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Okazaki fragments

Okazaki fragments are short sequences of DNA nucleotides (approximately 150 to 200 base pairs long in eukaryotes) which are synthesized discontinuously and later linked together by the enzyme DNA ligase to create the lagging strand during DNA replication. They were discovered in the 1960s by the Japanese molecular biologists Reiji and Tsuneko Okazaki, along with the help of some of their colleagues.

During DNA replication, the double helix is unwound and the complementary strands are separated by the enzyme DNA helicase, creating what is known as the DNA replication fork. Following this fork, DNA primase and DNA polymerase begin to act in order to create a new complementary strand. Because these enzymes can only work in the 5’ to 3’ direction, the two unwound template strands are replicated in different ways. One strand, the leading strand, undergoes a continuous replication process since its template strand has 3’ to 5’ directionality, allowing the polymerase assembling the leading strand to follow the replication fork without interruption. The lagging strand, however, cannot be created in a continuous fashion because its template strand has 5’ to 3’ directionality, which means the polymerase must work backwards from the replication fork. This causes periodic breaks in the process of creating the lagging strand. The primase and polymerase move in the opposite direction of the fork, so the enzymes must repeatedly stop and start again while the DNA helicase breaks the strands apart. Once the fragments are made, DNA ligase connects them into a single, continuous strand. The entire replication process is considered "semi-discontinuous" since one of the new strands is formed continuously and the other is not.

During the 1960s, Reiji and Tsuneko Okazaki conducted experiments involving DNA replication in the bacterium Escherichia coli. Before this time, it was commonly thought that replication was a continuous process for both strands, but the discoveries involving E. coli led to a new model of replication. The scientists found there was a discontinuous replication process by pulse-labeling DNA and observing changes that pointed to non-contiguous replication.

Experiments
The work of Kiwako Sakabe, Reiji Okazaki and Tsuneko Okazaki provided experimental evidence supporting the hypothesis that DNA replication is a discontinuous process. Previously, it was commonly accepted that replication was continuous in both the 3' to 5' and 5' to 3' directions. 3' and 5' are specifically numbered carbons on the deoxyribose ring in nucleic acids, and refer to the orientation or directionality of a strand. In 1967, Tsuneko Okazaki and Toru Ogawa suggested that there is no found mechanism that showed continuous replication in the 3' to 5' direction, only 5' to 3' using DNA polymerase, a replication enzyme. The team hypothesized that if discontinuous replication was used, short strands of DNA, synthesized at the replicating point, could be attached in the 5' to 3' direction to the older strand.

To distinguish the method of replication used by DNA experimentally, the team pulse-labeled newly replicated areas of Escherichia coli chromosomes, denatured, and extracted the DNA. A large number of radioactive short units meant that the replication method was likely discontinuous. The hypothesis was further supported by the discovery of polynucleotide ligase, an enzyme that links short DNA strands together.

In 1968, Reiji and Tsuneko Okazaki gathered additional evidence of nascent DNA strands. They hypothesized that if discontinuous replication, involving short DNA chains linked together by polynucleotide ligase, is the mechanism used in DNA synthesis, then "newly synthesized short DNA chains would accumulate in the cell under conditions where the function of ligase is temporarily impaired." E. coli were infected with bacteriophage T4 that produce temperature-sensitive polynucleotide ligase. The cells infected with the T4 phages accumulated a large number of short, newly synthesized DNA chains, as predicted in the hypothesis, when exposed to high temperatures. This experiment further supported the Okazakis' hypothesis of discontinuous replication and linkage by polynucleotide ligase. It disproved the notion that short chains were produced during the extraction process as well.

The Okazakis' experiments provided extensive information on the replication process of DNA and the existence of short, newly synthesized DNA chains that later became known as Okazaki fragments.

Pathways
Two pathways have been proposed to process Okazaki fragments: the short flap pathway and the long flap pathway.

Short Flap Pathway
In the short flap pathway in eukaryotes the lagging strand of DNA is primed in short intervals. In the short pathway only, the nuclease FEN1 is involved. Pol δ frequently encounters the downstream primed Okazaki fragment and displaces the RNA/DNA initiator primer into a 5′ flap. The FEN1 5’-3’ endonuclease recognizes that the 5’ flap is displaced, and it cleaves, creating a substrate for ligation. In this method the Pol a-synthesized primer is removed. Studies show that in the FEN1 suggest a ‘tracking; model where the nuclease moves from the 5’ flap to its base to preform cleavage. The Pol δ does not process a nuclease activity to cleave the displaced flap. The FEN1 cleaves the short flap immediately after they form. The cleavage is inhibited when the 5’ end of the DNA flap is blocked either with a complementary primer or a biotin-conjugated streptavidin moiety. DNA ligase seals the nick made by the FEN1 and it creates a functional continuous double strand of DNA. PCNA simulates enzymatic functions of proteins for both FEN1 and DNA ligase. The interaction is crucial in creating proper ligation of the lagging DNA strand. Sequential strand displacement and cleavage by Pol δ and FEN1, respectively, helps to remove the entire initiator RNA before ligation. Many displacements need to take place and cleavage reactions are required to remove the initiator primer. The flap that is created and processes and it is matured by the short flap pathway.

Long Flap Pathway
In some cases, the FEN1 lasts for only a short period of time and disengages from the replication complex. This causes a delay in the cleavage that the flaps displaced by Pol δ become long. When the RPA reaches a long enough length, it can bind stably. When the RPA bound flaps are refactorized to FEN1 cleavage the require another nuclease for processing, this has been identified as an alternate nuclease, DNA2. DNA2 has defects in the DEN1 overexpression. The DNA2 showed to work with FEN1 to process long flaps. DNA2 can dissociate the RPA from a long flap, it does this by using a mechanism like the FEN1. It binds the flap and threads the 5’ end of the flap. The nuclease cleaves the flap making it too short to bind to the RPA, the flap being too short means it is available for FEN1 and ligation. This is known as the long flap method. DNA2 can act as FEN1 as a backup for nuclease activity but it is not an efficient process.

Alternate pathway
Until recently, there were only two known pathways to process Okazaki fragments. However, current investigations have concluded that a new pathway for Okazaki fragmentation and DNA replication exists. This alternate pathway involves the enzymes Pol δ with Pif1 which perform the same flap removal process as Pol δ and FEN1.

Primase
Primase adds RNA primers onto the lagging strand, which allows synthesis of Okazaki fragments from 5' to 3'. However, primase creates RNA primers at a much lower rate than that at which DNA polymerase synthesizes DNA on the leading strand. DNA polymerase on the lagging strand also has to be continually recycled to construct Okazaki fragments following RNA primers. This makes the speed of lagging strand synthesis much lower than that of the leading strand. To solve this, primase acts as a temporary stop signal, briefly halting the progression of the replication fork during DNA replication. This molecular process prevents the leading strand from overtaking the lagging strand.

DNA polymerase δ
New DNA is made during this phase by enzymes which synthesize DNA in the 5’ to 3’ direction. DNA polymerase is essential for both the leading strand which is made as a continuous strand and lagging strand which is made in small pieces in DNA Synthesis. This process happens for extension of the newly synthesized fragment and expulsion of the RNA and DNA segment. Synthesis occurs in 3 phases with two different polymerases, DNA polymerase α-primase and DNA polymerase δ. This process starts with polymerase α-primase displacing from the RNA and DNA primer by the clamp loader replication Effect, this Effect leads the sliding clamp onto the DNA. After this, DNA polymerase δ begins to go into its holoenzyme form which then synthesis begins. The synthesis process will continue until the 5’end of the previous Okazaki fragment has arrived. Once arrived, Okazaki fragment processing proceeds to join the newly synthesized fragment to the lagging strand. Last function of DNA polymerase δ is to serve as a supplement to FEN1/RAD27 5’ Flap Endonuclease activity. The rad27-p allele is lethal in most combinations but was viable with the rad27-p polymerase and exo1. Both rad27-p polymerase and exo1 portray strong synergistic increases in CAN 1 duplication mutations. The only reason this mutation is viable is due to the double-strand break repair genes RAD50, RAD51 and RAD52. The RAD27/FEN1 creates nicks between adjacent Okazaki fragments by minimizing the amount of strand-expulsion in the lagging strand.

