White noise

In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density. The term is used, with this or similar meanings, in many scientific and technical disciplines, including physics, acoustical engineering, telecommunications, statistical forecasting. White noise refers to a statistical model for signals and signal sources, rather than to any specific signal. White noise draws its name from white light, although light that appears white does not have a flat power spectral density over the visible band. In discrete time, white noise is a discrete signal whose samples are regarded as a sequence of serially uncorrelated random variables with zero mean and finite variance. Depending on the context, one may require that the samples be independent and have identical probability distribution. In particular, if each sample has a normal distribution with zero mean, the signal is said to be additive white Gaussian noise; the samples of a white noise signal may be sequential in time, or arranged along one or more spatial dimensions.

In digital image processing, the pixels of a white noise image are arranged in a rectangular grid, are assumed to be independent random variables with uniform probability distribution over some interval. The concept can be defined for signals spread over more complicated domains, such as a sphere or a torus. An infinite-bandwidth white noise signal is a purely theoretical construction; the bandwidth of white noise is limited in practice by the mechanism of noise generation, by the transmission medium and by finite observation capabilities. Thus, random signals are considered "white noise" if they are observed to have a flat spectrum over the range of frequencies that are relevant to the context. For an audio signal, the relevant range is the band of audible sound frequencies; such a signal is heard by the human ear as a hissing sound, resembling the /h/ sound in a sustained aspiration. On the other hand, the / sh / sound in "ash" is a colored noise. In music and acoustics, the term "white noise" may be used for any signal that has a similar hissing sound.

The term white noise is sometimes used in the context of phylogenetically based statistical methods to refer to a lack of phylogenetic pattern in comparative data. It is sometimes used analogously in nontechnical contexts to mean "random talk without meaningful contents". Any distribution of values is possible. A binary signal which can only take on the values 1 or –1 will be white if the sequence is statistically uncorrelated. Noise having a continuous distribution, such as a normal distribution, can of course be white, it is incorrectly assumed that Gaussian noise refers to white noise, yet neither property implies the other. Gaussianity refers to the probability distribution with respect to the value, in this context the probability of the signal falling within any particular range of amplitudes, while the term'white' refers to the way the signal power is distributed over time or among frequencies. White noise is the generalized mean-square derivative of the Wiener Brownian motion. A generalization to random elements on infinite dimensional spaces, such as random fields, is the white noise measure.

White noise is used in the production of electronic music either directly or as an input for a filter to create other types of noise signal. It is used extensively in audio synthesis to recreate percussive instruments such as cymbals or snare drums which have high noise content in their frequency domain. A simple example of white noise is a nonexistent radio station. White noise is used to obtain the impulse response of an electrical circuit, in particular of amplifiers and other audio equipment, it is not used for testing loudspeakers as its spectrum contains too great an amount of high frequency content. Pink noise, which differs from white noise in that it has equal energy in each octave, is used for testing transducers such as loudspeakers and microphones. White noise is used as the basis of some random number generators. For example, uses a system of atmospheric antennae to generate random digit patterns from white noise. White noise is a common synthetic noise source used for sound masking by a tinnitus masker.

White noise machines and other white noise sources are sold as privacy enhancers and sleep aids and to mask tinnitus. Alternatively, the use of an FM radio tuned to unused frequencies is a simpler and more cost-effective source of white noise. However, white noise generated from a common commercial radio receiver tuned to an unused frequency is vulnerable to being contaminated with spurious signals, such as adjacent radio stations, harmonics from non-adjacent radio stations, electrical equipment in the vicinity of the receiving antenna causing interference, or atmospheric events such as solar flares and lightning. There is evidence that white noise exposure therapies may induce maladaptive changes in the brain that degrade neurological health and compromise cognition; the effects of white noise upon cognitive function are mixed. A small study found that white noise background stimulation improves cognitive functioning among secondary students with attention deficit hyperactivity disorder, while decreasing performance of non-ADHD students.

