On the Capacity of Multilevel NAND Flash Memory Channels

In this paper, we initiate a first information-theoretic study on multilevel NAND flash memory channels with intercell interference. More specifically, for a multilevel NAND flash memory channel under mild assumptions, we first prove that such a channel is indecomposable and it features asymptotic equipartition property; we then further prove that stationary processes achieve its information capacity, and consequently, as its order tends to infinity, its Markov capacity converges to its information capacity; eventually, we establish that its operational capacity is equal to its information capacity. Our results suggest that it is highly plausible to apply the ideas and techniques in the computation of the capacity of finite-state channels, which are relatively better explored, to that of the capacity of multilevel NAND flash memory channels.Comment: Submitted to IEEE Transactions on Information Theor

The Majorana spin in magnetic atomic chain systems

In this paper, we establish that Majorana zero modes emerging from a topological band structure of a chain of magnetic atoms embedded in a superconductor can be distinguished from trivial localized zero energy states that may accidentally form in this system using spin resolved measurements. To demonstrate this key Majorana diagnostics, we study the spin composition of magnetic impurity induced in-gap Shiba states in a superconductor using a quantum impurity model (at the mean-field level). By examining the spin and spectral densities in the context of the Bogoliubov-de Gennes (BdG) particle-hole symmetry, we derive a sum rule that relates the spin densities of localized Shiba states with those in the normal state without superconductivity. Extending our investigations to ferromagnetic chain of magnetic impurities, we identify key features of the spin properties of the extended Shiba state bands, as well as those associated with a localized Majorana end mode when the effect of spin-orbit interaction is included. We then formulate a phenomenological theory for the measurement of the local spin densities with spin-polarized scanning tunneling microscopy (STM) techniques. By combining the calculated spin densities and the measurement theory, we show that spin-polarized STM measurements can reveal a sharp contrast in spin polarization between an accidentally-zero-energy trivial Shiba state and a Majorana zero mode in a topological superconducting phase in atomic chains. We further confirm our results with numerical simulations that address generic parameter settings.Comment: 22 pages, 12 figures (references updated

Terrestrial ecosystem health under long-term metal inputs: modeling and risk assessment

Metal contamination of soils may pose long-term risks to ecosystem health if not properly managed. Future projection of contamination trends, coupled with ecological assessment, is needed to assess such risks. This can be achieved by coupling dynamic models of soil metal accumulation and loss with risk assessment on the basis of projected metal levels. In this study, we modeled the long-term dynamics of Cu, Zn, and Cd in agricultural topsoils of a northern Chinese catchment (Guanting reservoir) and related projected metal levels to 2060 to ecological risk. Past metal dynamics were simulated using historical metal inputs from atmospheric deposition, irrigation, fertilizers, and animal manures. Modeling future dynamics was done using scenarios of projected metal input rates. Ecological risk assessment was done using the Potentially Affected Fraction (PAF) approach to estimate the combined toxic pressure due to the three metals. Modeled labile soil metals agreed well with measurements from monitoring in 2009 following adjustment of the porewater dissolved organic concentration. Metals were predicted to be largely retained in the topsoil. Projections were sensitive to changes in imposed soil pH, organic matter, and porewater dissolved organic carbon. Modeling suggests that decreases in input rates to between 5% and 7.5% of 2009 levels are required to prevent further accumulation. Computed PAFs suggest zinc makes the greatest contribution to ecological risk. Under the most conservative estimate of PAF, the threshold of potential ecological risk was reached before 2060 in two of the three future input scenarios

Renyi Entropy Rate of Stationary Ergodic Processes

In this paper, we examine the Renyi entropy rate of stationary ergodic processes. For a special class of stationary ergodic processes, we prove that the Renyi entropy rate always exists and can be polynomially approximated by its defining sequence; moreover, using the Markov approximation method, we show that the Renyi entropy rate can be exponentially approximated by that of the Markov approximating sequence, as the Markov order goes to infinity. For the general case, by constructing a counterexample, we disprove the conjecture that the Renyi entropy rate of a general stationary ergodic process always converges to its Shannon entropy rate as {\alpha} goes to 1

Consensus Adversarial Defense Method Based on Augmented Examples

Deep learning has been used in many computer-vision-based industrial Internet of Things applications. However, deep neural networks are vulnerable to adversarial examples that have been crafted specifically to fool a system while being imperceptible to humans. In this study, we propose a consensus defense (Cons-Def) method to defend against adversarial attacks. Cons-Def implements classification and detection based on the consensus of the classifications of the augmented examples, which are generated based on an individually implemented intensity exchange on the red, green, and blue components of the input image. We train a convolutional neural network using augmented examples together with their original examples. For the test image to be assigned to a specific class, the class occurrence of the classifications on its augmented images should be the maximum and reach a defined threshold. Otherwise, it is detected as an adversarial example. The comparison experiments are implemented on MNIST, CIFAR-10, and ImageNet. The average defense success rate (DSR) against white-box attacks on the test sets of the three datasets is 80.3%. The average DSR against black-box attacks on CIFAR-10 is 91.4%. The average classification accuracies of Cons-Def on benign examples of the three datasets are 98.0%, 78.3%, and 66.1%. The experimental results show that Cons-Def shows a high classification performance on benign examples and is robust against white-box and black-box adversarial attacks