DNA ligase I
During lagging strand synthesis, DNA ligase I connects the Okazaki fragments, following replacement of the RNA primers with DNA nucleotides by DNA polymerase δ. Okazaki fragments that are not ligated could cause double-strand-breaks, which cleaves the DNA. Since only a small number of double-strand breaks are tolerated, and only a small number can be repaired, enough ligation failures could be lethal to the cell.

Further research implicates the supplementary role of proliferating cell nuclear antigen (PCNA) to DNA ligase I's function of joining Okazaki fragments. When the PCNA binding site on DNA ligase I is inactive, DNA ligase I's ability to connect Okazaki fragments is severely impaired. Thus, a proposed mechanism follows: after a PCNA-DNA polymerase δ complex synthesizes Okazaki fragments, the DNA polymerase δ is released. Then, DNA ligase I binds to the PCNA, which is clamped to the nicks of the lagging strand, and catalyzes the formation of phosphodiester bonds.

Flap endonuclease 1
Flap endonuclease 1 (FEN1) is responsible for processing Okazaki fragments. It works with DNA polymerase to remove the RNA primer of an Okazaki fragment and can remove the 5' ribonucleotide and 5' flaps when DNA polymerase displaces the strands during lagging strand synthesis. The removal of these flaps involves a process called nick translation and creates a nick for ligation. Thus, FEN1's function is necessary to Okazaki fragment maturation in forming a long continuous DNA strand. Likewise, during DNA base repair, the damaged nucleotide is displaced into a flap and subsequently removed by FEN1.

Dna2 endonuclease
Dna2 endonuclease does not have a specific structure and their properties are not well characterized, but could be referred as single-stranded DNA with free ends (ssDNA). Dna2 endonuclease is essential to cleave long DNA flaps that leave FEN1 during the Okazaki Process. Dna2 endonuclease is responsible for the removal of the initiator RNA segment on Okazaki Fragments. Also, Dna2 endonuclease has a pivotal role in the intermediates created during diverse DNA metabolisms and is functional in telomere maintenance.

Dna2 endonuclease becomes active when a terminal RNA segment attaches at the 5’ end, because it translocates in the 5’ to 3’ direction. In the presence of a single stranded DNA-binding protein RPA, the DNA 5' flaps become too long, and the nicks no longer fit as substrate for FEN1. This prevents the FEN1 from removing the 5′-flaps. Thus, Dna2's role is to reduce the 3′ end of these fragments, making it possible for FEN1 to cut the flaps, and the Okazaki fragment maturation more efficient. During the Okazaki Process, Dna2 helicase and endonuclease are inseparable. Dna2 Endonuclease does not depend on the 5’-tailed fork structure of its activity. Unproductive binding has been known to create blocks to FEN1 cleavage and tracking. It is known that ATP reduces activity, but promotes the release of the 3’-end label. Studies have suggested that a new model of Dna2 Endonuclease and FEN1 are partially responsible in Okazaki fragment maturation.

Biological function
Newly synthesized DNA, otherwise known as Okazaki fragments, are bound by DNA ligase, which forms a new strand of DNA. There are two strands that are created when DNA is synthesized. The leading strand is continuously synthesized and is elongated during this process to expose the template that is used for the lagging strand (Okazaki fragments). During the process of DNA replication, DNA and RNA primers are removed from the lagging strand of DNA to allow Okazaki fragments to bind to. Since this process is so common, Okazaki maturation will take place around a million times during one completion of DNA replication. For Okazaki maturation to occur, RNA primers must create segments on the fragments to be ligated. This is used as a building block for the synthesis of DNA in the lagging strand. On the template strand, polymerase will synthesize in the opposite direction from the replication fork. Once the template becomes discontinuous, it will create an Okazaki fragment. Defects in the maturation of Okazaki fragments can potentially cause strands in the DNA to break and cause different forms of chromosome abnormality. These mutations in the chromosomes can affect the appearance, the number of sets, or the number of individual chromosomes. Since chromosomes are fixed for each specific species, it can also change the DNA and cause defects in the genepool of that species.

Differences in prokaryotes and eukaryotes
Okazaki fragments are present in both prokaryotes and eukaryotes. DNA molecules in eukaryotes differ from the circular molecules of prokaryotes in that they are larger and usually have multiple origins of replication. This means that each eukaryotic chromosome is composed of many replicating units of DNA with multiple origins of replication. In comparison, prokaryotic DNA has only a single origin of replication. In eukaryotes, these replicating forks, which are numerous all along the DNA, form "bubbles" in the DNA during replication. The replication fork forms at a specific point called autonomously replicating sequences (ARS). Eukaryotes have a clamp loader complex and a six-unit clamp called the proliferating cell nuclear antigen. The efficient movement of the replication fork also relies critically on the rapid placement of sliding clamps at newly primed sites on the lagging DNA strand by ATP-dependent clamp loader complexes. This means that the piecewise generation of Okazaki fragments can keep up with the continuous synthesis of DNA on the leading strand. These clamp loader complexes are characteristic of all eukaryotes and separate some of the minor differences in the synthesis of Okazaki fragments in prokaryotes and eukaryotes. The lengths of Okazaki fragments in prokaryotes and eukaryotes are different as well. Prokaryotes have Okazaki fragments that are quite longer than those of eukaryotes. Eukaryotes typically have Okazaki fragments that are 100 to 200 nucleotides long, whereas fragments in prokaryotic E. coli can be 2,000 nucleotides long. The reason for this discrepancy is unknown.

Each eukaryotic chromosome is composed of many replicating units of DNA with multiple origins of replication. In comparison, the prokaryotic E. coli chromosome has only a single origin of replication. Replication in prokaryotes occurs inside of the cytoplasm, and this all begins the replication that is formed of about 100 to 200 or more nucleotides. Eukaryotic DNA molecules have a significantly larger number of replicons, about 50,000 or more; however, replication does not occur at the same time on all of the replicons. In eukaryotes, DNA replication takes place in the nucleus. A plethora replication form in just one replicating DNA molecule, the start of DNA replication is moved away by the multi-subunit protein. This replication is slow, and sometimes about 100 nucleotides per second are added.

We take from this that prokaryotic cells are simpler in structure, they have no nucleus, organelles, and very little of DNA, in the form of a single chromosome. Eukaryotic cells have nucleus with multiple organelles and more DNA arranged in linear chromosomes. We also see that the size is another difference between these prokaryotic and eukaryotic cells. The average eukaryotic cell has about 25 times more DNA than a prokaryotic cell does. Replication occurs much faster in prokaryotic cells than in eukaryotic cells; bacteria sometimes only take 40 minutes, while animal cells can take up to 400 hours. Eukaryotes also have a distinct operation for replicating the telomeres at the end of their last chromosomes. Prokaryotes have circular chromosomes, causing no ends to synthesize. Prokaryotes have a short replication process that occurs continuously; eukaryotic cells, on the other hand, only undertake DNA replication during the S-phase of the cell cycle.

The similarities are the steps for the DNA replication. In both prokaryotes and eukaryotes, replication is accomplished by unwinding the DNA by an enzyme called the DNA helicase. New strands are created by enzymes called DNA polymerases. Both of these follow a similar pattern, called semi-conservative replication, in which individual strands of DNA are produced in different directions, which makes a leading and lagging strand. These lagging strands are synthesized by the production of Okazaki fragments that are soon joined. Both of these organisms begin new DNA strands which also include small strands of RNA.

