Who owned Earls Colne in 1798....or how to squeeze more from the Land Tax

In this important article Richard Hoyle, one of the country’s leading historians of the early modern period, introduces new perspectives on the Land Tax and its use in the analysis of local communities in the late eighteenth and early nineteenth centuries. He uses as his case study the parish of Earls Colne in Essex, on which he has already written extensively with Professor Henry French. The article begins with an overview of the tax itself, explaining its history and the procedures for the collection of revenues – including the numerous changes which took place. The sizeable problems confronting any would-be analyst of the data are clearly identified, and Hoyle observes that because of these apparently insoluble difficulties the potential of the tax returns has never been fully realised. He then considers the surviving documentation in The National Archives, providing an accessible introduction to the sources and their arrangement, and describing the particularly important question o f the redemption of the tax by payment of a lump sum. The extent of redemption (in the years around 1800-1804) is discussed. Hoyle draws attention to the potential for linking the tax returns themselves with the redemption certificates (which have never been subjected to historical analysis and thereby proposes new ways of exploiting the evidence of the taxation as a whole. The article then discusses in detail the specific case of Earls Colne, with tabulated data showing the research potential. Topics analysed include the ownership of property ranked by size of payment, and calculations whereby the amount paid may be used to determine the worth of land and the structure of individual estates. The important question of absentee owners is investigated, and there is a very valuable consideration of the potential for looking at portfolio estate ownership, whereby owners held land in varying proportions in a number of parishes. It is suggested that such studies will allow us to be more aware of the entirety of property ownership, which a focus on a single community does not permit. In the concluding paragraph it is argued that using these sources we may see the rise and fall of estates, gain new information on landownership, landholding and farm size, and even approach the challenging topic of the distribution of wealth.

The role of myeloid receptors on murine plasmacytoid dendritic cells in induction of type I interferon

This study tested the hypothesis that a set of predominantly myeloid restricted receptors (F4/80, CD36, Dectin-1, CD200 receptor and mannan binding lectins) and the broadly expressed CD200 played a role in a key function of plasmacytoid DC (pDC), virally induced type I interferon (IFN) production. The Dectin-1 ligands zymosan, glucan phosphate and the anti-Dectin-1 monoclonal antibody (mAb) 2A11 had no effect on influenza virus induced IFNα/β production by murine splenic pDC. However, mannan, a broad blocking reagent against mannose specific receptors, inhibited IFNα/β production by pDC in response to inactivated influenza virus. Moreover, viral glycoproteins (influenza virus haemagglutinin and HIV-1 gp120) stimulated IFNα/β production by splenocytes in a mannan-inhibitable manner, implicating the function of a lectin in glycoprotein induced IFN production. Lastly, the effect of CD200 on IFN induction was investigated. CD200 knock-out macrophages produced more IFNα than wild-type macrophages in response to polyI:C, a MyD88-independent stimulus, consistent with CD200's known inhibitory effect on myeloid cells. In contrast, blocking CD200 with an anti-CD200 mAb resulted in reduced IFNα production by pDC-containing splenocytes in response to CpG and influenza virus (MyD88-dependent stimuli). This suggests there could be a differential effect of CD200 on MyD88 dependent and independent IFN induction pathways in pDC and macrophages. This study supports the hypothesis that a mannan-inhibitable lectin and CD200 are involved in virally induced type I IFN induction.

The Dirichlet-to-Neumann map for the elliptic sine Gordon

We analyse the Dirichlet problem for the elliptic sine Gordon equation in the upper half plane. We express the solution $q(x,y)$ in terms of a Riemann-Hilbert problem whose jump matrix is uniquely defined by a certain function $b(\la)$, $\la\in\R$, explicitly expressed in terms of the given Dirichlet data $g_0(x)=q(x,0)$ and the unknown Neumann boundary value $g_1(x)=q_y(x,0)$, where $g_0(x)$ and $g_1(x)$ are related via the global relation $\{b(\la)=0$, $\la\geq 0\}$. Furthermore, we show that the latter relation can be used to characterise the Dirichlet to Neumann map, i.e. to express $g_1(x)$ in terms of $g_0(x)$. It appears that this provides the first case that such a map is explicitly characterised for a nonlinear integrable {\em elliptic} PDE, as opposed to an {\em evolution} PDE.

Boundary value problems for the elliptic sine-Gordon equation in a semi-strip

We study boundary value problems posed in a semistrip for the elliptic sine-Gordon equation, which is the paradigm of an elliptic integrable PDE in two variables. We use the method introduced by one of the authors, which provides a substantial generalization of the inverse scattering transform and can be used for the analysis of boundary as opposed to initial-value problems. We first express the solution in terms of a 2 by 2 matrix Riemann-Hilbert problem whose \jump matrix" depends on both the Dirichlet and the Neumann boundary values. For a well posed problem one of these boundary values is an unknown function. This unknown function is characterised in terms of the so-called global relation, but in general this characterisation is nonlinear. We then concentrate on the case that the prescribed boundary conditions are zero along the unbounded sides of a semistrip and constant along the bounded side. This corresponds to a case of the so-called linearisable boundary conditions, however a major difficulty for this problem is the existence of non-integrable singularities of the function q_y at the two corners of the semistrip; these singularities are generated by the discontinuities of the boundary condition at these corners. Motivated by the recent solution of the analogous problem for the modified Helmholtz equation, we introduce an appropriate regularisation which overcomes this difficulty. Furthermore, by mapping the basic Riemann-Hilbert problem to an equivalent modified Riemann-Hilbert problem, we show that the solution can be expressed in terms of a 2 by 2 matrix Riemann-Hilbert problem whose jump matrix depends explicitly on the width of the semistrip L, on the constant value d of the solution along the bounded side, and on the residues at the given poles of a certain spectral function denoted by h. The determination of the function h remains open.

The elliptic sine-Gordon equation: a nonlinear elliptic integrable PDE

In this paper, we summarise this recent progress to underline the features specific to this nonlinear elliptic case, and we give a new classification of boundary conditions on the semistrip that satisfy a necessary condition for yielding a boundary value problem can be effectively linearised. This classification is based on formulation the equation in terms of an alternative Lax pair.