Pulse-code modulationPulse-code modulation (PCM) is a method used to digitally represent sampled analog signals. It is the standard form of digital audio in computers, compact discs, digital telephony and other digital audio applications. In a PCM stream, the amplitude of the analog signal is sampled at uniform intervals, and each sample is quantized to the nearest value within a range of digital steps. Linear pulse-code modulation (LPCM) is a specific type of PCM in which the quantization levels are linearly uniform.
Halting problemIn computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever. The halting problem is undecidable, meaning that no general algorithm exists that solves the halting problem for all possible program–input pairs. A key part of the formal statement of the problem is a mathematical definition of a computer and program, usually via a Turing machine.
Dense setIn topology and related areas of mathematics, a subset A of a topological space X is said to be dense in X if every point of X either belongs to A or else is arbitrarily "close" to a member of A — for instance, the rational numbers are a dense subset of the real numbers because every real number either is a rational number or has a rational number arbitrarily close to it (see Diophantine approximation). Formally, is dense in if the smallest closed subset of containing is itself.
Ice streamAn ice stream is a region of fast-moving ice within an ice sheet. It is a type of glacier, a body of ice that moves under its own weight. They can move upwards of a year, and can be up to in width, and hundreds of kilometers in length. They tend to be about deep at the thickest, and constitute the majority of the ice that leaves the sheet. In Antarctica, the ice streams account for approximately 90% of the sheet's mass loss per year, and approximately 50% of the mass loss in Greenland.
Subset sum problemThe subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset of integers and a target-sum , and the question is to decide whether any subset of the integers sum to precisely . The problem is known to be NP-hard. Moreover, some restricted variants of it are NP-complete too, for example: The variant in which all inputs are positive. The variant in which inputs may be positive or negative, and . For example, given the set , the answer is yes because the subset sums to zero.
Open setIn mathematics, an open set is a generalization of an open interval in the real line. In a metric space (a set along with a distance defined between any two points), an open set is a set that, along with every point P, contains all points that are sufficiently near to P (that is, all points whose distance to P is less than some value depending on P). More generally, an open set is a member of a given collection of subsets of a given set, a collection that has the property of containing every union of its members, every finite intersection of its members, the empty set, and the whole set itself.
Additive white Gaussian noiseAdditive white Gaussian noise (AWGN) is a basic noise model used in information theory to mimic the effect of many random processes that occur in nature. The modifiers denote specific characteristics: Additive because it is added to any noise that might be intrinsic to the information system. White refers to the idea that it has uniform power spectral density across the frequency band for the information system. It is an analogy to the color white which may be realized by uniform emissions at all frequencies in the visible spectrum.
Travelling salesman problemThe travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research. The travelling purchaser problem and the vehicle routing problem are both generalizations of TSP.
Sea levelMean sea level (MSL, often shortened to sea level) is an average surface level of one or more among Earth's coastal bodies of water from which heights such as elevation may be measured. The global MSL is a type of vertical datum a standardised geodetic datum that is used, for example, as a chart datum in cartography and marine navigation, or, in aviation, as the standard sea level at which atmospheric pressure is measured to calibrate altitude and, consequently, aircraft flight levels.
Typical setIn information theory, the typical set is a set of sequences whose probability is close to two raised to the negative power of the entropy of their source distribution. That this set has total probability close to one is a consequence of the asymptotic equipartition property (AEP) which is a kind of law of large numbers. The notion of typicality is only concerned with the probability of a sequence and not the actual sequence itself.