Medical concepts associated with Okazaki fragments
Although cells undergo multiple steps in order to ensure there are no mutations in the genetic sequence, sometimes specific deletions and other genetic changes during Okazaki fragment maturation go unnoticed. Because Okazaki fragments are the set of nucleotides for the lagging strand, any alteration including deletions, insertions, or duplications from the original strand can cause a mutation if it is not detected and fixed. Other causes of mutations include problems with the proteins that aid in DNA replication. For example, a mutation related to primase affects RNA primer removal and can make the DNA strand more fragile and susceptible to breaks. Another mutation concerns polymerase α, which impairs the editing of the Okazaki fragment sequence and incorporation of the protein into the genetic material. Both alterations can lead to chromosomal aberrations, unintentional genetic rearrangement, and a variety of cancers later in life.

In order to test the effects of the protein mutations on living organisms, researchers genetically altered lab mice to be homozygous for another mutation in protein related to DNA replication, flap endonuclease 1, or FEN1. The results varied based on the specific gene alterations. The homozygous knockout mutant mice experienced a "failure of cell proliferation" and "early embryonic lethality" (27). The mice with the mutation F343A and F344A (also known as FFAA) died directly after birth due to complications in birth including pancytopenia and pulmonary hypoplasia. This is because the FFAA mutation prevents the FEN1 from interacting with PCNA (proliferating cell nuclear antigen), consequently not allowing it to complete its purpose during Okazaki fragment maturation. The interaction with this protein is considered to be the key molecular function in the FEN1's biological function. The FFAA mutation causes defects in RNA primer removal and long-base pair repair, of which cause many breaks in the DNA. Under careful observation, cells homozygous for FFAA FEN1 mutations seem to display only partial defects in maturation, meaning mice heterozygous for the mutation would be able to survive into adulthood, despite sustaining multiple small nicks in their genomes. Inevitably however, these nicks prevent future DNA replication because the break causes the replication fork to collapse and causes double strand breaks in the actual DNA sequence. In time, these nicks also cause full chromosome breaks, which could lead to severe mutations and cancers. Other mutations have been implemented with altered versions of Polymerase α, leading to similar results.

title: Okazaki fragments


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Fluoro-richterite

Fluororichterite is a rare amphibole with formula Na(NaCa)Mg5Si8O22F2.

Occurrence
Fluororichterite was first reported from the Ilmen Nature Reserve, Ilmen Mountains, Chelyabinsk Oblast', Southern Urals, Russia. It was recognized by the International Mineralogical Association in 1994. Its name is derived from its fluorine content and relation to richterite.

At the type locality in the Ilmen Mountains fluororichterite occurs in carbonate veins in amphibolites and ultramafic rocks. In the Essonville occurrence in Wilberforce, Ontario it occurs in a limestone lens within a gneiss and is associated with phlogopite and calcite. It has also been reported from Austria, Germany, Italy, Spain and China. At Coyote Peak in the Coastal Range, Humboldt County, California, it occurs with a variety of rare minerals in an alkaline mafic diatreme.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Fluoro-richterite


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Belgae

The Belgae were a large confederation of tribes living in northern Gaul, between the English Channel, the west bank of the Rhine, and the northern bank of the river Seine, from at least the third century BC. They were discussed in depth by Julius Caesar in his account of his wars in Gaul. Some peoples in southern Britain were also called Belgae and had apparently moved from the continent. T. F. O'Rahilly believed that some had moved further west and he equated them with the Fir Bolg in Ireland. The Roman province of Gallia Belgica was named after the continental Belgae. The term continued to be used in the region until the present day and is reflected in the name of the modern country of Belgium.

Etymology
The consensus among linguists is that the ethnic name Belgae probably comes from the Proto-Celtic root *belg- or *bolg- meaning "to swell (particularly with anger/battle fury/etc.)", cognate with the Dutch adjective gebelgd "very angry" (weak perfect participle of the verb belgen "to become angry") and verbolgen "being angry" (strong perfect participle of obsolete verbelgen "to make angry"), as well as the Old English verb belgan, "to be angry" (from Proto-Germanic *balgiz), derived ultimately from the Proto-Indo-European root *bhelgh- ("to swell, bulge, billow"). Thus, a Proto-Celtic ethnic name *Bolgoi could be interpreted as "the people who swell (particularly with anger/battle fury)".

Origins of the Belgae
In Caesar's usage, Belgium is a geographical subregion comprising the Bellovaci, Ambiani, Atrebates, and Veromandui. These four communities are widely thought to have been the original Belgae in Gaul.

Julius Caesar describes Gaul at the time of his conquests (58–51 BC) as divided into three parts, inhabited by the Aquitani in the southwest, the Gauls in the biggest central part, who in their own language were called Celtae, and the Belgae in the north. Each of these three parts, he says, differed in terms of customs, laws and language. He noted that the Belgae, were "the bravest, because they are furthest from the civilization and refinement of [our] Province, and merchants least frequently resort to them, and import those things which tend to effeminate the mind; and they are the nearest to the Germans, who dwell beyond the Rhine, with whom they are continually waging war". Ancient sources such as Caesar are not always clear about the things used to define ethnicity today. While Caesar or his sources described the Belgae as distinctly different from the Gauls, Strabo stated that the differences between the Celts (Gauls) and Belgae in countenance, language, politics and way of life was a small one, unlike the difference between the Aquitanians and Celts. The fact that the Belgae were living in Gaul means that in one sense they were Gauls. This may be Caesar's meaning when he says "The Belgae have the same method of attacking a fortress as the rest of the Gauls".

Inconsistently, Caesar in Bello Gallico, II.4 also contrasted them with Gauls:
 * When Caesar inquired of them what states were in arms, how powerful they were, and what they could do, in war, he received the following information: that the greater part of the Belgae were sprung, from the Germans, and that having crossed the Rhine at an early period, they had settled there, on account of the fertility of the country, and had driven out the Gauls who inhabited those regions; and that they were the only people who, in the memory of our fathers [i.e. as far as we can remember], when all Gaul was overrun, had prevented the Teutones and the Cimbri from entering their territories; the effect of which was, that, from the recollection of those events, they assumed to themselves great authority and haughtiness in military matters.

So Caesar used the word "Germani" in two ways. He described a group of tribes within the Belgic alliance as the "Germani", distinguishing them from their neighbours. The most important of these tribes in relation to Caesar's campaigns were the Eburones. The other way he used the term was to refer to those related tribes east of the Rhine, who were not Celtic. So the Germani among the Belgae are called, based on Caesar's account, the Germani cisrhenani, to distinguish them from other Germani living east of the Rhine in what he understood to be their homeland. However, the later historian Tacitus was informed that the name Germania was known to have changed in meaning:
 * The first people to cross the Rhine and oust the Gauls, those now called Tungri, were then called Germani. It was the name of this nation, not a race, that gradually came into general use. And so, to begin with, they were all called Germani after the conquerors because of the terror these inspired, and then, once the name had been devised, they adopted it themselves.

In other words, Tacitus understood that the collective name Germani had first been used in Gaul, for a specific people there with connections beyond the Rhine, the Tungri being the name of the people living where the Eburones had lived in later imperial times, and was later adopted as a collective name for the non-Celtic peoples beyond the Rhine, the other, better-known way that Caesar used the term.

Culture
The cultural cohesion of Belgium as Caesar sketched it is suggested by the maintaining of these borders, more or less, in administrative divisions (pagi) mapped out later by the Romans and still evident in the parishes of the Carolingian era. Archaeology suggests cultural continuities from the third through the first centuries BC within this subregion, inhabited in the time of Caesar by Bellovaci, Ambiani, Atrebates, and Veromandui.

From 250 BC onward, the disposal of the dead was primarily through cremation, with some inhumation practiced. Ceramics and brooches are typical grave goods, while items of feasting appear in wealthier graves. The absence of weapons distinguishes these burials from the funerary practice of communities to the north and south.

Around this same time, a characteristic form of enclosed sanctuary began to be built, and from the late 2nd through the mid 1st centuries BC, fortifications with a high earthen rampart and a wide, flat-bottomed ditch are concentrated there.

The coinage of the Belgae in Gaul shows commonalities in design and distribution patterns from the 4th through the 1st centuries BC.

The Belgae of this period do not appear to have drunk beer.

