16,611 research outputs found
Subgame-Perfect Equilibria in Stochastic Timing Games
We introduce a notion of subgames for stochastic timing games and the related
notion of subgame-perfect equilibrium in possibly mixed strategies. While a
good notion of subgame-perfect equilibrium for continuous-time games is not
available in general, we argue that our model is the appropriate version for
timing games. We show that the notion coincides with the usual one for
discrete-time games. Many timing games in continuous time have only equilibria
in mixed strategies -- in particular preemption games, which often occur in the
strategic real option literature. We provide a sound foundation for some
workhorse equilibria of that literature, which has been lacking as we show. We
obtain a general constructive existence result for subgame-perfect equilibria
in preemption games and illustrate our findings by several explicit
applications.Comment: 27 pages, 1 figur
Covering compact metric spaces greedily
A general greedy approach to construct coverings of compact metric spaces by
metric balls is given and analyzed. The analysis is a continuous version of
Chvatal's analysis of the greedy algorithm for the weighted set cover problem.
The approach is demonstrated in an exemplary manner to construct efficient
coverings of the n-dimensional sphere and n-dimensional Euclidean space to give
short and transparent proofs of several best known bounds obtained from
deterministic constructions in the literature on sphere coverings.Comment: (v2) 10 pages, minor revision, accepted in Acta Math. Hunga
Possible Origin of Stagnation and Variability of Earth's Biodiversity
The magnitude and variability of Earth's biodiversity have puzzled scientists
ever since paleontologic fossil databases became available. We identify and
study a model of interdependent species where both endogenous and exogenous
impacts determine the nonstationary extinction dynamics. The framework provides
an explanation for the qualitative difference of marine and continental
biodiversity growth. In particular, the stagnation of marine biodiversity may
result from a global transition from an imbalanced to a balanced state of the
species dependency network. The predictions of our framework are in agreement
with paleontologic databases.Comment: 5 pages, 6 pages supplemen
Redistribution spurs growth by using a portfolio effect on human capital
We demonstrate by mathematical analysis and systematic computer simulations
that redistribution can lead to sustainable growth in a society. The human
capital dynamics of each agent is described by a stochastic multiplicative
process which, in the long run, leads to the destruction of individual human
capital and the extinction of the individualistic society. When agents are
linked by fully-redistributive taxation the situation might turn to individual
growth in the long run. We consider that a government collects a proportion of
income and reduces it by a fraction as costs for administration (efficiency
losses). The remaining public good is equally redistributed to all agents. We
derive conditions under which the destruction of human capital can be turned
into sustainable growth, despite the losses from the random growth process and
despite the administrative costs. Sustainable growth is induced by
redistribution. This effect could be explained by a simple portfolio-effect
which re-balances individual stochastic processes.
The findings are verified for three different tax schemes: proportional tax,
taking proportional more from the rich, and proportionally more from the poor.
We discuss which of these tax schemes is optimal with respect to maximize
growth under a fixed rate of administrative costs, or with respect to maximize
the governmental income. This leads us to some general conclusions about
governmental decisions, the relation to public good games, and the use of
taxation in a risk taking society.Comment: 12 pages, plus 8 Figures, plus matlab-code to run simulation and
produce figur
Phosphorus Nitride P3N5
Pure, stoichiometric, hydrogen-free, and crystalline phosphorus nitride P3N5 has been obtained for the first time by reaction of (PNCl2)3 and NH4Cl between 770 and 1050 K. The compound has been characterized by elemental analyses, 31P and 15N MAS NMR, EXAFS, IR spectroscopy, X-ray powder diffraction, and electron microscopy. In the solid a three-dimensional cross-linked network structure of corner sharing PN4 tetrahedra has been identified with 2/5 of the nitrogen atoms bonded to three P atoms and 3/5 of the nitrogen atoms bonded to two P atoms. By electron diffraction (ED) and high-resolution transmission electron microscopy (HRTEM) two distinguishable modifications α-P3N5 and β-P3N5 have been identified which differentiate only by the stacking order of identical sheets similar to the polytypes of SiC
Estimation of biochemical network parameter distributions in cell populations
Populations of heterogeneous cells play an important role in many biological
systems. In this paper we consider systems where each cell can be modelled by
an ordinary differential equation. To account for heterogeneity, parameter
values are different among individual cells, subject to a distribution function
which is part of the model specification.
Experimental data for heterogeneous cell populations can be obtained from
flow cytometric fluorescence microscopy. We present a heuristic approach to use
such data for estimation of the parameter distribution in the population. The
approach is based on generating simulation data for samples in parameter space.
By convex optimisation, a suitable probability density function for these
samples is computed.
To evaluate the proposed approach, we consider artificial data from a simple
model of the tumor necrosis factor (TNF) signalling pathway. Its main
characteristic is a bimodality in the TNF response: a certain percentage of
cells undergoes apoptosis upon stimulation, while the remaining part stays
alive. We show how our modelling approach allows to identify the reasons that
underly the differential response.Comment: 14 pages, 5 figure
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