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🔗 Physics

In physics, the fourth, fifth and sixth derivatives of position are defined as derivatives of the position vector with respect to time – with the first, second, and third derivatives being velocity, acceleration, and jerk, respectively. Unlike the first three derivatives, the higher-order derivatives are less common, thus their names are not as standardized, though the concept of a minimum snap trajectory has been used in robotics and is implemented in MATLAB.

The fourth derivative is often referred to as snap or jounce. The name "snap" for the fourth derivative led to crackle and pop for the fifth and sixth derivatives respectively, inspired by the Rice Krispies mascots Snap, Crackle, and Pop. These terms are occasionally used, though "sometimes somewhat facetiously".

🔗 Mathematics 🔗 Statistics 🔗 Systems 🔗 Robotics 🔗 Systems/Control theory

In statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, containing statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. Kálmán, one of the primary developers of its theory.

The Kalman filter has numerous applications in technology. A common application is for guidance, navigation, and control of vehicles, particularly aircraft, spacecraft and dynamically positioned ships. Furthermore, the Kalman filter is a widely applied concept in time series analysis used in fields such as signal processing and econometrics. Kalman filters also are one of the main topics in the field of robotic motion planning and control and can be used in trajectory optimization. The Kalman filter also works for modeling the central nervous system's control of movement. Due to the time delay between issuing motor commands and receiving sensory feedback, use of the Kalman filter supports a realistic model for making estimates of the current state of the motor system and issuing updated commands.

The algorithm works in a two-step process. In the prediction step, the Kalman filter produces estimates of the current state variables, along with their uncertainties. Once the outcome of the next measurement (necessarily corrupted with some amount of error, including random noise) is observed, these estimates are updated using a weighted average, with more weight being given to estimates with higher certainty. The algorithm is recursive. It can run in real time, using only the present input measurements and the previously calculated state and its uncertainty matrix; no additional past information is required.

Optimality of the Kalman filter assumes that the errors are Gaussian. In the words of Rudolf E. Kálmán: "In summary, the following assumptions are made about random processes: Physical random phenomena may be thought of as due to primary random sources exciting dynamic systems. The primary sources are assumed to be independent gaussian random processes with zero mean; the dynamic systems will be linear." Though regardless of Gaussianity, if the process and measurement covariances are known, the Kalman filter is the best possible linear estimator in the minimum mean-square-error sense.

Extensions and generalizations to the method have also been developed, such as the extended Kalman filter and the unscented Kalman filter which work on nonlinear systems. The underlying model is a hidden Markov model where the state space of the latent variables is continuous and all latent and observed variables have Gaussian distributions. Also, Kalman filter has been successfully used in multi-sensor fusion, and distributed sensor networks to develop distributed or consensus Kalman filter.

🔗 Poetry

"Dane-geld" is a poem by British writer Rudyard Kipling (1865-1936). It relates to the unwisdom of paying "Danegeld", or what is nowadays called blackmail and protection money. The most famous lines are "once you have paid him the Danegeld/ You never get rid of the Dane."

🔗 Mathematics 🔗 Physics

Earnshaw's theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges. This was first proven by British mathematician Samuel Earnshaw in 1842. It is usually referenced to magnetic fields, but was first applied to electrostatic fields.

Earnshaw's theorem applies to classical inverse-square law forces (electric and gravitational) and also to the magnetic forces of permanent magnets, if the magnets are hard (the magnets do not vary in strength with external fields). Earnshaw's theorem forbids magnetic levitation in many common situations.

If the materials are not hard, Braunbeck's extension shows that materials with relative magnetic permeability greater than one (paramagnetism) are further destabilising, but materials with a permeability less than one (diamagnetic materials) permit stable configurations.

