Uniform random generation of large acyclic digraphs

Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory networks, not only the estimation of model parameters but the reconstruction of the structure itself is of great interest. As well as for the assessment of different structure learning algorithms in simulation studies, a uniform sample from the space of directed acyclic graphs is required to evaluate the prevalence of certain structural features. Here we analyse how to sample acyclic digraphs uniformly at random through recursive enumeration, an approach previously thought too computationally involved. Based on complexity considerations, we discuss in particular how the enumeration directly provides an exact method, which avoids the convergence issues of the alternative Markov chain methods and is actually computationally much faster. The limiting behaviour of the distribution of acyclic digraphs then allows us to sample arbitrarily large graphs. Building on the ideas of recursive enumeration based sampling we also introduce a novel hybrid Markov chain with much faster convergence than current alternatives while still being easy to adapt to various restrictions. Finally we discuss how to include such restrictions in the combinatorial enumeration and the new hybrid Markov chain method for efficient uniform sampling of the corresponding graphs.Comment: 15 pages, 2 figures. To appear in Statistics and Computin

Control theory for principled heap sizing

We propose a new, principled approach to adaptive heap sizing based on control theory. We review current state-of-the-art heap sizing mechanisms, as deployed in Jikes RVM and HotSpot. We then formulate heap sizing as a control problem, apply and tune a standard controller algorithm, and evaluate its performance on a set of well-known benchmarks. We find our controller adapts the heap size more responsively than existing mechanisms. This responsiveness allows tighter virtual machine memory footprints while preserving target application throughput, which is ideal for both embedded and utility computing domains. In short, we argue that formal, systematic approaches to memory management should be replacing ad-hoc heuristics as the discipline matures. Control-theoretic heap sizing is one such systematic approach

A Short History of Polish-Ukrainian Terminography

A Short History of Polish-Ukrainian Terminography Specialised dictionaries fulfil a plethora of linguistic and cognitive functions in specialised communication. In particular, such reference works help introduce, harmonise and standardise national terminologies, thus playing an indispensable role in disseminating high quality specialised knowledge. An even more important role may be attributed to bilingual and multilingual specialised dictionaries, whose primary goal is to facilitate the flow of scientific and technical information at an international level. This function has come to the fore in today’s multinational and interconnected professional world. In light of the developing and ever stronger cooperation between Poland and Ukraine, an attempt is being made to evaluate bilingual and multilingual terminographic works containing Polish and Ukrainian which have been published in Poland to date. The aim is to assess the positive developments and to identify the gaps in Polish-Ukrainian terminography. It is hoped that the findings presented in this paper will be applied by terminographers in order to compile terminological dictionaries of higher quality, which satisfy the needs of specific users and follow terminographic principles.   Krótka historia terminografii polsko-ukraińskiej Słowniki specjalistyczne pełnią ważne funkcje lingwistyczne i kognitywne w komunikacji specjalistycznej. W szczególności dzieła terminograficzne umożliwiają rozpowszechnianie, harmonizację i standaryzację terminologii narodowych, stając się niezbędnym narzędziem w transferze wysokiej jakości wiedzy specjalistycznej. Jeszcze ważniejszą rolę można przypisać dwu- i wielojęzycznym słownikom specjalistycznym, których prymarnym celem jest ułatwienie przepływu informacji naukowej i technicznej w wymiarze globalnym, szczególnie w dzisiejszym jednoczącym się, wielonarodowościowym świecie. W świetle rozwijającej się coraz ściślejszej współpracy między Polską i Ukrainą w niniejszym artykule autor podejmuje się próby oceny opublikowanych w Polsce dwu- i wielojęzycznych dzieł terminograficznych z językami polskim i ukraińskim. Celem badania była ewaluacja pozytywnych oraz negatywnych aspektów praktyki terminograficznej polsko-ukraińskiej. Autor ma nadzieję, że wnioski przedstawione w niniejszej pracy znajdą zastosowanie w praktyce przy tworzeniu słowników coraz lepszej jakości, odpowiadających potrzebom konkretnych grup odbiorców oraz stosujących zasady współczesnej terminografii

Zero-one laws with respect to models of provability logic and two Grzegorczyk logics

It has been shown in the late 1960s that each formula of first-order logic without constants and function symbols obeys a zero-one law: As the number of elements of finite models increases, every formula holds either in almost all or in almost no models of that size. Therefore, many properties of models, such as having an even number of elements, cannot be expressed in the language of first-order logic. Halpern and Kapron proved zero-one laws for classes of models corresponding to the modal logics K, T, S4, and S5 and for frames corresponding to S4 and S5. In this paper, we prove zero-one laws for provability logic and its two siblings Grzegorczyk logic and weak Grzegorczyk logic, with respect to model validity. Moreover, we axiomatize validity in almost all relevant finite models, leading to three different axiom systems