Marking Shortest Paths On Pushdown Graphs Does Not Preserve MSO Decidability

In this paper we consider pushdown graphs, i.e. infinite graphs that can be described as transition graphs of deterministic real-time pushdown automata. We consider the case where some vertices are designated as being final and we built, in a breadth-first manner, a marking of edges that lead to such vertices (i.e., for every vertex that can reach a final one, we mark all out-going edges laying on some shortest path to a final vertex). Our main result is that the edge-marked version of a pushdown graph may itself no longer be a pushdown graph, as we prove that this enrich graph may have an undecidable MSO theory. In this paper we consider pushdown graphs, i.e. infinite graphs that can be described as transition graphs of deterministic real-time pushdown automata. We consider the case where some vertices are designated as being final and we build, in a breadth-first manner, a marking of edges that lead to such vertices (i.e., for every vertex that can reach a final one, we mark all out-going edges laying on some shortest path to a final vertex). Our main result is that the edge-marked version of a pushdown graph may itself no longer be a pushdown graph, as we prove that the MSO theory of this enriched graph may be undecidable.Comment: 11 pages, 2 figure

The FC-rank of a context-free language

We prove that the finite condensation rank (FC-rank) of the lexicographic ordering of a context-free language is strictly less than $\omega^\omega$

An analysis of the equational properties of the well-founded fixed point

Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study the logical properties of the (parametric) well-founded fixed point operation. We show that the operation satisfies several, but not all of the equational properties of fixed point operations described by the axioms of iteration theories

Knowledge flows and the geography of networks. A strategic model of small worlds formation.

This paper aims to demonstrate that the strategic approach of network formation can generate networks that share the main structural properties of most real social networks. We introduce a spatialized variation of the Connections model (Jackson and Wolinski, 1996) in which agents balance the benefits of forming links resulting from imperfect knowledge flows through bonds against their costs which increase with geographic distance. We show that, for intermediary levels of knowledge transferability, our time-inhomogeneous process selects networks which exhibit high clustering, short average distances and, when the costs of link formation are normally distributed across agents, skewed degree distributions.Strategic network formation ; Time-inhomogeneous process ; Knowledge flows ; Small worlds ; Monte Carlo simulations.

Who's Who in Patents. A Bayesian approach

This paper proposes a bayesian methodology to treat the who's who problem arising in individual level data sets such as patent data. We assess the usefullness of this methodology on the set of all French inventors appearing on EPO applications from 1978 to 2003.Patents; homonymy; Bayes rule

A strategic model of complex networks formation.

This paper introduces a spatialized variation of the Connections model of Jackson and Wolinski (1996). Agents benefit from their direct and indirect connections in a communication network. They are arranged on a circle and bear costs for maintaining direct connections which are linearly increasing with geographic distance. In a dynamic setting, this model is shown to generate networks that exhibit the small world properties shared by many real social and economic networks.Strategic Network Formation, Pairwise Stability, Small World, Monte Carlo.

The ‘problem of problem choice’: A model of sequential knowledge production within scientific communities cientific communities.

In this paper we present an original model of sequential problem choice within scientific communities. Disciplinary knowledge is accumulated by solving problems emerging in a growing tree-like web of research areas. Knowledge production is sequential since the problems solved generate new problems that may be handled. The model allows us to study how the reward system in science influences the scientific community in stochastically selecting at each period its research agendas, and the long term resulting disciplines. We present some evidence on a decrease in the generation of new areas, a path dependency in specialization, and circumstances under which collapsing dynamics arise.Sequential Problem Choice; Stochastic Process; Tree; Graph Theory; Scientific Knowledge; Academics; Reward System

Why do Academic Scientists Engage in Interdisciplinary Research ?

This article provides a first empirical study of the determinants of the propensity to which academic scholars tend to perform interdisciplinarity research. For that purpose we introduce a measure of interdisciplinarity as the diversity of their research production across scientific domains. Our dataset concerns more than nine hundred permanent researchers employed by a large French university which is ranked first among French universities in terms of Impact. As expected we find that the traditional academic career incentives do not stimulate interdisciplinary research while having connections with industry does. The context of work in the laboratory (size, colleagues’ status, age and affiliations) strongly affects the propensity to undertake interdisciplinary research.Economics of science, Academic incentives, Interdisciplinary research, Laboratory, University.

Dominance relations when both quantity and quality matter, and applications to the\r\ncomparison of US research universities and worldwide top departments in economics

In this article, we propose an extension of the concept of stochastic dominance intensively\r\nused in economics for the comparison of composite outcomes both the quality and the\r\nquantity of which do matter. Our theory also allows us to require unanimity of judgement\r\namong new classes of functions. We apply this theory to the ranking of US research\r\nuniversities, thereby providing a new tool to scientometricians (and the academic\r\ncommunities) who typically aim to compare research institutions taking into account both\r\nthe volume of publications and the impact of these articles. Another application is provided\r\nfor comparing and ranking academic departments when one takes into account both the size\r\nof the department and the prestige of each member.Ranking, dominance relations, citations.