Two algorithms are presented for the generation of full-length shift-register cycles, also referred to as de Bruijn sequences. The first algorithm generates 2 k’g(n,k) full cycles of length 2”, using 3n + k . g( n, k) bits of storage, where k is a free parameter in the range 1 2 k I 2((n-4)/2), and g(n, k) is of the ‘order of n 210g k. The second algorithm generates about 2 n2/4 full cycles of ...

This study reports on the development of a portable iodine-stabilized 543 nm sgreend length-standard laser, which is low cost and robust. All the needed optics and electronics were integrated into one box which measured 36 cm in length, 30 cm in width, and 15 cm in height. Simple circuits for third harmonic locking are presented and the laser’s frequency instability could be as small as 2310−12...

Consider communication over the binary erasure channel BEC(ǫ) using random low-density parity-check codes with finite-blocklength n from ‘standard’ ensembles. We show that large error events is conveniently described within a scaling theory, and explain how to estimate heuristically their effect. Among other quantities, we consider the finite length threshold ǫ∗(n), defined by requiring a block...

A novel method of generating a pseudorandom binary sequence (PRBS) test signal generator is presented. A traditional PRBS generator uses a linear feedback shift register (LFSR) which generates a single maximum length sequence pattern having a fixed period. In this paper, three shift registers with feedback connections are employed in which the preset inputs of the shift registers are changed on...

(Cell 170, 443–456.e1–e14; July 27, 2017) Our paper reported that Alzheimer’s disease-linked mutations in Presenilin and the amyloid precursor protein (APP) destabilize interactions between gamma-secretase APP leading to production of longer beta peptides. We have identified two errors Figure 3C manuscript. During preparation final figures, we mislabeled temperature values for PSEN1 mutants. Th...