Splaying Preorders and Postorders

Let $T$ be a binary search tree. We prove two results about the behavior of the Splay algorithm (Sleator and Tarjan 1985). Our first result is that inserting keys into an empty binary search tree via splaying in the order of either $T$'s preorder or $T$'s postorder takes linear time. Our proof uses the fact that preorders and postorders are pattern-avoiding: i.e. they contain no subsequences that are order-isomorphic to $(2,3,1)$ and $(3,1,2)$, respectively. Pattern-avoidance implies certain constraints on the manner in which items are inserted. We exploit this structure with a simple potential function that counts inserted nodes lying on access paths to uninserted nodes. Our methods can likely be extended to permutations that avoid more general patterns. Second, if $T'$ is any other binary search tree with the same keys as $T$ and $T$ is weight-balanced (Nievergelt and Reingold 1973), then splaying $T$'s preorder sequence or $T$'s postorder sequence starting from $T'$ takes linear time. To prove this, we demonstrate that preorders and postorders of balanced search trees do not contain many large "jumps" in symmetric order, and exploit this fact by using the dynamic finger theorem (Cole et al. 2000). Both of our results provide further evidence in favor of the elusive "dynamic optimality conjecture.

A Fistful of Dollars: Formalizing Asymptotic Complexity Claims via Deductive Program Verification

Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2018International audienceWe present a framework for simultaneously verifying the functional correctness and the worst-case asymptotic time complexity of higher-order imperative programs. We build on top of Separation Logic with Time Credits, embedded in an interactive proof assistant. We formalize the O notation, which is key to enabling modular specifications and proofs. We cover the subtleties of the multivariate case, where the complexity of a program fragment depends on multiple parameters. We propose a way of integrating complexity bounds into specifications, present lemmas and tactics that support a natural reasoning style, and illustrate their use with a collection of examples

Guidelines for the use and interpretation of assays for monitoring autophagy (4th edition)1.

In 2008, we published the first set of guidelines for standardizing research in autophagy. Since then, this topic has received increasing attention, and many scientists have entered the field. Our knowledge base and relevant new technologies have also been expanding. Thus, it is important to formulate on a regular basis updated guidelines for monitoring autophagy in different organisms. Despite numerous reviews, there continues to be confusion regarding acceptable methods to evaluate autophagy, especially in multicellular eukaryotes. Here, we present a set of guidelines for investigators to select and interpret methods to examine autophagy and related processes, and for reviewers to provide realistic and reasonable critiques of reports that are focused on these processes. These guidelines are not meant to be a dogmatic set of rules, because the appropriateness of any assay largely depends on the question being asked and the system being used. Moreover, no individual assay is perfect for every situation, calling for the use of multiple techniques to properly monitor autophagy in each experimental setting. Finally, several core components of the autophagy machinery have been implicated in distinct autophagic processes (canonical and noncanonical autophagy), implying that genetic approaches to block autophagy should rely on targeting two or more autophagy-related genes that ideally participate in distinct steps of the pathway. Along similar lines, because multiple proteins involved in autophagy also regulate other cellular pathways including apoptosis, not all of them can be used as a specific marker for bona fide autophagic responses. Here, we critically discuss current methods of assessing autophagy and the information they can, or cannot, provide. Our ultimate goal is to encourage intellectual and technical innovation in the field

InGaAs Quantum Dots Grown by Molecular Beam Epitaxy for Light Emission on Si Substrates

International audienceThe aim of this study is to achieve homogeneous, high density and dislocation free InGaAs quantum dots grown by molecular beam epitaxy for light emission on silicon substrates. This work is part of a project which aims at overcoming the severe limitation suffered by silicon regarding its optoelectronic applications, especially efficient light emission device. For this study, one of the key points is to overcome the expected type II InGaAs/Si interface by inserting the InGaAs quantum dots inside a thin silicon quantum well in SiO2 fabricated on a SOI substrate. Confinement effects of the Si/SiO2 quantum well are expected to heighten the indirect silicon bandgap and then give rise to a type I interface with the InGaAs quantum dots. Band structure and optical properties are modeled within the tight binding approximation: direct energy bandgap is demonstrated in SiO2/Si/InAs/Si/SiO2 heterostructures for very thin Si layers and absorption coefficient is calculated. Thinned SOI substrates are successfully prepared using successive etching process resulting in a 2 nm-thick Si layer on top of silica. Another key point to get light emission from InGaAs quantum dots is to avoid any dislocations or defects in the quantum dots. We investigate the quantum dot size distribution, density and structural quality at different V/III beam equivalent pressure ratios, different growth temperatures and as a function of the amount of deposited material. This study was performed for InGaAs quantum dots grown on Si(001) substrates. The capping of InGaAs quantum dots by a silicon epilayer is performed in order to get efficient photoluminescence emission from quantum dots. Scanning transmission electronic microscopy images are used to study the structural quality of the quantum dots. Dislocation free In50Ga50As QDs are successfully obtained on a (001) silicon substrate. The analysis of QDs capped with silicon by Rutherford Backscattering Spectrometry in a channeling geometry is also presented