Singular response to a dopant of an evaporating crystal surface

Moving crystal surfaces can undergo step-bunching instabilities, when subject to an electric current. We show analytically that an infinitesimal quantity of a dopant may invert the stability, whatever the sign of the current. Our study is relevant for experimental results [S. S. Kosolobov et al., JETP Lett. 81, 117 (2005)] on an evaporating Si(111) surface, which show a singular response to Au doping, whose density distribution is related to inhomogeneous Si diffusion.Comment: 5 pages. To be published in PRB-Rapid Communication

Lempel–Ziv-Like Parsing in Small Space

Lempel–Ziv (LZ77 or, briefly, LZ) is one of the most effective and widely-used compressors for repetitive texts. However, the existing efficient methods computing the exact LZ parsing have to use linear or close to linear space to index the input text during the construction of the parsing, which is prohibitive for long inputs. An alternative is Relative Lempel–Ziv (RLZ), which indexes only a fixed reference sequence, whose size can be controlled. Deriving the reference sequence by sampling the text yields reasonable compression ratios for RLZ, but performance is not always competitive with that of LZ and depends heavily on the similarity of the reference to the text. In this paper we introduce ReLZ, a technique that uses RLZ as a preprocessor to approximate the LZ parsing using little memory. RLZ is first used to produce a sequence of phrases, and these are regarded as metasymbols that are input to LZ for a second-level parsing on a (most often) drastically shorter sequence. This parsing is finally translated into one on the original sequence. We analyze the new scheme and prove that, like LZ, it achieves the kth order empirical entropy compression nHk+ o(nlog σ) with k= o(log σn) , where n is the input length and σ is the alphabet size. In fact, we prove this entropy bound not only for ReLZ but for a wide class of LZ-like encodings. Then, we establish a lower bound on ReLZ approximation ratio showing that the number of phrases in it can be Ω (log n) times larger than the number of phrases in LZ. Our experiments show that ReLZ is faster than existing alternatives to compute the (exact or approximate) LZ parsing, at the reasonable price of an approximation factor below 2.0 in all tested scenarios, and sometimes below 1.05, to the size of LZ. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.D. Kosolobov supported by the Russian Science Foundation (RSF), Project 18-71-00002 (for the upper bound analysis and a part of lower bound analysis). D. Valenzuela supported by the Academy of Finland (Grant 309048). G. Navarro funded by Basal Funds FB0001 and Fondecyt Grant 1-200038, Chile. S.J. Puglisi supported by the Academy of Finland (Grant 319454). This work started during Shonan Meeting 126 “Computation over Compressed Structured Data”. Funded in part by EU’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie Grant Agreement No. 690941 (project BIRDS)

Run compressed rank/select for large alphabets

Given a string of length n that is composed of r runs of letters from the alphabet 0,1,..,σ-1 such that 2 ≤ σ ≤ r, we describe a data structure that, provided r ≤ n/log ω(1) n, stores the string in rlog nσ/r + o(r log nσ/r) bits and supports select and access queries in O(log log(n/r)/loglogn) time and rank queries in O(log log(nσ/r)/log time. We show that r log n(σ-1)/r-O(log n/r) bits are necessary for any such data structure and, thus, our solution is succinct. We also describe a data structure that uses (1 + ϵ)r log nσ/r + O(r) bits, where ϵ > 0 is an arbitrary constant, with the same query times but without the restriction r ≤ n/log ω(1) n. By simple reductions to the colored predecessor problem, we show that the query times are optimal in the important case r ≥ 2logδ n, for an arbitrary constant δ > 0. We implement our solution and compare it with the state of the art, showing that the closest competitors consume 31-46% more space. © 2018 IEEE.Peer reviewe

Palindromic Decompositions with Gaps and Errors

Identifying palindromes in sequences has been an interesting line of research in combinatorics on words and also in computational biology, after the discovery of the relation of palindromes in the DNA sequence with the HIV virus. Efficient algorithms for the factorization of sequences into palindromes and maximal palindromes have been devised in recent years. We extend these studies by allowing gaps in decompositions and errors in palindromes, and also imposing a lower bound to the length of acceptable palindromes. We first present an algorithm for obtaining a palindromic decomposition of a string of length n with the minimal total gap length in time O(n log n * g) and space O(n g), where g is the number of allowed gaps in the decomposition. We then consider a decomposition of the string in maximal \delta-palindromes (i.e. palindromes with \delta errors under the edit or Hamming distance) and g allowed gaps. We present an algorithm to obtain such a decomposition with the minimal total gap length in time O(n (g + \delta)) and space O(n g).Comment: accepted to CSR 201

Towards Deep Integration of Electronics and Photonics

A combination of computational power provided by modern MOSFET-based devices with light assisted wideband communication at the nanoscale can bring electronic technologies to the next level. Obvious obstacles include a size mismatch between electronic and photonic components as well as a weak light–matter interaction typical for existing devices. Polariton modes can be used to overcome these difficulties at the fundamental level. Here, we review applications of such modes, related to the design and fabrication of electro–optical circuits. The emphasis is made on surface plasmon-polaritons which have already demonstrated their value in many fields of technology. Other possible quasiparticles as well as their hybridization with plasmons are discussed. A quasiparticle-based paradigm in electronics, developed at the microscopic level, can be used in future molecular electronics and quantum computing

Cold intense electron beams from LN2-cooled GaAs-photocathodes

To study electron-ion interactions at the Heidelberg heavy-ion storage ring, electron beams with low-energy spreads and dc-currents of milliamperes are desired. Measurements of the photoelectron energy distribution showed that electron beams with energy spreads of 5-8 meV can be obtained from GaAs photocathodes, cooled to about LN2-temperature. However, in order to get milliamperes beam currents, the laser illumination has to be increased up to 1 W, causing substantial cathode heating. The presented new electron gun design based on sapphire-substrate transmission-mode photocathodes, cooled by LN2, stabilizes the GaAs bulk temperature under 1 W laser illumination at about 95 K and thereby provides the prerequisites for an electron gun being operated at milliampere-currents with low-energy spreads

Pyramid-Like Si Structures Grown on the Step Bunched Si(111)-(7×7) Surface

Abstract – Pyramid-like Si structures have been observed on large (5 μm) atomically flat terraces of the step bunched Si (111)-(7×7) surface during Si deposition at T = 600°–760°C in the ultrahighvacuum reflection electron microscope (UHV REM). Such structures are the result of sequential twodimensional island nucleation and growth (2DNG) accompanied by reducing a terrace width after each monolayer formation. The critical terrace width, at which the next 2DNG layer starts, is measured depending on substrate temperature and Si deposition rate. Two different activation energies of 2DNG layer formation (E 2D) are found out: E 2D ≈ 2.4 eV at T < 700°C and E 2D ≈ 0.5 eV at T> 700°C. Based on experimental data a critical cluster size for 2Disland nucleation is determined to be 7–10 atoms. Index Terms – Silicon, homoepitaxial growth, morphology, superstructure