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In machine learning, the kernel embedding of distributions (also called the kernel mean or mean map) comprises a class of nonparametric methods in which a probability distribution is represented as an element of a reproducing kernel Hilbert space (RKHS). A generalization of the individual data-point feature mapping done in classical kernel methods, the embedding of distributions into infinite-dimensional feature spaces can preserve all of the statistical features of arbitrary distributions, while allowing one to compare and manipulate distributions using Hilbert space operations such as inner products, distances, projections, linear transformations, and spectral analysis. This learning framework is very general and can be applied to distributions over any space ${\displaystyle \Omega }$ on which a sensible kernel function (measuring similarity between elements of ${\displaystyle \Omega }$) may be defined. For example, various kernels have been proposed for learning from data which are: vectors in ${\displaystyle \mathbb {R} ^{d}}$, discrete classes/categories, strings, graphs/networks, images, time series, manifolds, dynamical systems, and other structured objects. The theory behind kernel embeddings of distributions has been primarily developed by Alex Smola, Le Song , Arthur Gretton, and Bernhard Schölkopf. A review of recent works on kernel embedding of distributions can be found in.

The analysis of distributions is fundamental in machine learning and statistics, and many algorithms in these fields rely on information theoretic approaches such as entropy, mutual information, or Kullback–Leibler divergence. However, to estimate these quantities, one must first either perform density estimation, or employ sophisticated space-partitioning/bias-correction strategies which are typically infeasible for high-dimensional data. Commonly, methods for modeling complex distributions rely on parametric assumptions that may be unfounded or computationally challenging (e.g. Gaussian mixture models), while nonparametric methods like kernel density estimation (Note: the smoothing kernels in this context have a different interpretation than the kernels discussed here) or characteristic function representation (via the Fourier transform of the distribution) break down in high-dimensional settings.

Methods based on the kernel embedding of distributions sidestep these problems and also possess the following advantages:

1. Data may be modeled without restrictive assumptions about the form of the distributions and relationships between variables
2. Intermediate density estimation is not needed
3. Practitioners may specify the properties of a distribution most relevant for their problem (incorporating prior knowledge via choice of the kernel)
4. If a characteristic kernel is used, then the embedding can uniquely preserve all information about a distribution, while thanks to the kernel trick, computations on the potentially infinite-dimensional RKHS can be implemented in practice as simple Gram matrix operations
5. Dimensionality-independent rates of convergence for the empirical kernel mean (estimated using samples from the distribution) to the kernel embedding of the true underlying distribution can be proven.
6. Learning algorithms based on this framework exhibit good generalization ability and finite sample convergence, while often being simpler and more effective than information theoretic methods

Thus, learning via the kernel embedding of distributions offers a principled drop-in replacement for information theoretic approaches and is a framework which not only subsumes many popular methods in machine learning and statistics as special cases, but also can lead to entirely new learning algorithms.

🔗 Caribbean 🔗 Football 🔗 Caribbean/Barbados 🔗 Grenada

On January 27, 1994, the national football teams of Barbados and Grenada played against each other as part of the qualification round for the 1994 Caribbean Cup. Barbados won 4-2 in extra time. In the last minutes of regular time, both teams attempted to score own goals. The result has been described as "one of the strangest matches ever".

In the 1994 Caribbean Cup, the tournament organisers implemented a variant of the golden goal rule: the first goal scored in extra-time not only won the match, but was also worth two goals. Barbados needed to win the match by a margin of at least two goals to qualify for the final tournament over Grenada. Barbados led the game 2-0 until Grenada scored at the 83rd minute, bringing the score to 2-1. Barbados then deliberately scored an own goal, tying the game at 2-2, to force extra-time so that they could take advantage of the golden goal rule to achieve their needed two-goal margin. This resulted in an unusual situation: for the last three minutes of the match, Grenada tried to score in both goals. Either outcome (3–2 on points, or 2–3 via goal difference) would have advanced them to the finals, while Barbados had to defend both goals. Ultimately, Barbados was able to prevent Grenada from scoring, forcing extra-time. Barbados then scored the golden goal to win the match.

