Implementing Write Compression in Flash Memory Using Zeckendorf Two-Round Rewriting Codes

Flash memory has become increasingly popular as the underlying storage technology for high-performance nonvolatile storage devices. However, while flash offers several benefits over alternative storage media, a number of limitations still exist within the current technology. One such limitation is that programming (altering a bit from its default value) and erasing (returning a bit to its default value) are asymmetric operations in flash memory devices: a flash memory can be programmed arbitrarily, but can only be erased in relatively large batches of storage bits called blocks, with block sizes ranging from 512K up to several megabytes. This creates a situation where relatively small write operations to the drive can potentially require reading out, erasing, and rewriting many times more data than the initial operation would normally require if that write would result in a bit erase operation. Prior work suggests that the performance impact of these costly block erase cycles can be mitigated by using a rewriting code, increasing the number of writes that can be performed on the same location in memory before an erase operation is required. This paper provides an implementation of this rewriting code, both as a software program written in C and as a SystemVerilog FPGA circuit specification, and discusses many of the additional design considerations that would be necessary to integrate such a rewriting code with current file storage techniques

Recent Application in Biometrics

In the recent years, a number of recognition and authentication systems based on biometric measurements have been proposed. Algorithms and sensors have been developed to acquire and process many different biometric traits. Moreover, the biometric technology is being used in novel ways, with potential commercial and practical implications to our daily activities. The key objective of the book is to provide a collection of comprehensive references on some recent theoretical development as well as novel applications in biometrics. The topics covered in this book reflect well both aspects of development. They include biometric sample quality, privacy preserving and cancellable biometrics, contactless biometrics, novel and unconventional biometrics, and the technical challenges in implementing the technology in portable devices. The book consists of 15 chapters. It is divided into four sections, namely, biometric applications on mobile platforms, cancelable biometrics, biometric encryption, and other applications. The book was reviewed by editors Dr. Jucheng Yang and Dr. Norman Poh. We deeply appreciate the efforts of our guest editors: Dr. Girija Chetty, Dr. Loris Nanni, Dr. Jianjiang Feng, Dr. Dongsun Park and Dr. Sook Yoon, as well as a number of anonymous reviewers

Quasiperiodic Renormalisation: Quasiperiodic Sums, Products and Composition Sum Operators

We study two topics in the renormalisation group theory of quasiperiodic systems, both topics having a number of important applications. Firstly we apply renormalisation techniques to a family of functions we designate quasiperiodic sums and products. These functions link the study of critical phenomena in diverse fields such as the emergence of strange non-chaotic attractors, critical KAM theory, convergence of ergodic averages, and q-series (much used in string theory). In pure mathematics they have also been studied extensively in complex power series analysis, partition theory, and Diophantine approximation. We set these currently dispersed results within a unified framework, and develop a more systematic approach to three key examples. We improve significantly on a series of number-theoretic results obtained by Sierpinsky, Hardy, Hecke, Lang et al; we provide a rigorous proof of some empirically obtained results recently reported by Knill et al (2011-12); and we settle (negatively) an open question of Erdos-Szekeres-Lubinsky dating initially from 1959. Secondly we study the fixed points of quasiperiodic renormalisation. These arise in the study of the Harper equation (almost Mathieu equation), barrier billiards, and a number of other scenarios. We identify the natural setting for their study as a certain class of linear operators (composition sum operators) acting on unbounded (non-Banach) function spaces. We develop the necessary foundations for this theory, and then apply it to construct the space of all fixed points of the golden renormalisation whose singularities are either poles, essential singularities, or logarithmic singularities of a certain simple type. This fixed point space is shown to include previously unknown fixed points

Second International Workshop on Harmonic Oscillators

The Second International Workshop on Harmonic Oscillators was held at the Hotel Hacienda Cocoyoc from March 23 to 25, 1994. The Workshop gathered 67 participants; there were 10 invited lecturers, 30 plenary oral presentations, 15 posters, and plenty of discussion divided into the five sessions of this volume. The Organizing Committee was asked by the chairman of several Mexican funding agencies what exactly was meant by harmonic oscillators, and for what purpose the new research could be useful. Harmonic oscillators - as we explained - is a code name for a family of mathematical models based on the theory of Lie algebras and groups, with applications in a growing range of physical theories and technologies: molecular, atomic, nuclear and particle physics; quantum optics and communication theory

Notes on the combinatorial fundamentals of algebra

This is a detailed survey -- with rigorous and self-contained proofs -- of some of the basics of elementary combinatorics and algebra, including the properties of finite sums, binomial coefficients, permutations and determinants. It is entirely expository (and written to a large extent as a repository for folklore proofs); no new results (and few, if any, new proofs) appear.Comment: 1360 pages. v2 corrects typos and adds Exercises 6.62--6.64. Not a textbook; rather a repository of proofs I could cite. Posted here for easier referencing (and long-term archival). This project is tracked on https://github.com/darijgr/detnote