ( for sufficiently large n ) than the best comparison-based sorting algorithms, which are all O ( n · log ( n )).

In particular, under the common ( but sometimes implicit ) assumption that all keys are distinct, then k must be at least of the order of log ( n ), however other sorting methods become O ( log ( n ) * log ( n ) * n ) under similar constraints as they also need to step through an ever increasing number of symbols to do the comparisons.

All attempts to log in and order Joshua to cancel the countdown fail, and all weapons will launch if the computer is disabled.

He also said that the log's role was primarily one of bringing prosperity and protection from evil-by keeping the remnant of the log all the year long the protection was said to remain across the year.

If the check in operation succeeds, then the version numbers of all files involved automatically increment, and the CVS-server writes a user-supplied description line, the date and the author's name to its log files.

An empirical analysis of all prime pairs up to 4. 35 · 10 < sup > 15 </ sup > shows that if the number of such pairs less than < var > x </ var > is f (< var > x </ var >)·< var > x </ var >/( log < var > x </ var >)< sup > 2 </ sup > then f (< var > x </ var >) is about 1. 7 for small < var > x </ var > and decreases towards about 1. 3 as < var > x </ var > tends to infinity.

There is equal energy in all octaves ( or similar log bundles ).

Where E is the number of edges in the graph and V is the number of vertices, Kruskal's algorithm can be shown to run in O ( E log E ) time, or equivalently, O ( E log V ) time, all with simple data structures.

Both types log all keyboard activity to their internal memory, which can be subsequently accessed, for example, by typing in a secret key sequence.

Essentially, the diode tells the computer whether or not the player hit something, and for < var > n </ var > objects, the sequence of the drawing of the targets tell the computer which target the player hit after 1 + ceil ( log < sub > 2 </ sub >(< var > n </ var >)) refreshes ( one refresh to determine if any target at all was hit and ceil ( log < sub > 2 </ sub >(< var > n </ var >)) to do a binary search for the object that was hit ).

These lumberjacks, called tie hacks, used saws to fell trees and cut to length, and a broadaxe to flatten two or all four sides of the log to create railroad ties.

* a log of all operational events