How cold will it be? Prospects for NHS funding: 2011- 2017

NHS spending in England may have more than doubled in real terms since 1999/2000, but the prospects for future funding now look bleak. Although there is consensus that the NHS faces a tough financial future, there is no agreement about just how cold the financial climate will be. Starting with a look at historical funding for the NHS, The King's Fund and the Institute for Fiscal Studies set out three plausible future funding scenarios and their consequences. The paper concludes with an assessment of each scenario and the options for funding up to 2017

A simple construction of complex equiangular lines

A set of vectors of equal norm in $\mathbb{C}^d$ represents equiangular lines if the magnitudes of the inner product of every pair of distinct vectors in the set are equal. The maximum size of such a set is $d^2$, and it is conjectured that sets of this maximum size exist in $\mathbb{C}^d$ for every $d \geq 2$. We describe a new construction for maximum-sized sets of equiangular lines, exposing a previously unrecognized connection with Hadamard matrices. The construction produces a maximum-sized set of equiangular lines in dimensions 2, 3 and 8.Comment: 11 pages; minor revisions and comments added in section 1 describing a link to previously known results; correction to Theorem 1 and updates to reference

On the local dynamics of polynomial difference equations with fading stochastic perturbations

We examine the stability-instability behaviour of a polynomial difference equa- tion with state-independent, asymptotically fading stochastic perturbations. We find that the set of initial values can be partitioned into a stability region, an instability region, and a region of unknown dynamics that is in some sense \small". In the ¯rst two cases, the dynamic holds with probability at least 1 ¡ °, a value corresponding to the statistical notion of a confidence level. Aspects of an equation with state-dependent perturbations are also treated. When the perturbations are Gaussian, the difference equation is the Euler-Maruyama dis- cretisation of an It^o-type stochastic differential equation with solutions displaying global a.s. asymptotic stability. The behaviour of any particular solution of the difference equation can be made consistent with the corresponding solution of the differential equation, with probability 1 ¡ °, by choosing the stepsize parameter sufficiently small. We present examples illustrating the relationship between h, ° and the size of the stability region

Conflict, cooperation and competition: The rise and fall of the Hull whaling trade during the seventeenth century

Ce document examine la montée et le déclin du commerce de pêche à la baleine à Hull au dix-septième siècle. Commençant par les voyages de pêche, y compris à la baleine, du port nordique à la fin du seizième et début du dix-septième siècle, il examine aussi bien la rivalité et la concurrence néfaste entre les aventuriers de Hull et la Compagnie de Moscovie de Londres, que le conflit entre les anglais et les hollandais pour l'accès aux baies du Spitzberg. Après un début prometteur, qui a été soutenu pendant les années 1630, le commerce de la pêche à la baleine de Hull a ensuite rencontré des difficultés. En dépit des efforts de le maintenir au cour des décennies tourmentées 1640 et 1650, ce commerce nouveau et potentiellement lucratif a été effectivement abandonné dès la deuxième moitié du dix-septième siècle

Initiatives to Engage Private-Practice Physicians in the Mission of Academic Medical Centers

Today\u27s healthcare market presents many challenges to academic healthcare centers and community-based physicians given the constrained resources and competition for healthcare dollars. Never before has the business sector infiltrated the healthcare market to this extent. Monies previously directed toward graduate medical education from government resources and cost-shifting practices have been abolished, and these changes have jeopardized the founding missions governing academic medical centers. However, community-based private practitioners-both educated and clinically trained at these centers of higher learning, provide an enormous pool of expertise to help rectify many current problems. Collaboration between these private practitioners and the medical centers could create positive change, to the mutual benefit of both groups. This research examines the problems facing medical schools in meeting their three-fold mission of education, clinical care, and research; and it presents a model for collaboration that could aid both the stakeholders and the healthcare system as a whole

