Given a graph H and an integer r ≥ 2, let G → (H, r) denote the Ramsey property of a graph G, that is, every r-coloring of the edges of G results in a monochromatic copy of H. Further, let m(G) = maxF⊆G |E(F )|/|V (F )| and define the Ramsey density minf (H, r) as the infimum of m(G) over all graphs G such that G → (H, r). In the first part of this paper we show that when H is a complete graph ...

Tim nineteenth-century artist Richard Dadd, who spent most of his working life confined in the Criminal Lunatic Asylums at Bethlem and Broadmoor, is quite well known, and ever increasingly so, to the art world; his name is less well known, perhaps, in the sphere of psychiatric history. Dadd was born at Chatham in 1817, the third son and fourth child of Robert Dadd, who owned a chemist's busines...

In this paper we describe the problem of painter classification, and propose a novel approach based on deep convolutional autoencoder neural networks. While previous approaches relied on image processing and manual feature extraction from paintings, our approach operates on the raw pixel level, without any preprocessing or manual feature extraction. We first train a deep convolutional autoencod...

Consider the following game between two players, Builder and Painter. Builder draws edges one at a time and Painter colours them, in either red or blue, as each appears. Builder’s aim is to force Painter to draw a monochromatic copy of a fixed graph G. The minimum number of edges which Builder must draw, regardless of Painter’s strategy, in order to guarantee that this happens is known as the o...

A definition of pictorial style in terms of distinctive combinations of pictorial devices characteristic of a particular culture or period or the work of an individual artist is proposed. Four kinds of pictorial structure are described: the drawing (spatial) systems, the denotation systems, the mark systems and the attributes systems. Three pictures by Poussin, Rembrandt and the Achilles painte...

We consider the important generalisation of Ramsey numbers, namely on-line numbers. It is easiest to understand them by considering a game between two players, Builder and Painter, on an infinite set vertices. In each round, joins non-adjacent vertices with edge, Painter colors edge red or blue. An number r˜(G,H) minimum rounds it takes force create copy graph G blue H, assuming that both play ...