Because our independent transcendentals act as indeterminates over, every permutation in the symmetric group on 5 letters induces an automorphism on that leaves fixed and permutes the elements.

Because no supernova is perfectly symmetric, the neutron star will be left with a small velocity relative to its original orbit.

Because of increased demand for symmetric services such as IP telephony, DOCSIS was revised to enhance upstream transmission speeds ; DOCSIS 2. 0 was released in December 2001.

( Because of the wider middle stripe and symmetric design, the design is sometimes classified as a " Canadian pale ".

Because of the antisymmetry-imposed restriction on possible rotational states, orthohydrogen has residual rotational energy at low temperature wherein nearly all the molecules are in the J = 1 state ( molecules in the symmetric spin-triplet state cannot fall into the lowest, symmetric rotational state ) and possesses nuclear-spin entropy due to the triplet state's threefold degeneracy.

Because of its double structure and symmetric tuning system, all the notes on one side of the bridge correspond to the lines of the musical staff and all the notes on the other side correspond to the staff spaces.

Because an RP is usually symmetric, horizontal and vertical lines correspond to each other, and, hence, only vertical lines are considered.

Because the P-array is 576 bits long, and the key bytes are XORed through all these 576 bits during the initialization, many implementations support key sizes up to 576 bits.

Because they lack this key defence, only 0. 5 % of cane toads are estimated to reach adulthood.

Because defining a GSSP depends on finding well-preserved geologic sections and identifying key events, this task becomes more difficult as one goes farther back in time.

Because of motivation's role in influencing workplace behavior and performance, it is key for organizations to understand and to structure the work environment to encourage productive behaviors and discourage those that are unproductive.

Because a magnet and sensor is required for each key, as well as custom control electronics, they are very expensive.

Because water is a key ingredient in beer it will not alter the flavor.

Because Ptolemy derived many of his key latitudes from crude longest day values, his latitudes are erroneous on average by roughly a degree ( 2 degrees for Byzantium, 4 degrees for Carthage ), though capable ancient astronomers knew their latitudes to more like a minute.

Because the principle allowing revocation authority for keys is very powerful, the mechanisms used to control it should involve both as many participants as possible ( to guard against malicious attacks of this type ), while at the same time as few as possible ( to ensure that a key can be revoked without dangerous delay ).

Because the key distinguishing characteristic Marsh noted for Pteranodon was its lack of teeth, any toothless pterosaur jaw fragment, wherever it was found in the world, tended to be attributed to Pteranodon during the late nineteenth and early twentieth centuries.

Because of the expansion of form ( those elements pertaining to form, key, instrumentation and the like ) within a typical composition, and the growing idiosyncrasies and expressiveness of the new composers from the new century, it thus became easier to identify an artist based on his work or style.

Because it presents essentially the same text in all three scripts ( with some minor differences between them ), it provided the key to the modern understanding of Egyptian hieroglyphs.

Because silent films had no synchronized sound for dialogue, onscreen intertitles were used to narrate story points, present key dialogue and sometimes even comment on the action for the cinema audience.

Because of this, the oligarchy that came into power after the " Meiji Restoration " of 1868 had a strong representation from the Satsuma province, with leaders such as Ōkubo Toshimichi and Saigō Takamori taking up key government positions.

Because of the key nature of DNA to living things, knowledge of DNA sequence may come in useful in practically any biological research.

Because the key is otherwise rarely used, programs that tie into other software often use it to prevent issues arising from both programs using the same key.

Because music written for early trumpets required the use of a different trumpet for each key — they did not have valves and therefore were not chromatic — and also because a player may choose to play a particular passage on a different trumpet from the one indicated on the written music, orchestra trumpet players are generally adept at transposing music at sight, sometimes playing music written for the B trumpet on the C trumpet, and vice versa.

Because volume measurements play a key role in titration, it is also known as volumetric analysis.

Because the trial of the Morgan conspirators was mishandled, and the Masons resisted further inquiries, many New Yorkers concluded that Masons " controlled key offices and used their official authority to promote the goals of the fraternity.

Because MORB basalt is considered a key to understanding plate tectonics, its compositions have been much studied.

Because it does not know the whole input, an online algorithm is forced to make decisions that may later turn out not to be optimal, and the study of online algorithms has focused on the quality of decision-making that is possible in this setting.

Because of this, many formulas in algorithms ( such as that for calculating hash table indices ) can be elegantly expressed in code using the modulo operation when array indices start at zero.

:" Because highly fit schemata of low defining length and low order play such an important role in the action of genetic algorithms, we have already given them a special name: building blocks.

Because of the astronomical number of possible cladograms, algorithms cannot guarantee that the solution is the overall best solution.

Because floating point versions of orthogonal matrices have advantageous properties, they are key to many algorithms in numerical linear algebra, such as QR decomposition.

* Because of the probabilities output, probabilistic pattern-recognition algorithms can be more effectively incorporated into larger machine-learning tasks, in a way that partially or completely avoids the problem of error propagation.

Because of the complexity of the optimization algorithms, most adaptive filters are digital filters.

Because of its tractability in practice, polynomial-time algorithms assuming the Riemann hypothesis, and other similar evidence, it was long suspected but not proven that primality could be solved in polynomial time.

Because there are fast algorithms for the DHT analogous to the fast Fourier transform ( FFT ), the DHT was originally proposed by R. N. Bracewell in 1983 as a more efficient computational tool in the common case where the data are purely real.

Because training sets are finite and the future is uncertain, learning theory usually does not yield guarantees of the performance of algorithms.

Because the traditional systolic array synthesis methods have been practiced by algebraic algorithms, only uniform arrays with only linear pipes can be obtained, so that the architectures are the same in all DPUs.

Because Python is currently implemented as an interpreter, mathematical algorithms written in it often run much more slowly than compiled equivalents.

Because indirection is a fundamental aspect of algorithms, pointers are often expressed as a fundamental data type in programming languages ; in statically ( or strongly ) typed programming languages, the type of a pointer determines the type of the datum to which the pointer points.

Because of the abundance of the sought strings, single-string searching algorithms are impractical.

Because of implementation costs, one may consider algorithms ( like those that follow ) that are similar to LRU, but which offer cheaper implementations.

Because modular exponentiation is an important operation in computer science, and there are efficient algorithms ( see above ) that are much faster than simply exponentiating and then taking the remainder, many programming languages and arbitrary-precision integer libraries have a dedicated function to perform modular exponentiation:

Because digital signature algorithms cannot sign a large amount of data efficiently, most implementations use a hash function to reduce (" compress ") the amount of data that needs to be signed down to a constant size.

Because computer algorithms and programs had been used as early as 1956 to test and validate mathematical theorems, such as the four color theorem, social scientists and systems dynamicists anticipated that similar computational approaches could " solve " and " prove " analogously formalized problems and theorems of social structures and dynamics.

Because these algorithms are only optimal in an asymptotic sense ( ignoring constant factors ), further machine-specific tuning may be required to obtain nearly optimal performance in an absolute sense.

Because of the versatility and power of modern re-identification algorithms, the absence of PII data does not mean that the remaining data does not identify individuals.

Because generic programming encourages simplifying interfaces to only what is required by the logic they support, the ITL algorithms resemble pseudocode, at least when compared with other implementations of the same algorithms.

Because Fast Infosets are compressed as part of the XML generation process, they are much faster than using Zip-style compression algorithms on an XML stream, although they can produce slightly larger files.