We investigate various aspects of operator quantum error-correcting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem codes using a counting argument similar to the quantum Gilbert-Varshamov bound. We derive linear programming bounds and other upper bounds. We answer the qu...

In this paper, a generic method to derive subsystem codes from existing subsystem codes is given that allows one to trade the dimensions of subsystem and co-subsystem while maintaining or improving the minimum distance. As a consequence, it is shown that all pure MDS subsystem codes are derived from MDS stabilizer codes. Furthermore, a simple construction of pure MDS subsystem codes is obtained...

A bstract We investigate the spontaneous breaking of subsystem symmetries directly in context continuum field theories by calculating correlation function charged operators. Our methods confirm lack symmetry some existing with symmetries, as had previously been established based on a careful analysis spectrum. present novel theory constructions that do exhibit whenever allowed general principle...

The concepts of learning and memory have fascinated man since before the advent of science. The evolutionary significance of these mechanisms is clear. If an organism is able to learn and remember information about its environment, it will have a distinct advantage in survival. Biologically, learning is described as the inherent process in which an organism senses an environmental stimulus and ...

An article by Xu et al. in the December 2014 issue of GENETICS can be used to illustrate epigenetic modification of gene expression, reverse genetic manipulation, genetic/epigenetic influence on behavioral studies, and studies using the Drosophila model organism applied to human disease. This Primer provides background information; technical explanations of genetic, biochemical, and behavioral ...

bin(k-1 ;n,p) = L n p xqn-x, the cumulative binomial function. k-1 ( ) x=o x C=the total of the cost of the subsystem itself plus the expected cost due to subsystem failure c1 = loss due to failure of the subsystem c3 =cost of a one module subsystem capable of full output c4 =cost of a module in a k-out-of-n:G (good) subsystem when k is fixed g(k) = the function relating cost of the subsystem t...

June 2013 / Vol. 63 No. 6 www.biosciencemag.org have generated extensive fundamental knowledge that now has us superbly positioned for “returning to the organism” (Stillman et al. 2011). The challenge is to extend, integrate, and exploit the insights from “outward” and “inward” gene-oriented biology to develop a deeper understanding of individual organisms’ higher-order emergent characteristics...