Search results for "recte"
showing 10 items of 463 documents
On Sturmian Graphs
2007
AbstractIn this paper we define Sturmian graphs and we prove that all of them have a certain “counting” property. We show deep connections between this counting property and two conjectures, by Moser and by Zaremba, on the continued fraction expansion of real numbers. These graphs turn out to be the underlying graphs of compact directed acyclic word graphs of central Sturmian words. In order to prove this result, we give a characterization of the maximal repeats of central Sturmian words. We show also that, in analogy with the case of Sturmian words, these graphs converge to infinite ones.
Using Search Algorithms for Modeling Economic Processes
2013
Abstract Economic issues are placed in formal practice, when is desired a modelling of the economic process, a manufacturing process, a device, etc. Each share of that economic process is denoted by a, b, c, d, these actions with defined time periods and action pairs are formed strings of the form, ab * cab * bc ., ab, bb, bc. so for them there are no other restrictions. If the graph is viewed as a system image, nodes representing components, then an immediate interpretation of an arc (xi, xj) are the component xi that is said to directly influence component xj. If nodes have the significance of possible states of a system when a spring (xi.xj) means that, the system can jump from state xi …
When can association graphs admit a causal interpretation?
1994
We discuss essentially linear structures which are adequately represented by association graphs called covariance graphs and concentration graphs. These do not explicitly indicate a process by which data could be generated in a stepwise fashion. Therefore, on their own, they do not suggest a causal interpretation. By contrast, each directed acyclic graph describes such a process and may offer a causal interpretation whenever this process is in agreement with substantive knowledge about causation among the variables under study. We derive conditions and procedures to decide for any given covariance graph or concentration graph whether all their pairwise independencies can be implied by some …
A comparison of compatible, finite, and inductive graph properties
1993
Abstract In the theory of hyperedge-replacement grammars and languages, one encounters three types of graph properties that play an important role in proving decidability and structural results. The three types are called compatible, finite, and inductive graph properties. All three of them cover graph properties that are well-behaved with respect to certain operations on hypergraphs. In this paper, we show that the three notions are essentially equivalent. Consequently, three lines of investigation in the theory of hyperedge replacement - so far separated - merge into one.
Optimal paths in weighted timed automata
2004
AbstractWe consider the optimal-reachability problem for a timed automaton with respect to a linear cost function which results in a weighted timed automaton. Our solution to this optimization problem consists of reducing it to computing (parametric) shortest paths in a finite weighted directed graph. We call this graph a parametric sub-region graph. It refines the region graph, a standard tool for the analysis of timed automata, by adding the information which is relevant to solving the optimal-reachability problem. We present an algorithm to solve the optimal-reachability problem for weighted timed automata that takes time exponential in O(n(|δ(A)|+|wmax|)), where n is the number of clock…
The Monadic Quantifier Alternation Hierarchy over Grids and Graphs
2002
AbstractThe monadic second-order quantifier alternation hierarchy over the class of finite graphs is shown to be strict. The proof is based on automata theoretic ideas and starts from a restricted class of graph-like structures, namely finite two-dimensional grids. Considering grids where the width is a function of the height, we prove that the difference between the levels k+1 and k of the monadic hierarchy is witnessed by a set of grids where this function is (k+1)-fold exponential. We then transfer the hierarchy result to the class of directed (or undirected) graphs, using an encoding technique called strong reduction. It is notable that one can obtain sets of graphs which occur arbitrar…
Estimating the length of minimal spanning trees in compression of files
1984
Compression of a formatted file by a minimal spanning tree (MST) is studied. Here the records of the file are considered as the nodes of a weighted undirected graph. Each record pair is connected in the graph and the corresponding arc is weighted by the sum of field lengths of those fields which differ in the two records. The actual compression is made by constructing an MST of the graph and by storing it in an economic way to preserve the information of the file. The length of the MST is a useful measure in the estimation of the power of the compression. In the paper we study upper bounds of this length, especially in the case where the field lengths of the different fields may vary. The u…
Minimum node weight spanning trees searching algorithm for broadcast transmission in sensor networks
2017
A minimum node weight spanning tree in a weighted, directed graph is a tree whose node with maximum out-weight is minimal among all spanning trees. This type of trees are important because they appear in the solutions of the maximum lifetime broadcasting problem in wireless sensor networks. In a complete graph build of N nodes there are NN-2 spanning trees and to find such trees it is necessary to perform more than O(NN-2) operations. In this paper we propose an algorithm for searching the minimum node weight spanning trees in the graph. In the proposed algorithm, instead of calculating the symbolic determinant of the generalized Laplacian matrix, numerical operations on its exponents are p…
Relations between structure and estimators in networks of dynamical systems
2011
The article main focus is on the identification of a graphical model from time series data associated with different interconnected entities. The time series are modeled as realizations of stochastic processes (representing nodes of a graph) linked together via transfer functions (representing the edges of the graph). Both the cases of non-causal and causal links are considered. By using only the measurements of the node outputs and without assuming any prior knowledge of the network topology, a method is provided to estimate the graph connectivity. In particular, it is proven that the method determines links to be present only between a node and its “kins”, where kins of a node consist of …
Organisation et conditions de la formation des doctorants dans le cadre de l'université française
2007
This research, refering to the theoretical framework of Pierre Bourdieu, shows that higher education can be considered as a “champ scientifique”, defined as a microcosm, relatively autonomous from the economic and social macrocosm, nevertheless strongly affected by its values and its evolution toward liberalism. This evolution is clearly perceveid in the structural reforms (contractualization, decentralization, increased autonomy...) inferred notably by the construction of the European Higher Education and Research Area. Higher education is structured in a hierarchy with dominating disciplines (mathematics, physique, chemistry...) at the center and, dominated disciplines (Social sciences an…