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R-trees are tree data structures used for spatial access methods, i.e., for indexing multi-dimensional information such as geographical coordinates, rectangles or polygons. The R-tree was proposed by Antonin Guttman in 1984 and has found significant use in both theoretical and applied contexts. A common real-world usage for an R-tree might be to store spatial objects such as restaurant locations or the polygons that typical maps are made of: streets, buildings, outlines of lakes, coastlines, etc. and then find answers quickly to queries such as "Find all museums within 2 km of my current location", "retrieve all road segments within 2 km of my location" (to display them in a navigation system) or "find the nearest gas station" (although not taking roads into account). The R-tree can also accelerate nearest neighbor search for various distance metrics, including great-circle distance.

This article compares variety of different X window managers. For an introduction to the topic, see X Window System.

The carpet at Portland International Airport (PDX) in Portland, Oregon, featured geometric shapes on a teal background, representing the intersection of the north and south runways seen by air traffic controllers from the airport's tower at night. SRG Partnership designed it in 1987, and since then, the carpet has received much media attention.

In 2013, the Port of Portland announced the carpet's replacement with a new pattern conceptualized by the Portland-based firm Zimmer Gunsul Frasca Architects. The announcement generated a social media "phenomenon" and gained attention from local and national news outlets. Removal of the original carpet began in January 2015, with the airport recycling worn portions and making remaining pieces available for sale by local retail vendors.

In 2015, Portland Trail Blazers point guard Damian Lillard released his first PDX carpet colorway on the Adidas D Lillard 1 sneaker. In 2016, Lillard released the colorway on the D Lillard 2, also inspired by the carpet.

In February of 2022, it was announced that the iconic carpet would be returning to the airport when a new terminal opens in 2024.

A gravity hill, also known as a magnetic hill, mystery hill, mystery spot, gravity road, or anti-gravity hill, is a place where the layout of the surrounding land produces an optical illusion, making a slight downhill slope appear to be an uphill slope. Thus, a car left out of gear will appear to be rolling uphill against gravity. There are hundreds of recognized gravity hills around the world.

The slope of gravity hills is an optical illusion, although sites are often accompanied by claims that magnetic or supernatural forces are at work. The most important factor contributing to the illusion is a completely or mostly obstructed horizon. Without a horizon, it becomes difficult to judge the slope of a surface as a reliable reference is missing. Objects which one would normally assume to be more or less perpendicular to the ground, such as trees, may actually be leaning, offsetting the visual reference.

A 2003 study looked into how the absence of a horizon can skew the perspective on gravity hills by recreating a number of antigravity places in the lab to see how volunteers would react. As a conclusion, researchers from Universities of Padova and Pavia in Italy found that without a true horizon in sight, landmarks such as trees and signs actually played these tricks on the human brain.

The illusion is similar to the Ames room, in which objects can also appear to roll against gravity.

The opposite phenomenon—an uphill road that appears flat—is known in bicycle racing as a "false flat".

The Luhn algorithm or Luhn formula, also known as the "modulus 10" or "mod 10" algorithm, named after its creator, IBM scientist Hans Peter Luhn, is a simple checksum formula used to validate a variety of identification numbers, such as credit card numbers, IMEI numbers, National Provider Identifier numbers in the United States, Canadian Social Insurance Numbers, Israel ID Numbers, South African ID Numbers, Greek Social Security Numbers (ΑΜΚΑ), and survey codes appearing on McDonald's, Taco Bell, and Tractor Supply Co. receipts. It is described in U.S. Patent No. 2,950,048, filed on January 6, 1954, and granted on August 23, 1960.

The algorithm is in the public domain and is in wide use today. It is specified in ISO/IEC 7812-1. It is not intended to be a cryptographically secure hash function; it was designed to protect against accidental errors, not malicious attacks. Most credit cards and many government identification numbers use the algorithm as a simple method of distinguishing valid numbers from mistyped or otherwise incorrect numbers.

In economics, hyperbolic discounting is a time-inconsistent model of delay discounting. It is one of the cornerstones of behavioral economics and its brain-basis is actively being studied by neuroeconomics researchers.

The discounted utility approach states that intertemporal choices are no different from other choices, except that some consequences are delayed and hence must be anticipated and discounted (i.e., reweighted to take into account the delay).

