Syntactic Complexity of R- and J-Trivial Regular Languages

The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of the class of regular languages is the maximal syntactic complexity of languages in that class, taken as a function of the state complexity n of these languages. We study the syntactic complexity of R- and J-trivial regular languages, and prove that n! and floor of [e(n-1)!] are tight upper bounds for these languages, respectively. We also prove that 2^{n-1} is the tight upper bound on the state complexity of reversal of J-trivial regular languages.Comment: 17 pages, 5 figures, 1 tabl

The finite tiling problem is undecidable in the hyperbolic plane

In this paper, we consider the finite tiling problem which was proved undecidable in the Euclidean plane by Jarkko Kari in 1994. Here, we prove that the same problem for the hyperbolic plane is also undecidable

The morphology, evolution and seismic visibility of partial melt at the core-mantle boundary: Implications for ULVZs

SUMMARY Seismic observations indicate that the lowermost mantle above the core–mantle boundary (CMB) is strongly heterogeneous. Body waves reveal a variety of ultra-low velocity zones (ULVZs), which extend not more than 100 km above the CMB and have shear velocity reductions of up to 30 per cent. While the nature and origin of these ULVZs remain uncertain, some have suggested they are evidence of partial melting at the base of mantle plumes. Here we use coupled geodynamic/thermodynamic modelling to explore the hypothesis that present-day deep mantle melting creates ULVZs and introduces compositional heterogeneity in the mantle. Our models explore the generation and migration of melt in a deforming and compacting host rock at the base of a plume in the lowermost mantle. We test whether the balance of gravitational and viscous forces can generate partially molten zones that are consistent with the seismic observations. We find that for a wide range of plausible melt densities, permeabilities and viscosities, lower mantle melt is too dense to be stirred into convective flow and instead sinks down to form a completely molten layer, which is inconsistent with observations of ULVZs. Only if melt is less dense or at most ca. 1 per cent more dense than the solid, or if melt pockets are trapped within the solid, can melt remain suspended in the partial melt zone. In these cases, seismic velocities would be reduced in a cone at the base of the plume. Generally, we find partial melt alone does not explain the observed ULVZ morphologies and solid-state compositional variation is required to explain the anomalies. Our findings provide a framework for testing whether seismically observed ULVZ shapes are consistent with a partial melt origin, which is an important step towards constraining the nature of the heterogeneities in the lowermost mantle and their influence on the thermal, compositional and dynamic evolution of the Earth.ER

The stability of dense oceanic crust near the core‐mantle boundary

The large low‐shear‐velocity provinces (LLSVPs) are thought to be thermo‐chemical in nature, with recycled oceanic crust (OC) being a contender for the source of the chemical heterogeneity. The melting process which forms OC concentrates heat producing elements (HPEs) within it which, over time, may cause any collected piles of OC to destabilize, limiting their suitability to explain LLSVPs. Despite this, most geodynamic studies which include recycling of OC consider only homogeneous heating rates. We perform a suite of spherical, three‐dimensional mantle convection simulations to investigate how buoyancy number, geochemical model and heating model affects the ability of recycled OC to accumulate at the core‐mantle boundary. Our results agree with others that only a narrow range of buoyancy numbers allow OC to form piles in the lower mantle which remain stable to present day. We demonstrate that heterogeneous radiogenic heating causes piles to destabilize more readily, reducing present day CMB coverage from 63% to 47%. Consequently, the choice of geochemical model can influence pile formation. Geochemical models which lead to high internal heating rates can cause more rapid replenishment of piles, increasing their longevity. Where piles do remain to present day, first order comparisons suggest that old (hot) OC material can produce seismic characteristics, such as Vs anomalies, similar to those of LLSVPs. Given the range of current density estimates for lower mantle mineral phases, subducted OC remains a contender for the chemical component of thermo‐chemical LLSVPs

Rape and respectability: ideas about sexual violence and social class

Women on low incomes are disproportionately represented among sexual violence survivors, yet feminist research on this topic has paid very little attention to social class. This article blends recent research on class, gender and sexuality with what we know about sexual violence. It is argued that there is a need to engage with classed distinctions between women in terms of contexts for and experiences of sexual violence, and to look at interactions between pejorative constructions of working-class sexualities and how complainants and defendants are perceived and treated. The classed division between the sexual and the feminine, drawn via the notion of respectability, is applied to these issues. This piece is intended to catalyse further research and debate, and raises a number of questions for future work on sexual violence and social class

Metalanguage in L1 English-speaking 12-year-olds: which aspects of writing do they talk about?

