426 research outputs found
Kinetic theory of age-structured stochastic birth-death processes
Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov-–Born–-Green–-Kirkwood-–Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution
The Quantum as an Emergent System
Double slit interference is explained with the aid of what we call
"21stcentury classical physics". We model a particle as an oscillator
("bouncer") in a thermal context, which is given by some assumed "zero-point"
field of the vacuum. In this way, the quantum is understood as an emergent
system, i.e., a steady-state system maintained by a constant throughput of
(vacuum) energy. To account for the particle's thermal environment, we
introduce a "path excitation field", which derives from the thermodynamics of
the zero-point vacuum and which represents all possible paths a particle can
take via thermal path fluctuations. The intensity distribution on a screen
behind a double slit is calculated, as well as the corresponding trajectories
and the probability density current. Further, particular features of the
relative phase are shown to be responsible for nonlocal effects not only in
ordinary quantum theory, but also in our classical approach.Comment: 24 pages, 2 figures, based on a talk given at "Emergent Quantum
Mechanics (Heinz von Foerster Conference 2011)",
http://www.univie.ac.at/hvf11/congress/EmerQuM.htm
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
"Meaning" as a sociological concept: A review of the modeling, mapping, and simulation of the communication of knowledge and meaning
The development of discursive knowledge presumes the communication of meaning
as analytically different from the communication of information. Knowledge can
then be considered as a meaning which makes a difference. Whereas the
communication of information is studied in the information sciences and
scientometrics, the communication of meaning has been central to Luhmann's
attempts to make the theory of autopoiesis relevant for sociology. Analytical
techniques such as semantic maps and the simulation of anticipatory systems
enable us to operationalize the distinctions which Luhmann proposed as relevant
to the elaboration of Husserl's "horizons of meaning" in empirical research:
interactions among communications, the organization of meaning in
instantiations, and the self-organization of interhuman communication in terms
of symbolically generalized media such as truth, love, and power. Horizons of
meaning, however, remain uncertain orders of expectations, and one should
caution against reification from the meta-biological perspective of systems
theory
"Open Innovation" and "Triple Helix" Models of Innovation: Can Synergy in Innovation Systems Be Measured?
The model of "Open Innovations" (OI) can be compared with the "Triple Helix
of University-Industry-Government Relations" (TH) as attempts to find surplus
value in bringing industrial innovation closer to public R&D. Whereas the firm
is central in the model of OI, the TH adds multi-centeredness: in addition to
firms, universities and (e.g., regional) governments can take leading roles in
innovation eco-systems. In addition to the (transversal) technology transfer at
each moment of time, one can focus on the dynamics in the feedback loops. Under
specifiable conditions, feedback loops can be turned into feedforward ones that
drive innovation eco-systems towards self-organization and the auto-catalytic
generation of new options. The generation of options can be more important than
historical realizations ("best practices") for the longer-term viability of
knowledge-based innovation systems. A system without sufficient options, for
example, is locked-in. The generation of redundancy -- the Triple Helix
indicator -- can be used as a measure of unrealized but technologically
feasible options given a historical configuration. Different coordination
mechanisms (markets, policies, knowledge) provide different perspectives on the
same information and thus generate redundancy. Increased redundancy not only
stimulates innovation in an eco-system by reducing the prevailing uncertainty;
it also enhances the synergy in and innovativeness of an innovation system.Comment: Journal of Open Innovations: Technology, Market and Complexity, 2(1)
(2016) 1-12; doi:10.1186/s40852-016-0039-
Socio-Economic Instability and the Scaling of Energy Use with Population Size
The size of the human population is relevant to the development of a sustainable world, yet the forces setting growth or declines in the human population are poorly understood. Generally, population growth rates depend on whether new individuals compete for the same energy (leading to Malthusian or density-dependent growth) or help to generate new energy (leading to exponential and super-exponential growth). It has been hypothesized that exponential and super-exponential growth in humans has resulted from carrying capacity, which is in part determined by energy availability, keeping pace with or exceeding the rate of population growth. We evaluated the relationship between energy use and population size for countries with long records of both and the world as a whole to assess whether energy yields are consistent with the idea of an increasing carrying capacity. We find that on average energy use has indeed kept pace with population size over long time periods. We also show, however, that the energy-population scaling exponent plummets during, and its temporal variability increases preceding, periods of social, political, technological, and environmental change. We suggest that efforts to increase the reliability of future energy yields may be essential for stabilizing both population growth and the global socio-economic system
A systematic review of the evidence for single stage and two stage revision of infected knee replacement
BACKGROUND:
Periprosthetic infection about the knee is a devastating complication that may affect between 1% and 5% of knee replacement. With over 79 000 knee replacements being implanted each year in the UK, periprosthetic infection (PJI) is set to become an important burden of disease and cost to the healthcare economy. One of the important controversies in treatment of PJI is whether a single stage revision operation is superior to a two-stage procedure. This study sought to systematically evaluate the published evidence to determine which technique had lowest reinfection rates.
