Convex Hull of Arithmetic Automata

Arithmetic automata recognize infinite words of digits denoting decompositions of real and integer vectors. These automata are known expressive and efficient enough to represent the whole set of solutions of complex linear constraints combining both integral and real variables. In this paper, the closed convex hull of arithmetic automata is proved rational polyhedral. Moreover an algorithm computing the linear constraints defining these convex set is provided. Such an algorithm is useful for effectively extracting geometrical properties of the whole set of solutions of complex constraints symbolically represented by arithmetic automata

On Functions Weakly Computable by Pushdown Petri Nets and Related Systems

We consider numerical functions weakly computable by grammar-controlled vector addition systems (GVASes, a variant of pushdown Petri nets). GVASes can weakly compute all fast growing functions $F_\alpha$ for $\alpha<\omega^\omega$, hence they are computationally more powerful than standard vector addition systems. On the other hand they cannot weakly compute the inverses $F_\alpha^{-1}$ or indeed any sublinear function. The proof relies on a pumping lemma for runs of GVASes that is of independent interest

Mountain trail formation and the active walker model

We extend the active walker model to address the formation of paths on gradients, which have been observed to have a zigzag form. Our extension includes a new rule which prohibits direct descent or ascent on steep inclines, simulating aversion to falling. Further augmentation of the model stops walkers from changing direction very rapidly as that would likely lead to a fall. The extended model predicts paths with qualitatively similar forms to the observed trails, but only if the terms suppressing sudden direction changes are included. The need to include terms into the model that stop rapid direction change when simulating mountain trails indicates that a similar rule should also be included in the standard active walker model.Comment: Introduction improved. Analysis of discretization errors added. Calculations from alternative scheme include

Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS

Vector Addition Systems with States (VASS) provide a well-known and fundamental model for the analysis of concurrent processes, parameterized systems, and are also used as abstract models of programs in resource bound analysis. In this paper we study the problem of obtaining asymptotic bounds on the termination time of a given VASS. In particular, we focus on the practically important case of obtaining polynomial bounds on termination time. Our main contributions are as follows: First, we present a polynomial-time algorithm for deciding whether a given VASS has a linear asymptotic complexity. We also show that if the complexity of a VASS is not linear, it is at least quadratic. Second, we classify VASS according to quantitative properties of their cycles. We show that certain singularities in these properties are the key reason for non-polynomial asymptotic complexity of VASS. In absence of singularities, we show that the asymptotic complexity is always polynomial and of the form $\Theta(n^k)$, for some integer $k\leq d$, where $d$ is the dimension of the VASS. We present a polynomial-time algorithm computing the optimal $k$. For general VASS, the same algorithm, which is based on a complete technique for the construction of ranking functions in VASS, produces a valid lower bound, i.e., a $k$ such that the termination complexity is $\Omega(n^k)$. Our results are based on new insights into the geometry of VASS dynamics, which hold the potential for further applicability to VASS analysis.Comment: arXiv admin note: text overlap with arXiv:1708.0925

Pinning an Ion with an Intracavity Optical Lattice

We report one-dimensional pinning of a single ion by an optical lattice. The lattice potential is produced by a standing-wave cavity along the rf-field-free axis of a linear Paul trap. The ion's localization is detected by measuring its fluorescence when excited by standing-wave fields with the same period, but different spatial phases. The experiments agree with an analytical model of the localization process, which we test against numerical simulations. For the best localization achieved, the ion's average coupling to the cavity field is enhanced from 50% to 81(3)% of its maximum possible value, and we infer that the ion is bound in a lattice well with over 97% probability.Comment: 5 pages, 4 figures; Text edited for clarity, results unchange

Antibody persistence and booster responses to split-virion H5N1 avian influenza vaccine in young and elderly adults

