* Typical algorithmic delay is 0. 125 ms, with no look-ahead delay

* Typical algorithmic delay is 0. 125 ms, with no look-ahead delay

For example, multiplying 7 by 6 is a simple algorithmic calculation.

Ray Solomonoff ( July 25, 1926 – December 7, 2009 ) was the inventor of algorithmic probability, and founder of algorithmic information theory, He was an originator of the branch of artificial intelligence based on machine learning, prediction and probability.

Lexical ambiguity can be addressed by algorithmic methods that automatically associate the appropriate meaning with a word in context, a task referred to as word sense disambiguation.

Babbage understood that the existence of an automatic computer would kindle interest in the field now known as algorithmic efficiency, writing in his Passages from the Life of a Philosopher, " As soon as an Analytical Engine exists, it will necessarily guide the future course of the science.

One such engine even develops sentient thought due to a recursive algorithmic loop.

In algorithmic information theory ( a subfield of computer science ), the Kolmogorov complexity of an object, such as a piece of text, is a measure of the computational resources needed to specify the object.

Kolmogorov complexity is also known as " descriptive complexity " ( not to be confused with descriptive complexity theory ), Kolmogorov – Chaitin complexity, algorithmic entropy, or program-size complexity.

The concept and theory of Kolmogorov Complexity is based on a crucial theorem first discovered by Ray Solomonoff, who published it in 1960, describing it in " A Preliminary Report on a General Theory of Inductive Inference " as part of his invention of algorithmic probability.

There are several other variants of Kolmogorov complexity or algorithmic information.

In the 1990s, Jürgen Schmidhuber described an algorithmic theory of beauty which takes the subjectivity of the observer into account and postulates: among several observations classified as comparable by a given subjective observer, the aesthetically most pleasing one is the one with the shortest description, given the observer ’ s previous knowledge and his particular method for encoding the data.

This is closely related to the principles of algorithmic information theory and minimum description length.

* Jürgen Schmidhuber: Papers on algorithmic theories of everything and the Anthropic Principle's lack of predictive power.

This can be used for algorithmic purposes as in the AGM method.

Other software including algorithmic beatmatching is Ableton Live, which allows for realtime music manipulation and deconstruction, or Mixmeister, a DJ Mixset creation tool.

* an algorithmic description.

In the computer science subfield of algorithmic information theory, a Chaitin constant ( Chaitin omega number ) or halting probability is a real number that informally represents the probability that a randomly constructed program will halt.

Two further major 1950s developments were the origins of digital sound synthesis by computer, and of algorithmic composition programs beyond rote playback.

Amongst other pioneers, the musical chemists Lejaren Hiller and Leonard Isaacson worked on a series of algorithmic composition experiments from 1956-9, manifested in the 1957 premiere of the Illiac Suite for string quartet.

Koenig produced algorithmic composition programs which were a generalisation of his own serial composition practice.

As with much algorithmic music, and algorithmic art in general, more depends on the way in which the parameters are mapped to aspects of these equations than on the equations themselves.

Diagram illustrating the position of CAAC in relation to other Generative music SystemsComputer-Aided Algorithmic Composition ( CAAC, pronounced " sea-ack ") is the implementation and use of algorithmic composition techniques in software.

The label algorithmic composition is likewise too broad, particularly in that it does not specify the use of a computer.

This is different from other improvisation methods with computers that use algorithmic composition to generate new music without performing analysis of existing music examples.

The theoretical background of compression is provided by information theory ( which is closely related to algorithmic information theory ) for lossless compression, and by rate – distortion theory for lossy compression.

The process is algorithmic and based on dependencies ( mathematical relations ) that exist among relations ' field types.

The data compression ratio can serve as an measure of the complexity of a data set or signal, in particular it is used to approximate the algorithmic complexity.

( editor ) " Report on the algorithmic language ALGOL 60 ", 1960, published in several journals, including Communication of the ACM 3, 5 ( May 1960 ), pp. 299 – 314

The computational complexity is quite low ( 5. 5 floating-point MIPS ) for an efficient high-quality compressor, and the algorithmic delay end-to-end is 40 ms. A 14 kHz ( 32 ksps ) extension, G. 722. 1 / Annex C, was approved by ITU-T on May 14, 2005.

The LD-CELP however, uses backward adaptation of predictors and gain to achieve an algorithmic delay of 0. 625 ms.

So the algorithmic delay for the coder is 30 ms with noise-suppression option B and 33 ms with noise-suppression option A.

The total algorithmic delay for the encoder and decoder is 36 ms.

This was a general change of methodology, since the needs of applications had up until then meant that much of mathematics was taught by means of algorithms ( or processes close to being algorithmic ).

The algorithmic means for establishing protein families on a large scale are based on a notion of similarity.

It offers an algorithmic approach for machine computation ( in that theta series span spaces of modular forms ); the theory is now considered by means of Brandt modules.

VoIP systems that try to be very bandwidth efficient may also add tens of milliseconds of algorithmic delay in the voice codec.

In contrast, TDMoIP maps TDM octets directly into the payload with no voice compression algorithms and no resultant algorithmic delay.

The discipline of computing is the systematic study of algorithmic

An arbitrary PID has much the same " structural properties " of a Euclidean domain ( or, indeed, even of the ring of integers ), but knowing an explicit algorithm for Euclidean division, and thus also for greatest common divisor computation, gives a concreteness which is useful for algorithmic applications.

In particular, files of random data cannot be consistently compressed by any conceivable lossless data compression algorithm: indeed, this result is used to define the concept of randomness in algorithmic complexity theory.

* Computational linguistics – study of linguistic issues in a way that is ' computationally responsible ', i. e., taking careful note of computational consideration of algorithmic specification and computational complexity, so that the linguistic theories devised can be shown to exhibit certain desirable computational properties implementations.

The encoder needs to be algorithmic or adaptive whereas the decoder is ' dumb ' and carries out fixed actions.

The algorithmic information content in a number is, roughly speaking, the length of the shortest computer program that will produce that number as output.

If, for instance, the algorithmic view is taken, then the reals as constructed here are essentially what classically would be called the computable numbers.

Multilinear algebra can be developed in greater generality than for scalars coming from a field, but the theory is then certainly less geometric, and computations more technical and less algorithmic.

In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a finitely generated group G is the algorithmic problem of deciding whether two words in the generators represent the same element.

The related but different uniform word problem for a class K of recursively presented groups is the algorithmic problem of deciding, given as input a presentation P for a group G in the class K and two words in the generators of G, whether the words represent the same element of G. Some authors require the class K to be definable by a recursively enumerable set of presentations.

A former student of George Perle, he is currently a professor of music composition at Princeton University, and in addition to his music is known as a pioneer in the development of computer music languages for algorithmic composition ( see Real-Time Cmix ).