Linear character-dependent models with constant time delay in population dynamics

AbstractWe reduce the extended MacKendrick-Von Foerster formalism of Gurney and Nisbet—an initial boundary value problem—to the solution of a single Volterra integral equation with a constant time lag. We then establish the existence, uniqueness and continuation of solutions for all t > 0, and reduce a simplified version of this model to a time-delay version of the classical MacKendrick model, for which the standard stability results for persistent distributions are available

Assessing bacterial quorum sensing through measuring bioluminescence with Vibrio fischeri exposed to simulated microgravity

Bacteria flourish in stressful environments when communicating with each other in a process known as Quorum Sensing. This process is accomplished by the production of small signaling molecules referred to as Autoinducers (AI). This communication allows the bacteria to alter their gene expression in an effort to regulate their cell number, behavior and sense the surrounding environment. The space environment provides stressful conditions for bacteria as they are exposed to radiation and microgravity (µG). Because of this, it could be possible that bacteria become more virulent and resistant to antibiotics. The purpose of this research was to expose Vibrio fischeri to simulated microgravity for its ability to produce AI and measure their quantity. The methods used include measurement of fluorescence via microbial biosensors (genetically modified microorganisms) that activate gene expression of markers once a specific autoinducer is detected, readings are recorded (using a microplate reader) and graphed. Results have demonstrated increased AI production and altered colony morphology under simulated microgravity

Scaling laws for the movement of people between locations in a large city

Large scale simulations of the movements of people in a ``virtual'' city and their analyses are used to generate new insights into understanding the dynamic processes that depend on the interactions between people. Models, based on these interactions, can be used in optimizing traffic flow, slowing the spread of infectious diseases or predicting the change in cell phone usage in a disaster. We analyzed cumulative and aggregated data generated from the simulated movements of 1.6 million individuals in a computer (pseudo agent-based) model during a typical day in Portland, Oregon. This city is mapped into a graph with $181,206$ nodes representing physical locations such as buildings. Connecting edges model individual's flow between nodes. Edge weights are constructed from the daily traffic of individuals moving between locations. The number of edges leaving a node (out-degree), the edge weights (out-traffic), and the edge-weights per location (total out-traffic) are fitted well by power law distributions. The power law distributions also fit subgraphs based on work, school, and social/recreational activities. The resulting weighted graph is a ``small world'' and has scaling laws consistent with an underlying hierarchical structure. We also explore the time evolution of the largest connected component and the distribution of the component sizes. We observe a strong linear correlation between the out-degree and total out-traffic distributions and significant levels of clustering. We discuss how these network features can be used to characterize social networks and their relationship to dynamic processes.Comment: 18 pages, 10 figure

Flashing annihilation term of a logistic kinetic as a mechanism leading to Pareto distributions

It is shown analytically that the flashing annihilation term of a Verhulst kinetic leads to the power--law distribution in the stationary state. For the frequency of switching slower than twice the free growth rate this provides the quasideterministic source of a Levy noises at the macroscopic level.Comment: 1 fi

Measurement of the production of a W boson in association with a charm quark in pp collisions at √s = 7 TeV with the ATLAS detector

The production of a W boson in association with a single charm quark is studied using 4.6 fb−1 of pp collision data at s√ = 7 TeV collected with the ATLAS detector at the Large Hadron Collider. In events in which a W boson decays to an electron or muon, the charm quark is tagged either by its semileptonic decay to a muon or by the presence of a charmed meson. The integrated and differential cross sections as a function of the pseudorapidity of the lepton from the W-boson decay are measured. Results are compared to the predictions of next-to-leading-order QCD calculations obtained from various parton distribution function parameterisations. The ratio of the strange-to-down sea-quark distributions is determined to be 0.96+0.26−0.30 at Q 2 = 1.9 GeV2, which supports the hypothesis of an SU(3)-symmetric composition of the light-quark sea. Additionally, the cross-section ratio σ(W + +c¯¯)/σ(W − + c) is compared to the predictions obtained using parton distribution function parameterisations with different assumptions about the s−s¯¯¯ quark asymmetry

Slightly generalized Generalized Contagion: Unifying simple models of biological and social spreading

We motivate and explore the basic features of generalized contagion, a model mechanism that unifies fundamental models of biological and social contagion. Generalized contagion builds on the elementary observation that spreading and contagion of all kinds involve some form of system memory. We discuss the three main classes of systems that generalized contagion affords, resembling: simple biological contagion; critical mass contagion of social phenomena; and an intermediate, and explosive, vanishing critical mass contagion. We also present a simple explanation of the global spreading condition in the context of a small seed of infected individuals.Comment: 8 pages, 5 figures; chapter to appear in "Spreading Dynamics in Social Systems"; Eds. Sune Lehmann and Yong-Yeol Ahn, Springer Natur

On the Modelling of Epidemics

18 pages, 1 article*On the Modelling of Epidemics* (Castillo-Chavez, C.; Cooke, K.; Levin, S. A.) 18 page