4,291 research outputs found
A finite difference method for Piecewise Deterministic Processes with memory
In this paper the numerical approximation of solutions of Liouville-Master
Equations for time-dependent distribution functions of Piecewise Deterministic
Processes with memory is considered. These equations are linear hyperbolic PDEs
with non-constant coefficients, and boundary conditions that depend on
integrals over the interior of the integration domain. We construct a finite
difference method of the first order, by a combination of the upwind method,
for PDEs, and by a direct quadrature, for the boundary condition. We analyse
convergence of the numerical solution for distribution functions evolving
towards an equilibrium. Numerical results for two problems, whose analytical
solutions are known in closed form, illustrate the theoretical finding.Comment: 20 pages, 7 figure
Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience
This essay is presented with two principal objectives in mind: first, to
document the prevalence of fractals at all levels of the nervous system, giving
credence to the notion of their functional relevance; and second, to draw
attention to the as yet still unresolved issues of the detailed relationships
among power law scaling, self-similarity, and self-organized criticality. As
regards criticality, I will document that it has become a pivotal reference
point in Neurodynamics. Furthermore, I will emphasize the not yet fully
appreciated significance of allometric control processes. For dynamic fractals,
I will assemble reasons for attributing to them the capacity to adapt task
execution to contextual changes across a range of scales. The final Section
consists of general reflections on the implications of the reviewed data, and
identifies what appear to be issues of fundamental importance for future
research in the rapidly evolving topic of this review
Precision of readout at the hunchback gene: analyzing short transcription time traces in living fly embryos
The simultaneous expression of the hunchback gene in the numerous nuclei of
the developing fly embryo gives us a unique opportunity to study how
transcription is regulated in living organisms. A recently developed MS2-MCP
technique for imaging nascent messenger RNA in living Drosophila embryos allows
us to quantify the dynamics of the developmental transcription process. The
initial measurement of the morphogens by the hunchback promoter takes place
during very short cell cycles, not only giving each nucleus little time for a
precise readout, but also resulting in short time traces of transcription.
Additionally, the relationship between the measured signal and the promoter
state depends on the molecular design of the reporting probe. We develop an
analysis approach based on tailor made autocorrelation functions that overcomes
the short trace problems and quantifies the dynamics of transcription
initiation. Based on live imaging data, we identify signatures of bursty
transcription initiation from the hunchback promoter. We show that the
precision of the expression of the hunchback gene to measure its position along
the anterior-posterior axis is low both at the boundary and in the anterior
even at cycle 13, suggesting additional post-transcriptional averaging
mechanisms to provide the precision observed in fixed embryos
The iEBE-VISHNU code package for relativistic heavy-ion collisions
The iEBE-VISHNU code package performs event-by-event simulations for
relativistic heavy-ion collisions using a hybrid approach based on
(2+1)-dimensional viscous hydrodynamics coupled to a hadronic cascade model. We
present the detailed model implementation, accompanied by some numerical code
tests for the package. iEBE-VISHNU forms the core of a general theoretical
framework for model-data comparisons through large scale Monte-Carlo
simulations. A numerical interface between the hydrodynamically evolving medium
and thermal photon radiation is also discussed. This interface is more
generally designed for calculations of all kinds of rare probes that are
coupled to the temperature and flow velocity evolution of the bulk medium, such
as jet energy loss and heavy quark diffusion.Comment: 47 pages, 21 figures. Manuscript was accepted by Computer Physics
Communication
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