Periodic Strategies: A New Solution Concept and an Algorithm for NonTrivial Strategic Form Games

We introduce a new solution concept, called periodicity, for selecting optimal strategies in strategic form games. This periodicity solution concept yields new insight into non-trivial games. In mixed strategy strategic form games, periodic solutions yield values for the utility function of each player that are equal to the Nash equilibrium ones. In contrast to the Nash strategies, here the payoffs of each player are robust against what the opponent plays. Sometimes, periodicity strategies yield higher utilities, and sometimes the Nash strategies do, but often the utilities of these two strategies coincide. We formally define and study periodic strategies in two player perfect information strategic form games with pure strategies and we prove that every non-trivial finite game has at least one periodic strategy, with non-trivial meaning non-degenerate payoffs. In some classes of games where mixed strategies are used, we identify quantitative features. Particularly interesting are the implications for collective action games, since there the collective action strategy can be incorporated in a purely non-cooperative context. Moreover, we address the periodicity issue when the players have a continuum set of strategies available.Comment: Revised version, similar to the one published in Advances in Complex System

Blending of Polyhydroxybutyrate-co-valerate with Polylactic Acid for Packaging Applications – Reflections on Miscibility and Effects on the Mechanical and Barrier Properties

Biopolymers for packaging applications offer many advantages and are therefore of increasing interest. In order to develop a sustainable alternative for petrochemical-based polymers the biobased and biodegradable polymers, the focus of this work are polyhydroxybutyrate-co-valerate (PHBV) and polylactic acid (PLA) (and copolymers). Blending of these two biopolymers was reviewed under thermodynamic aspects and backed with own results. Additionally, different ways of improving the miscibility were performed by compatibilisers, peroxides, transesterification catalysts, and by blending PHBV with modified molecular weight. These blends were extruded as cast films, and characterised by means of mechanical and barrier properties. This study analyses the miscibility of PLA and PHB-copolyester (with approximately equal molar masses) and reports on the unusually high barrier properties in PLA and PHBV blends. However, the quality of blending, especially regarding barrier properties to interphase boundaries, depends on the compatibility of the components and the morphology of the blend. Our results suggest that a PHBV content of 20–35 % in PLA is the most suitable blend system in terms of compatibility and high barrier properties

INVERSE DYNAMICS OF TAKE-OFF ON SKI-JUMPING SIMULATOR

A special take-off simulator for ski-jumping was constructed to enable training of jumping skills. An inverse dynamics model was used to evaluate a take-off technique on that simulator. A 3D video based kinematical system was used to obtain body coordinates, which were then transformed to 2D sagittal plane. From a five link segment model the joint forces in horizontal and vertical direction as well as joint torques were calculated. Results showed sufficient sensitiveness of the method for a take-off assessment. A vibration effect, probably due to the low approaching velocity and thus a poorer balance, was observable, what was not a case in a normal snow conditions

Mode spectrum and temporal soliton formation in optical microresonators

The formation of temporal dissipative solitons in optical microresonators enables compact, high repetition rate sources of ultra-short pulses as well as low noise, broadband optical frequency combs with smooth spectral envelopes. Here we study the influence of the resonator mode spectrum on temporal soliton formation. Using frequency comb assisted diode laser spectroscopy, the measured mode structure of crystalline MgF2 resonators are correlated with temporal soliton formation. While an overal general anomalous dispersion is required, it is found that higher order dispersion can be tolerated as long as it does not dominate the resonator's mode structure. Mode coupling induced avoided crossings in the resonator mode spectrum are found to prevent soliton formation, when affecting resonator modes close to the pump laser. The experimental observations are in excellent agreement with numerical simulations based on the nonlinear coupled mode equations, which reveal the rich interplay of mode crossings and soliton formation

Representation of Markov chains by random maps: existence and regularity conditions

We systematically investigate the problem of representing Markov chains by families of random maps, and which regularity of these maps can be achieved depending on the properties of the probability measures. Our key idea is to use techniques from optimal transport to select optimal such maps. Optimal transport theory also tells us how convexity properties of the supports of the measures translate into regularity properties of the maps via Legendre transforms. Thus, from this scheme, we cannot only deduce the representation by measurable random maps, but we can also obtain conditions for the representation by continuous random maps. Finally, we present conditions for the representation of Markov chain by random diffeomorphisms.Comment: 22 pages, several changes from the previous version including extended discussion of many detail

Transport and thermoelectric properties of the LaAlO3_3/SrTiO3_3 interface

The transport and thermoelectric properties of the interface between SrTiO$_3$ and a 26-monolayer thick LaAlO$_3$-layer grown at high oxygen-pressure have been investigated at temperatures from 4.2 K to 100 K and in magnetic fields up to 18 T. For $T>$ 4.2 K, two different electron-like charge carriers originating from two electron channels which contribute to transport are observed. We probe the contributions of a degenerate and a non-degenerate band to the thermoelectric power and develop a consistent model to describe the temperature dependence of the thermoelectric tensor. Anomalies in the data point to an additional magnetic field dependent scattering.Comment: 7 pages, 4 figure