Language
Caesar's book Commentarii de Bello Gallico begins: "All Gaul is divided into three parts, one of which the Belgae inhabit, the Aquitani another, those who in their own language are called Celts, in ours Gauls, the third. All these differ from each other in language, customs and laws." However, many modern scholars believe that the Belgae were a Celtic-speaking group. On the other hand, at least part of the Belgae may also have had significant cultural and historical connections to peoples east of the Rhine, including Germanic peoples, judging from archaeological, placename and textual evidence. It has also been argued based on placename studies that the older language of the area, though apparently Indo-European, was not Celtic (see Nordwestblock) and that Celtic, though influential amongst the elite, might never have been the main language of the part of the Belgic area north of the Ardennes. For example, Maurits Gysseling suggested that prior to Celtic and Germanic influences the Belgae may have comprised a distinct Indo-European branch, termed Belgian.

However, most of the Belgic tribal and personal names recorded are identifiably Gaulish, including those of the Germani cisrhenani, and this is indeed also true of the tribes immediately over the Rhine at this time, such as the Tencteri and Usipetes. Surviving inscriptions also indicate that Gaulish was spoken in at least part of Belgic territory.

The Romans were not precise in their ethnography of northern barbarians: by "Germanic", Caesar may simply have meant "originating east of the Rhine" (the homeland of the Germani cisrhenani) with no distinction of language intended. The east of the Rhine was not necessarily inhabited by Germanic speakers at this time. It has been remarked that Germanic speakers might have been no closer than the river Elbe in the time of Caesar. However, studies of place names, such as those of Maurits Gysseling, have been argued to show evidence of the pre-Roman presence of early Germanic languages throughout the Belgic area north of the Ardennes, where the Germani cisrhenani lived. The sound changes described by "Grimm's law" appear to have affected names with older forms, apparently already in the second century BC. Strong evidence for old Celtic placenames, though, is found in the Ardennes and to the south of them. According to Strabo, the country of the Belgae extended along the coast where 15 tribes were living from the Rhenus (Rhine) to the Liger (Loire). Strabo also says that "Augustus Caesar, when dividing the country into four parts, united the Keltae to the Narbonnaise; the Aquitani he preserved the same as Julius Caesar, but added thereto fourteen other nations of those who dwelt between the Garonne and the river Loire, and dividing the rest into two parts, the one extending to the upper districts of the Rhine (Gallia Lugdunensis) he made dependent upon Lugdunum, the other [he assigned] to the Belgae (Gallia Belgica)."

Apart from the Germani, the report of Caesar seems to indicate that more of the Belgae had some Germanic ethnicity, but this is not necessarily what defines a tribe as Belgic. Edith Wightman proposed that Caesar can be read as treating only the southwestern Belgic tribes, the Suessiones, Viromandui and Ambiani and perhaps some of their neighbours, as the true ethnic Belgae, as opposed to those in a political and military alliance with them. She reads Caesar as implying a "transition zone" of mixed ethnicity and ancestry for the Menapii, Nervii and Morini, all living in the northwest of the Belgic region, neighbours to the Germani cisrhenani in the northeast. (Caesar also mentions his allies the Remi being closest to the Celts amongst the Belgae. )

It seems that, whatever their ancestry, at least some of the Belgic tribes spoke a variety of Gaulish as their main language by Caesar's time, and all of them used such languages in at least some contexts. Luc van Durme summarizes competing evidence of Celtic and Germanic influence at the time of Caesar by saying that "one has to accept the rather remarkable conclusion that Caesar must have witnessed a situation opposing Celtic and Germanic in Belgium, in a territory slightly more to the south than the early medieval Romance-Germanic language border", but van Durme accepts that Germanic did not block "Celticisation coming from the south" so "both phenomena were simultaneous and interfering".

The medieval Gesta Treverorum compiled by monks of Trier claims that the Belgae were descendants of Trebeta, an otherwise unattested legendary founder of Trier, the Roman Augusta Treverorum, "Augusta of the Treveri".

Tribes of the Belgae
Caesar names the following as Belgic tribes, which can be related to later Roman provinces: Later, Tacitus mentioned a tribe called the Tungri living where the Germani cisrhenani had lived, and he also stated that they had once been called the Germani (although Caesar had claimed to have wiped out the name of the main tribe, the Eburones). Other tribes that may have been included among the Belgae in some contexts were the Leuci, Treveri and Mediomatrici. Posidonius includes the Armoricani, as well.

Conquest of the Belgae
Caesar conquered the Belgae, beginning in 57 BC. He writes that the Belgae were conspiring and arming themselves in response to his earlier conquests; to counter this threat, he raised two new legions and ordered his Gallic allies, the Aedui, to invade the territory of the Bellovaci, the largest and fiercest of the Belgae tribes. Wary of the numbers and bravery of the Belgae, Caesar initially avoided a pitched battle, resorting mainly to cavalry skirmishes to probe their strengths and weaknesses. Once he was satisfied his troops were a match for them, he made camp on a low hill protected by a marsh at the front and the river Aisne behind, near Bibrax (between modern Laon and Reims) in the territory of the Remi.

The Belgae attacked over the river, but were repulsed after a fierce battle. Realising they could not dislodge the Romans and aware of the approach of the Aedui into the lands of the Bellovaci, the Belgae decided to disband their combined force and return to their own lands. Caesar's informants advised him that whichever tribe Caesar attacked first, the others would come to their defence. They broke camp shortly before midnight. At daybreak, satisfied the retreat was not a trap, Caesar sent cavalry to harass the rear guard, followed by three legions. Many of the Belgae were killed in battle.

Caesar next marched into the territory of the Suessiones and besieged the town of Noviodunum (Soissons). Seeing the Romans' siege engines, the Suessiones surrendered, whereupon Caesar turned his attention to the Bellovaci, who had retreated into the fortress of Bratuspantium (between modern Amiens and Beauvais). They quickly surrendered, as did the Ambiani.

The Nervii, along with the Atrebates and Viromandui, decided to fight (the Atuatuci had also agreed to join them, but had not yet arrived). They concealed themselves in the forests and attacked the approaching Roman column at the river Sabis (previously thought to be the Sambre, but recently the Selle is thought to be more probable). Their attack was quick and unexpected. The element of surprise briefly left the Romans exposed. Some of the Romans did not have time to take the covers off their shields or to even put on their helmets. However, Caesar grabbed a shield, made his way to the front line, and quickly organised his forces. The two Roman legions guarding the baggage train at the rear finally arrived and helped to turn the tide of the battle. Caesar says the Nervii were almost annihilated in the battle, and is effusive in his tribute to their bravery, calling them "heroes" (for more details see Battle of the Sabis).

The Atuatuci, who were marching to their aid, turned back on hearing of the defeat and retreated to one stronghold, were put under siege, and soon surrendered and handed over their arms. However, the surrender was a ploy, and the Atuatuci, armed with weapons they had hidden, tried to break out during the night. The Romans had the advantage of position and killed 4,000. The rest, about 53,000, were sold into slavery.

In 53 BC, the Eburones, led by Ambiorix, along with the Nervii, Menapii and Morini, revolted again and wiped out fifteen cohorts, only to be put down by Caesar. The Belgae fought in the uprising of Vercingetorix in 52 BC.

After their final subjugation, Caesar combined the three parts of Gaul, the territory of the Belgae, Celtae and Aquitani, into a single unwieldy province (Gallia Comata, "long-haired Gaul") that was reorganized by the emperor Augustus into its traditional cultural divisions. The province of Gallia Belgica was bounded on its east by the Rhine and extended all the way from the North Sea to Lake Constance (Lacus Brigantinus), including parts of what is now western Switzerland, with its capital at the city of the Remi (Reims). Under Diocletian, Belgica Prima (capital Augusta Trevirorum, Trier) and Belgica Secunda (capital Reims) formed part of the diocese of Gaul.