Other work indicates it is effective in impro

Megali Idea

The Megali Idea was an irredentist concept that expressed the goal of reviving the Byzantine Empire, by establishing a Greek state, which would include the large Greek populations that were still under Ottoman rule after the end of the Greek War of Independence and all the regions that traditionally belonged to Greeks since ancient times. The term appeared for the first time during the debates of Prime Minister Ioannis Kolettis with King Otto that preceded the promulgation of the 1844 constitution; this was a visionary nationalist aspiration, to dominate foreign relations and, to a significant extent, determine domestic politics of the Greek state for much of the first century of independence. The expression was new in 1844 but the concept had roots in the Greek popular psyche, which long had hopes of liberation from Turkish rule and restoration of the Byzantine Empire. Πάλι με χρόνια με καιρούς, πάλι δικά μας θα'ναι!. The Megali Idea implied the goal of reviving the Eastern Roman Empire, by establishing a Greek state, which would be, as ancient geographer Strabo wrote, a Greek world encompassing the former Byzantine lands from the Ionian Sea to the west, to Asia Minor and the Black Sea to the east and from Thrace and Epirus to the north, to Crete and Cyprus to the south.

This new state would have Constantinople as its capital: it would be the "Greece of Two Continents and Five Seas". The Megali Idea dominated foreign policy and domestic politics of Greece from the War of Independence in the 1820s through the Balkan wars in the beginning of the 20th century, it started to fade after the defeat of Greece in the Greco-Turkish War and the Great Fire of Smyrna in 1922, followed by the Population exchange between Greece and Turkey in 1923. Despite the end of the Megali Idea project in 1922, the Greek state expanded five times in its history, either through military conquest or diplomacy. After the creation of Greece in 1830, it annexed the Ionian Islands, Macedonia, Crete and the Eastern Aegean Islands, Western Thrace and the Dodecanese, making them Greek territory; the Byzantine Empire was Roman in origin and was called the "Roman Empire" by its inhabitants and the entire world, until some 120 years after its fall, when Hieronymus Wolf coined the usage of "Byzantium".

It became Hellenistic with time to the point where Greek replaced Latin as the official language in AD 610, owing to several factors: Its religion, being Christian, with the New Testament written in Greek. Byzantium held out against the invasions of the centuries with a vitality that the Western Roman Empire lost, repelling the Visigoths, the Huns, the Saracens, the Mongols and the Turks. Constantinople, the capital of Byzantium, fell to the Fourth Crusaders in the early years of the 13th century; the city was liberated by the Empire of Nicaea, a Byzantine successor, the Empire was restored. However, the city fell to a different foe in 1453—the Ottoman Turks—and this fall of Constantinople marked the nadir of Byzantine civilization. Following the conquest of Constantinople, the capture of the remainder of the Byzantine territories was accomplished by the Ottomans. In the Millet system in force during the Ottoman Empire, the population was classified according to religion rather than language or ethnicity.

Orthodox Greeks were seen as part of the millet-i Rûm which included all Orthodox Christians, including beside Greeks Bulgarians, Vlachs, Georgians, Arabs and Albanians, despite their differences in ethnicity and language and despite the fact that the religious hierarchy was Greek dominated. It is not clear to what extent one can speak of a Greek identity during those times as opposed to a Christian or Orthodox identity. In the late 1780s, Catherine II of Russia and Joseph II of Austria intended to reclaim the Byzantine heritage and restore the Greek statehood as part of their joint Greek Plan, it is notable that during the Middle Ages and the Ottoman period, Greek-speaking Christians identified as Romans and thought of themselves as the descendants of the Roman Empire. Indeed, the term Roman was interpreted as synonymous with Christian throughout Europe and the Mediterranean during this time; the terms Greek or Hellene were seen by Ottoman Christians as referring to the ancient pagan peoples of the region.