English privateering during the Spanish and French wars, 1625-1630

From 1625 to 1630 England was actively involved in that wider, more general conflict which was sweeping across Europe during the first half of the seventeenth century. The main interest of King Charles lay in his determination to see the Palatinate restored to his brother-in-law. It was for this reason that Charles took up arms against Spain: in 1625 a major naval expedition was sent to the Spanish coast to seize the treasure fleet returning from the New World. The disastrous failure of this expedition, perhaps the "low water mark" of English seamanship, increased the King's determination to repeat the operation in 1626. Success again eluded the English fleet. The expedition of 1626 was the last to be sent against Spain for the rest of the war; during the course of that year England became enmeshed in a web of disputes with France. The result was another major naval expedition to aid the Huguenots in the port of La Rochelle. The expedition was under the supreme command of the King's favourite, the Duke of Buckingham. The failure of this expedition goaded Charles into another effort to relieve the Protestant city in 1628. Buckingham was again to take personal charge but following his assassination in August the expedition was eventually led by the Earl of Denbigh. The successive failure of these expeditions to the continent, or of their inability to achieve even a modicum of success, sapped the English military effort and contributed to the alienation of opinion of many at home: Sir Simonds D'Ewes was not alone in lamenting, during 1628, that "the Protestant cause was well near ruined this year by the unfortunate and unseasonable assistance of England". Dogged by serious mismanagement and financial debility, despite prodigious efforts to raise money, the English military machine was structurally incapable of successfully fighting both Spain and France. These disastrous expeditions were accompanied by, and related to, growing parliamentary turbulence which affected both the House of Commons and Lords. Feeding upon the failure of the expedition to Cadiz in 1625, the opposition and indignation felt against Buckingham exploded in 1626 with an attempt to impeach him. In 1628, parliament refused to consider any motion concerning supply until the crown accepted the Petition of Right. Relations between crown and parliament failed to improve, despite the King's acceptance of the Petition and the removal of Buckingham from the political scene. With dissidence seeping out from the confines of Westminster into the mercantile community of London and the county communities, a "decade of tension"3 was brought to an end by the dissolution of parliament, following scenes of gross disorder in the House of Commons.By the latter part of 1628 it was evident that the war effort was being crippled by internal dissension and financial weakness. The futility of continuing the Gars was painfully apparent: early in 1629, therefore, peace was made with France, to be followed in November 1630 by peace with Spain.The large naval expeditions of the 1620s were accompanied by a privateering war, carried on by hundreds of English vessels which put to sea on voyages of reprisal between 1625 and 1630. This was a very different story to the unrelieved misery and failure of the large-scale expeditions. Sailing alone, or sometimes in packs of three or four, English privateers plundered in the English Channel, the Bay of Biscay, the Mediterranean and the Caribbean. While the fortunes of the King's fleet, waned those of the privateers waxed, as prize upon prize was seized and returned to England. The success of many privateers recalled the Elizabethan sea war against Spain, which many in the 1620s looked on as a golden age of English maritime plunder and as a model for the warlike efforts of their own generation

The EU Ban on Battery Cages: History and Prospects

On June 15, 1999, the European Union (EU) passed a directive on the welfare of laying hens, requiring that battery cages (so called because they are arranged in batteries of rows and tiers) be phased out by 2012. Enriched laying cages (which may also be arranged in batteries but which provide increased area and height, when compared with conventional cages, and a perch, nest box, and litter area) will still be allowed. This chapter outlines how this directive came about, and the social, economic, and political issues involved. It considers prospects for the future, both within and outside the EU, and implications for welfare of laying hens in the United States

On the interpretation of lateral manganin gauge stress measurements in polymers

Encapsulated wire-element stress gauges enable changes in lateral stress during shock loading to be directly monitored. However, there is substantial debate with regards to interpretation of observed changes in stress behind the shock front; a phenomenon attributed both to changes in material strength and shock- dispersion within the gauge-encapsulation. Here, a pair of novel techniques which both modify or remove the embedding medium where such stress gauges are placed within target materials have been used to try and inform this debate. The behavior of three polymeric materials of differing complexity was considered, namely polystyrene, the commercially important resin transfer moulding RTM 6 resin and a commercially available fat lard. Comparison to the response of embedded gauges has suggested a possible slight decrease in the absolute magnitude of stress. However, changing the encapsulation has no detectable effect on the gradient behind the shock in such polymeric systems

SIC~POVMs and Clifford groups in prime dimensions

We show that in prime dimensions not equal to three, each group covariant symmetric informationally complete positive operator valued measure (SIC~POVM) is covariant with respect to a unique Heisenberg--Weyl (HW) group. Moreover, the symmetry group of the SIC~POVM is a subgroup of the Clifford group. Hence, two SIC~POVMs covariant with respect to the HW group are unitarily or antiunitarily equivalent if and only if they are on the same orbit of the extended Clifford group. In dimension three, each group covariant SIC~POVM may be covariant with respect to three or nine HW groups, and the symmetry group of the SIC~POVM is a subgroup of at least one of the Clifford groups of these HW groups respectively. There may exist two or three orbits of equivalent SIC~POVMs for each group covariant SIC~POVM, depending on the order of its symmetry group. We then establish a complete equivalence relation among group covariant SIC~POVMs in dimension three, and classify inequivalent ones according to the geometric phases associated with fiducial vectors. Finally, we uncover additional SIC~POVMs by regrouping of the fiducial vectors from different SIC~POVMs which may or may not be on the same orbit of the extended Clifford group.Comment: 30 pages, 1 figure, section 4 revised and extended, published in J. Phys. A: Math. Theor. 43, 305305 (2010