Analytical solution of a model for complex food webs

We investigate numerically and analytically a recently proposed model for food webs [Nature {\bf 404}, 180 (2000)] in the limit of large web sizes and sparse interaction matrices. We obtain analytical expressions for several quantities with ecological interest, in particular the probability distributions for the number of prey and the number of predators. We find that these distributions have fast-decaying exponential and Gaussian tails, respectively. We also find that our analytical expressions are robust to changes in the details of the model.Comment: 4 pages (RevTeX). Final versio

Invariant and polynomial identities for higher rank matrices

We exhibit explicit expressions, in terms of components, of discriminants, determinants, characteristic polynomials and polynomial identities for matrices of higher rank. We define permutation tensors and in term of them we construct discriminants and the determinant as the discriminant of order $d$, where $d$ is the dimension of the matrix. The characteristic polynomials and the Cayley--Hamilton theorem for higher rank matrices are obtained there from

The invariant-comb approach and its relation to the balancedness of multipartite entangled states

The invariant-comb approach is a method to construct entanglement measures for multipartite systems of qubits. The essential step is the construction of an antilinear operator that we call {\em comb} in reference to the {\em hairy-ball theorem}. An appealing feature of this approach is that for qubits (or spins 1/2) the combs are automatically invariant under SL(2,\CC), which implies that the obtained invariants are entanglement monotones by construction. By asking which property of a state determines whether or not it is detected by a polynomial SL(2,\CC) invariant we find that it is the presence of a {\em balanced part} that persists under local unitary transformations. We present a detailed analysis for the maximally entangled states detected by such polynomial invariants, which leads to the concept of {\em irreducibly balanced} states. The latter indicates a tight connection with SLOCC classifications of qubit entanglement. \\ Combs may also help to define measures for multipartite entanglement of higher-dimensional subsystems. However, for higher spins there are many independent combs such that it is non-trivial to find an invariant one. By restricting the allowed local operations to rotations of the coordinate system (i.e. again to the SL(2,\CC)) we manage to define a unique extension of the concurrence to general half-integer spin with an analytic convex-roof expression for mixed states.Comment: 17 pages, revtex4. Substantially extended manuscript (e.g. proofs have been added); title and abstract modified

Comparing Static and Dynamic Weighted Software Coupling Metrics

Coupling metrics that count the number of inter-module connections in a software system are an established way to measure internal software quality with respect to modularity. In addition to static metrics, which are obtained from the source or compiled code of a program, dynamic metrics use runtime data gathered, e.g., by monitoring a system in production. Dynamic metrics have been used to improve the accuracy of static metrics for object-oriented software. We study weighted dynamic coupling that takes into account how often a connection (e.g., a method call) is executed during a system’s run. We investigate the correlation between dynamic weighted metrics and their static counterparts. To compare the different metrics, we use data collected from four different experiments, each monitoring production use of a commercial software system over a period of four weeks. We observe an unexpected level of correlation between the static and the weighted dynamic case as well as revealing differences between class- and package-level analyses

Hematological Changes in Women and Infants Exposed to an AZT-Containing Regimen for Prevention of Mother-to-child-transmission of HIV in Tanzania.

Tanzanian guidelines for prevention of mother-to-child-transmission of HIV (PMTCT) recommend an antiretroviral combination regimen involving zidovudine (AZT) during pregnancy, single-dosed nevirapine at labor onset, AZT plus Lamivudine (3TC) during delivery, and AZT/3TC for 1-4 weeks postpartum. As drug toxicities are a relevant concern, we assessed hematological alterations in AZT-exposed women and their infants. A cohort of HIV-positive women, either with AZT intake (n = 82, group 1) or without AZT intake (n = 62, group 2) for PMTCT during pregnancy, was established at Kyela District Hospital, Tanzania. The cohort also included the infants of group 1 with an in-utero AZT exposure ≥4 weeks, receiving AZT for 1 week postpartum (n = 41), and infants of group 2 without in-utero AZT exposure, receiving a prolonged 4-week AZT tail (n = 58). Complete blood counts were evaluated during pregnancy, birth, weeks 4-6 and 12. For women of group 1 with antenatal AZT intake, we found a statistically significant decrease in hemoglobin level, red blood cells, white blood cells, granulocytes, as well as an increase in red cell distribution width and platelet count. At delivery, the median red blood cell count was significantly lower and the median platelet count was significantly higher in women of group 1 compared to group 2. At birth, infants from group 1 showed a lower median hemoglobin level and granulocyte count and a higher frequency of anemia and granulocytopenia. At 4-6 weeks postpartum, the mean neutrophil granulocyte count was significantly lower and neutropenia was significantly more frequent in infants of group 2. AZT exposure during pregnancy as well as after birth resulted in significant hematological alterations for women and their newborns, although these changes were mostly mild and transient in nature. Research involving larger cohorts is needed to further analyze the impact of AZT-containing regimens on maternal and infant health

