An unexpected application of minimization theory to module decompositions

The aim of this work is to show how we can decompose a module (if decomposable) into an indecomposable module with the help of the minimization process.Comment: 15-02-200

Algebraic Elimination of epsilon-transitions

We present here algebraic formulas associating a k-automaton to a k-epsilon-automaton. The existence depends on the definition of the star of matrices and of elements in the semiring k. For this reason, we present the theorem which allows the transformation of k-epsilon-automata into k-automata. The two automata have the same behaviour.Comment: 13 decembre 200

Extending the scalars of minimizations

In the classical theory of formal languages, finite state automata allow to recognize the words of a rational subset of $\Sigma^*$ where $\Sigma$ is a set of symbols (or the alphabet). Now, given a semiring (\K,+,.), one can construct \K-subsets of $\Sigma^*$ in the sense of Eilenberg , that are alternatively called noncommutative formal power series for which a framework very similar to language theory has been constructed Particular noncommutative formal power series, which are called rational series, are the behaviour of a family of weighted automata (or \K-automata). In order to get an efficient encoding, it may be interesting to point out one of them with the smallest number of states. Minimization processes of \K-automata already exist for \K being:\\ {\bf a)} a field ,\\ {\bf b)} a noncommutative field ,\\ {\bf c)} a PID .\\ When \K is the bolean semiring, such a minimization process (with isomorphisms of minimal objects) is known within the category of deterministic automata. Minimal automata have been proved to be isomorphic in cases {\bf (a)} and {\bf (b)}. But the proof given for (b) is not constructive. In fact, it lays on the existence of a basis for a submodule of \K^n. Here we give an independent algorithm which reproves this fact and an example of a pair of nonisomorphic minimal automata. Moreover, we examine the possibility of extending {\bf (c)}. To this end, we provide an {\em Effective Minimization Process} (or {\em EMP}) which can be used for more general sets of coefficients

Direct and dual laws for automata with multiplicities

We present here theoretical results coming from the implementation of the package called AMULT (automata with multiplicities in several noncommutative variables). We show that classical formulas are ``almost every time'' optimal, characterize the dual laws preserving rationality and also relators that are compatible with these laws

Multilinear representations of Free PROs

We describe a structure of PRO on hypermatrices. This structure allows us to define multilinear representations of PROs and in particular of free Pros. As an example of applications, we investigate the relations of the representations of Pros with the theory of automata.Comment: 39 page

Observed methods of cuneiform tablet reconstruction in virtual and real world environments

The reconstruction of fragmented artefacts is a tedious process that consumes many valuable work hours of scholars' time. We believe that such work can be made more efficient via new techniques in interactive virtual environments. The purpose of this research is to explore approaches to the reconstruction of cuneiform tablets in the real and virtual environment, and to address the potential barriers to virtual reconstruction of fragments. In this paper we present the results of an experiment exploring the reconstruction strategies employed by individual users working with tablet fragments in real and virtual environments. Our findings have identified physical factors that users find important to the reconstruction process and further explored the subjective usefulness of stereoscopic 3D in the reconstruction process. Our results, presented as dynamic graphs of interaction, compare the precise order of movement and rotation interactions, and the frequency of interaction achieved by successful and unsuccessful participants with some surprising insights. We present evidence that certain interaction styles and behaviours characterise success in the reconstruction process

A Survey of Geometric Analysis in Cultural Heritage

We present a review of recent techniques for performing geometric analysis in cultural heritage (CH) applications. The survey is aimed at researchers in the areas of computer graphics, computer vision and CH computing, as well as to scholars and practitioners in the CH field. The problems considered include shape perception enhancement, restoration and preservation support, monitoring over time, object interpretation and collection analysis. All of these problems typically rely on an understanding of the structure of the shapes in question at both a local and global level. In this survey, we discuss the different problem forms and review the main solution methods, aided by classification criteria based on the geometric scale at which the analysis is performed and the cardinality of the relationships among object parts exploited during the analysis. We finalize the report by discussing open problems and future perspectives

The Global Risk Approach Should Be Better Applied in French Hypertensive Patients: A Comparison between Simulation and Observation Studies

The prediction of the public health impact of a preventive strategy provides valuable support for decision-making. International guidelines for hypertension management have introduced the level of absolute cardiovascular risk in the definition of the treatment target population. The public health impact of implementing such a recommendation has not been measured.We assessed the efficiency of three treatment scenarios according to historical and current versions of practice guidelines on a Realistic Virtual Population representative of the French population aged from 35 to 64 years: 1) BP≥160/95 mm Hg; 2) BP≥140/90 mm Hg and 3) BP≥140/90 mm Hg plus increased CVD risk. We compared the eligibility following the ESC guidelines with the recently observed proportion of treated amongst hypertensive individuals reported by the Etude Nationale Nutrition Santé survey. Lowering the threshold to define hypertension multiplied by 2.5 the number of eligible individuals. Applying the cardiovascular risk rule reduced this number significantly: less than 1/4 of hypertensive women under 55 years and less than 1/3 of hypertensive men below 45 years of age. This was the most efficient strategy. Compared to the simulated guidelines application, men of all ages were undertreated (between 32 and 60%), as were women over 55 years (70%). By contrast, younger women were over-treated (over 200%).The global CVD risk approach to decide for treatment is more efficient than the simple blood pressure level. However, lack of screening rather than guideline application seems to explain the low prescription rates among hypertensive individuals in France. Multidimensional analyses required to obtain these results are possible only through databases at the individual level: realistic virtual populations should become the gold standard for assessing the impact of public health policies at the national level