Selection theorem for systems with inheritance

The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has generically finite-dimensional asymptotics. Such systems are apparent in many areas of biology, physics (the theory of parametric wave interaction), chemistry and economics. This conservation of support has a biological interpretation: inheritance. The finite-dimensional asymptotics demonstrates effects of "natural" selection. Estimations of the asymptotic dimension are presented. After some initial time, solution of a kinetic equation with conservation of support becomes a finite set of narrow peaks that become increasingly narrow over time and move increasingly slowly. It is possible that these peaks do not tend to fixed positions, and the path covered tends to infinity as t goes to infinity. The drift equations for peak motion are obtained. Various types of distribution stability are studied: internal stability (stability with respect to perturbations that do not extend the support), external stability or uninvadability (stability with respect to strongly small perturbations that extend the support), and stable realizability (stability with respect to small shifts and extensions of the density peaks). Models of self-synchronization of cell division are studied, as an example of selection in systems with additional symmetry. Appropriate construction of the notion of typicalness in infinite-dimensional space is discussed, and the notion of "completely thin" sets is introduced. Key words: Dynamics; Attractor; Evolution; Entropy; Natural selectionComment: 46 pages, the final journal versio

A Concurrency-Optimal Binary Search Tree

The paper presents the first \emph{concurrency-optimal} implementation of a binary search tree (BST). The implementation, based on a standard sequential implementation of an internal tree, ensures that every \emph{schedule} is accepted, i.e., interleaving of steps of the sequential code, unless linearizability is violated. To ensure this property, we use a novel read-write locking scheme that protects tree \emph{edges} in addition to nodes. Our implementation outperforms the state-of-the art BSTs on most basic workloads, which suggests that optimizing the set of accepted schedules of the sequential code can be an adequate design principle for efficient concurrent data structures

On Concurrent Solutions in Differential Games

We examine solutions in which neither player is worse off from the leadership of one in a policy maker-public game. The loop model of dynamic games is used. Outcome space is dotted with equivalence classes of solutions. The Dynamic Stochastic General Equilibrium (DSGE) results and their New Keynesian variants might represent one category. The economy is the neighborhood of a market-clearing equilibrium with Pareto-optimal properties modulo frictions. Our interest lies in the ‘old’ Keynesian genus where the representative state is one of involuntary unemployment. Two information sets are relevant. In the first case, agents look to the past and the present. In the second, they are bound by the information provided in the present. The standard analysis pertains to DSGE models under full information. We show, in contrast, that in a situation of structural disequilibrium and feedback information, all parties are better off reneging on the social compact to achieve a superior class of solutions.information structures, time consistency, credibility and reputation