Great Britain
The Belgae had made their way across the English Channel into southern Britain in Caesar's time. Caesar asserts they had first crossed the channel as raiders, only later establishing themselves on the island. The precise extent of their conquests is unknown. After the Roman conquest of Great Britain, the civitas of the Belgae was bordered to the north by the British Atrebates, who were also a Belgic tribe, and to the east by the Regni, who were probably linked to the Belgae as well. The arrival and spread of Aylesford-Swarling pottery across the southeastern corner of Britain has been related to the Belgic invasion since Arthur Evans published his excavation of Aylesford in 1890, which was then thought to show "the demonstrable reality of a Belgic invasion", according to Sir Barry Cunliffe, although more recent studies tend to downplay the role of migration in favour of increasing trade links; the question remains unclear.

A large number of coins of the Ambiani dating to the mid-second century BC have been found in southern Britain and the remains of a possible Belgic fort have been unearthed in Kent. Within memory of Caesar's time, a king of the Suessiones (also referred to as Suaeuconi) called Diviciacus was not only the most powerful king of Belgic Gaul, but also ruled territory in Britain. Commius of the Atrebates, Caesar's former ally, fled to Britain after participating in Vercingetorix's rebellion and either joined or established a British branch of his tribe. Based on the development of imagery on coins, by the time of the Roman conquest, some of the tribes of south-eastern Britain likely were ruled by a Belgic nobility and were culturally influenced by them. The later civitas (administrative division) of Roman Britain had towns including Portus Adurni (Portchester) and Clausentum (Southampton). The civitas capital was at Venta Belgarum (Winchester), which was built on top of an Iron Age oppidum (this was itself built on the site of two earlier abandoned hillforts); Winchester remains Hampshire's county town to this day. In addition to Venta Belgarum, the ancient geographer Ptolemy lists Aquae Calidae (Bath) and Iscalis as poleis of the Belgae.

Ireland?
In his theory of Ireland's prehistory, T. F. O'Rahilly suggested in 1946 that a branch of the Belgae settled in Ireland around the 5th century BC, later becoming the historical Iverni (Érainn) and their offshoots. He believes the memory of Belgae settlers was preserved in medieval Irish legend as the Fir Bolg. O'Rahilly's theory has been challenged by historians and archaeologists, and is no longer accepted.

Fintan O'Toole suggested the Keshcarrigan Bowl is evidence for the movement of people into Ireland following upheaval and displacement, triggered by the Belgae arriving into Britain as refugees.

title: Belgae


text:
Talk:Nottingham

Shopping
The 'shopping' category needs an update regarding the Victoria Centre and Broadmarsh. With developments for the former well underway and clear plans for the Broadmarsh submitted. — Preceding unsigned comment added by Gilb3rn4tor (talk • contribs) 12:55, 9 April 2015 (UTC)

External links modified
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I have just added archive links to 3 one external links on Nottingham. Please take a moment to review my edit. If necessary, add after the link to keep me from modifying it. Alternatively, you can add to keep me off the page altogether. I made the following changes:
 * Added archive https://web.archive.org/20131103232808/http://musicnottingham.com/2013/08/23/georgie-rose-in-session-at-rofl-audio-for-this-weekends-sound-of-nottingham/ to http://musicnottingham.com/2013/08/23/georgie-rose-in-session-at-rofl-audio-for-this-weekends-sound-of-nottingham/
 * Added archive https://web.archive.org/20150402152505/http://www.confetti.uk.com/about/confetti-tv-channel-bid/ to http://www.confetti.uk.com/about/confetti-tv-channel-bid/
 * Added archive https://web.archive.org/20150722155636/http://www.flyfm.co.uk/ to http://www.flyfm.co.uk

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City Image
I'd quite like to see an updated image representing the city; something along the lines of Manchester or Birmingham's header image. Thoughts? — Preceding unsigned comment added by AshenTheSettler (talk • contribs) 17:52, 23 October 2015 (UTC)

History - Edward III and Roger Mortimer
Roger Mortimer, effectively acting as Edward III's regent during his minority, was captured at Nottingham Castle by Edward and some young Turks. This is from Mortimer's page on wiki:-

The jealousy and anger of many nobles were aroused by Mortimer's use of power. Henry, Earl of Lancaster, one of the principals behind Edward II's deposition, tried to overthrow Mortimer, but the action was ineffective as the young king passively stood by. Then, in March 1330, Mortimer ordered the execution of Edmund, Earl of Kent, the half-brother of Edward II. After this execution Henry Lancaster prevailed upon the young king, Edward III, to assert his independence. In October 1330, a Parliament was summoned to Nottingham, just days before Edward's eighteenth birthday, and Mortimer and Isabella were seized by Edward and his companions from inside Nottingham Castle. In spite of Isabella's entreaty to her son, "Fair son, have pity on the gentle Mortimer," Mortimer was conveyed to the Tower. Accused of assuming royal power and of various other high misdemeanours, he was condemned without trial and ignominiously hanged at Tyburn on 29 November 1330, his vast estates forfeited to the crown. His body hung at the gallows for two days and nights in full view of the populace. Mortimer's widow Joan received a pardon in 1336 and survived till 1356. She was buried beside Mortimer at Wigmore, but the site was later destroyed.

Some or all of this story would fit well in the History section of this page on Nottingham, being one of the most dramatic events in the city's history when Edward III finally took charge of the country.

86.140.142.236 (talk) 23:57, 23 April 2016 (UTC) Dantes Warden

Weather boxes
Why is Sutton Bonnington, which is outside of the city, used in the climate section? Surely a weather box for Watnall is all that is needed - if Sutton Bonnington is used it should be either on the article for the village itself, or on the Loughborough article, nearest town.2A02:C7F:C812:FD00:C541:F7F5:2531:957F (talk) 23:01, 27 July 2017 (UTC)
 * Watnall is also outside of the city, and having more information (that can be easily hidden) isn't making the article worse? —Kusma (t·c) 08:46, 28 July 2017 (UTC)

 * Climate is better covered at the county level article. Microclimate can vary over a few miles, so the detail is likely to be incorrect for the city. I have removed these boxes in the past, only to have them put back by a weather enthusiast. I prpose removing the boxes and restricting weather to a short prose description per WP:PROSE.Charles (talk) 09:41, 28 July 2017 (UTC)

External links modified
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 * Added archive https://web.archive.org/web/20150924002318/http://www.espon.eu/export/sites/default/Documents/Projects/ESPON2006Projects/StudiesScientificSupportProjects/UrbanFunctions/fr-1.4.3_April2007-final.pdf to http://www.espon.eu/export/sites/default/Documents/Projects/ESPON2006Projects/StudiesScientificSupportProjects/UrbanFunctions/fr-1.4.3_April2007-final.pdf
 * Added archive https://web.archive.org/web/20151222112901/http://www.nottinghampost.com/Nottingham-named-UNESCO-City-Literature/story-28347373-detail/story.html to http://www.nottinghampost.com/Nottingham-named-UNESCO-City-Literature/story-28347373-detail/story.html
 * Added archive https://web.archive.org/web/20120808091729/http://www.hesa.ac.uk/content/view/1897/239 to http://www.hesa.ac.uk/content/view/1897/239/
 * Corrected formatting/usage for http://www.flyfm.co.uk/
 * Added archive https://web.archive.org/web/20130626075304/http://www.ljubljana.si/si/ljubljana/pobratena-mesta-zdruzenja/ to http://www.ljubljana.si/si/ljubljana/pobratena-mesta-zdruzenja/

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"Within the city" and "around the city" locations
It would be helpful if the "Around the city" section gave some criterion for inclusion - one place was recently removed as "Quite a distance from the city itself", while others in the list are further away. Pam D  23:29, 11 November 2021 (UTC)
 * What exactly does this list of places around or in the city actually do? A lot of it is subjective especially in the case of Langley Mill and Ilkeston which while are near Nottingham. Would be better placed in the Greater Nottingham article than here for the city alone given the actual urban area includes Derby, Sutton-in-Ashfield, Mansfield, Alfreton Belper, Ripley Heanor. etc...I really don't see how the around the city bit works whereas those which are in the city like Bulwell, Arnold, Beeston, West Bridgford, Hucknall and Daybrook are better placed to be mentioned than others like Langley Mill Ilkeston Long Eaton Sandiacre and Ruddington which are not directly near the city area...DragonofBatley (talk) 00:14, 12 November 2021 (UTC)

Overcrowding in the early 19th century
In The Bleak Age, a book by J. L. and Barbara Hammond (1947 edition), the following passage occurs on page 57:

"..it is safe to say that the worst overcrowding was to be found in the old quarters of existing towns. Manchester, Liverpool, London, were hard to beat; Leeds could show districts where overcrowding could hardly be carried further; but Nottingham was the worst example. Nottingham could not grow easily, and it contained in a narrow space 11,000 inhabited houses laid out in narrow streets, many of them 'built in confined courts and alleys, the entrance of which is usually through a tunnel from 30 to 36 inches wide, about 8 feet high, and from 25 to 30 feet long.' Of the 11,000 houses, upwards of 7,000 were built 'back to back and side to side.'"

