These estimates provide an insight into reasonable directions of search for efficient algorithms.

These algorithms almost all rely on psychoacoustics to eliminate less audible or meaningful sounds, thereby reducing the space required to store or transmit them.

These can be implemented as analog circuits ( for instance, using a Sallen Key filter topology, a type of active filter ), or as algorithms in digital signal processing systems.

These brute-force algorithms are computationally manageable for n = 8, but would be intractable for problems of n ≥ 20, as 20!

These algorithms model diffuse inter-reflection which is a very important part of global illumination ; however most of these ( excluding radiosity ) also model specular reflection, which makes them more accurate algorithms to solve the lighting equation and provide a more realistically illuminated scene.

These algorithms are numerical approximations to the rendering equation.

These macros are similar to the algorithms in pseudocode typically used in teaching computer science.

These same interpolation formulas nevertheless continue to be used as part of the software algorithms for solving differential equations.

These algorithms take as input a large set of " features " that are generated from the input data.

These algorithms are not practicable for hand written computation, but are available in any Computer algebra system ( see Berlekamp's algorithm for the case in which the coefficients belong to a finite field or the Berlekamp – Zassenhaus algorithm when working over the rational numbers ).

These algorithms compute an estimate of the likely distribution of annihilation events that led to the measured data, based on statistical principles.

These leaves need not be explicit in computer memory — a null child pointer can encode the fact that this child is a leaf — but it simplifies some algorithms for operating on red – black trees if the leaves really are explicit nodes.

These algorithms first convert the SMILES to an internal representation of the molecular structure and do not simply manipulate strings as is sometimes thought.

These techniques are superficially comparable to weather models that show hurricane storm tracks ; each of several algorithms independently models a complex system ( the weather, in this case ) somewhat differently from each of its sister weather algorithms, and the average of all the algorithms ' output is taken to be the most likely " storm track ".

These algorithms do not work if out-of-order execution is utilized on the platform that executes them.

These asymmetric key algorithms allow one key to be made public while retaining the private key in only one location.

These algorithms use data compression to achieve higher throughput.

These algorithms arrange all particles in a tree, a quadtree in the two-dimensional case and an octree in the three-dimensional case.

These two algorithms form the basis for many variations including LZW, LZSS, LZMA and others.

These applications typically employ complex algorithms and data structures and require high performance.

These algorithms usually come in the form of a flowchart, incorporating ' yes / no ' type decisions, making the algorithm easier to memorize.

These specialists perform valuable services by helping teachers learn to identify children who need special attention, by suggesting ways of meeting the needs of individual children in the regular classroom, and by providing clinical services for severely maladjusted children.

These qualities are the ultimate source of human happiness, and the need for them lies at the very core of our being " ( Dalai Lama ).

These finishes protect the adobe wall from water damage, but need to be reapplied periodically, or the walls can be finished with other nontraditional plasters providing longer protection.

These songs were typically performed while adjusting the rigging, raising anchor, and other tasks where men would need to pull in rhythm.

These communities use extemporaneous forms of administration at the discretion of the minister, who need not be a pastor.

These teachings discuss the ministry and atonement of Jesus, the laws of justice and mercy, the need for repentance, and the resurrection and judgment of all people.

These buses often need to undergo a degree of vehicle restoration to restore them to their original condition, and will have their livery and other details such as internal notices and rollsigns restored to be authentic to a specific time in the bus's actual history.

These need not be greater numerical losses-if one side is much more numerous than the other than pursuing a strategy based on attrition can work even if casualties on both sides are about equal.

These do not need to be defeated to complete the level, and disappear once a player's life is lost.

These rest states need not be symmetric with respect to stored energy.

These damages need not be set forth in statute as they already exist in the tradition of common law.

These are bets that may not be settled on the first roll and may need any number of subsequent rolls before an outcome is determined.

These clutches had long operating lives, cycling for tens, maybe hundreds of millions of cycles without need of maintenance other than occasional lubrication with recommended oil.

These tubes didn't need gas in them to work, so they were evacuated to a lower pressure, around 10 < sup >− 9 </ sup > atm ( 10 < sup >− 4 </ sup > P ).

These have a lower infection risk, are much less prone to phlebitis or extravasation, and abolish the need for repeated insertion of peripheral cannulae.

These have more to do with the simplified models of bulk matter used, and in any case have nothing to do with general relativity, and need to be excluded.

These special circumstances need to be excluded by some hypothesis.

These programs in schools everywhere need a wide variety of clothes suited for the many productions they put on each year.

; Integrated data warehouse: These data warehouses assemble data from different areas of business, so users can look up the information they need across other systems.

These semiconductor radiation detectors need efficient and uniform charge collection and low leakage current.

These set-ups are taken for granted by the genre conventions, and need not be explained for the reader anew ... though it should also be noted that these elements can easily be treated subversively as well, playing with some of the preconceptions inherent in formula fiction.

These solutions are often ideally suited for users who only very occasionally need to use fax services.

These typically need to be close to where the children live, for practical logistics.

These used a small number of standard components, all small enough to be readily transportable in areas with poor or non-existent roads, and were joined together using bolts rather than rivets, reducing the need for skilled labour on site.