Ronald Fisher

Sir Ronald Aylmer Fisher was a British statistician and geneticist. For his work in statistics, he has been described as "a genius who single-handedly created the foundations for modern statistical science" and "the single most important figure in 20th century statistics". In genetics, his work used mathematics to combine natural selection. For his contributions to biology, Fisher has been called "the greatest of Darwin’s successors". From 1919 onward, he worked at the Rothamsted Experimental Station for 14 years, he established his reputation there in the following years as a biostatistician. He is known as one of the three principal founders of population genetics, he outlined Fisher's principle, the Fisherian runaway and sexy son hypothesis theories of sexual selection. His contributions to statistics include the maximum likelihood, fiducial inference, the derivation of various sampling distributions, founding principles of the design of experiments, much more. Fisher held strong views on race.

Throughout his life, he was a prominent supporter of eugenics, an interest which led to his work on statistics and genetics. Notably, he was a dissenting voice in the 1950 UNESCO statement The Race Question, insisting on racial differences. Fisher was born in East Finchley in London, into a middle-class household, he was one of twins, with the other twin being still-born and grew up the youngest, with three sisters and one brother. From 1896 until 1904 they lived at Inverforth House in London, where English Heritage installed a blue plaque in 2002, before moving to Streatham, his mother, died from acute peritonitis when he was 14, his father lost his business 18 months later. Lifelong poor eyesight caused his rejection by the British Army for World War I, but developed his ability to visualize problems in geometrical terms, not in writing mathematical solutions, or proofs, he entered Harrow School won the school's Neeld Medal in mathematics. In 1909, he won a scholarship to study Mathematics at Cambridge.

In 1912, he gained a First in Mathematics. In 1915 he published a paper The evolution of sexual preference on sexual mate choice. During 1913–1919, Fisher worked for six years as a statistician in the City of London and taught physics and maths at a sequence of public schools, at the Thames Nautical Training College, at Bradfield College. There he settled with Eileen Guinness, with whom he had two sons and six daughters. In 1918 he published "The Correlation Between Relatives on the Supposition of Mendelian Inheritance", in which he introduced the term variance and proposed its formal analysis, he put forward a genetics conceptual model showing that continuous variation amongst phenotypic traits measured by biostatisticians could be produced by the combined action of many discrete genes and thus be the result of Mendelian inheritance. This was the first step towards establishing population genetics and quantitative genetics, which demonstrated that natural selection could change allele frequencies in a population, resulting in reconciling its discontinuous nature with gradual evolution.

Joan Box, Fisher's biographer and daughter says that Fisher had resolved this problem in 1911. In 1919, he began working at the Rothamsted Experimental Station for 14 years, where he analysed its immense data from crop experiments since the 1840s, developed the analysis of variance. In 1919, he was offered a position at the Galton Laboratory in University College London led by Karl Pearson, but instead accepted a temporary job at Rothamsted in Harpenden to investigate the possibility of analysing the vast amount of crop data accumulated since 1842 from the "Classical Field Experiments", he analysed the data recorded over many years and in 1921, published Studies in Crop Variation, his first application of the analysis of variance ANOVA. In 1928, Joseph Oscar Irwin began a three-year stint at Rothamsted and became one of the first people to master Fisher's innovations. Between 1912 and 1922 Fisher recommended and vastly popularized Maximum likelihood. Fisher's 1924 article On a distribution yielding the error functions of several well known statistics presented Pearson's chi-squared test and William Gosset's Student's t-distribution in the same framework as the Gaussian distribution and is where he developed Fisher's z-distribution a new statistical method used decades as the F distribution.

