Posets are easily testable

Alon and Shapira proved that every monotone class (closed under taking subgraphs) of undirected graphs is strongly testable, that is, under the promise that a given graph is either in the class or ɛ -far from it, there is a test using a constant number of samples (depending on ɛ only) that rejects every graph not in the class with probability at least one half, and always accepts a graph in the class. However, their bound on the number of samples is quite large since they heavily rely on Szemerédi’s regularity lemma. We study the case of posets and show that every monotone class of posets is easily testable, that is, a polynomial (of ɛ ) number of samples is sufficient. We achieve this via proving a polynomial removal lemma for posets. We give a simple classification: for every monotone class of posets, there is an such that the class is indistinguishable (every large enough poset in one class is ɛ -close to a poset in the other class) from the class of -free posets, where denotes the chain with elements. This allows us to test every monotone class of posets using ɛ samples. The test has a two-sided error, but it is almost complete: the probability of refuting a poset in the class is polynomially small in the size of the poset. The analogous results hold for comparability graphs, too

A Virtuális Glóbuszok Múzeuma az iskolai oktatás szolgálatában

Following a brief description of the laws that formed the educational basis for the use of globes in schools, the history of the Hungarian globes, including Earth and celestial globes produced by the most important makers and publishers in different periods is reviewed. The paper briefly describes the Virtual Globes’ Museum founded in 2007, with special respect to some peculiar globes, and presents its various uses in education. It is drawing attention to the importance of using the globe as a tool in creating a comprehensive picture of our Earth in the students’ mind so that the globe should not only be used as a decorative element of apartments, but also as a useful device in the acquisition of geographical and historical knowledge

A szakfordító mint a többnyelvű uniós jog szövegezője

Az uniós jog többnyelvű rendszerében a fordításnak és a fordításokat készítő szakfordítóknak kiemelt szerepük van, hiszen az uniós jog keletkezésének sajátosságai okán az egyaránt hiteles és hivatalos különböző nyelvi változatok tényleges előállítói lesznek. Tekintve, hogy az uniós jog nyelve a tagállami jogi nyelvek szókészletét használja, valamint az uniós jogi terminusok e jogi nyelvek részévé válnak, az uniós fordító nyelvi választásaival befolyásolhatja az egyes tagállamok nyelvpolitikáját is. Éppen ezért esetükben az általános fordítói kompetenciákon felül kiemelt szerep jut a különböző nemzeti, valamint az uniós jogrendszerek közötti átjárhatóságot felismerő transzfer, illetve interkulturális kompetenciáknak, a fordítóknak ugyanis nem csupán rendszerek közötti horizontális, hanem az uniós és a nemzeti jogrendszerek közötti vertikális fordítást is el kell végezniük

Spirit in a Carafe

In the early modern period, accusations of treasure hunting became increasingly common in Inquisition trials in the Principality of Catalonia. The reason for this shift was the Church's attitude towards judicial astrology, most notably after the bull of Pope Sixtus V, Coeli et terrae creator , was issued. This paper presents the facts and contexts of a treasure hunting trial that took place between 1641 and 1644 at the Tribunal of the Inquisition at Barcelona, with a special focus on various European practices of catoptromancy. Through contemporary parallels, we can see side by side the diversity of divination methods, witness the circulation and reproduction of manuscripts, and the popularization and practical use of an earlier, written body of knowledge

The devil's staircase for chip‐firing on random graphs and on graphons

We study the behavior of the activity of the parallel chip‐firing upon increasing the number of chips on an Erdős–Rényi random graph. We show that in various situations the resulting activity diagrams converge to a devil's staircase as we increase the number of vertices. Such a phenomenon was proved in an earlier paper by Levine for complete graphs, by relating the activity to the rotation number of a cycle map. Our method in this article is to generalize the parallel chip‐firing to graphons. Then we show that the earlier results on complete graphs generalize to constant graphons. Moreover, we prove a continuity result for the activity on graphons. These statements enable us to prove results on the activity of the parallel chip‐firing on large random graphs. We also address several problems concerning chip‐firing on graphons, and pose open problems. In particular, we show that the activity of a chip configuration on a graphon does not necessarily exist, but it does exist for every chip configuration on a large class of graphons