Modal Logics of Topological Relations

Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham's modal logic of time intervals based on the Allen relations, we introduce a family of modal logics equipped with eight modal operators that are interpreted by the Egenhofer-Franzosa (or RCC8) relations between regions in topological spaces such as the real plane. We investigate the expressive power and computational complexity of logics obtained in this way. It turns out that our modal logics have the same expressive power as the two-variable fragment of first-order logic, but are exponentially less succinct. The complexity ranges from (undecidable and) recursively enumerable to highly undecidable, where the recursively enumerable logics are obtained by considering substructures of structures induced by topological spaces. As our undecidability results also capture logics based on the real line, they improve upon undecidability results for interval temporal logics by Halpern and Shoham. We also analyze modal logics based on the five RCC5 relations, with similar results regarding the expressive power, but weaker results regarding the complexity

Hybridization of institutions

Extended version including all proofsModal logics are successfully used as specification logics for reactive systems. However, they are not expressive enough to refer to individual states and reason about the local behaviour of such systems. This limitation is overcome in hybrid logics which introduce special symbols for naming states in models. Actually, hybrid logics have recently regained interest, resulting in a number of new results and techniques as well as applications to software specification. In this context, the first contribution of this paper is an attempt to ‘universalize’ the hybridization idea. Following the lines of [DS07], where a method to modalize arbitrary institutions is presented, the paper introduces a method to hybridize logics at the same institution-independent level. The method extends arbitrary institutions with Kripke semantics (for multi-modalities with arbitrary arities) and hybrid features. This paves the ground for a general result: any encoding (expressed as comorphism) from an arbitrary institution to first order logic (FOL) deter- mines a comorphism from its hybridization to FOL. This second contribution opens the possibility of effective tool support to specification languages based upon logics with hybrid features.Fundação para a Ciência e a Tecnologia (FCT

Structure of the hDmc1-ssDNA filament reveals the principles of its architecture

In eukaryotes, meiotic recombination is a major source of genetic diversity, but its defects in humans lead to abnormalities such as Down's, Klinefelter's and other syndromes. Human Dmc1 (hDmc1), a RecA/Rad51 homologue, is a recombinase that plays a crucial role in faithful chromosome segregation during meiosis. The initial step of homologous recombination occurs when hDmc1 forms a filament on single-stranded (ss) DNA. However the structure of this presynaptic complex filament for hDmc1 remains unknown. To compare hDmc1-ssDNA complexes to those known for the RecA/Rad51 family we have obtained electron microscopy (EM) structures of hDmc1-ssDNA nucleoprotein filaments using single particle approach. The EM maps were analysed by docking crystal structures of Dmc1, Rad51, RadA, RecA and DNA. To fully characterise hDmc1-DNA complexes we have analysed their organisation in the presence of Ca2+, Mg2+, ATP, AMP-PNP, ssDNA and dsDNA. The 3D EM structures of the hDmc1-ssDNA filaments allowed us to elucidate the principles of their internal architecture. Similar to the RecA/Rad51 family, hDmc1 forms helical filaments on ssDNA in two states: extended (active) and compressed (inactive). However, in contrast to the RecA/Rad51 family, and the recently reported structure of hDmc1-double stranded (ds) DNA nucleoprotein filaments, the extended (active) state of the hDmc1 filament formed on ssDNA has nine protomers per helical turn, instead of the conventional six, resulting in one protomer covering two nucleotides instead of three. The control reconstruction of the hDmc1-dsDNA filament revealed 6.4 protein subunits per helical turn indicating that the filament organisation varies depending on the DNA templates. Our structural analysis has also revealed that the N-terminal domain of hDmc1 accomplishes its important role in complex formation through domain swapping between adjacent protomers, thus providing a mechanistic basis for coordinated action of hDmc1 protomers during meiotic recombination

The chemical evolution of the solar neighbourhood for planet-hosting stars

Theoretical physical-chemical models for the formation of planetary systems depend on data quality for the Sun's composition, that of stars in the solar neighbourhood, and of the estimated "pristine" compositions for stellar systems. The effective scatter and the observational uncertainties of elements within a few hundred parsecs from the Sun, even for the most abundant metals like carbon, oxygen and silicon, are still controversial. Here we analyse the stellar production and the chemical evolution of key elements that underpin the formation of rocky (C, O, Mg, Si) and gas/ice giant planets (C, N, O, S). We calculate 198 galactic chemical evolution (GCE) models of the solar neighbourhood to analyse the impact of different sets of stellar yields, of the upper mass limit for massive stars contributing to GCE ($M_{\rm up}$) and of supernovae from massive-star progenitors which do not eject the bulk of the iron-peak elements (faint supernovae). Even considering the GCE variation produced via different sets of stellar yields, the observed dispersion of elements reported for stars in the Milky Way disk is not reproduced. Among others, the observed range of super-solar [Mg/Si] ratios, sub-solar [S/N], and the dispersion of up to 0.5 dex for [S/Si] challenge our models. The impact of varying $M_{\rm up}$ depends on the adopted supernova yields. Thus, observations do not provide a constraint on the M$_{\rm up}$ parametrization. When including the impact of faint supernova models in GCE calculations, elemental ratios vary by up to 0.1-0.2 dex in the Milky Way disk; this modification better reproduces observations.Comment: 36 pages, 26 figures, 1 Table, 1 Appendix, Accepted for publication in MNRA