🔗 Computing 🔗 Computing/Computer hardware

The Pentium FDIV bug is a hardware bug affecting the floating-point unit (FPU) of the early Intel Pentium processors. Because of the bug, the processor would return incorrect binary floating point results when dividing certain pairs of high-precision numbers. The bug was discovered in 1994 by Thomas R. Nicely, a professor of mathematics at Lynchburg College. Missing values in a lookup table used by the FPU's floating-point division algorithm led to calculations acquiring small errors. While these errors would in most use-cases only occur rarely and result in small deviations from the correct output values, in certain circumstances the errors can occur frequently and lead to more significant deviations.

The severity of the FDIV bug is debated. Though rarely encountered by most users (Byte magazine estimated that 1 in 9 billion floating point divides with random parameters would produce inaccurate results), both the flaw and Intel's initial handling of the matter were heavily criticized by the tech community.

In December 1994, Intel recalled the defective processors in what was the first full recall of a computer chip. In its 1994 annual report, Intel said it incurred "a $475 million pre-tax charge ... to recover replacement and write-off of these microprocessors."

🔗 Aviation 🔗 Aviation/aircraft 🔗 Automobiles

The AVE Mizar (named after the star Mizar) was a roadable aircraft built between 1971 and 1973 by Advanced Vehicle Engineers (AVE) of Van Nuys, Los Angeles, California. The company was started by Henry Smolinski and Harold Blake, both graduates of Northrop Institute of Technology's aeronautical engineering school.

🔗 Video games 🔗 Computing

The FM Towns (Japanese: エフエムタウンズ, Hepburn: Efu Emu Taunzu) is a Japanese personal computer built by Fujitsu from February 1989 to the summer of 1997. It started as a proprietary PC variant intended for multimedia applications and PC games, but later became more compatible with IBM PC compatibles. In 1993, the FM Towns Marty was released, a game console compatible with existing FM Towns games.

The "FM" part of the name means "Fujitsu Micro" like their earlier products, while the "Towns" part is derived from the code name the system was assigned while in development, "Townes". This refers to Charles Townes, one of the winners of the 1964 Nobel Prize in Physics, following a custom of Fujitsu at the time to code name PC products after Nobel Prize winners. The e in "Townes" was dropped when the system went into production to make it clearer that the term was to be pronounced like the word "towns" rather than the potential "tow-nes".

🔗 Psychology 🔗 Education

Bloom's 2 sigma problem refers to an educational phenomenon observed by educational psychologist Benjamin Bloom and initially reported in 1984 in the journal Educational Researcher. Bloom found that the average student tutored one-to-one using mastery learning techniques performed two standard deviations better than students who learn via conventional instructional methods — that is, "the average tutored student was above 98% of the students in the control class". Additionally, the variation of the students' achievement changed: "about 90% of the tutored students ... attained the level of summative achievement reached by only the highest 20%" of the control class. Bloom's graduate students J. Anania and A. J. Burke conducted studies of this effect at different grade levels and in different schools, observing students with "great differences in cognitive achievement, attitudes, and academic self-concept".

🔗 Computer science 🔗 Mathematics 🔗 Systems 🔗 Cryptography 🔗 Cryptography/Computer science 🔗 Systems/Operations research

The knapsack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items. The problem often arises in resource allocation where the decision makers have to choose from a set of non-divisible projects or tasks under a fixed budget or time constraint, respectively.

The knapsack problem has been studied for more than a century, with early works dating as far back as 1897. The name "knapsack problem" dates back to the early works of mathematician Tobias Dantzig (1884–1956), and refers to the commonplace problem of packing the most valuable or useful items without overloading the luggage.

🔗 Literature 🔗 Folklore

The Aarne–Thompson–Uther Index (ATU Index) is a catalogue of folktale types used in folklore studies. The ATU Index is the product of a series of revisions and expansions by an international group of scholars: Originally composed in German by Finnish folklorist Antti Aarne (1910); the index was translated into English, revised, and expanded by American folklorist Stith Thompson (1928, 1961); and later further revised and expanded by German folklorist Hans-Jörg Uther (2004). The ATU Index, along with Thompson's Motif-Index of Folk-Literature (1932) (with which it is used in tandem) is an essential tool for folklorists.