METHODS:
A systematic review of the literature was undertaken using the MEDLINE and EMBASE databases with the aim to identify existing studies that present the outcomes of each surgical technique. Reinfection rate was the primary outcome measure. Studies of specific subsets of patients such as resistant organisms were excluded.
RESULTS:
63 studies were identified that met the inclusion criteria. The majority of which (58) were reports of two-stage revision. Reinfection rated varied between 0% and 41% in two-stage studies, and 0% and 11% in single stage studies. No clinical trials were identified and the majority of studies were observational studies.
CONCLUSIONS:
Evidence for both one-stage and two-stage revision is largely of low quality. The evidence basis for two-stage revision is significantly larger, and further work into direct comparison between the two techniques should be undertaken as a priority
A Path Integral Approach to Age Dependent Branching Processes
Age dependent population dynamics are frequently modeled with generalizations of the classic McKendrick-von Foerster equation. These are deterministic systems, and a stochastic generalization was recently reported in [1,2]. Here we develop a fully stochastic theory for age-structured populations via quantum field theoretical Doi-Peliti techniques. This results in a path integral formulation where birth and death events correspond to cubic and quadratic interaction terms. This formalism allows us to efficiently recapitulate the results in [1,2], exemplifying the utility of Doi-Peliti methods. Furthermore, we find that the path integral formulation for age-structured moments has an exact perturbative expansion that explicitly relates to the hereditary structure between correlated individuals. These methods are then generalized with a binary fission model of cell division
Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins
In this review we demonstrate how the algebraic Bethe ansatz is used for the
calculation of the energy spectra and form factors (operator matrix elements in
the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As
examples we apply the theory to several models of current interest in the study
of Bose-Einstein condensates, which have been successfully created using
ultracold dilute atomic gases. The first model we introduce describes Josephson
tunneling between two coupled Bose-Einstein condensates. It can be used not
only for the study of tunneling between condensates of atomic gases, but for
solid state Josephson junctions and coupled Cooper pair boxes. The theory is
also applicable to models of atomic-molecular Bose-Einstein condensates, with
two examples given and analysed. Additionally, these same two models are
relevant to studies in quantum optics. Finally, we discuss the model of
Bardeen, Cooper and Schrieffer in this framework, which is appropriate for
systems of ultracold fermionic atomic gases, as well as being applicable for
the description of superconducting correlations in metallic grains with
nanoscale dimensions. In applying all of the above models to physical
situations, the need for an exact analysis of small scale systems is
established due to large quantum fluctuations which render mean-field
approaches inaccurate.Comment: 49 pages, 1 figure, invited review for J. Phys. A., published version
available at http://stacks.iop.org/JPhysA/36/R6
Lessons from complexity science for urban health and well-being
From a complexity science perspective, urban health and well-being challenges emerge due to the complexity of urban systems. Adverse urban health outcomes emerge from failing to respond to that complexity by taking a systems approach in knowledge and action which would open opportunity spaces for human agents to create benefits which in turn would generate salutogenic health and well-being outcomes. Lessons learned from complexity science suggest that adverse urban health outcomes emerge from a poor understanding of their complexity and from not engaging with them in a transdisciplinary, integrated fashion. A conceptual framework is presented which combines systems models from the natural and social sciences and explains how opportunities for advancing health and well-being can be co-created. The framework demonstrates that taking a systems approach is a necessary cognitive response from learning the lessons of complexity science and from understanding that humans are an inextricable part of the systems they aim at understanding and managing. Such response is at the core of systems intelligence. The implications are far reaching for the science of urban health and well-being
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