Aspects of noncommutative Lorentzian geometry for globally hyperbolic spacetimes

Connes' functional formula of the Riemannian distance is generalized to the Lorentzian case using the so-called Lorentzian distance, the d'Alembert operator and the causal functions of a globally hyperbolic spacetime. As a step of the presented machinery, a proof of the almost-everywhere smoothness of the Lorentzian distance considered as a function of one of the two arguments is given. Afterwards, using a $C^*$-algebra approach, the spacetime causal structure and the Lorentzian distance are generalized into noncommutative structures giving rise to a Lorentzian version of part of Connes' noncommutative geometry. The generalized noncommutative spacetime consists of a direct set of Hilbert spaces and a related class of $C^*$-algebras of operators. In each algebra a convex cone made of self-adjoint elements is selected which generalizes the class of causal functions. The generalized events, called {\em loci}, are realized as the elements of the inductive limit of the spaces of the algebraic states on the $C^*$-algebras. A partial-ordering relation between pairs of loci generalizes the causal order relation in spacetime. A generalized Lorentz distance of loci is defined by means of a class of densely-defined operators which play the r\^ole of a Lorentzian metric. Specializing back the formalism to the usual globally hyperbolic spacetime, it is found that compactly-supported probability measures give rise to a non-pointwise extension of the concept of events.Comment: 43 pages, structure of the paper changed and presentation strongly improved, references added, minor typos corrected, title changed, accepted for publication in Reviews in Mathematical Physic

Positronium S state spectrum: analytic results at O(m alpha^6)

We present an analytic calculation of the O(m alpha^6) recoil and radiative recoil corrections to energy levels of positronium nS states and their hyperfine splitting. A complete analytic formula valid to O(m alpha^6) is given for the spectrum of S states. Technical aspects of the calculation are discussed in detail. Theoretical predictions are given for various energy intervals and compared with experimental results.Comment: 29 pages, revte

Systems biologists seek fuller integration of systems biology approaches in new cancer research programs

Systems biology takes an interdisciplinary approach to the systematic study of complex interactions in biological systems. This approach seeks to decipher the emergent behaviors of complex systems rather than focusing only on their constituent properties. As an increasing number of examples illustrate the value of systems biology approaches to understand the initiation, progression, and treatment of cancer, systems biologists from across Europe and the United States hope for changes in the way their field is currently perceived among cancer researchers. In a recent EU-US workshop, supported by the European Commission, the German Federal Ministry for Education and Research, and the National Cancer Institute of the NIH, the participants discussed the strengths, weaknesses, hurdles, and opportunities in cancer systems biology

Evolving networks with disadvantaged long-range connections

We consider a growing network, whose growth algorithm is based on the preferential attachment typical for scale-free constructions, but where the long-range bonds are disadvantaged. Thus, the probability to get connected to a site at distance $d$ is proportional to $d^{-\alpha}$, where $\alpha$ is a tunable parameter of the model. We show that the properties of the networks grown with $\alpha <1$ are close to those of the genuine scale-free construction, while for $\alpha >1$ the structure of the network is vastly different. Thus, in this regime, the node degree distribution is no more a power law, and it is well-represented by a stretched exponential. On the other hand, the small-world property of the growing networks is preserved at all values of $\alpha$.Comment: REVTeX, 6 pages, 5 figure

Thermal sensitivity of feeding and burrowing activity of an invasive crayfish in UK waters

Climate change and invasive species are among the biggest threats to global biodiversity and ecosystem function. Although the individual impacts of climate change and invasive species are commonly assessed, we know far less about how a changing climate may impact invading species. Increases in water temperature due to climate change are likely to alter the thermal regime of UK rivers, and this in turn may influence the performance of invasive species such as signal crayfish (Pacifastacus leniusculus), which are known to have deleterious impacts on native ecosystems. We evaluate the relationship between water temperature and two key performance traits in signal crayfish—feeding and burrowing rate—using thermal experiments on wild‐caught individuals in a laboratory environment. Although water temperature was found to have no significant influence on burrowing rate, it did have a strong effect on feeding rate. Using the thermal performance curve for feeding rate, we evaluate how the thermal suitability of three UK rivers for signal crayfish may change as a result of future warming. We find that warming rivers may increase the amount of time that signal crayfish can achieve high feeding rate levels. These results suggest that elevated river water temperatures as a result of climate change may promote higher signal crayfish performance in the future, further exacerbating the ecological impact of this invasive species

A Taxonomy of Causality-Based Biological Properties

We formally characterize a set of causality-based properties of metabolic networks. This set of properties aims at making precise several notions on the production of metabolites, which are familiar in the biologists' terminology. From a theoretical point of view, biochemical reactions are abstractly represented as causal implications and the produced metabolites as causal consequences of the implication representing the corresponding reaction. The fact that a reactant is produced is represented by means of the chain of reactions that have made it exist. Such representation abstracts away from quantities, stoichiometric and thermodynamic parameters and constitutes the basis for the characterization of our properties. Moreover, we propose an effective method for verifying our properties based on an abstract model of system dynamics. This consists of a new abstract semantics for the system seen as a concurrent network and expressed using the Chemical Ground Form calculus. We illustrate an application of this framework to a portion of a real metabolic pathway

Terrestrial laser scanning survey in support of unstable slopes analysis. The case of Vulcano Island (Italy)

The capability to measure at distance dense cloud of 3D point has improved the relevance of geomatic techniques to support risk assessment analysis related to slope instability. This work focuses on quantitative analyses carried out to evaluate the effects of potential failures in the Vulcano Island (Italy). Terrestrial laser scanning was adopted to reconstruct the geometry of investigated slopes that is required for the implementation of numerical modeling adopted to simulate runout areas. Structural and morphological elements, which influenced past instabilities or may be linked to new events, were identified on surface models based on ground surveying. Terrestrial laser scanning was adopted to generate detailed 3D models of subvertical slopes allowing to characterize the distribution and orientation of the rock discontinuities that affect instability mechanism caused by critical geometry. Methods for obtaining and analyzing 3D topographic data and to implement simulation analyses contributing to hazard and risk assessment are discussed for two case studies (Forgia Vecchia slope and Lentia rock walls)

Edge overload breakdown in evolving networks

We investigate growing networks based on Barabasi and Albert's algorithm for generating scale-free networks, but with edges sensitive to overload breakdown. the load is defined through edge betweenness centrality. We focus on the situation where the average number of connections per vertex is, as the number of vertices, linearly increasing in time. After an initial stage of growth, the network undergoes avalanching breakdowns to a fragmented state from which it never recovers. This breakdown is much less violent if the growth is by random rather than preferential attachment (as defines the Barabasi and Albert model). We briefly discuss the case where the average number of connections per vertex is constant. In this case no breakdown avalanches occur. Implications to the growth of real-world communication networks are discussed.Comment: To appear in Phys. Rev.