He pioneered the principles of the design of experiments and the statistics of small samples and the analysis of real data. In 1925 he published Statistical Methods for Research Workers, one of the 20th century's most influential books on statistical methods. Fisher's method is a technique for data fusion or "meta-analysis"; this book popularized the p-value, plays a central role in his approach. Fisher proposes the level p=0.05, or a 1 in 20 chance of being exceeded by chance, as a limit for statistical significance, applies this to a normal distribution, thus yielding the rule of two standard deviations for statistical significance. The 1.96, the approximate value of the 97.5 percentile point of the normal distribution used in probability and statistics originated in this book. "The value for which P=0.05, or 1 in 20, is 1.96 or n


The Muller C-element is a small digital block used in design of asynchronous circuits and systems. It has been first used in ILLIAC II computer. In terms of the theory of lattices, the C-element is a semimodular distributive circuit, whose operation in time is described by a Hasse diagram; the C-element is related to the rendezvous and join elements, where an input is not allowed to change twice in succession. In some cases, when relations between delays are known, the C-element can be realized as a sum-of-product circuit. Earlier techniques for implementing the C-element include Schmidt trigger, Eccles-Jordan flip-flop and last moving point flip-flop. For two input signals the C-element is defined by the equation y n = x 1 x 2 + y n − 1, which corresponds to the following truth table: This table can be turned into a circuit using the Karnaugh map. However, the obtained implementation is naive. To understand under what conditions the obtained circuit is workable, it is necessary to do additional analysis, which reveals that delay1 is a propagation delay from node 1 via environment to node 3, delay2 is a propagation delay from node 1 via internal feedback to node 3, delay1 must be greater than delay2.

Thus, the naive implementation is correct only for slow environment. Note that the definition of C-element can be generalized for multiple-valued logic or for continuous signals: if x 1 = x 2 =... = x m y n = any, else y n = y n − 1. For example, the truth table for a balanced ternary C-element with two inputs is Depending on the requirements to the switching speed and power consumption, the C-element can be realized as a coarse- or fine-grain circuit. One should distinguish between single-output and differential realizations of C-element. Differential realization is possible using only NANDs. A single-output realization is workable if and only if: The circuit, where each input of a C-element is connected through a separate inverter to its output, is semimodular to the state, where all the inverters are excited; this state is live for the output gate of C-element. There is a number of different single-output circuits of C-element built on logic gates. In particular, the so-called Maevsky's implementation is a non-distributive circuit loosely based on.

Non-distributivity is introduced sometimes to increase concurrency. The 3NAND gate in this circuit can be replaced by two 2NAND gates; the C-element using only two-input gates has been proposed by Tsirlin and synthesized by Starodoubtsev et al. using Taxogram language This circuit coincides with that attributed to Bartky and can operate without the input latch. Yet another version of the C-element built on two RS latches has been synthesized by Murphy using Petrify tool. However, this circuit includes inverter connected to one if the inputs; this inverter should have small delay. However, there are realizations of RS latches that have one inverted input, for example. Note that some speed-independent approaches assume that zero-delay input inverters are available on all gates, a violation of true speed-independence but is safe in practice. Other examples of using this assumption exist. In his report Muller proposed to realize C-element as a majority gate with feedback. However, to avoid hazards linked with skews of internal delays, the majority gate must have as small number of transistors as possible.

C-elements with different timing assumptions can be built on AND-OR-Invert or its dual, OR-AND-Invert gate and inverter. Yet another option patented by Varshavsky et al. is to shunt the input signals when they are not equal each other. Being simple, these realizations dissipate more power due to the short-circuits. Note that connecting an additional majority gate to the inverted output of C-element, we obtain inclusive OR function: z n = x 1 x 2 + y n ¯. Note that some simple asynchronous circuits like pulse distributors can be built on majority gates. Semistatic C-element stores its previous state using two cross-coupled inverters, similar to an SRAM cell. One of the inverters is weaker than the rest of the circuit, so it can be overpowered by the pull-up and pull-down networks. If both inputs are 0 the pull-up network changes the latch's state, the C-element outputs a 0. If both inputs are 1 the pull-down network changes the latch's state, making the C-element output a 1. Otherwise, the input of the latch is not connected to either V


Quintus Ennius was a writer and poet who lived during the Roman Republic. He is considered the father of Roman poetry, he was born in Rudiae a small town located near modern Lecce in the heel of Italy, could speak Oscan as well as Latin and Greek. Although only fragments of his works survive, his influence in Latin literature was significant in his use of Greek literary models. Little is reliably known about the life of Ennius, his contemporaries hardly mentioned him and much, related about him could have been embroidered from references to himself in his now fragmentary writings. Some lines of the Annales, as well as ancient testimonies, for example, suggest that Ennius opened his epic with a recollection of a dream in which the ancient epic-writer Homer informed him that his spirit had been reborn into Ennius, it is true that the doctrine of the transmigration of souls once flourished in the areas of Italy settled by Greeks, but the statement might have been no more than a literary flourish.

