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

Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS

This article presents a finite element reduced order model for the nonlinear vibrations of piezoelectric layered beams with application to NEMS. In this model, the geometrical nonlinearities are taken into account through a von Kármán nonlinear strain–displacement relationship. The originality of the finite element electromechanical formulation is that the system electrical state is fully described by only a couple of variables per piezoelectric patches, namely the electric charge contained in the electrodes and the voltage between the electrodes. Due to the geometrical nonlinearity, the piezoelectric actuation introduces an original parametric excitation term in the equilibrium equation. The reduced-order formulation of the discretized problem is obtained by expanding the mechanical displacement unknown vector onto the short-circuit eigenmode basis. A particular attention is paid to the computation of the unknown nonlinear stiffness coefficients of the reduced-order model. Due to the particular form of the von Kármán nonlinearities, these coefficients are computed exactly, once for a given geometry, by prescribing relevant nodal displacements in nonlinear static solutions settings. Finally, the low-order model is computed with an original purely harmonic-based continuation method. Our numerical tool is then validated by computing the nonlinear vibrations of a mechanically excited homogeneous beam supported at both ends referenced in the literature. The more difficult case of the nonlinear oscillations of a layered nanobridge piezoelectrically actuated is also studied. Interesting vibratory phenomena such as parametric amplification or patch length dependence of the frequency output response are highlighted in order to help in the design of these nanodevices.This research is part of the NEMSPIEZO project, under funds from the French National Research Agency (Project ANR-08-NAN O-015-04), for which the authors are grateful

Modeling cardiac rhythm and heart rate using BFO and DOLCE

This paper presents an application ontology for modeling cardiac rhythm and its anomalies such as tachycardia and bradycardia. We use BFO and DOLCE as ontological reference framework in order to compare their impact on ontology design. 

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Job Creation, Job Destruction and the Life Cycle

This paper originally incorporates life-cycle features into the job creation - job destruction framework. Once a finite horizon is introduced, this workhorse labor market model naturally delivers the empirically uncontroversial prediction that the employment rate of workers decreases with age due to lower hirings and higher firings of older workers. This age profile of hirings and firings is in addition found to be optimal in a competitive search equilibrium context. If search externalities are not internalized and unemployment benefits distort equilibrium, there is a room for labor market policy differentiated by age. This lastly allows us to debate the incidence of labor demand policies which have been introduced in many countries to favor the older worker employment. We show that hiring subsidies and firing costs should be decreasing with age when unemployment benefits are sufficiently high, as in the Europe. On the contrary, if unemployment benefits are low, as in the US, optimal hiring subsidies and firing taxes should be increasing with age. In this latter case, the introduction of anti-discrimination laws is a good proxy of this first best policy.Job creations and destructions, Life cycle, Older workers

Life-Cycle Equilibrium Unemployment

This paper develops a life-cycle approach to equilibrium unemployment. Workers only differ respectively to their distance from deterministic retirement. A non age-directed search equilibrium is then typically featured by increasing (decreasing) firing (hiring) rates with age and a hump-shaped age profile for employment. Because of intergenerational inefficiencies, the Hosios condition no longer achieves efficiency. We then explore the optimal age-pattern of some policy tools to restore this efficiency. The optimal profile for employment subsidies should increase with age, whereas firing taxes and hirings subsidies would have to be hump-shaped. Lastly, we examine the robustness of our results. We show that age-directed recruitment policies cannot exist in equilibrium even if it would have been ex-ante possible, and that introducing endogenous search effort of unemployed workers reinforces our main results.job search, matching, life cycle

Age-Dependent Employment Protection

This paper examines the age-related design of firing taxes by extending the theory of job creation and job destruction to account for a finite working life-time. We first argue that the potential employment gains related to employment protection are high for older workers, but higher firing taxes for these workers increase job destruction rates for the younger generations. On the other hand, age-decreasing firing taxes can lead to lower job destruction rates at all ages. Furthermore, from a normative standpoint, because firings of older (younger) workers exert a negative (positive) externality on the matching process, we find that the first best age-dynamic of firing taxes and hiring subsidies is typically hump-shaped. Taking into account distortions related to unemployment benefits and bargaining power shows the robustness of this result, in contradiction with the existing policies in most OECD countries.foo