Articles Demographic Dimensions of World Politics: P. M. Hauser .......................... 1641 Population explosion has implications for the coinflict between the free world and the Communist bloc. Sir Francis Simon: P. W. Bridgman ...... .................................. 1647 Knowledge of the properties of matter at tenmperatures near absolute zero has been increased greatly by his work. Cha...

Let K be a finitely generated extension of Q and A a non-zero abelian variety over K. Let K̃ be the algebraic closure of K and Gal(K) = Gal(K̃/K) the absolute Galois group of K equipped with its Haar measure. For each σ ∈ Gal(K) let K̃(σ) be the fixed field of σ in K̃. We prove that for almost all σ ∈ Gal(K) there exist infinitely many prime numbers l such that A has a non-zero K̃(σ)-rational point ...

Let A be a m × m complex matrix with zero trace. Then there are m ×m matrices B and C such that A = [B,C] and ‖B‖‖C‖2 ≤ (logm + O(1))‖A‖2 where ‖D‖ is the norm of D as an operator on `2 and ‖D‖2 is the Hilbert–Schmidt norm of D. Moreover, the matrix B can be taken to be normal. Conversely there is a zero trace m × m matrix A such that whenever A = [B,C], ‖B‖‖C‖2 ≥ | logm−O(1)|‖A‖2 for some abso...

We make distributed stochastic gradient descent faster by exchanging sparse updates instead of dense updates. Gradient updates are positively skewed as most updates are near zero, so we map the 99% smallest updates (by absolute value) to zero then exchange sparse matrices. This method can be combined with quantization to further improve the compression. We explore different configurations and a...

Luttinger's contributions abound in different parts of many-body physics. Here I review the ones that appear when one uses the Renormalization Group (RG) to study the subject: the Luttinger Liquid, Luttinger's Theorem (on the volume of the Fermi surface) and the Kohn-Luttinger Theorem on the superconducting instability of all metals as one approaches absolute zero.

The so–called affine projection algorithm has become a popular tool in the context of acoustic echo cancellation. Regularisation is an absolute necessity in an affine projection algorithm to avoid near end noise amplification. This paper describes a method to achieve zero overhead regularisation while allowing stable algorithms to be employed to update the inverse covariance matrix that is used...

A method to obtain the absolute measure of the position is by means of the autocorrelation of two zero reference marks. In one-axis measurement systems one dimensional mark are used and the design of these marks is relatively complex. When the movement is in two-axes, two dimensional reference marks are required and they are even harder to design. We report a method of global optimization to ca...

Let A be a non-zero abelian variety defined over a number field K and let K be a fixed algebraic closure of K. For each element σ of the absolute Galois group Gal(K/K), let K(σ) be the fixed field in K of σ. We show that the torsion subgroup of A(K(σ)) is infinite for all σ ∈ Gal(K/K) outside of some set of Haar measure zero. This proves the number field case of a conjecture of W.-D. Geyer and ...

This report considers low resolution scalar quantization. Specifically, it considers entropyconstrained scalar quantization for memoryless Gaussian and Laplacian sources with both squared and absolute error distortion measures. The slope of the operational rate-distortion functions of scalar quantization for these sources and distortion measures is found. It is shown that in three of the four c...

Spatiotemporal chaos in the complex Ginzburg–Landau equation is known to be associated with a rapid increase in the density of defects, which are isolated points at which the solution amplitude is zero and the phase is undefined. Recently there have been significant advances in understanding the details and interactions of defects and other coherent structures, and in the theory of convective a...