This, changed during the late stages of the Ottoman Empire and the emergence of the Greek independence movement. After the Greek War of Independence ended in 1829, a new southern Greek state was established, with assistance from the United Kingdom and Imperial Russia. However, this new Greek state under John Capodistria after the Greek War of Independence was, with Serbia, one of the only two countries of the era whose population was smaller than the population of the same ethnicity outside its borders; this version of Greece was designed by the Great Power

World War I reparations

World War I reparations were war reparations imposed during the Paris Peace Conference upon the Central Powers following their defeat in the First World War by the Allied and Associate Powers. Each of the defeated powers were required to make payments in either cash or kind; because of the financial situation Austria and Turkey found themselves in after the war, few to no reparations were paid and the requirements for reparations were cancelled. Bulgaria, having paid only a fraction of what was required, saw its reparation figure reduced and cancelled. Historians have recognized the German requirement to pay reparations as the "chief battleground of the post-war era" and "the focus of the power struggle between France and Germany over whether the Versailles Treaty was to be enforced or revised"; the Treaty of Versailles and the 1921 London Schedule of Payments required Germany to pay 132 billion gold marks in reparations to cover civilian damage caused during the war. This figure was divided into three categories of bonds: A, B, C.

Of these, Germany was required to pay towards'A' and'B' bonds totaling 50 billion marks unconditionally. The payment of the remaining'C' bonds was interest free and contingent on the Weimar Republic's ability to pay, as was to be assessed by an Allied committee. Due to the lack of reparation payments by Germany, France occupied the Ruhr in 1923 to enforce payments, causing an international crisis that resulted in the implementation of the Dawes Plan in 1924; this plan outlined a new payment method and raised international loans to help Germany to meet its reparation commitments. Despite this, by 1928 Germany called for a new payment plan, resulting in the Young Plan that established the German reparation requirements at 112 billion marks and created a schedule of payments that would see Germany complete payments by 1988. With the collapse of the German economy in 1931, reparations were suspended for a year and in 1932 during the Lausanne Conference they were cancelled altogether. Between 1919 and 1932, Germany paid less than 21 billion marks in reparations.

The German people saw reparations as a national humiliation. British economist John Maynard Keynes called the treaty a Carthaginian peace that would economically destroy Germany, his arguments had a profound effect on historians and the public at large. Despite Keynes' arguments and those by historians supporting or reinforcing Keynes' views, the consensus of contemporary historians is that reparations were not as intolerable as the Germans or Keynes had suggested and were within Germany's capacity to pay had there been the political will to do so. Following the Second World War, West Germany took up payments; the 1953 London Agreement on German External Debts resulted in an agreement to pay 50 per cent of the remaining balance. The final payment was made on 3 October 2010, settling German loan debts in regard to reparations. In 1914, the First World War broke out. For the next four years fighting raged across Europe, the Middle East and Asia. On 8 January 1918, United States President Woodrow Wilson issued a statement that became known as the Fourteen Points.

In part, this speech called for Germany to withdraw from the territory it had occupied and for the formation of a League of Nations. During the fourth quarter of 1918, the Central Powers began to collapse. In particular, the German military was decisively defeated on the Western Front and the German navy mutinied, prompting domestic uprisings that became known as the German Revolution. Most of the war's major battles occurred in France and the French countryside was scarred in the fighting. Furthermore, in 1918 during the German retreat, German troops devastated France's most industrialized region in the north-east. Extensive looting took place as German forces removed whatever material they could use and destroyed the rest. Hundreds of mines were destroyed along with railways and entire villages. Prime Minister of France Georges Clemenceau was determined, for these reasons, that any just peace required Germany to pay reparations for the damage it had caused. Clemenceau viewed reparations as a way of weakening Germany to ensure it could never threaten France again.

Reparations would go towards the reconstruction costs in other countries, including Belgium, directly affected by the war. British Prime Minister David Lloyd George opposed harsh reparations, arguing for a smaller sum, less damaging to the German economy so that Germany could remain a viable economic power and trading partner, he argued that reparations should include war pensions for disabled veterans and allowances for war widows, which would reserve a larger share of the reparations for the British Empire. Wilson opposed these positions and was adamant that no indemnity should be imposed upon Germany; the Paris Peace Conference opened on 18 January 1919, aiming to establish a lasting peace between the Allied and Central Powers. Demanding compensation from the defeated party was a common feature of peace treaties. However, the financial terms of treaties signed during the peace conference were labelled reparations to distinguish them from punitive settlements known as indemnities, which were intended for reconstruction and compensating families, bereaved by the war.

The opening article of the reparation section of the Treaty of Versailles, Article 231, served as a legal basis for the following articles, which obliged Germany to pay compensation and limited German responsibility to civilian damages. The same article, with the signatory's name changed, was in