Tits also have a variety of methods for attracting mates, primarily through their intricate, bouncing mating dance.

Insularity also affects clutch size, with Great Tits on offshore islands laying smaller clutches with larger eggs than mainland birds.

In mathematics, a building ( also Tits building, Bruhat – Tits building, named after François Bruhat and Jacques Tits ) is a combinatorial and geometric structure which simultaneously generalizes certain aspects of flag manifolds, finite projective planes, and Riemannian symmetric spaces.

Initially introduced by Jacques Tits as a means to understand the structure of exceptional groups of Lie type, the theory has also been used to study the geometry and topology of homogeneous spaces of p-adic Lie groups and their discrete subgroups of symmetries, in the same way that trees have been used to study free groups.

Iwahori – Matsumoto, Borel – Tits and Bruhat – Tits demonstrated that in analogy with Tits ' construction of spherical buildings, affine buildings can also be constructed from certain groups, namely, reductive algebraic groups over a local non-Archimedean field.

He also is blackmailed by a parole officer he calls Mucho, after she describes herself as " Mucho Hair, Mucho Tits ," and by Mel's old boyfriend, Jeff, now an ex-con.

Derivation and structure algebras also form part of Tits ' construction of the Freudenthal magic square.

During the 1970s Rivers worked closely with Diana Molinari and Michel Auder on many video tape projects, including the infamous Tits, and also worked in neon.

They were invented by the mathematician Jacques Tits, and are also sometimes known as Tits systems.

They also include the Varied and probably the White-fronted Tit ( which were sometimes separated in Sittiparus ), and possibly the White-browed and Caspian Tits.

Tits proved a remarkable theorem: all spherical buildings of rank at least three are connected with a group ; moreover, if a building of rank at least two is connected with a group then the group is essentially determined by the building.

Tits proved that any label-preserving automorphism of the affine building arises from an element of SL < sub > n </ sub >( Q < sub > p </ sub >).

Tits proved that all irreducible spherical buildings ( i. e. with finite Weyl group ) of rank greater than 2 are associated to simple algebraic or classical groups.

Analogues of the Tits alternative have been proved for many other classes of groups, such as fundamental groups of 2-dimensional simplicial complexes of non-positive curvature.

" Nonetheless, neither the band nor the album proved to be a big commercial success in the US: major chain store Wal-Mart refused to stock it, claiming on its website that it contained " a snarling, swaggering attack on conservatism " in the form of the song " Tits on the Radio ".

Tits demonstrated how to every such group G one can associate a simplicial complex Δ = Δ ( G ) with an action of G, called the spherical building of G. The group G imposes very strong combinatorial regularity conditions on the complexes Δ that can arise in this fashion.

For finitely generated linear groups, however, the von Neumann conjecture is true by the Tits alternative: every subgroup of GL ( n, k ) with k a field either has a normal solvable subgroup of finite index ( and therefore is amenable ) or contains the free group on two generators.

Tits have settled North America twice, probably at some time during the Early-Mid Pliocene.

Another study in the United Kingdom found that during winter and while foraging, Marsh Tits spent more time than Blue Tits in the wood's understorey, and more time lower in the woodland canopy and understorey.

In her spare time she was briefly a backing singer along with friend Lindsay Forrest in the Leeds-based pop group Dawn Chorus and the Blue Tits, fronted by radio DJ Liz Kershaw during the early 1980s.

The Tits group is one of the simple N-groups, and was overlooked in John G. Thompson's first announcement of the classification of simple N-groups, as it had not been discovered at the time.

Famous lyrics " Hips, Tits, Lips, Power " adorned a popular T-shirt of the time.

The notion of a building was invented by Jacques Tits as a means of describing simple algebraic groups over an arbitrary field.

By treating these conditions as axioms for a class of simplicial complexes, Tits arrived at his first definition of a building.

Tits later reworked the foundational aspects of the theory of buildings using the notion of a chamber system, encoding the building solely in terms of adjacency properties of simplices of maximal dimension ; this leads to simplifications in both spherical and affine cases.

If a group G acts simplicially on a building X, transitively on pairs of chambers C and apartments A containing them, then the stabilisers of such a pair define a BN pair or Tits system.

The results of Tits on determination of a group by its building have deep connections with rigidity theorems of George Mostow and Grigory Margulis, and with Margulis arithmeticity.

Variations in the exploratory behaviour of Great Tits ( Parus major ) have been found to be linked with a gene orthologous to the human gene DRD4 ( Dopamine receptor D4 ) which is known to be associated with novelty-seeking behaviour.

*: The Tits group is generally considered of this form, though strictly speaking it is not of Lie type, but rather index 2 in a group of Lie type.

The Marsh Tit Poecile palustris is a passerine bird in the tit family Paridae and genus Poecile, closely related to the Willow, Père David's and Songar Tits.

Plumage characteristics include the lack of a pale wing panel ( formed by pale edges to the secondary feathers in the Willow Tit ), the Marsh Tit's glossier black cap and smaller black ' bib ', although none of these is ' completely reliable '; for example, juvenile Marsh Tits can show a pale wing panel.

Most Marsh Tits stay in their breeding territories year-round ; presumably this is related to their food-storing strategy.

Conservation work is now undergoing to determine the cause of the Willow Tits decline in population, and to try and identify ways to improve said causes.

Communication with other Blue Tits is the most important motivation for the use of calls.

It is generally resident, and most Great Tits do not migrate except in extremely harsh winters.

There is little geographic variation in calls, but tits from the two south Asian groups recently split from the Great Tit do not recognise or react to the calls of the temperate Great Tits.

Great Tits combine dietary versatility with a considerable amount of intelligence and the ability to solve problems with insight learning, that is to solve a problem through insight rather than trial and error.

Great Tits are cavity nesters, breeding in a hole that is usually inside a tree, although occasionally in a wall or rock face, and they will readily take to nest boxes.

The Eurasian Sparrowhawk is a predator of Great Tits, with the young from second broods being at higher risk partly because of the hawk ’ s greater need for food for its own developing young.

The hen flea Ceratophyllus gallinae is exceedingly common in the nests of Blue and Great Tits.

In woodland, Eurasian Sparrowhawks account for the deaths of a third of all young Great Tits ; the two alarm calls given by Great Tits when mobbing a predator, and when fleeing from a nearby hawk, are within the optimum hearing range of both prey and predator ; however, the high-pitched alarm call given when a distant flying Eurasian Sparrowhawk is seen " can only be heard well by the tit.

Sometimes ( such as by John Conway ) the Tits group is regarded as a sporadic group ( because it is not strictly a group of Lie type ), in which case there are 27 sporadic groups.

* There are 27 sporadic groups, if the Tits group is included.