Reduction (complexity)In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem. A sufficiently efficient reduction from one problem to another may be used to show that the second problem is at least as difficult as the first. Intuitively, problem A is reducible to problem B, if an algorithm for solving problem B efficiently (if it existed) could also be used as a subroutine to solve problem A efficiently. When this is true, solving A cannot be harder than solving B.
Validity (statistics)Validity is the main extent to which a concept, conclusion or measurement is well-founded and likely corresponds accurately to the real world. The word "valid" is derived from the Latin validus, meaning strong. The validity of a measurement tool (for example, a test in education) is the degree to which the tool measures what it claims to measure. Validity is based on the strength of a collection of different types of evidence (e.g. face validity, construct validity, etc.) described in greater detail below.
Ecological validityIn the behavioral sciences, ecological validity is often used to refer to the judgment of whether a given study's variables and conclusions (often collected in lab) are sufficiently relevant to its population (e.g. the "real world" context). Psychological studies are usually conducted in laboratories though the goal of these studies is to understand human behavior in the real-world. Ideally, an experiment would have generalizable results that predict behavior outside of the lab, thus having more ecological validity.
Internal validityInternal validity is the extent to which a piece of evidence supports a claim about cause and effect, within the context of a particular study. It is one of the most important properties of scientific studies and is an important concept in reasoning about evidence more generally. Internal validity is determined by how well a study can rule out alternative explanations for its findings (usually, sources of systematic error or 'bias').
Dimensionality reductionDimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension. Working in high-dimensional spaces can be undesirable for many reasons; raw data are often sparse as a consequence of the curse of dimensionality, and analyzing the data is usually computationally intractable (hard to control or deal with).
Byzantine Empire under the Komnenos dynastyThe Byzantine Empire was ruled by emperors of the Komnenos dynasty for a period of 104 years, from 1081 to about 1185. The Komnenian (also spelled Comnenian) period comprises the reigns of five emperors, Alexios I, John II, Manuel I, Alexios II and Andronikos I. It was a period of sustained, though ultimately incomplete, restoration of the military, territorial, economic and political position of the Byzantine Empire.
Noise reductionNoise reduction is the process of removing noise from a signal. Noise reduction techniques exist for audio and images. Noise reduction algorithms may distort the signal to some degree. Noise rejection is the ability of a circuit to isolate an undesired signal component from the desired signal component, as with common-mode rejection ratio. All signal processing devices, both analog and digital, have traits that make them susceptible to noise.
Hirohito surrender broadcastThe Hirohito surrender broadcast was a radio broadcast of surrender given by Hirohito, the emperor of Japan, on 15 August 1945. It announced to the Japanese people that the Japanese government had accepted the Potsdam Declaration demanding the unconditional surrender of the Japanese military at the end of World War II. Following the Hiroshima bombing on August 6, the Soviet declaration of war and the Nagasaki bombing on August 9, the Emperor's speech was broadcast at noon Japan Standard Time on 15 August 1945, and referred to the atomic bombs as a reason for the surrender.
Turing reductionIn computability theory, a Turing reduction from a decision problem to a decision problem is an oracle machine which decides problem given an oracle for (Rogers 1967, Soare 1987). It can be understood as an algorithm that could be used to solve if it had available to it a subroutine for solving . The concept can be analogously applied to function problems. If a Turing reduction from to exists, then every algorithm for can be used to produce an algorithm for , by inserting the algorithm for at each place where the oracle machine computing queries the oracle for .
Maurice (emperor)Maurice (Mauricius; Maurikios; 539 – 27 November 602) was Byzantine emperor from 582 to 602 and the last member of the Justinian dynasty. A successful general, Maurice was chosen as heir and son-in-law by his predecessor Tiberius II. Maurice's reign was troubled by almost constant warfare. After he became emperor, he brought the war with Sasanian Persia to a victorious conclusion. The empire's eastern border in the South Caucasus was vastly expanded and, for the first time in nearly two centuries, the Romans were no longer obliged to pay the Persians thousands of pounds of gold annually for peace.
