Design and Experimental Performance of a Two Stage Partial Admission Turbine, Task B.1/B.4

A three-inch mean diameter, two-stage turbine with partial admission in each stage was experimentally investigated over a range of admissions and angular orientations of admission arcs. Three configurations were tested in which first stage admission varied from 37.4 percent (10 of 29 passages open, 5 per side) to 6.9 percent (2 open, 1 per side). Corresponding second stage admissions were 45.2 percent (14 of 31 passages open, 7 per side) and 12.9 percent (4 open, 2 per side). Angular positions of the second stage admission arcs with respect to the first stage varied over a range of 70 degrees. Design and off-design efficiency and flow characteristics for the three configurations are presented. The results indicated that peak efficiency and the corresponding isentropic velocity ratio decreased as the arcs of admission were decreased. Both efficiency and flow characteristics were sensitive to the second stage nozzle orientation angles

Flatness is a Criterion for Selection of Maximizing Measures

For a full shift with Np+1 symbols and for a non-positive potential, locally proportional to the distance to one of N disjoint full shifts with p symbols, we prove that the equilibrium state converges as the temperature goes to 0. The main result is that the limit is a convex combination of the two ergodic measures with maximal entropy among maximizing measures and whose supports are the two shifts where the potential is the flattest. In particular, this is a hint to solve the open problem of selection, and this indicates that flatness is probably a/the criterion for selection as it was conjectured by A.O. Lopes. As a by product we get convergence of the eigenfunction at the log-scale to a unique calibrated subaction

Robust simplifications of multiscale biochemical networks

<p>Abstract</p> <p>Background</p> <p>Cellular processes such as metabolism, decision making in development and differentiation, signalling, etc., can be modeled as large networks of biochemical reactions. In order to understand the functioning of these systems, there is a strong need for general model reduction techniques allowing to simplify models without loosing their main properties. In systems biology we also need to compare models or to couple them as parts of larger models. In these situations reduction to a common level of complexity is needed.</p> <p>Results</p> <p>We propose a systematic treatment of model reduction of multiscale biochemical networks. First, we consider linear kinetic models, which appear as "pseudo-monomolecular" subsystems of multiscale nonlinear reaction networks. For such linear models, we propose a reduction algorithm which is based on a generalized theory of the limiting step that we have developed in <abbrgrp><abbr bid="B1">1</abbr></abbrgrp>. Second, for non-linear systems we develop an algorithm based on dominant solutions of quasi-stationarity equations. For oscillating systems, quasi-stationarity and averaging are combined to eliminate time scales much faster and much slower than the period of the oscillations. In all cases, we obtain robust simplifications and also identify the critical parameters of the model. The methods are demonstrated for simple examples and for a more complex model of NF-<it>κ</it>B pathway.</p> <p>Conclusion</p> <p>Our approach allows critical parameter identification and produces hierarchies of models. Hierarchical modeling is important in "middle-out" approaches when there is need to zoom in and out several levels of complexity. Critical parameter identification is an important issue in systems biology with potential applications to biological control and therapeutics. Our approach also deals naturally with the presence of multiple time scales, which is a general property of systems biology models.</p

Ergodicity conditions for zero-sum games

See also arXiv: 1405.4658International audienceA basic question for zero-sum repeated games consists in determining whether the mean payoff per time unit is independent of the initial state. In the special case of "zero-player" games, i.e., of Markov chains equipped with additive functionals, the answer is provided by the mean ergodic theorem. We generalize this result to repeated games. We show that the mean payoff is independent of the initial state for all state-dependent perturbations of the rewards if and only if an ergodicity condition is verified. The latter is characterized by the uniqueness modulo constants of non-linear harmonic functions (fixed point of the recession operator of the Shapley operator), or, in the special case of stochastic games with finite action spaces and perfect information, by a reachability condition involving conjugated subsets of states in directed hypergraphs. We show that the ergodicity condition for games only depend on the support of the transition probability, and that it can be checked in polynomial time when the number of states is fixed

Isometries of polyhedral Hilbert geometries

We show that the isometry group of a polyhedral Hilbert geometry coincides with its group of collineations (projectivities) if and only if the polyhedron is not an n-simplex with n ? 2. Moreover, we determine the isometry group of the Hilbert geometry on the n-simplex for all n ? 2, and find that it has the collineation group as an index-two subgroup. The results confirm several conjectures of P. de la Harpe for the class of polyhedral Hilbert geometries

Max Plus Decision Processes in Planning Problems for Unmanned Air Vehicle Teams

Many aspects of unmanned air vehicle (UAV) operations In this paper, we consider some idempotent modifications of stochastic and Bayesian analysis suitable for decision making in mixed initiative and multi-agent systems. Of particular interest are techniques for mixed initiative and highly autonomous operation. We examine certain Markov Decision Processes (MDPs) within the context of max-plus probability, and we discuss their application to problems of control of unmanned air sensing assets