Ennius seems to have been given to making large claims, as in the report by Maurus Servius Honoratus that he claimed descent from Messapus, the legendary king of his native district. The Hellenised city of Rudiae, his place of birth, was in the area settled by the Messapians, and this, he used to say, according to Aulus Gellius, had endowed him with a triple linguistic and cultural heritage, fancifully described as "three hearts… Greek and Latin”. The public career of Ennius first emerges in middle life, when he was serving in the army with the rank of centurion during the Second Punic War. While in Sardinia in the year 204 BC, he is said to have attracted the attention of Cato the Elder and was taken by him to Rome. There he taught Greek and adapted Greek plays for a livelihood, by his poetical compositions gained the friendship of some of the greatest men in Rome whose achievements he praised. Amongst these were Scipio Africanus and Fulvius Nobilior, whom he accompanied on his Aetolian campaign.

Afterwards he made the capture of Ambracia, at which he was present, the subject of a play and of an episode in the Annales. It was through the influence of Nobilior's son Quintus that Ennius subsequently obtained Roman citizenship, but he himself lived plainly and in the literary quarter on the Aventine Hill with the poet Caecilius Statius, a fellow adapter of Greek plays. At about the age of 70 Ennius died after producing his tragedy Thyestes. In the last book of his epic poem, in which he seems to have given various details of his personal history, he mentioned that he was in his 67th year at the date of its composition, he compared himself, in contemplation of the close of the great work of his life, to a gallant horse which, after having won the prize at the Olympic Games, obtained his rest when weary with age. A similar feeling of pride at the completion of a great career is expressed in the memorial lines which he composed to be placed under his bust after death: “Let no one weep for me, or celebrate my funeral with mourning.

Ennius continued the nascent literary tradition by writing plays in Greek and Roman style, as well as his most famous work, a historic epic in hexameters called the Annales. Other minor works include the Epicharmus, the Euhemerus, the Hedyphagetica, Praecepta/Protrepticus, Saturae and Sota; the Annales was an epic poem in fifteen books expanded to eighteen, covering Roman history from the fall of Troy in 1184 BC down to the censorship of Cato the Elder in 184 BC. It was the first Latin poem to adopt the dactylic hexameter metre used in Greek epic and didactic poetry, leading it to become the standard metre for these genres in Latin poetry; the Annals became a school text for Roman schoolchildren supplanted by Virgil's Aeneid. About 600 lines survive. A copy of the work is among the Latin rolls of the Herculaneum library; the Epicharmus was inspired by the philosophical hypotheses developed by the Sicilian poet and philosopher Epicharmus of Kos, after which Ennius's work took its name. In the Epicharmus, the poet describes a dream he had in which he died and was transported to some place of heavenly enlightenment.

Here, he met Epicharmus, who explained the nature of the gods and taught Ennius the physics of the universe. The Euhemerus presented a theological doctrine based on the ideas Greek of Euhemerus of Messene, who argued that the gods of Olympus were not supernatural powers that interference in the lives of humans, but rather heroes of old who after death were regarded as deities due to their valor, bravery, or cultural impact. Both Cicero and Lactantius write that the Euhemerus was a "translat and a recount" of Euhemerus's original work the Sacred History, but it is unclear if this means Ennius translated the original from Greek into Latin, or added in his own elements. Most of what is preserved of this work comes to us from Lactantius, these snippets suggest that the Euhemerus was a prose text; the Hedyphagetica took much of its substance from the gastronomical epic of Archestratus of Gela. The extant portions of Ennius's poem discuss. Most of the fragments, replete with unique terms for fish and numerous place names, are corrupt or damaged.

The Hedyphagetica is written in hexameters, but differs from the Annales in regards to "metrical practices". The titles Praecepta and Protrepticus were used to refer to the same wo