Given two similar rewards, humans show a preference for one that arrives sooner rather than later. Humans are said to discount the value of the later reward, by a factor that increases with the length of the delay. In the financial world, this process is normally modeled in the form of exponential discounting, a time-consistent model of discounting. A large number of psychological studies have since demonstrated deviations in instinctive preference from the constant discount rate assumed in exponential discounting. Hyperbolic discounting is an alternative mathematical model that agrees more closely with these findings.

According to hyperbolic discounting, valuations fall relatively rapidly for earlier delay periods (as in, from now to one week), but then fall more slowly for longer delay periods (for instance, more than a few days). For example, in an early study subjects said they would be indifferent between receiving $15 immediately or $30 after 3 months, $60 after 1 year, or $100 after 3 years. These indifferences reflect annual discount rates that declined from 277% to 139% to 63% as delays got longer. This contrasts with exponential discounting, in which valuation falls by a constant factor per unit delay and the discount rate stays the same.

The standard experiment used to reveal a test subject's hyperbolic discounting curve is to compare short-term preferences with long-term preferences. For instance: "Would you prefer a dollar today or three dollars tomorrow?" or "Would you prefer a dollar in one year or three dollars in one year and one day?" It has been claimed that a significant fraction of subjects will take the lesser amount today, but will gladly wait one extra day in a year in order to receive the higher amount instead. Individuals with such preferences are described as "present-biased".

The most important consequence of hyperbolic discounting is that it creates temporary preferences for small rewards that occur sooner over larger, later ones. Individuals using hyperbolic discounting reveal a strong tendency to make choices that are inconsistent over time – they make choices today that their future self would prefer not to have made, despite knowing the same information. This dynamic inconsistency happens because hyperbolas distort the relative value of options with a fixed difference in delays in proportion to how far the choice-maker is from those options.

Octopolis and Octlantis are two separate non-human underwater settlements built by the gloomy octopuses. The first settlement, named Octopolis by biologists, was found in 2009. The individual structures in Octopolis consist of burrows around a piece of scrap metal. In 2016, a second settlement was found, named Octlantis, which instead of burrows, has dens and is built with seashells.

In navigation, a rhumb line, rhumb (), or loxodrome is an arc crossing all meridians of longitude at the same angle, that is, a path with constant bearing as measured relative to true north.

An automated vacuum waste collection system, also known as pneumatic refuse collection, or automated vacuum collection (AVAC), transports waste at high speed through underground pneumatic tubes to a collection station where it is compacted and sealed in containers. When the container is full, it is transported away and emptied. The system helps facilitate separation and recycling of waste.

The process begins with the deposit of trash into intake hatches, called portholes, which may be specialized for waste, recycling, or compost. Portholes are located in public areas and on private property where the owner has opted in. The waste is then pulled through an underground pipeline by air pressure difference created by large industrial fans, in response to porthole sensors that indicate when the trash needs to be emptied and help ensure that only one kind of waste material is travelling through the pipe at a time. The pipelines converge on a central processing facility that uses automated software to direct the waste to the proper container, from there to be trucked to its final location, such as a landfill or composting plant.

The turboencabulator or turbo-encabulator (and its later incarnations, the retroencabulator or retro-encabulator and Micro Encabulator) is a fictional machine whose alleged existence became an in-joke and subject of professional humor among engineers. The explanation of the supposed product makes extensive use of technobabble.

The gag was popular for many years. The following quote is from the original Students' Quarterly Journal article written by J. H. Quick in 1944. The citation in the later Time article misspells several of the technical terms. General Electric, Chrysler and Rockwell Automation use many of the same words.

The original machine had a base plate of prefabulated amulite, surmounted by a malleable logarithmic casing in such a way that the two main spurving bearings were in a direct line with the panametric fan. The latter consisted simply of six hydrocoptic marzlevanes, so fitted to the ambifacient lunar waneshaft that side fumbling was effectively prevented. The main winding was of the normal lotus-o-deltoid type placed in panendermic semi-boloid slots in the stator, every seventh conductor being connected by a nonreversible tremmie pipe to the differential girdlespring on the "up" end of the grammeters.