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

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

Generalized shuffles related to Nijenhuis and TD-algebras

Shuffle and quasi-shuffle products are well-known in the mathematics literature. They are intimately related to Loday's dendriform algebras, and were extensively used to give explicit constructions of free commutative Rota-Baxter algebras. In the literature there exist at least two other Rota-Baxter type algebras, namely, the Nijenhuis algebra and the so-called TD-algebra. The explicit construction of the free unital commutative Nijenhuis algebra uses a modified quasi-shuffle product, called the right-shift shuffle. We show that another modification of the quasi-shuffle product, the so-called left-shift shuffle, can be used to give an explicit construction of the free unital commutative TD-algebra. We explore some basic properties of TD-operators and show that the free unital commutative Nijenhuis algebra is a TD-algebra. We relate our construction to Loday's unital commutative dendriform trialgebras, including the involutive case. The concept of Rota-Baxter, Nijenhuis and TD-bialgebras is introduced at the end and we show that any commutative bialgebra provides such objects.Comment: 20 pages, typos corrected, accepted for publication in Communications in Algebr

SEM-EDS analyses of small craters in stardust aluminium foils: implications for the Wild-2 dust distribution

Implications for the Wild-2 dust distribution of the statistical results obtained by SEM-EDS from nearly 300 impact craters on aluminium foils of the Stardust sample tray assembly

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

Fabrication and Optical Properties of a Fully Hybrid Epitaxial ZnO-Based Microcavity in the Strong Coupling Regime

In order to achieve polariton lasing at room temperature, a new fabrication methodology for planar microcavities is proposed: a ZnO-based microcavity in which the active region is epitaxially grown on an AlGaN/AlN/Si substrate and in which two dielectric mirrors are used. This approach allows as to simultaneously obtain a high-quality active layer together with a high photonic confinement as demonstrated through macro-, and micro-photoluminescence ({\mu}-PL) and reflectivity experiments. A quality factor of 675 and a maximum PL emission at k=0 are evidenced thanks to {\mu}-PL, revealing an efficient polaritonic relaxation even at low excitation power.Comment: 12 pages, 3 figure

Patterned silicon substrates: a common platform for room temperature GaN and ZnO polariton lasers

A new platform for fabricating polariton lasers operating at room temperature is introduced: nitride-based distributed Bragg reflectors epitaxially grown on patterned silicon substrates. The patterning allows for an enhanced strain relaxation thereby enabling to stack a large number of crack-free AlN/AlGaN pairs and achieve cavity quality factors of several thousands with a large spatial homogeneity. GaN and ZnO active regions are epitaxially grown thereon and the cavities are completed with top dielectric Bragg reflectors. The two structures display strong-coupling and polariton lasing at room temperature and constitute an intermediate step in the way towards integrated polariton devices

Characterization of potential biomarkers of reactogenicity of licensed antiviral vaccines: randomized controlled clinical trials conducted by the BIOVACSAFE consortium

Funding text The authors are grateful for the vital contributions of the participating study volunteers, clinicians, nurses, and laboratory technicians at the Surrey study site. The work by Roberto Leone, laboratory technician at Humanitas Clinical and Research Center, is gratefully acknowledged. Finally, they thank Ellen Oe (GSK) for scientific writing assistance. The research leading to these results has received support from the Innovative Medicines Initiative Joint Undertaking under grant agreement n°115308, resources of which are composed of financial contribution from the European Union’s Seventh Framework Programme (FP7/2007–2013) and EFPIA companies’ in-kind contribution. The contribution of the European Commission to the Advanced Immunization Technologies (ADITEC) project (grant agreement n° 280873) is also gratefully acknowledged. Publisher Copyright: © 2019, The Author(s).Biomarkers predictive of inflammatory events post-vaccination could accelerate vaccine development. Within the BIOVACSAFE framework, we conducted three identically designed, placebo-controlled inpatient/outpatient clinical studies (NCT01765413/NCT01771354/NCT01771367). Six antiviral vaccination strategies were evaluated to generate training data-sets of pre-/post-vaccination vital signs, blood changes and whole-blood gene transcripts, and to identify putative biomarkers of early inflammation/reactogenicity that could guide the design of subsequent focused confirmatory studies. Healthy adults (N = 123; 20–21/group) received one immunization at Day (D)0. Alum-adjuvanted hepatitis B vaccine elicited vital signs and inflammatory (CRP/innate cells) responses that were similar between primed/naive vaccinees, and low-level gene responses. MF59-adjuvanted trivalent influenza vaccine (ATIV) induced distinct physiological (temperature/heart rate/reactogenicity) response-patterns not seen with non-adjuvanted TIV or with the other vaccines. ATIV also elicited robust early (D1) activation of IFN-related genes (associated with serum IP-10 levels) and innate-cell-related genes, and changes in monocyte/neutrophil/lymphocyte counts, while TIV elicited similar but lower responses. Due to viral replication kinetics, innate gene activation by live yellow-fever or varicella-zoster virus (YFV/VZV) vaccines was more suspended, with early IFN-associated responses in naïve YFV-vaccine recipients but not in primed VZV-vaccine recipients. Inflammatory responses (physiological/serum markers, innate-signaling transcripts) are therefore a function of the vaccine type/composition and presence/absence of immune memory. The data reported here have guided the design of confirmatory Phase IV trials using ATIV to provide tools to identify inflammatory or reactogenicity biomarkers.Peer reviewe

LO-phonon assisted polariton lasing in a ZnO based microcavity

Polariton relaxation mechanisms are analysed experimentally and theoretically in a ZnO-based polariton laser. A minimum lasing threshold is obtained when the energy difference between the exciton reservoir and the bottom of the lower polariton branch is resonant with the LO phonon energy. Tuning off this resonance increases the threshold, and exciton-exciton scattering processes become involved in the polariton relaxation. These observations are qualitatively reproduced by simulations based on the numerical solution of the semi-classical Boltzmann equations

On Multiphase-Linear Ranking Functions

Multiphase ranking functions ($\mathit{M{\Phi}RFs}$) were proposed as a means to prove the termination of a loop in which the computation progresses through a number of "phases", and the progress of each phase is described by a different linear ranking function. Our work provides new insights regarding such functions for loops described by a conjunction of linear constraints (single-path loops). We provide a complete polynomial-time solution to the problem of existence and of synthesis of $\mathit{M{\Phi}RF}$ of bounded depth (number of phases), when variables range over rational or real numbers; a complete solution for the (harder) case that variables are integer, with a matching lower-bound proof, showing that the problem is coNP-complete; and a new theorem which bounds the number of iterations for loops with $\mathit{M{\Phi}RFs}$. Surprisingly, the bound is linear, even when the variables involved change in non-linear way. We also consider a type of lexicographic ranking functions, $\mathit{LLRFs}$, more expressive than types of lexicographic functions for which complete solutions have been given so far. We prove that for the above type of loops, lexicographic functions can be reduced to $\mathit{M{\Phi}RFs}$, and thus the questions of complexity of detection and synthesis, and of resulting iteration bounds, are also answered for this class.Comment: typos correcte