Why could Nottingham not grow easily? Was it a matter of the steepness of the Trent valley, or was there marshy ground where housing would otherwise be easily built, or was there perhaps some other reason? Harfarhs (talk) 21:09, 6 July 2023 (UTC)

 * From 'To the Castle' from = People's Histreh =
 * Nottingham Radical History Group
 * "Nottingham was surrounded by areas to which various protagonists claimed ‘inviolable’ property rights. On the west the expansion of the town was blocked by the Duke of Newcastle’s Nottingham Park and Lord Middleton’s Wollaton Park. On the east there was Colwick parish, owned by the Musters family. To the North and the South were the common fields and meadows, which have
 * been described as ‘the biggest stumbling block of all’. The common lands were not as common as the name suggests, as they were mostly controlled by burgesses and freeholders, vigorously defending their users’ rights. A frequent though paradoxical argument by the opponents of enclosure were health reasons, as they claimed that public interest demanded the preservation of
 * Nottingham’s open spaces. But it can be assumed that opposition to enclosure was primarily upheld for economical reasons. Some who held users’ rights on the commons were renting them out as grazing spaces and others were landlords who wanted to keep their overcrowded town properties occupied." 84.64.51.122 (talk) 14:36, 26 October 2023 (UTC)

The Demonym is missing from the pale-blue box at top right
The info-box should be a standard template for every municipality about which there is an article. That box contains the demonym for that municipality in almost all Wikipedia articles about municipalities that I've read here. I assume it started out life as standard, and that someone has DELETED the demonym. Please fix Wikipedia so that this kind of information is standardized across all municipalities. I came here for one quick look to see if people from Nottingham are called "Nottinghammers" and that is NOT here. This is how Wikipedia wastes people's time when information is standardized across many, but not all, articles within a category of things such as "municipalities". Uniform templates are of the utmost importance.2600:1700:6759:B000:E894:BFCC:705D:880 (talk) 22:05, 20 February 2024 (UTC)Christopher Lawrence Simpson

Notingham is insolvent
bbc.com: Equal pay claims of up to £760m are among the bills it cannot afford. (10 October 2023)

(also Birmingham is insolvent) Search'n'write (talk) 17:08, 3 May 2024 (UTC)

White British
Is there a Wikipedia reason that I am unaware of for why the 2021 Census figure of 57.3% White British has been deleted, and why under the Demographics header the number of White British is misrepresented as 65.9% which is actually the 2021 percentage for Whites as a whole? The same thing seems to have happened for other boroughs and districts too so obviously I must be unaware of some new knowledge that contradicts the Census. Aletheiaxxx (talk) 14:37, 20 May 2024 (UTC)

 * What is your source for 57.3% White British? That does not seem to be in the census results cited. I agree that the source just says "White" so it should not be presented as "White British" (the collapsed section in the infobox does it correctly). —Kusma (talk) 15:20, 20 May 2024 (UTC)
 * You can look for yourself on the Nomis official census and labour market statistics website.
 * https://www.nomisweb.co.uk/datasets/c2021ts021
 * Geography: District/Unitary: Nottingham:
 * White: English, Welsh, Scottish, Northern Irish or British
 * 185,580 which is 57.3% Aletheiaxxx (talk) 19:18, 20 May 2024 (UTC)
 * I see. It can be computed from the information in the detailed database of results, but is not in the overview that is cited in the article. I have changed the article to say "White" instead of "White British". —Kusma (talk) 20:11, 20 May 2024 (UTC)

title: Talk:Nottingham


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Dori | Talk 14:32, Mar 5, 2004 (UTC)

Hello! I noticed your great work on pistols and pages standards. Check out WikiProject_Weaponry and add your standards if you want. It just started so its not formalized. Greyengine5 06:37, 4 May 2004 (UTC)

Hi, was there any reason you blanked Beretta 8045 Mini cougar F? Angela. 22:50, May 16, 2004 (UTC)

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Beretta 92
Please consider putting a "see talk page" note in your edit summary (and explaination in the talk page) rather than leaving it blank when deleting a large amount of text, as such edits taken by themselves at first glance appear to be page-blanking vandalism. Triona 16:29, 28 December 2005 (UTC)

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Nomination of List of Beretta 92 models for deletion
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title: User talk:Meswiss


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User talk:Sietse

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Dori | Talk 14:32, Mar 5, 2004 (UTC)

Sietse - I'll maybe give the Scottish Freedom movements article a go. Not sure what sort of article it would be. Maybe just a list, or perhaps a bit more history. Not sure. Cheers for getting in touch anyway. Big Jim Fae Scotland, March 8 2004

Verwarming | Talk 13:27, Jun 19, 2018 (CEST)

hey Sietse kom je 7 juli naar de Gender gap meeting bij wikimedia? https://nl.wikimedia.org/wiki/WikiZaterdag#7_juli_2018

Proposed deletion of Litsa Spathi

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 * Hi UnitedStatesian,
 * Thank you for informing me. I cannot remember creating that page at all, nor do I know the subject; nor does the original edit look like my own writing style as I know it. My MediaWiki account is a merger of my own (Sietse on en.wikipedia.org) and an unused one (Sietse on nl.wikipedia.org); perhaps the edit came in to my edit history via that route. That would also explain a few other edits in my early history: there are some edits there that I haven't noticed before, which are clearly vandalism, and which I definitely did not make. So, either another user or I was careless with my password at the time.
 * At any rate, I have no opinion on the page's notability or whether it should be deleted. I'll repeat this message on the deletion proposal page. Hope this helps you! --Sietse (talk) 11:01, 14 February 2019 (UTC)

Nomination of Litsa Spathi for deletion
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Dori | Talk 14:33, Mar 5, 2004 (UTC)

Quick yes/no question. Are you User:Cautious under another username? The allegation has been made elsewhere, and I'd just like to know if you could either confirm or deny this (since you're the person who knows...) Fennec 01:59, 25 Mar 2004 (UTC)

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Saltcoats

Saltcoats (Baile an t-Salainn; Scots: Saulcuts) is a town on the west coast of North Ayrshire, Scotland. The name is derived from the town's earliest industry when salt was harvested from the sea water of the Firth of Clyde, carried out in small cottages along the shore. It is part of the 'Three Towns' conurbation along with Ardrossan and Stevenston and is the third largest town in North Ayrshire.

Origins, 1200s
The history of Saltcoats can be traced back to when the monks of Kilwinning Abbey discovered easily accessible coastal coal seams at Saltcoats in the 1200s, it expanded from small scattering of buildings. The coal proved an efficient source of heat for evaporating saltwater for the manufacturing of salt, and by the 1500s, King James V-funded sheds along the shoreline, leading to a successful salt pans industry. This sector of the economy is where Saltcoats gets its name.

