Now it is easy to convince oneself that the set X could not possibly be measurable for any rotation-invariant countably additive finite measure on S. Hence one couldn't expect to find an algorithm to find a point in each orbit, without using the axiom of choice.

The choice of which element to remove from the input is arbitrary, and can be made using almost any choice algorithm.

The choice of embedding algorithm in the most cases is driven by the results of the steganographic channel robustness analysis.

The first level of protection is determined only by the choice of embedding algorithm.

The quantum circuits used for this algorithm are custom designed for each choice of N and the random a used in f ( x ) = a < sup > x </ sup > mod N. Given N, find Q = 2 < sup > q </ sup > such that < math > N ^ 2

The first phase is a choice of algorithm parameters which may be shared between different users of the system, while the second phase computes public and private keys for a single user.

Adoption of technical standards for digital signatures have lagged behind much of the legislation, delaying a more or less unified engineering position on interoperability, algorithm choice, key lengths, and so on what the engineering is attempting to provide.

This limits which data structures a given algorithm can be applied to and such complexity requirements are a major determinant of data structure choice.

As mentioned above, choice of individual assembler instructions ( or even sometimes just their order of execution ) on particular machines can affect the efficiency of an algorithm.

For instance, a class that performs validation on incoming data may use a strategy pattern to select a validation algorithm based on the type of data, the source of the data, user choice, and / or other discriminating factors.

In any recursive algorithm, there is considerable freedom in the choice of the base cases, the small subproblems that are solved directly in order to terminate the recursion.

The algorithm used may also be a modification of an existing algorithm and may be an important consideration in the choice of a dive computer.

Another common choice is to terminate when the best solution found by the algorithm has not been improved in a given number of steps.

The relative simplicity of the algorithm makes it a popular first choice amongst optimizing algorithms.

The algorithm may be easily modified to deal with collinearity, including the choice whether it should report only extreme points ( vertices of the convex hull ) or all points that lie on the convex hull.

Certain steps of the algorithms are " choice points ", points at which a variable can be given either of two different truth values, and later steps in the algorithm may cause it to backtrack to one of these choice points.

* If there is a clause in which both of the variables are set, in a way that falsifies the clause, then the algorithm backtracks to its most recent choice point, undoing the assignments it made since that choice, and reverses the decision made at that choice.

We now consider how the choice of description language affects the value of K, and show that the effect of changing the description language is bounded.

The way a CPU represents numbers is a design choice that affects the most basic ways in which the device functions.

The player's choice of civilization also prevents the computer from being able to play as that civilization or the other civilization of the same color, and since computer-controlled opponents display certain traits of their civilizations this affects gameplay as well.

The choice of modulation affects the cost and performance of a system and these two factors must be balanced carefully by the engineer.

Unlike the related battles over operating systems, programming languages, and even source code indent style, choice of editor usually only affects oneself.

The choice of switch technology affects key response ( the positive feedback that a key has been pressed ) and travel ( the distance needed to push the key to enter a character reliably ).

Monopolies, monopsonies and oligopolies are all situations such that one or a few of the entities have market power and therefore interact with their customers ( monopoly ), suppliers ( monopsony ) and the other companies ( oligopoly ) in a game theoretic manner – meaning that expectations about their behavior affects other players ' choice of strategy and vice versa.

However, whereas in Quake, the only option was to change the color of the player's uniform unless third party modifications were used, now the game comes with a selection of three different player models: a male marine, a female marine, and a male cyborg ; choice of player model also affects the speech effects the player's character will make, such as exhaling in effort while jumping or groaning when injured.

Externality: the basic idea is that an externality exists when a person makes a choice that affects other people that are not accounted for in the market price.

The latitude where the garlic is grown affects the choice of type as garlic can be day-length sensitive.

The terms heavy-weight and light-weight are often used to describe buildings with different thermal mass strategies, and affects the choice of numerical factors used in subsequent calculations to describe their thermal response to heating and cooling.

The choice of symbol for the decimal mark also affects the choice of symbol for the thousands separator used in digit grouping, so the latter is also treated in this article.

Note that the choice of a variable bitrate ( VBR ) method only affects the encoding process.

The choice of buffer also affects the electrophoretic mobility of the buffer counterions and thereby the resolution of the gel.

An example of how lens choice affects angle of view.

