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We study certain physically-relevant subgeometries of binary symplectic polar spaces W(2N−1,2) of small rank N, when the points of these spaces canonically encode N-qubit observables. Key characteristics of a subspace of such a space W(2N−1,2) are: the number of its negative lines, the distribution of types of observables, the character of the geometric hyperplane the subspace shares with the distinguished (non-singular) quadric of W(2N−1,2) and the structure of its Veldkamp space. In particular, we classify and count polar subspaces of W(2N−1,2) whose rank is N−1. W(3,2) features three negative lines of the same type and its W(1,2)’s are of five different types. W(5,2) is endowed with 90 negative lines of two types and its W(3,2)’s split into 13 types. A total of 279 out of 480 W(3,2)’s with three negative lines are composite, i.e., they all originate from the two-qubit W(3,2). Given a three-qubit W(3,2) and any of its geometric hyperplanes, there are three other W(3,2)’s possessing the same hyperplane. The same holds if a geometric hyperplane is replaced by a ‘planar’ tricentric triad. A hyperbolic quadric of W(5,2) is found to host particular sets of seven W(3,2)’s, each of them being uniquely tied to a Conwell heptad with respect to the quadric. There is also a particular type of W(3,2)’s, a representative of which features a point each line through which is negative. Finally, W(7,2) is found to possess 1908 negative lines of five types and its W(5,2)’s fall into as many as 29 types. A total of 1524 out of 1560 W(5,2)’s with 90 negative lines originate from the three-qubit W(5,2). Remarkably, the difference in the number of negative lines for any two distinct types of four-qubit W(5,2)’s is a multiple of four.

A magic three-qubit Veldkamp line of W ( 5 , 2 ) , i.e., the line comprising a hyperbolic quadric Q + ( 5 , 2 ) , an elliptic quadric Q − ( 5 , 2 ) and a quadratic cone Q ^ ( 4 , 2 ) that share a parabolic quadric Q ( 4 , 2 ) , the doily, is shown to provide an interesting model for the Veldkamp space of the doily. The model is based on the facts that: (a) the 20 off-doily points of Q + ( 5 , 2 ) form ten complementary pairs, each corresponding to a unique grid of the doily; (b) the 12 off-doily points of Q − ( 5 , 2 ) form six complementary pairs, each corresponding to a unique ovoid of the doily; and (c) the 15 off-doily points of Q ^ ( 4 , 2 ) , disregarding the nucleus of Q ( 4 , 2 ) , are in bijection with the 15 perp-sets of the doily. These findings lead to a conjecture that also parapolar spaces can be relevant for quantum information.

Edward Doyley led English Jamaica for most of its first decade. Sent as part of a military force intent on conquering the island, he rose to a position of command in the army as a result of his survival and seniority. Eventually he took charge of the navy and civilian affairs as well. Wielding theoretically vast powers he lacked official authorization from any central authority for much of his tenure. His correspondence requesting support for the island reveals the needs of a newly conquered colony, enumerating the requirements that an expanding imperial center must fill as England moved more decisively toward engagement in the wider world. Scholarly debates over state building that emphasize military and naval expansion as a driving force, and debates about state formation focusing on negotiations between central and local authorities, speak to the experience of early Jamaica. Doyley's circumstances place him in a position between the two ideal situations described in that literature.

\"We're fortunate to have a place like [Gillian]'s Place to provide support in our community,\" said [Leona Moore]. \"They're not just a shelter - they also provide outreach and other programs.\" \"Domestic violence affects everyone,\" said [Michele Auger], who is on the board of directors for Gillian's Place. \"We all have a responsibility to raise awareness, and speak out.\" \"Everyone needs to be able to find security and comfort if it's needed,\" said [Lina Kennedy]. \"I wish there was a place like this in every community.\"

\"The walk is a symbolic gesture,\" said Joanne Doyley, fundraising and special events coordinator for [Gillian]'s Place, \"It's a great way to raise awareness.\" Adding, \"It gives men the opportunity to take a stand.\" Doyley knows just how important this day is. \"The shelter has been at full capacity since January.\" she said. \"The need has increased. Now more than ever we need to raise awareness.\" \"We're really excited for our fifth anniversary,\" said Doyley. \"We hope it's our best year yet.\"

In an instant, it catapulted [Watford]'s longestserving player into the ranks of \"Brazilian\" greats - move over Ronaldinho and Jairzinho, who needs the Copacabana when we've got Lloydinho from Whitechapel? [Lloyd Doyley]'s equaliser, the catalyst for a 3-1 win which sent QPR's dressing room into a seismic squabble, made his mate Andy Collins - who organises Watford's end-ofseason dinners - leap so high out of his armchair at home in Aylesbury that he cracked his head on an oak beam and needed hospital treatment. \"Heidar Helguson, who is the best header of a ball I've ever seen, came up afterwards and said 'nice finish' which, from him, is a real compliment. Now the lads are taking the mickey out of me for my goal celebration because I didn't know where to turn, but it's all good fun.\" \"Next thing I knew there were thousands of fans in the Rookery chanting 'We've got Lloydinho'. The nearest I'll get to playing for Brazil is a handful of coffee, but I'll take it as a compliment even if it's a joke.\"

In an instant, it catapulted [Watford]'s longestserving player into the ranks of \"Brazilian\" greats - move over Ronaldinho and Jairzinho, who needs the Copacabana when we've got Lloydinho from Whitechapel? \"Heidar Helguson, who is the best header of a ball I've ever seen, came up afterwards and said 'nice finish' which, from him, is a real compliment. Now the lads are taking the mickey out of me for my goal celebration because I didn't know where to turn, but it's all good fun.\" \"Next thing I knew there were thousands of fans in the Rookery chanting 'We've got Lloydinho'. The nearest I'll get to playing for Brazil is a handful of coffee, but I'll take it as a compliment even if it's a joke.\"

An emotional [Lloyd Doyley] said: 'I dedicate that goal to my mum, who passed away five months ago. I'm sure she's looking down on me and will be very proud.' Patrick Agyemang opened the scoring for QPR after an intelligent pass from Alejandro Faurlin.

Watford v Preston WATFORD are hoping to bring back defender Lloyd Doyley for tonight's visit by struggling Preston.