Production of intense highly charged ion beams with SERSE

The source SERSE is operational at LNS since June 1998 and many improvements have been carried out in this period. The frequency has been increased from 14.5 GHz to 18 GHz and the use of two frequency heating has given positive results. Metallic ion production has been tested by means of a high temperature oven and the preliminary results are described. Tests of magnetic field scaling and frequency scaling have confirmed the results of previous tests with SC-ECRIS at lower frequency and seems to suggest that the upgrading of the source to higher frequency may be considered

Can we avoid high coupling?

It is considered good software design practice to organize source code into modules and to favour within-module connections (cohesion) over between-module connections (coupling), leading to the oft-repeated maxim "low coupling/high cohesion". Prior research into network theory and its application to software systems has found evidence that many important properties in real software systems exhibit approximately scale-free structure, including coupling; researchers have claimed that such scale-free structures are ubiquitous. This implies that high coupling must be unavoidable, statistically speaking, apparently contradicting standard ideas about software structure. We present a model that leads to the simple predictions that approximately scale-free structures ought to arise both for between-module connectivity and overall connectivity, and not as the result of poor design or optimization shortcuts. These predictions are borne out by our large-scale empirical study. Hence we conclude that high coupling is not avoidable--and that this is in fact quite reasonable

Classification of qubit entanglement: SL(2,C) versus SU(2) invariance

The role of SU(2) invariants for the classification of multiparty entanglement is discussed and exemplified for the Kempe invariant I_5 of pure three-qubit states. It is found to being an independent invariant only in presence of both W-type entanglement and threetangle. In this case, constant I_5 admits for a wide range of both threetangle and concurrences. Furthermore, the present analysis indicates that an SL^3 orbit of states with equal tangles but continuously varying I_5 must exist. This means that I_5 provides no information on the entanglement in the system in addition to that contained in the tangles (concurrences and threetangle) themselves. Together with the numerical evidence that I_5 is an entanglement monotone this implies that SU(2) invariance or the monotone property are too weak requirements for the characterization and quantification of entanglement for systems of three qubits, and that SL(2,C) invariance is required. This conclusion can be extended to general multipartite systems (including higher local dimension) because the entanglement classes of three-qubit systems appear as subclasses.Comment: 9 pages, 10 figures, revtex

On the Black-Hole/Qubit Correspondence

The entanglement classification of four qubits is related to the extremal black holes of the 4-dimensional STU model via a time-like reduction to three dimensions. This correspondence is generalised to the entanglement classification of a very special four-way entanglement of eight qubits and the black holes of the maximally supersymmetric N = 8 and exceptional magic N = 2 supergravity theories.Comment: 32 pages, very minor changes at the start of Sec. 4.1. Version to appear in The European Physical Journal - Plu

Dense active matter model of motion patterns in confluent cell monolayers

Epithelial cell monolayers show remarkable displacement and velocity correlations over distances of ten or more cell sizes that are reminiscent of supercooled liquids and active nematics. We show that many observed features can be described within the framework of dense active matter, and argue that persistent uncoordinated cell motility coupled to the collective elastic modes of the cell sheet is sufficient to produce swirl-like correlations. We obtain this result using both continuum active linear elasticity and a normal modes formalism, and validate analytical predictions with numerical simulations of two agent-based cell models, soft elastic particles and the self-propelled Voronoi model together with in-vitro experiments of confluent corneal epithelial cell sheets. Simulations and normal mode analysis perfectly match when tissue-level reorganisation occurs on times longer than the persistence time of cell motility. Our analytical model quantitatively matches measured velocity correlation functions over more than a decade with a single fitting parameter.Comment: updated version accepted for publication in Nat. Com