Note that the choice of concentration scale affects both the activity and the standard state chemical potential, which is especially important when the reference state is the infinite dilution of a solute in a solvent.

The choice of the aperture also affects image quality ( aberrations ) and depth of field ( see below ).

Gender choice is also a factor, which slightly affects stats.

; Monopoly: A monopoly is a price maker in that its choice of output level affects the price paid by consumers.

The plant life available in a region affects the choice of material, which in turn influences the weaving technique.

Whatever affects one directly, affects all indirectly … Anyone who lives inside the United States can never be considered an outsider …” King expressed his remorse that the demonstrations were taking place in Birmingham but felt that the white power structure left the black community with no other choice.

The measure of combat efficiency in an indecisive campaign is a matter of personal choice.

A good randomizing function is ( barring computational efficiency concerns ) generally a good choice as a hash function, but the converse need not be true.

Concepts and methods from economic science ( as rational choice, social choice or game theory ) have also been applied for understanding the efficiency of scientific communities in the production of epistemic outputs.

The consent takes the form of a compensation principle like Pareto efficiency for making a policy change and unanimity at least no opposition as a point of departure for social choice.

However, once the product reaches the point at which it does everything that it is designed to do, the manufacturer is left with the choice of adding unneeded functions, sometimes at the cost of efficiency, or sticking with the old version, at the cost of a perceived lack of improvement.

There are social choice theory definitions of seemingly reasonable criteria that are a measure of the fairness of certain aspects of voting, including non-dictatorship, unrestricted domain, non-imposition, Pareto efficiency, and independence of irrelevant alternatives but Arrow's impossibility theorem states that no voting system can meet all these standards.

For a discussion on how the choice of particular instructions available on a specific machine effect efficiency, see later section ' Choice of instruction and data type '.

Particularly in an Assembly language ( although also applicable to HLL statements ), the choice of a particular ' instruction ' or data type, can have a large impact on execution efficiency.

While this may affect the choice of an antenna, an antenna's impedance can also be adapted to the desired impedance level of a system using an matching network while maintaining the other characteristics ( except for a possible loss of efficiency ).

Because of a Schottky diodes ’ low forward voltage drop, less energy is wasted as heat making them the most efficient choice for applications sensitive to efficiency.

Designed with a Volcano shaped cook chamber for high efficiency, a draft ring to control air intake, the ability to collapse to form a very small footprint, and a carrying case make these an ideal choice for those who want more heat output than can typically be provided by portable stoves that use hexamine, trioxane or a fuel canister.

Its efficiency as a fire extinguishing agent has also led it to be the predominant choice of fire extinguishing agent on commercial aircraft and is typically found in cylindrical hand-held canisters.

Although there are different standards of evaluation for the concept of allocative efficiency, the basic principle asserts that in any economic system, choices in resource allocation produce both " winners " and " losers " relative to the choice being evaluated.

Numerous process parameters, such as preparation of the initial graphite powder, the choice of ultrasonic power, synthesis time and the solvent, are not yet optimized, leaving a window for potential improvement of the efficiency and reduction of the cost of the ultrasonic synthesis.

Such techniques are fast and efficient, however the original " purely parametric " formulation ( due to Kass and Terzopoulos in 1987 and known as " snakes "), is generally criticized for its limitations regarding the choice of sampling strategy, the internal geometric properties of the curve, topology changes ( curve splitting and merging ), addressing problems in higher dimensions, etc .. Nowadays, efficient " discretized " formulations have been developed to address these limitations while maintaining high efficiency.

This time, the heat event consisted of a single paper of Multiple choice problems to improve the efficiency in marking papers.

The efficiency of implementing the arithmetic depends on the underlying finite field, in practice it turns out that finite fields of characteristic 2 are a good choice for hardware implementations while software is usually faster in odd characteristic.

The choice of carrier gas ( mobile phase ) is important, hydrogen has a larger range of flowrates that are comparable to helium in efficiency.

Linux is the operating system ( OS ) of choice for IRLP, as it allows the best in reliability, programmability, efficiency, and functionality.

In it, Ellul set forth seven characteristics of modern technology that make efficiency a necessity: rationality, artificiality, automatism of technical choice, self-augmentation, monism, universalism, and autonomy.

Bradshaw was a controversial choice as Lord President, and opinions of his efficiency as a judge varied.