On the Gap between Random Dynamical Systems and Continuous Skew Products

AMS 2000 subject classification: primary 37-02, 37B20, 37H05; secondary 34C27, 37A20.We review the recent notion of a nonautonomous dynamical system (NDS), which has been introduced as an abstraction of both random dynamical systems and continuous skew product flows. Our focus is on fundamental analogies and discrepancies brought about by these two classes of NDS. We discuss base dynamics mainly through almost periodicity and almost automorphy, and we emphasize the importance of these concepts for NDS which are generated by differential and difference equations. Nonautonomous dynamics is presented by means of representative examples. We also mention several natural yet unresolved questions

On Almost Automorphic Dynamics in Symbolic Lattices

1991 Mathematics Subject Classification. Primary Primary 37B10, 37A35, 43A60; Secondary 37B20, 54H20.We study the existence, structure, and topological entropy of almost automorphic arrays in symbolic lattice dynamical systems. In particular we show that almost automorphic arrays with arbitrarily large entropy are typical in symbolic lattice dynamical systems. Applications to pattern formation and spatial chaos in infinite dimensional lattice systems are considered, and the construction of chaotic almost automorphic signals is discussed.The first author was supported by a Max Kade Postdoctoral Fellowship (at Georgia Tech). The second author was partially supported by DFG grant Si 801 and CDSNS, Georgia Tech. The third author was partially supported by NSF Grant DMS-0204119

Force-dependent unbinding rate of molecular motors from stationary optical trap data

Molecular motors walk along filaments until they detach stochastically with a force-dependent unbinding rate. Here, we show that this unbinding rate can be obtained from the analysis of experimental data of molecular motors moving in stationary optical traps. Two complementary methods are presented, based on the analysis of the distribution for the unbinding forces and of the motor's force traces. In the first method, analytically derived force distributions for slip bonds, slip-ideal bonds, and catch bonds are used to fit the cumulative distributions of the unbinding forces. The second method is based on the statistical analysis of the observed force traces. We validate both methods with stochastic simulations and apply them to experimental data for kinesin-1

The Micro Dynamic of Exporting-Evidence from French Firms

This paper describes the dynamics of rms' exports to dierent countries. Using a panel of almost 19,000 French exporters, we dene an export-relation as an observed positive export ow from a French rm to a destination. We establish the following facts: 1. There is a great deal of dynamics in rms' export relations that washes out at a more aggregate level; 2. Export values shipped by individual rms to specic destinations are very volatile: most of the changes occur within established export relations (intensive margin), with new relations or relations that are terminated (extensive margin)contributing little to adjustments in export value at rm level ; 3. Export ows within a newly-created relation involve very small values, often inferior to 1000 euros; 4. Export-relations are also very volatile. Moreover, from year to year single rms create and destroy relations simultaneously, and countries are simultaneously involved in the formation and termination of relations; 5. Formation or termination of export relations and changes in export values are explained mostly by rm-country specic shocks; 6. The share of relations continued from one year to the next is correlated with country characteristics: it is higher in bigger and closer markets. We discuss how those ndings could be related to dierent kinds of heterogeneous rm models and to a relation-specic trade model, arguing that the second one seems to t more naturally all the documented facts.

The Micro Dynamics of Exporting: Evidence from French Firms

This paper describes the dynamics of firms' exports to different countries. Using a panel of almost 19,000 French exporters, we define an export-relation as an observed positive export flow from a French firm to a destination. We establish the following facts: 1. There is a great deal of dynamics in firms' export relations that washes out at a more aggregate level; 2. Export values shipped by individual firms to specific destinations are very volatile: most of the changes occur within established export relations (intensive margin), with new relations or relations that are terminated (extensive margin)contributing little to adjustments in export value at firm level ; 3. Export flows within a newly-created relation involve very small values, often inferior to 1000 euros; 4. Export-relations are also very volatile. Moreover, from year to year single firms create and destroy relations simultaneously, and countries are simultaneously involved in the formation and termination of relations; 5. Formation or termination of export relations and changes in export values are explained mostly by firm-country specific shocks; 6. The share of relations continued from one year to the next is correlated with country characteristics: it is higher in bigger and closer markets. We discuss how those findings could be related to different kind of heterogeneous firm models and to a relation-specific trade model, arguing that the second one seems to fit more naturally all the documented facts.firm level trade, trade dynamics, state dependence, extensive/intensive margin

Class vs. Nation, Class and the Nation, Between Class and Nation? Labour's Response to the National Question c.1870-1939, with Special Reference to Britain and Germany

Few historians would doubt the huge influence of the metanarratives of “nation” and “class” on nineteenth- and twentieth-century history. Both had risen to prominence in the midst of the massive upheaval that followed nineteenth-century industrialization. Both were hugely successful defensive mechanisms promising stable identities and continuity in a rapidly changing world. In the second half of the nineteenth century, the nascent European labour movements began to build their political claims on the language of “class”, while being shaped to a considerable extent by their respective national frameworks. The tension between this “national” framework and the more international aspirations of the language of class was present from the beginning of the modern labour movement. Examples from Britain and Germany show how organized labour constructed identities that attempted to reconcile the languages of these seemingly antagonistic concepts.Peu d’historiens douteraient de l’énorme influence qu’ont eue les métanarratifs de « nation » et de « classe » sur l’histoire du XIXe et du XXe siècles. Tous deux avaient atteint la prééminence lors des bouleversements consécutifs à l’industrialisation du XIXe siècle. Tous deux ont remporté énormément de succès comme mécanismes de défense, promettant des identités stables et la continuité dans un monde évoluant rapidement. Durant la deuxième moitié du XIXe siècle, les mouvements ouvriers naissants d’Europe commencèrent à revendiquer la langue des « classes » sur la scène politique tout en étant façonnés dans une large mesure par leurs cadres nationaux respectifs. La tension entre ce cadre « national » et les aspirations plus internationales de la langue des classes était présente dès le début du mouvement ouvrier moderne. Des exemples de Grande-Bretagne et d’Allemagne montrent comment le travail organisé a construit des identités qui tentaient de concilier les langues de ces concepts en apparence contradictoires