Stream diatom biodiversity in islands and continents—A global perspective on effects of area, isolation and environment

Aim The species-area relationship (SAR) is one of the most distinctive biogeographic patterns, but global comparisons of the SARs between island and mainland are lacking for microbial taxa. Here, we explore whether the form of the SAR and the drivers of species richness, including area, environmental heterogeneity, climate and physico-chemistry, differ between islands and similarly sized areas on mainland, referred to as continental area equivalents (CAEs). Location Global. Taxon Stream benthic diatoms. Methods We generated CAEs on six continental datasets and examined the SARs of CAEs and islands (ISAR). Then, we compared CAEs and islands in terms of total richness and richness of different ecological guilds. We tested the factors contributing to richness in islands and CAEs with regressions. We used structural equation models to determine the effects of area versus environmental heterogeneity, climate and local conditions on species richness. Results We found a non-significant ISAR, but a significant positive SAR in CAEs. Richness in islands was related to productivity. Richness in CAEs was mainly dependent on area and climate, but not directly on environmental heterogeneity. Species richness within guilds exhibited inconsistent relationships with island isolation and area. Main conclusions Ecological and evolutionary processes shaping diatom island biogeography do not depend on area at the worldwide scale probably due to the presence of distinct species pool across islands. Conversely, area was an important driver of diatom richness in continents, and this effect could be attributed to dispersal. Continents had greater richness than islands, but this was a consequence of differences in environmental conditions such as specific island climatic conditions. We stress the need for more island data on benthic diatoms, particularly from archipelagos, to better understand the biogeography of this most speciose group of algae

The Blue Stragglers of the Old Open Cluster NGC 188

The old (7 Gyr) open cluster NGC 188 has yielded a wealth of astrophysical insight into its rich blue straggler population. Specifically, the NGC 188 blue stragglers are characterized by: A binary frequency of 80% for orbital periods less than $10^4$ days;Typical orbital periods around 1000 days;Typical secondary star masses of 0.5 M$_{\odot}$; At least some white dwarf companion stars; Modestly rapid rotation; A bimodal radial spatial distribution; Dynamical masses greater than standard stellar evolution masses (based on short-period binaries); Under-luminosity for dynamical masses (short-period binaries). Extensive $N$-body modeling of NGC 188 with empirical initial conditions reproduces the properties of the cluster, and in particular the main-sequence solar-type binary population. The current models also reproduce well the binary orbital properties of the blue stragglers, but fall well short of producing the observed number of blue stragglers. This deficit could be resolved by reducing the frequency of common-envelope evolution during Roche lobe overflow. Both the observations and the $N$-body models strongly indicate that the long-period blue-straggler binaries - which dominate the NGC 188 blue straggler population - are formed by asymptotic-giant (primarily) and red-giant mass transfer onto main sequence stars. The models suggest that the few non-velocity-variable blue stragglers formed from mergers or collisions. Several remarkable short-period double-lined binaries point to the importance of subsequent dynamical exchange encounters, and provide at least one example of a likely collisional origin for a blue straggler.Comment: Chapter 3, in Ecology of Blue Straggler Stars, H.M.J. Boffin, G. Carraro & G. Beccari (Eds), Astrophysics and Space Science Library, Springe

Testing spooky action at a distance

In science, one observes correlations and invents theoretical models that describe them. In all sciences, besides quantum physics, all correlations are described by either of two mechanisms. Either a first event influences a second one by sending some information encoded in bosons or molecules or other physical carriers, depending on the particular science. Or the correlated events have some common causes in their common past. Interestingly, quantum physics predicts an entirely different kind of cause for some correlations, named entanglement. This new kind of cause reveals itself, e.g., in correlations that violate Bell inequalities (hence cannot be described by common causes) between space-like separated events (hence cannot be described by classical communication). Einstein branded it as spooky action at a distance. A real spooky action at a distance would require a faster than light influence defined in some hypothetical universally privileged reference frame. Here we put stringent experimental bounds on the speed of all such hypothetical influences. We performed a Bell test during more than 24 hours between two villages separated by 18 km and approximately east-west oriented, with the source located precisely in the middle. We continuously observed 2-photon interferences well above the Bell inequality threshold. Taking advantage of the Earth's rotation, the configuration of our experiment allowed us to determine, for any hypothetically privileged frame, a lower bound for the speed of this spooky influence. For instance, if such a privileged reference frame exists and is such that the Earth's speed in this frame is less than 10^-3 that of the speed of light, then the speed of this spooky influence would have to exceed that of light by at least 4 orders of magnitude.Comment: Preliminary version of Nature 454, 861-864 (14 August 2008). 5 pages and 5 figure