The municipal archives of the City of New York

Ith some 100,000 cubic feet of civic documents, vital and building records, libers, films and photographs, New York City's Municipal Archives is a magnet for researchers. Among those who benefit from centralized access to the wealth of material deposited in the Archives by city government agencies are genealogists, urban scholars and architectural historians

A globally convergent flow for computing the best low rank approximation of a matrix

We work in the space of $m$-by-$n$ real matrices with the Frobenius inner product. Consider the following Problem: Given an m-by-n real matrix A and a positive integer k, find the m-by-n matrix with rank k that is closest to A. I discuss a rank-preserving differential equation (d.e.) which solves this problem. If X(t) is a solution of this d.e., then the distance between $X(t)$ and $A$ decreases as t increases; this distance function is a Lyapunov function for the d.e. If $A$ has distinct positive singular values (which is a generic condition) then this d.e. has only one stable equilibrium point. The other equilibrium points are finite in number and unstable. In other words, the basin of attraction of the stable equilibrium point on the manifold of matrices with rank $k$ consists of almost all matrices. This special equilibrium point is the solution of the given problem. Usually constrained optimization problems have many local minimums (most of which are undesirable). So the constrained optimization problem considered here is very special

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Time-spliced X-ray Diffraction Imaging

Diffraction imaging of non-equilibrium dynamics at atomic resolution is becoming possible with X-ray free-electron lasers. However, there are unresolved problems with applying this method to objects that are confined in only one dimension. Here I show that one-dimensional coherent diffraction imaging is possible by splicing together images recovered from different delays in a time-resolved experiment. This is used to image the time and space evolution of antiferromagnetic order in a complex oxide heterostructure from measurements of a resonant soft X-ray diffraction peak. Mid-infrared excitation of the substrate is shown to lead to a magnetic front that propagates at a velocity exceeding the speed of sound, a critical observation for the understanding of driven phase transitions in complex condensed matter

The Legend of the Wehrmacht’s “Clean Hands”: The Attempt to Remove Nazism from the German Military

The legend of the Wehrmacht’s “clean hands” was created with the Himmerdoer Memorandum of 1950 and sought to disassociate the German military with its Nazi past. The legend gained popularity in the minds of the German people and successfully led to Germany’s rearmament after World War Two. Beginning in 1990, the legend was destroyed as the actions of the Wehrmacht during World War Two created a different picture than that of the legend. The Wehrmacht’s hands were far from “clean” and instead were very dirty