Status and Prospects for the AWAKE Experiment

The AWAKE Collaboration is pursuing a demonstration of proton-driven plasma wakefield acceleration of electrons. The AWAKE experiment uses a \SI{400}{GeV/c} proton bunch from the CERN SPS, with a rms bunch length of $6$-\SI{15}{cm}, to drive wakefields in a \SI{10}{m} long rubidium plasma with an electron density of $10^{14}-10^{15}$cm$^{-3}$. Since the drive bunch length is much longer than the plasma wavelength ($\lambda_{pe}<$\SI{3}{mm}) for these plasma densities, AWAKE performed experiments to prove that the long proton bunch self-modulates in the plasma (2017). The next step is to demonstrate acceleration of electrons in the wakefields driven by the self-modulated bunch (2018). We summarize the concept of the self-modulation measurements and describe the plans and challenges for the electron acceleration experiments

On simplicial commutative algebras with Noetherian homotopy

In this paper, a strategy is developed studying a simplicial commutative algebra A whose zeroth homotopy group is a Noetherian ring B and whose higher homotopy groups are finite over B. The strategy replaces A with a connected simplicial supplemented k(q)-algebra, for each prime ideal q in B, which preserves much of the Andre-Quillen homology of A. The methods for this construction involves a mixture of methods of homotopy theory (e.g. Postnikov towers) with methods of commutative algebras (e.g. completions, Cohen factorizations). We finish by indicating how these methods resolve a more general form of a conjecture posed by Quillen.Comment: 10 page

Chemical structure matching using correlation matrix memories

This paper describes the application of the Relaxation By Elimination (RBE) method to matching the 3D structure of molecules in chemical databases within the frame work of binary correlation matrix memories. The paper illustrates that, when combined with distributed representations, the method maps well onto these networks, allowing high performance implementation in parallel systems. It outlines the motivation, the neural architecture, the RBE method and presents some results of matching small molecules against a database of 100,000 models

Simplicial commutative algebras with vanishing Andre-Quillen homology

In this paper, we study the Andr\'e-Quillen homology of simplicial commutative $\ell$-algebras, $\ell$ a field, having certain vanishing properties. When $\ell$ has non-zero characteristic, we obtain an algebraic version of a theorem of J.-P. Serre and Y. Umeda that characterizes such simplicial algebras having bounded homotopy groups. We further discuss how this theorem fails in the rational case and, as an application, indicate how the algebraic Serre theorem can be used to resolve a conjecture of D. Quillen for algebras of finite type over Noetherian rings, which have non-zero characteristic.Comment: 11 page