Stack graphs: Name resolution at scale

We present stack graphs, an extension of Visser et al.'s scope graphs framework. Stack graphs power Precise Code Navigation at GitHub, allowing users to navigate name binding references both within and across repositories. Like scope graphs, stack graphs encode the name binding information about a program in a graph structure, in which paths represent valid name bindings. Resolving a reference to its definition is then implemented with a simple path-finding search. GitHub hosts millions of repositories, containing petabytes of total code, implemented in hundreds of different programming languages, and receiving thousands of pushes per minute. To support this scale, we update the graph construction and path-finding judgments to be file-incremental. For each source file, we create an isolated subgraph without any knowledge of, or visibility into, any other file in the program. This lets us eliminate the storage and compute costs of reanalyzing file versions that we have already seen. Since most commits change a small fraction of the files in a repository, this greatly amortizes the operational costs of indexing large, frequently changed repositories over time. To handle type-directed name lookups (which require "pausing" the current lookup to resolve another name), our path-finding algorithm maintains a stack of the currently paused (but still pending) lookups. Stack graphs can be constructed via a purely syntactic analysis of the program's source code, using a new declarative graph construction language. This means that we can extract name binding information for every repository without any per-package configuration, and without having to invoke an arbitrary, untrusted, package-specific build process.Comment: 8 pages, submitted to Eelco Visser Commemorative Symposium 202

Nilpotency of skew braces and multipermutation solutions of the Yang-Baxter equation

We study relations between different notions of nilpotency in the context of skew braces and applications to the structure of solutions to the Yang-Baxter equation. In particular, we consider annihilator nilpotent skew braces, an important class that turns out to be a brace-theoretic analog to the class of nilpotent groups. In this vein, several well-known theorems in group theory are proved in the more general setting of skew braces.Comment: 18 pages. Postprint versio

Factorizations of skew braces

We introduce strong left ideals of skew braces and prove that they produce non-trivial decomposition of set-theoretic solutions of the Yang–Baxter equation. We study factorization of skew left braces through strong left ideals and we prove analogs of Itô’s theorem in the context of skew left braces. As a corollary, we obtain applications to the retractability problem of involutive non-degenerate solutions of the Yang–Baxter equation. Finally, we classify skew braces that contain no non-trivial proper characteristic ideals.Fil: Jespers, E.. Vrije Unviversiteit Brussel; BélgicaFil: Kubat, L.. Vrije Unviversiteit Brussel; BélgicaFil: Van Antwerpen, A.. Vrije Unviversiteit Brussel; BélgicaFil: Vendramin, Claudio Leandro. Institute of Mathematical Sciences at NYU Shanghai; China. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

On various types of nilpotency of the structure monoid and group of a set-theoretic solution of the Yang--Baxter equation

Given a finite bijective non-degenerate set-theoretic solution $(X,r)$ of the Yang--Baxter equation we characterize when its structure monoid $M(X,r)$ is Malcev nilpotent. Applying this characterization to solutions coming from racks, we rediscover some results obtained recently by Lebed and Mortier, and by Lebed and Vendramin on the description of finite abelian racks and quandles. We also investigate bijective non-degenerate multipermutation (not necessarily finite) solutions $(X,r)$ and show, for example, that this property is equivalent to the solution associated to the structure monoid $M(X,r)$ (respectively structure group $G(X,r)$) being a multipermuation solution and that $G=G(X,r)$ is solvable of derived length not exceeding the multipermutation level of $(X,r)$ enlarged by one, generalizing results of Gateva-Ivanova and Cameron obtained in the involutive case. Moreover, we also prove that if $X$ is finite and $G=G(X,r)$ is nilpotent, then the torsion part of the group $G$ is finite, it coincides with the commutator subgroup $[G,G]_+$ of the additive structure of the skew left brace $G$ and $G/[G,G]_+$ is a trivial left brace.Comment: 35 page

Consultancy haalbaarheid Klimrekscherm

Deze haalbaarheidstudie heeft als doel de mogelijkheden van het klimrek systeem in de glastuinbouw in kaart te brengen in een semi-gesloten teelt concept teneinde te komen tot energiebesparing, productieverhoging, betere kwaliteit, betere CO2 benutting en minder uitval ten gevolge van vochtproblemen door een te hoge RV

Higgs boson as a gluon trigger: the study of QCD in high pile-up environments

In the forthcoming high-luminosity phase of the LHC many of the most interesting measurements for precision QCD studies are hampered by large pile-up conditions, especially at not very high transverse momenta. However, with the recently discovered Higgs boson, which couples in the heavy top limit directly to gluons, we have access to a novel production process to probe QCD by a colour-singlet current. In this study we compare observables in Higgs boson and Drell-Yan production and investigate whether measuring ratios or subtractions can yield results that are stable in high pile-up environments, and yet sensitive to (small-$p_{\text{T}}$) QCD physics in gluon fusion processes. We present results of Monte Carlo event generator calculations for a few specific examples.Comment: 7 pages, 10 figures, DIS2014 conference proceeding

Gauging the three-nucleon spectator equation

We derive relativistic three-dimensional integral equations describing the interaction of the three-nucleon system with an external electromagnetic field. Our equations are unitary, gauge invariant, and they conserve charge. This has been achieved by applying the recently introduced gauging of equations method to the three-nucleon spectator equations where spectator nucleons are always on mass shell. As a result, the external photon is attached to all possible places in the strong interaction model, so that current and charge conservation are implemented in the theoretically correct fashion. Explicit expressions are given for the three-nucleon bound state electromagnetic current, as well as the transition currents for the scattering processes \gamma He3 -> NNN, Nd -> \gamma Nd, and \gamma He3 -> Nd. As a result, a unified covariant three-dimensional description of the NNN-\gamma NNN system is achieved.Comment: 23 pages, REVTeX, epsf, 4 Postscript figure