Dynamic Complexity of Formal Languages

The paper investigates the power of the dynamic complexity classes DynFO, DynQF and DynPROP over string languages. The latter two classes contain problems that can be maintained using quantifier-free first-order updates, with and without auxiliary functions, respectively. It is shown that the languages maintainable in DynPROP exactly are the regular languages, even when allowing arbitrary precomputation. This enables lower bounds for DynPROP and separates DynPROP from DynQF and DynFO. Further, it is shown that any context-free language can be maintained in DynFO and a number of specific context-free languages, for example all Dyck-languages, are maintainable in DynQF. Furthermore, the dynamic complexity of regular tree languages is investigated and some results concerning arbitrary structures are obtained: there exist first-order definable properties which are not maintainable in DynPROP. On the other hand any existential first-order property can be maintained in DynQF when allowing precomputation.Comment: Contains the material presenten at STACS 2009, extendes with proofs and examples which were omitted due lack of spac

Ferropericlase Control of Lower Mantle Rheology : Impact of Phase Morphology

Abstract The rheological properties of Earth's lower mantle play a key role for global mantle dynamics. The mineralogy of the lower mantle can be approximated as a bridgmanite‐ferropericlase mixture. Previous work has suggested that the deformation of this mixture might be dramatically affected by the large differences in viscosity between bridgmanite and ferropericlase. Here, we employ numerical models to establish a connection between ferropericlase morphology and the effective rheology of the Earth's lower mantle using a numerical‐statistical approach. Using this approach, we link the statistical properties of the two‐phase composite to its effective viscosity tensor using analytical approximations. We find that ferropericlase develops elongated structures within the bridgmanite matrix that result in significantly lowered viscosity. While our findings confirm previous endmember models that suggested a change of mantle viscosity due to the formation of interconnected weak layers, we show that significant rheological weakening can thus be already achieved even when ferropericlase does not form an interconnected network. Additionally, the alignment of weak ferropericlase leads to a pronounced viscous anisotropy that develops with total strain, which may have implications for understanding the viscosity structure of Earth's lower mantle as well as for modeling the behavior of subducting slabs. We show that to capture the effect of ferropericlase elongation on the effective viscosity tensor (and its anisotropy) in large‐scale mantle convection models, the analytical approximations that have been derived to describe the evolution of the effective viscosity of a two‐phase medium with aligned elliptical inclusions can be used

Sense Smart, Not Hard: A Layered Cognitive Radar Architecture

In this chapter, we present a cognitive radar architecture based on the three-layer model by Rasmussen. The skill-based-layer is characterized by adaptive signal-processing approaches and target matched waveforms. The rule-based-layer comprises reactive execution of optimal illumination policies and resource-management. The knowledge-based layer allows for long term, goal-oriented mission- and trajectory planning. Each layer is illustrated by example algorithms and applications for implementation

Replicating financial market dynamics with a simple self-organized critical lattice model

We explore a simple lattice field model intended to describe statistical properties of high frequency financial markets. The model is relevant in the cross-disciplinary area of econophysics. Its signature feature is the emergence of a self-organized critical state. This implies scale invariance of the model, without tuning parameters. Prominent results of our simulation are time series of gains, prices, volatility, and gains frequency distributions, which all compare favorably to features of historical market data. Applying a standard GARCH(1,1) fit to the lattice model gives results that are almost indistinguishable from historical NASDAQ data.Comment: 20 pages, 33 figure

Distortion Product Otoacoustic Emissions Evoked by Tone Complexes

Distortion product otoacoustic emissions (DPOAEs) are traditionally evoked by two-tone stimuli. In this study, emission data from Mongolian gerbils are reported that were obtained with stimuli consisting of six to 10 tones. The stimuli were constructed by replacing one of the tones of a tone pair by a narrowband multitone complex. This produced rich spectra of the ear canal sound pressure in which many of the third-order DPOAEs originated from the interaction of triplets of stimulus components. A careful choice of the stimulus frequencies ensured that none of these DPOAE components coincided. Three groups of DPOAEs are reported, two of which are closely related to DPOAEs evoked by tone pairs. The third group has no two-tone equivalent and only arises when using a multitone stimulus. We analyzed the relation between multitone-evoked DPOAEs and DPOAEs evoked by tone pairs, and explored the new degrees of freedom offered by the multitone paradigm

Responses of Auditory Nerve and Anteroventral Cochlear Nucleus Fibers to Broadband and Narrowband Noise: Implications for the Sensitivity to Interaural Delays

The quality of temporal coding of sound waveforms in the monaural afferents that converge on binaural neurons in the brainstem limits the sensitivity to temporal differences at the two ears. The anteroventral cochlear nucleus (AVCN) houses the cells that project to the binaural nuclei, which are known to have enhanced temporal coding of low-frequency sounds relative to auditory nerve (AN) fibers. We applied a coincidence analysis within the framework of detection theory to investigate the extent to which AVCN processing affects interaural time delay (ITD) sensitivity. Using monaural spike trains to a 1-s broadband or narrowband noise token, we emulated the binaural task of ITD discrimination and calculated just noticeable differences (jnds). The ITD jnds derived from AVCN neurons were lower than those derived from AN fibers, showing that the enhanced temporal coding in the AVCN improves binaural sensitivity to ITDs. AVCN processing also increased the dynamic range of ITD sensitivity and changed the shape of the frequency dependence of ITD sensitivity. Bandwidth dependence of ITD jnds from AN as well as AVCN fibers agreed with psychophysical data. These findings demonstrate that monaural preprocessing in the AVCN improves the temporal code in a way that is beneficial for binaural processing and may be crucial in achieving the exquisite sensitivity to ITDs observed in binaural pathways