Evolutionary computation in dynamic and uncertain environments

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Editorial to special issue on evolutionary computation in dynamic and uncertain environments

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Collusion with private and aggregate information

This paper considers three linear asymmetric oligopoly models with (i) a representative consumer, (ii) horizontal differentiation and (iii) vertical differentiation. We show that firms could maximize the joint-profit only based on private and aggregate information. They can choose the “correct“ colluding prices without knowing the demand or profit function. The collusive outcome is a natural focal point despite firms are asymmetric. Collusion can be incentive compatible even though individual actions (prices) are not observed. -- Der Beitrag untersucht drei linear asymmetrische Oligopol-Modelle mit (i) einem repräsentativen Verbraucher, (ii) horizontaler Differenzierung und (iii) vertikaler Differenzierung. Es wird gezeigt, daß Firmen in der Lage sind, den Gesamtprofit allein auf der Grundlage privater und gemeinschaftlicher Information zu maximieren. Sie können zur „richtigen“ Absprache des Preises gelangen, ohne die Nachfrage- oder Gewinn-Funktion zu kennen. Die Absprache stellt einen natürlichen Gleichgewichtspunkt dar, ungeachtet asymmetrischer Verhältnisse. Die Absprache kann anreizkompatibel sein, auch wenn individuelle Aktionen (Preise) nicht beobachtet werden.

Bounded perturbation resilience of projected scaled gradient methods

We investigate projected scaled gradient (PSG) methods for convex minimization problems. These methods perform a descent step along a diagonally scaled gradient direction followed by a feasibility regaining step via orthogonal projection onto the constraint set. This constitutes a generalized algorithmic structure that encompasses as special cases the gradient projection method, the projected Newton method, the projected Landweber-type methods and the generalized Expectation-Maximization (EM)-type methods. We prove the convergence of the PSG methods in the presence of bounded perturbations. This resilience to bounded perturbations is relevant to the ability to apply the recently developed superiorization methodology to PSG methods, in particular to the EM algorithm.Comment: Computational Optimization and Applications, accepted for publicatio

Minimal Models for Axion and Neutrino

The PQ mechanism resolving the strong CP problem and the seesaw mechanism explaining the smallness of neutrino masses may be related in a way that the PQ symmetry breaking scale and the seesaw scale arise from a common origin. Depending on how the PQ symmetry and the seesaw mechanism are realized, one has different predictions on the color and electromagnetic anomalies which could be tested in the future axion dark matter search experiments. Motivated by this, we construct various PQ seesaw models which are minimally extended from the (non-) supersymmetric Standard Model and thus set up different benchmark points on the axion-photon-photon coupling in comparison with the standard KSVZ and DFSZ models.Comment: 12 pages and 2 figures, references added, matched with the published version in PL

Random induced subgraphs of Cayley graphs induced by transpositions

In this paper we study random induced subgraphs of Cayley graphs of the symmetric group induced by an arbitrary minimal generating set of transpositions. A random induced subgraph of this Cayley graph is obtained by selecting permutations with independent probability, $\lambda_n$. Our main result is that for any minimal generating set of transpositions, for probabilities $\lambda_n=\frac{1+\epsilon_n}{n-1}$ where $n^{-{1/3}+\delta}\le \epsilon_n0$, a random induced subgraph has a.s. a unique largest component of size $\wp(\epsilon_n)\frac{1+\epsilon_n}{n-1}n!$, where $\wp(\epsilon_n)$ is the survival probability of a specific branching process.Comment: 18 pages, 1 figur