The outcome of the match was criticised by Grenadian coach James Clarkson, who felt that his team had been unfairly prevented from advancing to the finals. However, given the fact that the unusual tournament rules had not been broken, FIFA cleared Barbados of any wrongdoing.

🔗 Food and drink 🔗 Iceland

Although Iceland is reliant upon fishing, tourism and aluminium production as the mainstays of its economy, the production of vegetables and fruit in greenhouses is a growing sector. Until the 1960s this included commercial production of bananas.

In 1941, the first bananas in Iceland were produced. They have been produced since that time, about 100 clusters a year each about 5–20 kg (11–44 lb), but are not currently sold. In the wake of World War II, the combination of inexpensive geothermal power (which had recently become available) and high prices for imported fruit led to the construction of a number of greenhouses where bananas were produced commercially from 1945 to as late as 1958 or 1959. In 1960, the government removed import duties on fruit. Domestically grown bananas were no longer able to compete with imported ones and soon disappeared from the market. Icelandic banana production was much slower due to low levels of sunlight; Icelandic bananas took two years to mature, while it only takes a few months near the equator.

The urban myth that Iceland is Europe’s largest producer or exporter of bananas has been propagated in various books and other media. It was mentioned, in an episode of the BBC quiz programme QI, and on a forum connected with the show. According to FAO statistics, the largest European producer of bananas is France (in Martinique and Guadeloupe), followed by Spain (primarily in the Canary Islands). Other banana-producing countries in Europe include Portugal (on Madeira), Greece, and Italy.

Although a small number of banana plants still exist in greenhouses and produce fruit every year, Iceland imports nearly all of the bananas consumed in the country, with imports now amounting to over 18 kg (40 lb) per capita per annum. The Agricultural University of Iceland maintains the last such farm with 600-700 banana plants in its tropical greenhouse, which were received as donations from producers when they shut down (then the Horticultural College). Bananas grown there are consumed by the students and staff and are not sold.

🔗 Computing 🔗 Computing/Software

In computer programming, a poltergeist (or gypsy wagon) is a short-lived, typically stateless object used to perform initialization or to invoke methods in another, more permanent class. It is considered an anti-pattern. The original definition is by Michael Akroyd 1996 - Object World West Conference:

"As a gypsy wagon or a poltergeist appears and disappears mysteriously, so does this short lived object. As a consequence the code is more difficult to maintain and there is unnecessary resource waste. The typical cause for this anti-pattern is poor object design."

A poltergeist can often be identified by its name; they are often called "manager_", "controller_", "supervisor", "start_process", etc.

Sometimes, poltergeist classes are created because the programmer anticipated the need for a more complex architecture. For example, a poltergeist arises if the same method acts as both the client and invoker in a command pattern, and the programmer anticipates separating the two phases. However, this more complex architecture may actually never materialize.

Poltergeists should not be confused with long-lived, state-bearing objects of a pattern such as model–view–controller, or tier-separating patterns such as business-delegate.

To remove a poltergeist, delete the class and insert its functionality in the invoked class, possibly by inheritance or as a mixin.

🔗 Biography 🔗 England 🔗 Middle Ages 🔗 Middle Ages/History 🔗 Biography/arts and entertainment 🔗 East Anglia 🔗 East Anglia/Suffolk

Roland the Farter (known in contemporary records as Roland le Fartere, Roulandus le Fartere or Roland le Petour) was a medieval flatulist who lived in twelfth-century England. He was given Hemingstone manor in Suffolk and 12 hectares (30 acres) of land in return for his services as a jester for King Henry II. Each year he was obliged to perform "Unum saltum et siffletum et unum bumbulum" (one jump, one whistle, and one fart) for the King's court at Christmas.

Roland is listed in the thirteenth-century English Liber Feodorum (Book of Fees).