Traditional psycholinguistic approaches to metalinguistic awareness in L1 learners elicit responses containing metalanguage that demonstrates metalinguistic awareness of pre-determined aspects of language knowledge. This paper, which takes a more ethnographic approach, demonstrates how pupils are able to engage their own focus of metalanguage when reflecting on their everyday learning activities involving written language. What is equally significant is what their metalanguage choices reveal about their understanding and application of written language concepts

Effect of Fe3+ on Phase Relations in the Lower Mantle : Implications for Redox Melting in Stagnant Slabs

Recent studies have revealed that Earth's deep mantle may have a wider range of oxygen fugacities than previously thought. Such a large heterogeneity might be caused by material subducted into the deep mantle. However, high-pressure phase relations are poorly known in systems including Fe3+ at the top of the lower mantle, where the subducted slab may be stagnant. We therefore conducted high-pressure and high-temperature experiments using a multi-anvil apparatus to study the phase relations in a Fe3+-bearing system at 26 GPa and 1573–2073 K, at conditions prevailing at the top of the lower mantle. At temperatures below 1923 K, MgSiO3-rich bridgmanite, an Fe3+-rich oxide phase, and SiO2 coexist in the recovered sample. Quenched partial melt was observed above 1973 K, which is significantly lower than the solidus temperature of an equivalent Fe3+-free bulk composition. The partial melt obtained from the Fe3+-rich bulk composition has a higher iron content than coexisting bridgmanite, similar to the Fe2+-dominant system. The results suggest that strong mantle oxygen fugacity anomalies might alter the subsolidus and melting phase relations under lower mantle conditions. We conclude that (1) a small amount of melt may be generated from an Al-depleted region of a stagnant slab, such as subducted former banded-iron-formation, and (2) Fe3+ is not transported into the deep part of the lower mantle because of its incompatibility during melting

Mutation of Directed Graphs -- Corresponding Regular Expressions and Complexity of Their Generation

Directed graphs (DG), interpreted as state transition diagrams, are traditionally used to represent finite-state automata (FSA). In the context of formal languages, both FSA and regular expressions (RE) are equivalent in that they accept and generate, respectively, type-3 (regular) languages. Based on our previous work, this paper analyzes effects of graph manipulations on corresponding RE. In this present, starting stage we assume that the DG under consideration contains no cycles. Graph manipulation is performed by deleting or inserting of nodes or arcs. Combined and/or multiple application of these basic operators enable a great variety of transformations of DG (and corresponding RE) that can be seen as mutants of the original DG (and corresponding RE). DG are popular for modeling complex systems; however they easily become intractable if the system under consideration is complex and/or large. In such situations, we propose to switch to corresponding RE in order to benefit from their compact format for modeling and algebraic operations for analysis. The results of the study are of great potential interest to mutation testing

Near-Field Seismic Propagation and Coupling Through Mars’ Regolith:Implications for the InSight Mission

NASA’s InSight Mission will deploy two three-component seismometers on Mars in 2018. These short period and very broadband seismometers will be mounted on a three-legged levelling system, which will sit directly on the sandy regolith some 2–3 meters from the lander. Although the deployment will be covered by a wind and thermal shield, atmospheric noise is still expected to couple to the seismometers through the regolith. Seismic activity on Mars is expected to be significantly lower than on Earth, so a characterisation of the extent of coupling to noise and seismic signals is an important step towards maximising scientific return. In this study, we conduct field testing on a simplified model of the seismometer assembly. We constrain the transfer function between the wind and thermal shield and tripod-mounted seismometers over a range of frequencies (1–40 Hz) relevant to the deployment on Mars. At 1–20 Hz the displacement amplitude ratio is approximately constant, with a value that depends on the site (0.03–0.06). The value of the ratio in this range is 25–50% of the value expected from the deformation of a homogeneous isotropic elastic halfspace. At 20–40 Hz, the ratio increases as a result of resonance between the tripod mass and regolith. We predict that mounting the InSight instruments on a tripod will not adversely affect the recorded amplitudes of vertical seismic energy, although particle motions will be more complex than observed in recordings generated by more conventional buried deployments. Higher frequency signals will be amplified by tripod-regolith resonance, probably reaching peak-amplification at ∼50 Hz. The tripod deployment will lose sensitivity at frequencies >50 Hz as a result of the tripod mass and compliant regolith. We also investigate the attenuation of seismic energy within the shallow regolith covering the range of seismometer deployment distances