Edward Cator Seaton

Edward Jenner

cow-pox of one human being from another: the first of a long series of protective inoculations upon which, for a hundred years, man has been dependent for his protection against one of the most terrible disease^ to which he is exposed. From this inoculation has grown our national system of vaccination, in the creation of which the name of this Society and its former president, Edward Seaton, wi...

Infant mortality in three East Midland towns: similarities and differences, 1890-1910

Until the end of the nineteenth century the problem of infant mortality was still an area which was mainly regarded as a problem of the home circumstances that the child were born into. Interfering in an individual’s life was abhorrent to the status quo, so little was done to investigate the problem and it was only at the beginning of the twentieth century that a real interest began to take pla...

Learning Arbitrarily Complex Weight Uncertainties in Neural Networks

A shape theorem and semi-infinite geodesics for the Hammersley model with random weights

In this paper we will prove a shape theorem for the last-passage percolation model on a two dimensional F -compound Poisson process, called the Hammersley model with random weights. We will also provide diffusive upper bounds for shape fluctuations. Finally we will indicate how these results can be used to prove existence and coalescence of semi-infinite geodesics in some fixed direction α, fol...

Second Class Particles and Cube Root Asymptotics for Hammersley’s Process by Eric Cator

We show that, for a stationary version of Hammersley’s process, with Poisson sources on the positive x-axis and Poisson sinks on the positive y-axis, the variance of the length of a longest weakly North–East path L(t, t) from (0,0) to (t, t) is equal to 2E(t −X(t))+, where X(t) is the location of a second class particle at time t . This implies that both E(t −X(t))+ and the variance of L(t, t) ...