Burgh status, 1528
In 1528, Saltcoats was granted status as a burgh leading to the creation of a market. By the middle of the 1600s, Saltcoats' primary sources of income were the import of corn and butter, as well as the sale of cattle and fish (mostly herring) to Ireland. Local farmers produced cheese, butter, wheat, oats, and potatoes. Cottage labourers in the town were given access to hand looms so they could weave muslins for the Glasgow and Paisley markets. On the outskirts of the town, chemical operations that produce magnesium and Epsom salts ran on waste materials from the salt-panning business.

In the late 18th century, several shipyards operated at Saltcoats, producing some 60 to 70 ships. The leading shipbuilder was William Ritchie, but in 1790 he moved his business to Belfast. In 1793, it was recorded that Saltcoats had around 400 houses, with 3 operational shipyards remaining. By 1820, this had climbed to 600 houses, with a population of 3,413 being noted.

Recent history
By the early 19th century, the town had stopped producing ships. Saltcoats Town Hall, which dates back to 1826, is a Category B listed building.

Saltcoats had various amenities, lodging, and entertainment required to develop into a prosperous seaside resort as a result of the vast, protected bay known as "South Beach" between Saltcoats and Ardrossan and a Beach Pavilion built in the 1920s. Its importance as a holiday destination declined with the onset of cheap air travel and mass summer migrations to the Mediterranean.

Governance
Saltcoats is part of the North Ayrshire and Arran constituency in the House of Commons. From 2005, the seat was represented by Scottish Labour however, more recently in 2015, the seat was won by Patricia Gibson of the Scottish National Party. She was returned in 2017 albeit a smaller majority, but in 2019 her majority increased.

Historically, Saltcoats has been part of the UK parliament constituencies North Ayrshire (1868–1918), Bute and Northern Ayrshire (1918–1983) and Cunninghame North (1983–2005). These constituencies historically returned Conservative or Unionist MPs until 1987, when the constituency was won by the Labour Party.

For the devolved Scottish Parliament, the town is a part of the Cunninghame North constituency. This seat has been represented by Kenneth Gibson since the 2007 Scottish Parliament election, where it was the seat with the smallest majority at only 48 votes. It was previously represented by Scottish Labour since its creation in 1999.

Transport
The harbour was designed by James Jardine in 1811, however no cargo or passenger services run from the harbour any more.

Saltcoats is served by regular bus and railway services. Primary bus services are provided by Stagecoach West Scotland, while rail services are operated by ScotRail. These rail services are frequent and serve nearby Glasgow, as well as Largs, Ardrossan and Kilwinning.

Although Saltcoats currently only has a single railway station, the town was once served by a second railway station located in the north of the town, originally as part of the Lanarkshire and Ayrshire Railway. This station ceased regular passenger services on 4 July 1932, and there is no trace of the station today bar a nearby bridge.

Notable people

 * Alexander Allan (1780–1854), founder of the Allan Line Royal Mail Steamers
 * Andrew Allan (1822–1901), of the Allan Line Royal Mail Steamers
 * Sir Hugh Allan (1810–82), of the Allan Line Royal Mail Steamers
 * George Biagi (b.1985), Italian national rugby player
 * William Burns (1809–76), historian
 * Kenneth Campbell (1917–1941), recipient of the Victoria Cross
 * Steve Clarke (b.1963), professional footballer, Scotland national team manager
 * Hamish Fraser (1913–1986), former communist, traditionalist Catholic writer and local councillor
 * Janice Galloway (b.1955), author
 * Michael Garrett (b.1964), first Sir Bernard Lovell chair in astrophysics, Director of Jodrell Bank Centre for Astrophysics
 * Colin Hay (b.1953), musician, singer-songwriter, leader of Men at Work
 * Al Howie (1945–2016), long-distance runner
 * Bobby Lennox (b.1943), professional footballer
 * Fiona Macpherson (b.1971), philosopher
 * James Manson (1845–1935), engineer
 * Hugh McMahon (1906–97), professional footballer
 * Betsy Miller (1792–1864), sea captain
 * Hugh Munro (1856–1919), mountaineer, author
 * Graeme Obree (b.1965), cyclist
 * Robert Thornton (b.1967), professional darts player

In popular culture
The activities of Glaswegians in Saltcoats during the Glasgow Fair are celebrated by Billy Connolly in his song Saltcoats at the Fair, first released on The Humblebums' First Collection of Merry Melodies album (Transatlantic TRA186, February 1969).

title: Saltcoats


text:
User talk:Fruggo

Press Release
I see you contributed to the creation of the press release. Might you be willing to follow these steps, and send off the press release? -- user:zanimum

Sushi
Really nice photos of sushi. Is Loyaukee a friend of yours? If so, give him/her my complements. - Xamian 02:41, 15 Sep 2004 (UTC)

I have several questions about this image,. It looks all wrong for a piece of sushi with fish sliced into an uneven flat rectangle, wasabi dripping out, and rice packed too tightly. In short, it looks like a sloppy work. Also in the back, temakizushi seem to be piled on top of one another. Was this taken in an authentic sushi restaurant?Revth 14:54, 20 Nov 2004 (UTC)

 * I really have no idea. I got the picture from the sxc-website (here). If it is not a correct representation of Sushi, please nominate the image for deletion. Fruggo 20:06, 20 Nov 2004 (UTC)

Image:Arnhem Nederrijn ochtend apr04.jpg
Thank you for uploading this image. Do you license it under Creative Commons Attribution-ShareAlike 1.0 and 2.0? --Ellmist 07:07, 13 Mar 2005 (UTC)

 * I really have no idea what the difference is. I don't really care anyway, I'll change it to GNU-FDL. That seems to be the easiest choice :) Fruggo 15:47, 19 Mar 2005 (UTC)

Quarto
I noticed your question to User:Sj about Quarto. If it's a template you're having trouble with, this may help: m:Help:Template. It's the 'definitive' guide on Meta. Quinobi 20:04, 22 Jun 2005 (UTC)
 * That template wasn't well named in any case. I substituted it directly into the page. +sj  +  20:32, 22 Jun 2005 (UTC)
 * Thank you both. Fruggo 21:38, 22 Jun 2005 (UTC)

ArbCom elections are now open!
MediaWiki message delivery (talk) 08:53, 23 November 2015 (UTC)

title: User talk:Fruggo


text:
3SUM

In computational complexity theory, the 3SUM problem asks if a given set of $$n$$ real numbers contains three elements that sum to zero. A generalized version, k-SUM, asks the same question on k elements, rather than simply 3. 3SUM can be easily solved in $$O(n^2)$$ time, and matching $$\Omega(n^{\lceil k/2 \rceil})$$ lower bounds are known in some specialized models of computation.

It was conjectured that any deterministic algorithm for the 3SUM requires $$ \Omega(n^2) $$ time. In 2014, the original 3SUM conjecture was refuted by Allan Grønlund and Seth Pettie who gave a deterministic algorithm that solves 3SUM in $$O(n^2 / ({\log n} / {\log \log n})^{2/3})$$ time. Additionally, Grønlund and Pettie showed that the 4-linear decision tree complexity of 3SUM is $$ O(n^{3/2}\sqrt{\log n}) $$. These bounds were subsequently improved. The current best known algorithm for 3SUM runs in $$O(n^2 (\log \log n)^{O(1)} / {\log^2 n}) $$ time. Kane, Lovett, and Moran showed that the 6-linear decision tree complexity of 3SUM is $$O(n{\log^2 n})$$. The latter bound is tight (up to a logarithmic factor). It is still conjectured that 3SUM is unsolvable in $$O(n^{2-\Omega(1)})$$ expected time.

When the elements are integers in the range $$[-N, \dots, N]$$, 3SUM can be solved in $$O(n + N\log N)$$ time by representing the input set $$S$$ as a bit vector, computing the set $$S+S$$ of all pairwise sums as a discrete convolution using the fast Fourier transform, and finally comparing this set to $$S$$.

Quadratic algorithm
Suppose the input array is $$S[0..n-1]$$. In integer (word RAM) models of computing, 3SUM can be solved in $$O(n^2)$$ time on average by inserting each number $$S[i]$$ into a hash table, and then, for each index $$i$$ and $$j$$, checking whether the hash table contains the integer $$-(S[i]+S[j])$$.

