Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems

A new class of non-homogeneous state-affine systems is introduced for use in reservoir computing. Sufficient conditions are identified that guarantee first, that the associated reservoir computers with linear readouts are causal, time-invariant, and satisfy the fading memory property and second, that a subset of this class is universal in the category of fading memory filters with stochastic almost surely uniformly bounded inputs. This means that any discrete-time filter that satisfies the fading memory property with random inputs of that type can be uniformly approximated by elements in the non-homogeneous state-affine family.Comment: 41 page

How post-Civil War segregation helped to shape the patterns of racial inequality that we see today

In the wake of recent tragic killings of blacks by whites in Ferguson, Baltimore, and Charleston, the issue of black-white segregation has come to the fore once again. In new research Angelina Grigoryeva and Martin Ruef examine the history of segregation in the aftermath of the Civil War. They find that in the North, as today, segregation was largely in the form of racialized African-American districts, while in the South, segregation was more fine-grained with black families relegated to side streets and alleys in more mixed communities, reproducing the racial inequality found under slavery. They write that examining early forms of racial segregation and how they varied by region may be useful in explaining regional differences in racial unrest in the contemporary United States