Avian influenza continues to circulate and remains a global health threat not least because of the associated high mortality. In this study antibody persistence, booster vaccine response and cross-clade immune response between two influenza A(H5N1) vaccines were compared. Participants aged over 18-years who had previously been immunized with a clade 1, A/Vietnam vaccine were re-immunized at 6-months with 7.5 mu g of the homologous strain or at 22-months with a clade 2, alum-adjuvanted, A/Indonesia vaccine. Blood sampled at 6, 15 and 22-months after the primary course was used to assess antibody persistence. Antibody concentrations 6-months after primary immunisation with either A/Vietnam vaccine 30 mu g alum-adjuvanted vaccine or 7.5 mu g dose vaccine were lower than 21days after the primary course and waned further with time. Re-immunization with the clade 2, 30 mu g alum-adjuvanted vaccine confirmed cross-clade reactogenicity. Antibody crossreactivity between A(H5N1) clades suggests that in principle a prime-boost vaccination strategy may provide both early protection at the start of a pandemic and improved antibody responses to specific vaccination once available

Measuring techniques in induced polarisation imaging

Multi-electrode geoelectrical imaging has become very popular and is used for many different purposes. For some of these, the inclusion of IP data would be desirable as it would allow the interpreter to distinguish between, e.g. sand formations with saltwater infiltration and clay formations or help delineate landfills. However, present-day IP measuring techniques require the use of nonpolarisable potential electrodes and special wire layout and are thus cumbersome and expensive. In this paper, we suggest making IP measurements with multi-electrode cables and just one set of steel electrodes. The polarisation potentials on the potential electrodes are corrected for by subtracting the polarisation potential measured when no primary current and no IP signal are present. Test measurements indicate that the polarisation potentials vary slowly and that the correction procedure is feasible. At two sites in southern Sweden, we have compared measurements with only stainless steel electrodes and measurements with both stainless steel and Pb-PbCl nonpolarisable electrodes using one or two sets of multicore cables, respectively. Almost no difference between the two data sets was observed. At one site, the charge-up effect on the potential electrodes was not important, while at the other site, the correction procedure was crucial. Though only two sites have been studied so far, it seems that time-domain IP imaging measurements can be taken with only steel electrodes and ordinary multicore cables. Coupling in the multicore cables has not presented any problems at the investigated sites where grounding resistances were moderate, making the coupling effect small. High grounding resistance sites have not yet been investigated. (C) 2002 Published by Elsevier Science B.V

Pregnancy has a minimal impact on the acute transcriptional signature to vaccination.

Vaccination in pregnancy is an effective tool to protect both the mother and infant; vaccines against influenza, pertussis and tetanus are currently recommended. A number of vaccines with a specific indication for use in pregnancy are in development, with the specific aim of providing passive humoral immunity to the newborn child against pathogens responsible for morbidity and mortality in young infants. However, the current understanding about the immune response to vaccination in pregnancy is incomplete. We analysed the effect of pregnancy on early transcriptional responses to vaccination. This type of systems vaccinology approach identifies genes and pathways that are altered in response to vaccination and can be used to understand both the acute inflammation in response to the vaccine and to predict immunogenicity. Pregnant women and mice were immunised with Boostrix-IPV, a multivalent vaccine, which contains three pertussis antigens. Blood was collected from women before and after vaccination and RNA extracted for analysis by microarray. While there were baseline differences between pregnant and non-pregnant women, vaccination induced characteristic patterns of gene expression, with upregulation in interferon response and innate immunity gene modules, independent of pregnancy. We saw similar patterns of responses in both women and mice, supporting the use of mice for preclinical screening of novel maternal vaccines. Using a systems vaccinology approach in pregnancy demonstrated that pregnancy does not affect the initial response to vaccination and that studies in non-pregnant women can provide information about vaccine immunogenicity and potentially safety

Renormalization : A number theoretical model

We analyse the Dirichlet convolution ring of arithmetic number theoretic functions. It turns out to fail to be a Hopf algebra on the diagonal, due to the lack of complete multiplicativity of the product and coproduct. A related Hopf algebra can be established, which however overcounts the diagonal. We argue that the mechanism of renormalization in quantum field theory is modelled after the same principle. Singularities hence arise as a (now continuously indexed) overcounting on the diagonals. Renormalization is given by the map from the auxiliary Hopf algebra to the weaker multiplicative structure, called Hopf gebra, rescaling the diagonals.Comment: 15 pages, extended version of talks delivered at SLC55 Bertinoro,Sep 2005, and the Bob Delbourgo QFT Fest in Hobart, Dec 200