It is also possible to solve the problem in the same time in a comparison-based model of computing or real RAM, for which hashing is not allowed. The algorithm below first sorts the input array and then tests all possible pairs in a careful order that avoids the need to binary search for the pairs in the sorted list, achieving worst-case $$O(n^2)$$ time, as follows. sort(S); for i = 0 to n - 2 do a = S[i]; start = i + 1; end = n - 1; while (start < end) do b = S[start] c = S[end]; if (a + b + c == 0) then output a, b, c;            // Continue search for all triplet combinations summing to zero. // We need to update both end and start together since the array values are distinct. start = start + 1; end = end - 1; else if (a + b + c > 0) then end = end - 1; else start = start + 1; end end

The following example shows this algorithm's execution on a small sorted array. Current values of a are shown in red, values of b and c are shown in magenta. -25 -10 -7 -3 2 4 8 10 (a+b+c==-25) -25 -10 -7 -3 2 4 8 10 (a+b+c==-22) . . . -25 -10 -7 -3 2 4 8 10  (a+b+c==-7) -25 -10 -7 -3 2 4 8 10 (a+b+c==-7) -25 -10 -7 -3 2 4 8 10 (a+b+c==-3) -25 -10 -7 -3 2 4 8 10 (a+b+c==2) -25 -10 -7 -3 2 4 8 10 (a+b+c==0)

The correctness of the algorithm can be seen as follows. Suppose we have a solution a + b + c = 0. Since the pointers only move in one direction, we can run the algorithm until the leftmost pointer points to a. Run the algorithm until either one of the remaining pointers points to b or c, whichever occurs first. Then the algorithm will run until the last pointer points to the remaining term, giving the affirmative solution.

Non-zero sum
Instead of looking for numbers whose sum is 0, it is possible to look for numbers whose sum is any constant C. The simplest way would be to modify the original algorithm to search the hash table for the integer $(C -(S[i]+S[j]))$.

Another method:
 * Subtract C/3 from all elements of the input array.
 * In the modified array, find 3 elements whose sum is 0.

For example, if A=[1,2,3,4] and if you are asked to find 3SUM for C=4, then subtract 4/3 from all the elements of A, and solve it in the usual 3sum way, i.e., $(a-C/3) + (b-C/3) + (c-C/3) = 0$.

Three different arrays
Instead of searching for the 3 numbers in a single array, we can search for them in 3 different arrays. I.e., given three arrays X, Y and Z, find three numbers $a∈X, b∈Y, c∈Z$, such that $a+b+c=0$. Call the 1-array variant 3SUM×1 and the 3-array variant 3SUM×3.

Given a solver for 3SUM×1, the 3SUM×3 problem can be solved in the following way (assuming all elements are integers): By the way we transformed the arrays, it is guaranteed that $a∈X, b∈Y, c∈Z$.
 * For every element in X, Y and Z, set: $X[i] \gets X[i]*10+1$, $Y[i] \gets Y[i]*10+2$, $Z[i] \gets Z[i]*10-3$.
 * Let S be a concatenation of the arrays X, Y and Z.
 * Use the 3SUM×1 oracle to find three elements $a' \in S,\ b' \in S,\ c' \in S$ such that $a'+b'+c'=0$.
 * Return $a \gets (a'-1)/10,\ b \gets (b'-2)/10,\ c \gets (c'+3)/10$.

Convolution sum
Instead of looking for arbitrary elements of the array such that:
 * $$S[k]=S[i]+S[j]$$

the convolution 3sum problem (Conv3SUM) looks for elements in specific locations:
 * $$S[i+j]=S[i]+S[j]$$

Reduction from Conv3SUM to 3SUM
Given a solver for 3SUM, the Conv3SUM problem can be solved in the following way.
 * Define a new array T, such that for every index i: $$T[i]=2n S[i]+i$$ (where n is the number of elements in the array, and the indices run from 0 to n-1).
 * Solve 3SUM on the array T.

Correctness proof:
 * If in the original array there is a triple with $$S[i+j]=S[i]+S[j]$$, then $$T[i+j]=2n S[i+j]+i+j = (2n S[i] + i) + (2n S[j] + j)=T[i]+T[j]$$, so this solution will be found by 3SUM on T.
 * Conversely, if in the new array there is a triple with $$T[k]=T[i]+T[j]$$, then $$2n S[k] + k = 2n(S[i]+S[j]) + (i+j)$$. Because $$i+j<2n$$, necessarily $$S[k] = S[i]+S[j]$$ and $$k=i+j$$, so this is a valid solution for Conv3SUM on S.

Reduction from 3SUM to Conv3SUM
Given a solver for Conv3SUM, the 3SUM problem can be solved in the following way.

The reduction uses a hash function. As a first approximation, assume that we have a linear hash function, i.e. a function h such that:
 * $$h(x+y)=h(x)+h(y)$$

Suppose that all elements are integers in the range: 0...N-1, and that the function h maps each element to an element in the smaller range of indices: 0...n-1. Create a new array T and send each element of S to its hash value in T, i.e., for every x in S($\forall x \in S$):
 * $$T[h(x)] = x$$

Initially, suppose that the mappings are unique (i.e. each cell in T accepts only a single element from S). Solve Conv3SUM on T. Now:
 * If there is a solution for 3SUM: $$z=x+y$$, then: $$T[h(z)]=T[h(x)]+T[h(y)]$$ and $$h(z)=h(x)+h(y)$$, so this solution will be found by the Conv3SUM solver on T.
 * Conversely, if a Conv3SUM is found on T, then obviously it corresponds to a 3SUM solution on S since T is just a permutation of S.

This idealized solution doesn't work, because any hash function might map several distinct elements of S to the same cell of T. The trick is to create an array $T^*$ by selecting a single random element from each cell of T, and run Conv3SUM on $T^*$. If a solution is found, then it is a correct solution for 3SUM on S. If no solution is found, then create a different random $T^*$ and try again. Suppose there are at most R elements in each cell of T. Then the probability of finding a solution (if a solution exists) is the probability that the random selection will select the correct element from each cell, which is $$(1/R)^3$$. By running Conv3SUM $$R^3$$ times, the solution will be found with a high probability.

Unfortunately, we do not have linear perfect hashing, so we have to use an almost linear hash function, i.e. a function h such that:
 * $$h(x+y)=h(x)+h(y)$$ or
 * $$h(x+y)=h(x)+h(y)+1$$

This requires to duplicate the elements of S when copying them into T, i.e., put every element $$x\in S$$ both in $$T[h(x)]$$ (as before) and in $$T[h(x)]-1$$. So each cell will have 2R elements, and we will have to run Conv3SUM $$(2R)^3$$ times.

3SUM-hardness
A problem is called 3SUM-hard if solving it in subquadratic time implies a subquadratic-time algorithm for 3SUM. The concept of 3SUM-hardness was introduced by. They proved that a large class of problems in computational geometry are 3SUM-hard, including the following ones. (The authors acknowledge that many of these problems are contributed by other researchers.)

 * Given a set of lines in the plane, are there three that meet in a point?
 * Given a set of non-intersecting axis-parallel line segments, is there a line that separates them into two non-empty subsets?
 * Given a set of infinite strips in the plane, do they fully cover a given rectangle?
 * Given a set of triangles in the plane, compute their measure.
 * Given a set of triangles in the plane, does their union have a hole?
 * A number of visibility and motion planning problems, e.g.,
 * Given a set of horizontal triangles in space, can a particular triangle be seen from a particular point?
 * Given a set of non-intersecting axis-parallel line segment obstacles in the plane, can a given rod be moved by translations and rotations between a start and finish positions without colliding with the obstacles?

By now there are a multitude of other problems that fall into this category. An example is the decision version of X + Y sorting: given sets of numbers $X$ and $Y$ of $n$ elements each, are there $n²$ distinct $x + y$ for $x ∈ X, y ∈ Y$?

title: 3SUM