16,657 research outputs found
Ordering dynamics in the voter model with aging
The voter model with memory-dependent dynamics is theoretically and
numerically studied at the mean-field level. The `internal age', or time an
individual spends holding the same state, is added to the set of binary states
of the population, such that the probability of changing state (or activation
probability ) depends on this age. A closed set of integro-differential
equations describing the time evolution of the fraction of individuals with a
given state and age is derived, and from it analytical results are obtained
characterizing the behavior of the system close to the absorbing states. In
general, different age-dependent activation probabilities have different
effects on the dynamics. When the activation probability is an increasing
function of the age , the system reaches a steady state with coexistence of
opinions. In the case of aging, with being a decreasing function, either
the system reaches consensus or it gets trapped in a frozen state, depending on
the value of (zero or not) and the velocity of approaching
. Moreover, when the system reaches consensus, the time ordering of
the system can be exponential () or power-law like ().
Exact conditions for having one or another behavior, together with the
equations and explicit expressions for the exponents, are provided
Stochastic and deterministic models for age-structured populations with genetically variable traits
Understanding how stochastic and non-linear deterministic processes interact
is a major challenge in population dynamics theory. After a short review, we
introduce a stochastic individual-centered particle model to describe the
evolution in continuous time of a population with (continuous) age and trait
structures. The individuals reproduce asexually, age, interact and die. The
'trait' is an individual heritable property (d-dimensional vector) that may
influence birth and death rates and interactions between individuals, and vary
by mutation. In a large population limit, the random process converges to the
solution of a Gurtin-McCamy type PDE. We show that the random model has a long
time behavior that differs from its deterministic limit. However, the results
on the limiting PDE and large deviation techniques \textit{\`a la}
Freidlin-Wentzell provide estimates of the extinction time and a better
understanding of the long time behavior of the stochastic process. This has
applications to the theory of adaptive dynamics used in evolutionary biology.
We present simulations for two biological problems involving life-history trait
evolution when body size is plastic and individual growth is taken into
account.Comment: This work is a proceeding of the CANUM 2008 conferenc
Stochastic heating of cooling flows
It is generally accepted that the heating of gas in clusters of galaxies by
active galactic nuclei (AGN) is a form of feedback. Feedback is required to
ensure a long term, sustainable balance between heating and cooling. This work
investigates the impact of proportional stochastic feedback on the energy
balance in the intracluster medium. Using a generalised analytical model for a
cluster atmosphere, it is shown that an energy equilibrium can be reached
exponentially quickly. Applying the tools of stochastic calculus it is
demonstrated that the result is robust with regard to the model parameters,
even though they affect the amount of variability in the system.Comment: 7 pages, 6 figures, accepted by MNRAS,
http://www.astro.soton.ac.uk/~gbp/pub/pavlovski_stochh.pd
Toward an integrated workforce planning framework using structured equations
Strategic Workforce Planning is a company process providing best in class,
economically sound, workforce management policies and goals. Despite the
abundance of literature on the subject, this is a notorious challenge in terms
of implementation. Reasons span from the youth of the field itself to broader
data integration concerns that arise from gathering information from financial,
human resource and business excellence systems. This paper aims at setting the
first stones to a simple yet robust quantitative framework for Strategic
Workforce Planning exercises. First a method based on structured equations is
detailed. It is then used to answer two main workforce related questions: how
to optimally hire to keep labor costs flat? How to build an experience
constrained workforce at a minimal cost
Examples of mathematical modeling tales from the crypt
Mathematical modeling is being increasingly recognized within the biomedical sciences as an important tool that can aid the understanding of biological systems. The heavily regulated cell renewal cycle in the colonic crypt provides a good example of how modeling can be used to find out key features of the system kinetics, and help to explain both the breakdown of homeostasis and the initiation of tumorigenesis. We use the cell population model by Johnston et al. (2007) Proc. Natl. Acad. Sci. USA 104, 4008-4013, to illustrate the power of mathematical modeling by considering two key questions about the cell population dynamics in the colonic crypt. We ask: how can a model describe both homeostasis and unregulated growth in tumorigenesis; and to which parameters in the system is the model most sensitive? In order to address these questions, we discuss what type of modeling approach is most appropriate in the crypt. We use the model to argue why tumorigenesis is observed to occur in stages with long lag phases between periods of rapid growth, and we identify the key parameters
A jump-growth model for predator-prey dynamics: derivation and application to marine ecosystems
This paper investigates the dynamics of biomass in a marine ecosystem. A
stochastic process is defined in which organisms undergo jumps in body size as
they catch and eat smaller organisms. Using a systematic expansion of the
master equation, we derive a deterministic equation for the macroscopic
dynamics, which we call the deterministic jump-growth equation, and a linear
Fokker-Planck equation for the stochastic fluctuations. The McKendrick--von
Foerster equation, used in previous studies, is shown to be a first-order
approximation, appropriate in equilibrium systems where predators are much
larger than their prey. The model has a power-law steady state consistent with
the approximate constancy of mass density in logarithmic intervals of body mass
often observed in marine ecosystems. The behaviours of the stochastic process,
the deterministic jump-growth equation and the McKendrick--von Foerster
equation are compared using numerical methods. The numerical analysis shows two
classes of attractors: steady states and travelling waves.Comment: 27 pages, 4 figures. Final version as published. Only minor change
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