172 research outputs found
Finite-Size Effects in Stochastic Models of Population Dynamics: Applications to Biomedicine and Biology
Population dynamics constitutes a widespread branch of investigations which finds important applications within the realm of life science. The classical deterministic (macroscopic) approach aims at characterizing the time evolution of families of homologous entities, so to unravel the global mechanisms which drive their dynamics. As opposed to this formulation, a microscopic level of modeling can be invoked which instead focuses on the explicit rules governing the interactions among individuals. A viable tool that enables to bridge the gap between the two approaches is the van Kampen's system size expansion. In this thesis we use this method to show how the finite-size effects accounted by the microscopic level might significantly alter the dynamics of biological phenomena
Phase equilibria of polydisperse hydrocarbons: moment free energy method analysis
We analyze the phase equilibria of systems of polydisperse hydrocarbons by
means of the recently introduced moment method. Hydrocarbons are modelled with
the Soave-Redlick-Kwong and Peng-Robinson equations of states. Numerical
results show no particular qualitative difference between the two equations of
states. Furthermore, in general the moment method proves to be an excellent
method for solving phase equilibria of polydisperse systems, showing excellent
agreement with previous results and allowing a great improvement in generality
of the numerical scheme and speed of computation.Comment: 12 pages, 2 figure
The second will be first: competition on directed networks
Multiple sinks competition is investigated for a walker diffusing on directed
complex networks. The asymmetry of the imposed spatial support makes the system
non transitive. As a consequence, it is always possible to identify a suitable
location for the second absorbing sink that screens at most the flux of agents
directed against the first trap, whose position has been preliminarily
assigned. The degree of mutual competition between pairs of nodes is
analytically quantified through apt indicators that build on the topological
characteristics of the hosting graph. Moreover, the positioning of the second
trap can be chosen so as to minimize, at the same time the probability of being
in turn shaded by a thirdly added trap. Supervised placing of absorbing traps
on a asymmetric disordered and complex graph is hence possible, as follows a
robust optimization protocol. This latter is here discussed and successfully
tested against synthetic data
Ginzburg-Landau approximation for self-sustained oscillators weakly coupled on complex directed graphs
A normal form approximation for the evolution of a reaction-diffusion system
hosted on a directed graph is derived, in the vicinity of a supercritical Hopf
bifurcation. Weak diffusive couplings are assumed to hold between adjacent
nodes. Under this working assumption, a Complex Ginzburg-Landau equation (CGLE)
is obtained, whose coefficients depend on the parameters of the model and the
topological characteristics of the underlying network. The CGLE enables one to
probe the stability of the synchronous oscillating solution, as displayed by
the reaction-diffusion system above Hopf bifurcation. More specifically,
conditions can be worked out for the onset of the symmetry breaking instability
that eventually destroys the uniform oscillatory state. Numerical tests
performed for the Brusselator model confirm the validity of the proposed
theoretical scheme. Patterns recorded for the CGLE resemble closely those
recovered upon integration of the original Brussellator dynamics
Multiple scale theory of topology driven pattern on directed networks
Dynamical processes on networks are currently being considered in different
domains of cross-disciplinary interest. Reaction-diffusion systems hosted on
directed graphs are in particular relevant for their widespread applications,
from neuroscience, to computer networks and traffic systems. Due to the
peculiar spectrum of the discrete Laplacian operator, homogeneous fixed points
can turn unstable, on a directed support, because of the topology of the
network, a phenomenon which cannot be induced on undirected graphs. A linear
analysis can be performed to single out the conditions that underly the
instability. The complete characterization of the patterns, which are
eventually attained beyond the linear regime of exponential growth, calls
instead for a full non linear treatment. By performing a multiple time scale
perturbative calculation, we here derive an effective equation for the non
linear evolution of the amplitude of the most unstable mode, close to the
threshold of criticality. This is a Stuart-Landau equation whose complex
coefficients appear to depend on the topological features of the embedding
directed graph. The theory proves adequate versus simulations, as confirmed by
operating with a paradigmatic reaction-diffusion model
Noise Processing by MicroRNA-Mediated Circuits: the Incoherent Feed-Forward Loop, Revisited
The intrinsic stochasticity of gene expression is usually mitigated in higher
eukaryotes by post-transcriptional regulation channels that stabilise the
output layer, most notably protein levels. The discovery of small non-coding
RNAs (miRNAs) in specific motifs of the genetic regulatory network has led to
identifying noise buffering as the possible key function they exert in
regulation. Recent in vitro} and in silico studies have corroborated this
hypothesis. It is however also known that miRNA-mediated noise reduction is
hampered by transcriptional bursting in simple topologies. Here, using
stochastic simulations validated by analytical calculations based on van
Kampen's expansion, we revisit the noise-buffering capacity of the
miRNA-mediated Incoherent Feed Forward Loop (IFFL), a small module that is
widespread in the gene regulatory networks of higher eukaryotes, in order to
account for the effects of intermittency in the transcriptional activity of the
modulator gene. We show that bursting considerably alters the circuit's ability
to control static protein noise. By comparing with other regulatory
architectures, we find that direct transcriptional regulation significantly
outperforms the IFFL in a broad range of kinetic parameters. This suggests
that, under pulsatile inputs, static noise reduction may be less important than
dynamical aspects of noise and information processing in characterising the
performance of regulatory elements.Comment: 25 pages (Main Text and Supplementary Information), 5 figure
Noise processing by microRNA-mediated circuits: The Incoherent Feed-Forward Loop, revisited
The intrinsic stochasticity of gene expression is usually mitigated in higher eukaryotes by post-transcriptional regulation channels that stabilise the output layer, most notably protein levels. The discovery of small non-coding RNAs (miRNAs) in specific motifs of the genetic regulatory network has led to identifying noise buffering as the possible key function they exert in regulation. Recent in vitro and in silico studies have corroborated this hypothesis. It is however also known that miRNA-mediated noise reduction is hampered by transcriptional bursting in simple topologies. Here, using stochastic simulations validated by analytical calculations based on van Kampen's expansion, we revisit the noise-buffering capacity of the miRNA-mediated Incoherent Feed Forward Loop (IFFL), a small module that is widespread in the gene regulatory networks of higher eukaryotes, in order to account for the effects of intermittency in the transcriptional activity of the modulator gene. We show that bursting considerably alters the circuit's ability to control static protein noise. By comparing with other regulatory architectures, we find that direct transcriptional regulation significantly outperforms the IFFL in a broad range of kinetic parameters. This suggests that, under pulsatile inputs, static noise reduction may be less important than dynamical aspects of noise and information processing in characterising the performance of regulatory elements
Hopping in the crowd to unveil network topology
We introduce a nonlinear operator to model diffusion on a complex undirected
network under crowded conditions. We show that the asymptotic distribution of
diffusing agents is a nonlinear function of the nodes' degree and saturates to
a constant value for sufficiently large connectivities, at variance with
standard diffusion in the absence of excluded-volume effects. Building on this
observation, we define and solve an inverse problem, aimed at reconstructing
the a priori unknown connectivity distribution. The method gathers all the
necessary information by repeating a limited number of independent measurements
of the asymptotic density at a single node that can be chosen randomly. The
technique is successfully tested against both synthetic and real data, and
shown to estimate with great accuracy also the total number of nodes
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