Cage

Cage may refer to:

Technology

Cage (graph theory)

In the mathematical area of graph theory, a cage is a regular graph that has as few vertices as possible for its girth.

Formally, an (r,g)-graph is defined to be a graph in which each vertex has exactly r neighbors, and in which the shortest cycle has length exactly g. It is known that an (r,g)-graph exists for any combination of r ≥ 2 and g ≥ 3. An (r,g)-cage is an (r,g)-graph with the fewest possible number of vertices, among all (r,g)-graphs.

If a Moore graph exists with degree r and girth g, it must be a cage. Moreover, the bounds on the sizes of Moore graphs generalize to cages: any cage with odd girth g must have at least

vertices, and any cage with even girth g must have at least

vertices. Any (r,g)-graph with exactly this many vertices is by definition a Moore graph and therefore automatically a cage.

There may exist multiple cages for a given combination of r and g. For instance there are three nonisomorphic (3,10)-cages, each with 70 vertices : the Balaban 10-cage, the Harries graph and the Harries–Wong graph. But there is only one (3,11)-cage : the Balaban 11-cage (with 112 vertices).

Cage (enclosure)

A cage is an enclosure made of mesh, bars or wires, used to confine, contain or protect something or someone. A cage can serve many purposes, including keeping an animal in captivity, capturing, and being used for display of an animal at a zoo.

Humans

In history, prisoners were sometimes kept in a cage. They would sometimes be chained up inside into uncomfortable positions to intensify suffering.

History

Cages have been usually been used to capture or trapping a certain life form. For this reason, they've been known as a hunting accessory, often used for poaching animals or simply seizing them.

In captivity

Cages are often used now as a source to confine animals. These provide as a habitat to the animal, and since they've advanced so greatly, they are now specially designed to fit that species of animal. Captive breeds of birds, rodents, reptiles, and even larger animals have also been known to be confined in a cage as a domesticated animal (also known as a pet). Captivity is a common purpose of the cage.

Echelon (band)

Echelon were a four-piece band hailing from Essex, England.

Biography

Guitarist Mark Brandon, bassist Owain North and vocalist Paul Usher met at an early age and played together in various lineups, however became serious about a career as a band following the recruitment of drummer Andrew Grant. Following a series of local gigs, the band caught the ear of rock legend Alan McGee in early 2004 who would subsequently sign the band to his Poptones label later that year.

The band gained momentum, supporting bands such as The Others and The Boxer Rebellion and doing their own headline tour surrounding the release of their first single Plus. The single received airplay from renowned DJs such as Steve Lamacq and Tom Robinson, who made it single of the week on his BBC 6 Music evening show. The single also received airplay from XFM where the band did a live session. The debut single Plus was released on 8 November to positive reviews, and charted at Number 57 in the Official Charts, a great accomplishment for a relatively unknown band.

Echelon formation

An echelon formation is a (usually military) formation in which its units are arranged diagonally. Each unit is stationed behind and to the right (a "right echelon"), or behind and to the left ("left echelon"), of the unit ahead. The name of the formation comes from the French word échelon, meaning a rung of a ladder, which describes the shape that this formation has when viewed from above or below.

Use of the formation dates back to ancient infantry and cavalry warfare when attempting to flank an enemy or to break one wing with overwhelming numbers. One of the earliest uses was at the Battle of Leuctra when the Thebans attacked the Spartan right with a column 48 men deep while their weaker center and right were refused. The echelon formation was also used by Hannibal at the Battle of Cannae, Alexander the Great at the Battle of Gaugamela, Frederick II of Prussia, and the Confederate army at the Battle of Gettysburg

The tactic persists up to the present day, where it is regularly employed by all branches of the modern armed forces. Tactically, echelon formations are used because of the excellent range of vision offered to each participant in the formation. In particular, it is commonly employed by armored cavalry because of the large, overlapping fields of fire that it gives to each tank in the formation, and by combat aircraft, where the close, streamlined flight formation can allow the planes to dramatically reduce fuel consumption by "surfing" the updraft created by the wingtip vortices of the aircraft ahead.

Echelon (card game)

Echelon is a turn-based, customizable World War II strategy card game from Echelon Games .