Analysis of Petri Net Models through Stochastic Differential Equations

It is well known, mainly because of the work of Kurtz, that density dependent Markov chains can be approximated by sets of ordinary differential equations (ODEs) when their indexing parameter grows very large. This approximation cannot capture the stochastic nature of the process and, consequently, it can provide an erroneous view of the behavior of the Markov chain if the indexing parameter is not sufficiently high. Important phenomena that cannot be revealed include non-negligible variance and bi-modal population distributions. A less-known approximation proposed by Kurtz applies stochastic differential equations (SDEs) and provides information about the stochastic nature of the process. In this paper we apply and extend this diffusion approximation to study stochastic Petri nets. We identify a class of nets whose underlying stochastic process is a density dependent Markov chain whose indexing parameter is a multiplicative constant which identifies the population level expressed by the initial marking and we provide means to automatically construct the associated set of SDEs. Since the diffusion approximation of Kurtz considers the process only up to the time when it first exits an open interval, we extend the approximation by a machinery that mimics the behavior of the Markov chain at the boundary and allows thus to apply the approach to a wider set of problems. The resulting process is of the jump-diffusion type. We illustrate by examples that the jump-diffusion approximation which extends to bounded domains can be much more informative than that based on ODEs as it can provide accurate quantity distributions even when they are multi-modal and even for relatively small population levels. Moreover, we show that the method is faster than simulating the original Markov chain

Thixotropy in macroscopic suspensions of spheres

An experimental study of the viscosity of a macroscopic suspension, i.e. a suspension for which Brownian motion can be neglected, under steady shear is presented. The suspension is prepared with a high packing fraction and is density-matched in a Newtonian carrier fluid. The viscosity of the suspension depends on the shear rate and the time of shearing. It is shown for the first time that a macroscopic suspension shows thixotropic viscosity, i.e. shear-thinning with a long relaxation time as a unique function of shear. The relaxation times show a systematic decrease with increasing shear rate. These relaxation times are larger when decreasing the shear rates, compared to those observed after increasing the shear. The time scales involved are about 10000 times larger than the viscous time scale and about 1000 times smaller than the thermodynamic time scale. The structure of the suspension at the outer cylinder of a viscometer is monitored with a camera, showing the formation of a hexagonal structure. The temporal decrease of the viscosity under shear coincides with the formation of this hexagonal pattern

Accounting for nature: assessing habitats in the UK countryside.

Countryside Survey 2000 (CS2000) and the Northern Ireland Countryside Survey 2000 (NICS2000) have been designed to provide detailed information about the habitats and landscape features that are important elements of our countryside. They can tell us about the ‘stock’ of these resources, that is how much of them we have and where they are to be found, and they can give us an insight into their condition based on the variety and abundance of the plant species associated with them. Using information from previous surveys, we can also gain an understanding of how the stock and condition of these habitats and landscape features are changing over time. We can build up a sort of balance sheet or an account of natural assets in the UK countryside. In this report we look in particular at the period between the last two surveys, 1990 and 1998

SARS-CoV-2 mRNA vaccine design enabled by prototype pathogen preparedness

A vaccine for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is needed to control the coronavirus disease 2019 (COVID-19) global pandemic. Structural studies have led to the development of mutations that stabilize Betacoronavirus spike proteins in the prefusion state, improving their expression and increasing immunogenicity1. This principle has been applied to design mRNA-1273, an mRNA vaccine that encodes a SARS-CoV-2 spike protein that is stabilized in the prefusion conformation. Here we show that mRNA-1273 induces potent neutralizing antibody responses to both wild-type (D614) and D614G mutant2 SARS-CoV-2 as well as CD8+ T cell responses, and protects against SARS-CoV-2 infection in the lungs and noses of mice without evidence of immunopathology. mRNA-1273 is currently in a phase III trial to evaluate its efficacy

Evaluation of the mRNA-1273 Vaccine against SARS-CoV-2 in Nonhuman Primates

Background: Vaccines to prevent coronavirus disease 2019 (Covid-19) are urgently needed. The effect of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccines on viral replication in both upper and lower airways is important to evaluate in nonhuman primates. Methods: Nonhuman primates received 10 or 100 μg of mRNA-1273, a vaccine encoding the prefusion-stabilized spike protein of SARS-CoV-2, or no vaccine. Antibody and T-cell responses were assessed before upper- and lower-airway challenge with SARS-CoV-2. Active viral replication and viral genomes in bronchoalveolar-lavage (BAL) fluid and nasal swab specimens were assessed by polymerase chain reaction, and histopathological analysis and viral quantification were performed on lung-tissue specimens. Results: The mRNA-1273 vaccine candidate induced antibody levels exceeding those in human convalescent-phase serum, with live-virus reciprocal 50% inhibitory dilution (ID50) geometric mean titers of 501 in the 10-μg dose group and 3481 in the 100-μg dose group. Vaccination induced type 1 helper T-cell (Th1)-biased CD4 T-cell responses and low or undetectable Th2 or CD8 T-cell responses. Viral replication was not detectable in BAL fluid by day 2 after challenge in seven of eight animals in both vaccinated groups. No viral replication was detectable in the nose of any of the eight animals in the 100-μg dose group by day 2 after challenge, and limited inflammation or detectable viral genome or antigen was noted in lungs of animals in either vaccine group. Conclusions: Vaccination of nonhuman primates with mRNA-1273 induced robust SARS-CoV-2 neutralizing activity, rapid protection in the upper and lower airways, and no pathologic changes in the lung. (Funded by the National Institutes of Health and others.)

Phase Behavior of Aqueous Na-K-Mg-Ca-CI-NO3 Mixtures: Isopiestic Measurements and Thermodynamic Modeling

A comprehensive model has been established for calculating thermodynamic properties of multicomponent aqueous systems containing the Na{sup +}, K{sup +}, Mg{sup 2+}, Ca{sup 2+}, Cl{sup -}, and NO{sub 3}{sup -} ions. The thermodynamic framework is based on a previously developed model for mixed-solvent electrolyte solutions. The framework has been designed to reproduce the properties of salt solutions at temperatures ranging from the freezing point to 300 C and concentrations ranging from infinite dilution to the fused salt limit. The model has been parameterized using a combination of an extensive literature database and new isopiestic measurements for thirteen salt mixtures at 140 C. The measurements have been performed using Oak Ridge National Laboratory's (ORNL) previously designed gravimetric isopiestic apparatus, which makes it possible to detect solid phase precipitation. Water activities are reported for mixtures with a fixed ratio of salts as a function of the total apparent salt mole fraction. The isopiestic measurements reported here simultaneously reflect two fundamental properties of the system, i.e., the activity of water as a function of solution concentration and the occurrence of solid-liquid transitions. The thermodynamic model accurately reproduces the new isopiestic data as well as literature data for binary, ternary and higher-order subsystems. Because of its high accuracy in calculating vapor-liquid and solid-liquid equilibria, the model is suitable for studying deliquescence behavior of multicomponent salt systems