A Lower Bound on the Entropy Rate for a Large Class of Stationary Processes and its Relation to the Hyperplane Conjecture

We present a new lower bound on the differential entropy rate of stationary processes whose sequences of probability density functions fulfill certain regularity conditions. This bound is obtained by showing that the gap between the differential entropy rate of such a process and the differential entropy rate of a Gaussian process with the same autocovariance function is bounded. This result is based on a recent result on bounding the Kullback-Leibler divergence by the Wasserstein distance given by Polyanskiy and Wu. Moreover, it is related to the famous hyperplane conjecture, also known as slicing problem, in convex geometry originally stated by J. Bourgain. Based on an entropic formulation of the hyperplane conjecture given by Bobkov and Madiman we discuss the relation of our result to the hyperplane conjecture.Comment: presented at the 2016 IEEE Information Theory Workshop (ITW), Cambridge, U

Oversampling Increases the Pre-Log of Noncoherent Rayleigh Fading Channels

We analyze the capacity of a continuous-time, time-selective, Rayleigh block-fading channel in the high signal-to-noise ratio (SNR) regime. The fading process is assumed stationary within each block and to change independently from block to block; furthermore, its realizations are not known a priori to the transmitter and the receiver (noncoherent setting). A common approach to analyzing the capacity of this channel is to assume that the receiver performs matched filtering followed by sampling at symbol rate (symbol matched filtering). This yields a discrete-time channel in which each transmitted symbol corresponds to one output sample. Liang & Veeravalli (2004) showed that the capacity of this discrete-time channel grows logarithmically with the SNR, with a capacity pre-log equal to $1-{Q}/{N}$. Here, $N$ is the number of symbols transmitted within one fading block, and $Q$ is the rank of the covariance matrix of the discrete-time channel gains within each fading block. In this paper, we show that symbol matched filtering is not a capacity-achieving strategy for the underlying continuous-time channel. Specifically, we analyze the capacity pre-log of the discrete-time channel obtained by oversampling the continuous-time channel output, i.e., by sampling it faster than at symbol rate. We prove that by oversampling by a factor two one gets a capacity pre-log that is at least as large as $1-1/N$. Since the capacity pre-log corresponding to symbol-rate sampling is $1-Q/N$, our result implies indeed that symbol matched filtering is not capacity achieving at high SNR.Comment: To appear in the IEEE Transactions on Information Theor

Evolution Of The Unnecessary : Investigating How fMet Became Central In Bacterial Translation Initiation

All bacteria initiate translation using formylated methionine, yet directly after translation, the formyl-group is removed. This sequence of addition and removal appears futile, yet every sequenced bacterial genome encodes the enzymes for formylation and deformylation, suggesting this process is essential. Puzzlingly, the process is absent from both Archaea and Eukaryotes, and moreover, bacterial mutants lacking both the formylase and deformylase activities are viable, albeit with a diminished growth rate. We created an Escherichia coli strain devoid of formylase and deformylase activity. This strain was then allowed to evolve over 1500 generations whereupon it reached wild-type growth rate, demonstrating that formylation can be completely dispensed with. This raises an additional question: if the formylation cycle is unnecessary, how did it emerge and why has it persisted? Our results show that the formylation-deformylation cycle could have evolved as a toxin-antitoxin pair (TA) with post-segregational killing (PSK) activity. TAs ‘addict’ cells to the plasmids that carry them by inducing PSK. We measured the stability of formylase-deformylase encoding plasmids and their ability to elicit PSK in our evolved E. coli strain. We report several lines of evidence consistent with the formylation-cycle having evolved from a plasmid-borne PSK element: 1) in the absence of deformylation, formyl-methionine on proteins is cytotoxic in bacteria 2) deformylation relieves the cytotoxicity of formyl-methionine, 3) the loss of a plasmid containing formylase and deformylase genes from evolved cells results in cessation of growth – a standard PSK phenotype. In addition, we introduced the E. coli formylase and deformylase genes into yeast and demonstrate that Met-tRNA formylation is not lethal, even in the absence of deformylation. This suggests PSK would be ineffectual in yeast, accounting for the absence of formylation from eukaryotic cytoplasmic translation. We also report the presence of formylase and deformylase genes in the two representative members of the archaeal Methanocopusculum genus. Moreover, we demonstrate that these genes have been acquired by a recent horizontal gene transfer from bacteria. Our results indicate that formylmethionine use in bacteria evolved, not through a direct functional benefit to cells, but through competition between infectious genetic elements

Организация бережливого производства в здравоохранении

В данной статье изучены принципы концепции бережливого производства, а так же приведены особенности и организация бережливого производства в здравоохранении