Partial norms and the convergence of general products of matrices

Motivated by the theory of inhomogeneous Markov chains, we determine a sufficient condition for the convergence to 0 of a general product formed from a sequence of real or complex matrices. When the matrices have a common invariant subspace $H$, we give a sufficient condition for the convergence to 0 on $H$ of a general product. Our result is applied to obtain a condition for the weak ergodicity of an inhomogeneous Markov chain. We compare various types of contractions which may be defined for a single matrix, such as paracontraction, $l$--contraction, and $H$--contraction, where $H$ is an invariant subspace of the matrix

Electronic Dynamics Due to Exchange Interaction with Holes in Bulk GaAs

We present an investigation of electron-spin dynamics in p-doped bulk GaAs due to the electron-hole exchange interaction, aka the Bir-Aronov-Pikus mechanism. We discuss under which conditions a spin relaxation times for this mechanism is, in principle, accessible to experimental techniques, in particular to 2-photon photoemission, but also Faraday/Kerr effect measurements. We give numerical results for the spin relaxation time for a range of p-doping densities and temperatures. We then go beyond the relaxation time approximation and calculate numerically the spin-dependent electron dynamics by including the spin-flip electron-hole exchange scattering and spin-conserving carrier Coulomb scattering at the level of Boltzmann scattering integrals. We show that the electronic dynamics deviates from the simple spin-relaxation dynamics for electrons excited at high energies where the thermalization does not take place faster than the spin relaxation time. We also present a derivation of the influence of screening on the electron-hole exchange scattering and conclude that it can be neglected for the case of GaAs, but may become important for narrow-gap semiconductors.Comment: 14 pages, 5 figures, formatted using SPIE templat

Allowing for household preferences in emission trading-A contribution to the climate policy debate

In the context of emission trading it seems to be taken as given that people's preferences can be ignored with respect to the whole process of fixing emission targets and allocating emission permits to polluters. With this paper we want to reopen the debate on how citizens can be involved in this process. We try to show how citizen preferences can be included in the process of pollution control through emission trading. We propose an emission trading system where all emission permits are initially allocated to households who are then allowed to sell them in the permit market or to withhold (at least some of) them in order to reduce total pollution. This proposal tries to overcome the fundamental disadvantage of traditional permit systems which neglect consumer preferences by solely distributing emission permits to producers / polluters. In our system the property right to nature is re-allocated to the households who obtain the opportunity of reducing actual emissions according to their personal preferences by withholding a part or all of the emission permits allotted to them. Such a change in environmental policy would mark a return to the traditional principles of consumer sovereignty by involving households (at least partially) in the social abatement decision process instead of excluding them. Another advantage of admitting households to the TEP market as sellers or buyers of permits is that this increases the number of agents in the permit market and thus significantly reduces the possibilities of strategic market manipulations.Environmental policy; tradable emission permits; climate policy; consumer sovereignty

Allowing for Household Preferences in Emission Trading - A Contribution to the Climate Policy Debate

In the context of emission trading it seems to be taken as given that people's preferences can be ignored with respect to the whole process of fixing emission targets and allocating emission permits to polluters. With this paper we want to reopen the debate on how citizens can be involved in this process. We try to show how citizen preferences can be included in the process of pollution control through emission trading. We propose an emission trading system where all emission permits are initially allocated to households who are then allowed to sell them in the permit market or to withhold (at least some of) them in order to reduce total pollution. This proposal tries to overcome the fundamental disadvantage of traditional permit systems which neglect consumer preferences by solely distributing emission permits to producers/polluters. In our system the property right to nature is re-allocated to the households who obtain the opportunity of reducing actual emissions according to their personal preferences by withholding a part or all of the emission permits allotted to them. Such a change in environmental policy would mark a return to the traditional principles of consumer sovereignty by involving households (at least partially) in the social abatement decision process instead of excluding them. Another advantage of admitting households to the TEP market as sellers or buyers of permits is that this increases the number of agents in the permit market and thus significantly reduces the possibilities of strategic market manipulations.Environmental policy, tradable emission permits, climate policy, consumer sovereignty

PotLLL: A Polynomial Time Version of LLL With Deep Insertions

Lattice reduction algorithms have numerous applications in number theory, algebra, as well as in cryptanalysis. The most famous algorithm for lattice reduction is the LLL algorithm. In polynomial time it computes a reduced basis with provable output quality. One early improvement of the LLL algorithm was LLL with deep insertions (DeepLLL). The output of this version of LLL has higher quality in practice but the running time seems to explode. Weaker variants of DeepLLL, where the insertions are restricted to blocks, behave nicely in practice concerning the running time. However no proof of polynomial running time is known. In this paper PotLLL, a new variant of DeepLLL with provably polynomial running time, is presented. We compare the practical behavior of the new algorithm to classical LLL, BKZ as well as blockwise variants of DeepLLL regarding both the output quality and running time.Comment: 17 pages, 8 figures; extended version of arXiv:1212.5100 [cs.CR