MBI Videos

Videos by Joint 2012 MBI-NIMBioS-CAMBAM Summer Graduate Workshop: Stochastics Applied to Biological Systems

  • Persistence, coexistence and spatial spread in a fluctuating environment
    Sebastian Schreiber
    All populations experience stochastic
    uctuations in abiotic factors such as temperature, nutrient avail-
    ability, precipitation. This environmental stochasticity in conjunction with biotic interactions can facilitate
    or disrupt persistence. One approach to examining the interplay between these deterministic and stochastic
    forces is the construc...
  • Anomalous diffusion in biological fluids
    Scott McKinley
    Rapid recent progress in advanced microscopy has revealed that nano-particles
    immersed in biological
    uids exhibit rich and widely varied behaviors. In some
    cases, biology serves to enhance the mobility of small scale entities. Cargo-laden
    vesicles in axons undergo stark periods of forward and backward motion, inter-
    rupted by sudden paus...
  • Anomalous diffusion in biological fluids
    Scott McKinley
    Rapid recent progress in advanced microscopy has revealed that nano-particles
    immersed in biological
    uids exhibit rich and widely varied behaviors. In some
    cases, biology serves to enhance the mobility of small scale entities. Cargo-laden
    vesicles in axons undergo stark periods of forward and backward motion, inter-
    rupted by sudden paus...
  • Flux and fixation for the one-dimensional Axelrod model
    Nicolas Lanchier
    As a warming up, we will start with a brief overview of the main results about the voter model: clustering versus coexistence, cluster size and occupation time. The voter model is an example of interacting particle system - individual-based model - that models social influence, the tendency of individuals to become more similar when they interact. Each vertex of the lattic...
  • Individualâ€?based stochastic spatial models
    Steve Krone
    We will work through some of the basic ideas involved in modeling various types of interactions in spatial population biology using interacting particle systems (sometimes referred to as stochastic cellular automata). Some of the essential ingredients and behaviors come from simple models like the contact process and the voter model. These components can be combined and tw...
  • Flux and fixation for the voter model and the Axelrod model
    Nicolas Lanchier
    As a warming up, we will start with a brief overview of the main results about the voter model: clustering versus coexistence, cluster size and occupation time. The voter model is an example of interacting particle system - individual-based model - that models social influence, the tendency of individuals to become more similar when they interact. Each vertex of the lattic...
  • Individualâ€?based stochastic spatial models
    Steve Krone
    We will work through some of the basic ideas involved in modeling various types of interactions in spatial population biology using interacting particle systems (sometimes referred to as stochastic cellular automata). Some of the essential ingredients and behaviors come from simple models like the contact process and the voter model. These components can be combined and tw...
  • An introduction to thinking like a probabilist about biology
    Louis Gross
    This set of lectures and discussions will provide a quick one-day conceptual overview of stochastic issues in biology. Time permitting, I will point out the major conceptual approaches to stochasticity as typically applied in biology (random walks, Markov chains, birth and death processes, branching processes, agent-based models, stochastic DEs, diffusion processes, statis...
  • A Practical Introduction to Stochastic Differential Equations in Mathematical Biology
    Edward Allen
    Properties of the Wiener process are reviewed and stochastic integration is explained. Stochastic diļ¬€erential equations are introduced and some of their properties
    are described. Equivalence of SDE systems is explained. Commonly used numerical
    procedures are discussed for computationally solving systems of stochastic diļ¬€erentia...
  • A Practical Introduction to Stochastic Differential Equations in Mathematical Biology
    Edward Allen
    Properties of the Wiener process are reviewed and stochastic integration is explained. Stochastic diļ¬€erential equations are introduced and some of their properties are described. Equivalence of SDE systems is explained. Commonly used numerical procedures are discussed for computationally solving systems of stochastic diļ¬€erential equations. A...
  • An Introduction to Stochastic Epidemic Models
    Linda Allen
    A brief introduction is presented to modeling in stochastic epidemiology. Several
    useful epidemiological concepts such as the basic reproduction number and the nal size
    of an epidemic are de ned. Three well-known stochastic modeling formulations are in-
    troduced: discrete-time Markov chains, continuous-time Markov chains, and stochastic
    di eren...

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