🔗 Biography 🔗 Mathematics 🔗 Philosophy 🔗 Philosophy/Logic 🔗 Philosophy/Social and political philosophy 🔗 Biography/science and academia 🔗 Philosophy/Philosophy of science 🔗 Linguistics 🔗 Linguistics/Theoretical Linguistics 🔗 Philosophy/Philosophers 🔗 Philosophy/Epistemology 🔗 Sociology 🔗 Politics of the United Kingdom 🔗 Philosophy/Philosophy of language 🔗 Chicago 🔗 Philosophy/Metaphysics 🔗 Linguistics/Philosophy of language 🔗 Philosophy/Analytic philosophy 🔗 Atheism 🔗 Biography/Peerage and Baronetage

Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, historian, writer, essayist, social critic, political activist, and Nobel laureate. At various points in his life, Russell considered himself a liberal, a socialist and a pacifist, although he also confessed that his sceptical nature had led him to feel that he had "never been any of these things, in any profound sense." Russell was born in Monmouthshire into one of the most prominent aristocratic families in the United Kingdom.

In the early 20th century, Russell led the British "revolt against idealism". He is considered one of the founders of analytic philosophy along with his predecessor Gottlob Frege, colleague G. E. Moore and protégé Ludwig Wittgenstein. He is widely held to be one of the 20th century's premier logicians. With A. N. Whitehead he wrote Principia Mathematica, an attempt to create a logical basis for mathematics, the quintessential work of classical logic. His philosophical essay "On Denoting" has been considered a "paradigm of philosophy". His work has had a considerable influence on mathematics, logic, set theory, linguistics, artificial intelligence, cognitive science, computer science (see type theory and type system) and philosophy, especially the philosophy of language, epistemology and metaphysics.

Russell was a prominent anti-war activist and he championed anti-imperialism. Occasionally, he advocated preventive nuclear war, before the opportunity provided by the atomic monopoly had passed and he decided he would "welcome with enthusiasm" world government. He went to prison for his pacifism during World War I. Later, Russell concluded that war against Adolf Hitler's Nazi Germany was a necessary "lesser of two evils" and criticised Stalinist totalitarianism, attacked the involvement of the United States in the Vietnam War and was an outspoken proponent of nuclear disarmament. In 1950, Russell was awarded the Nobel Prize in Literature "in recognition of his varied and significant writings in which he champions humanitarian ideals and freedom of thought".

🔗 Business

Founder's syndrome (also founderitis) is the difficulty faced by organizations where one or more founders maintain disproportionate power and influence following the effective initial establishment of the project, leading to a wide range of problems for the organization. The passion and charisma of the founder(s), sources of the initial creativity and productivity of the organization, become limiting or destructive factors. The syndrome occurs in both non-profit and for-profit organizations. It may simply limit further growth and success of the project, or it may lead to bitter factionalism and divisions as the scale of demands made on the organization increases, or it may result in outright failure. There are ways in which a founder or organization can respond and grow beyond this situation.

🔗 Energy

The gravitation water vortex power plant is a type of micro hydro vortex turbine system which is capable of converting energy in a moving fluid to rotational energy using a low hydraulic head of 0.7–3 metres (2 ft 4 in–9 ft 10 in). The technology is based on a round basin with a central drain. Above the drain the water forms a stable line vortex which drives a water turbine.

It was first patented by Greek-Australian Lawyer & Inventor Paul Kouris in 1996, who was searching for a way to harness the power inherent in a vortex.

Later, Austrian Inventor Franz Zotlöterer created a similar turbine while attempting to find a way to aerate water without an external power source.

🔗 Mathematics

Pentagramma mirificum (Latin for miraculous pentagram) is a star polygon on a sphere, composed of five great circle arcs, all of whose internal angles are right angles. This shape was described by John Napier in his 1614 book Mirifici logarithmorum canonis descriptio (Description of the wonderful rule of logarithms) along with rules that link the values of trigonometric functions of five parts of a right spherical triangle (two angles and three sides). The properties of pentagramma mirificum were studied, among others, by Carl Friedrich Gauss.