234 research outputs found
Asymptotic analysis of first passage time in complex networks
The first passage time (FPT) distribution for random walk in complex networks
is calculated through an asymptotic analysis. For network with size and
short relaxation time , the computed mean first passage time (MFPT),
which is inverse of the decay rate of FPT distribution, is inversely
proportional to the degree of the destination. These results are verified
numerically for the paradigmatic networks with excellent agreement. We show
that the range of validity of the analytical results covers networks that have
short relaxation time and high mean degree, which turn out to be valid to many
real networks.Comment: 6 pages, 4 figures, 1 tabl
Singularity Structure, Symmetries and Integrability of Generalized Fisher Type Nonlinear Diffusion Equation
In this letter, the integrability aspects of a generalized Fisher type
equation with modified diffusion in (1+1) and (2+1) dimensions are studied by
carrying out a singularity structure and symmetry analysis. It is shown that
the Painlev\'e property exists only for a special choice of the parameter
(). A B\"acklund transformation is shown to give rise to the linearizing
transformation to the linear heat equation for this case (). A Lie
symmetry analysis also picks out the same case () as the only system among
this class as having nontrivial infinite dimensional Lie algebra of symmetries
and that the similarity variables and similarity reductions lead in a natural
way to the linearizing transformation and physically important classes of
solutions (including known ones in the literature), thereby giving a group
theoretical understanding of the system. For nonintegrable cases in (2+1)
dimensions, associated Lie symmetries and similarity reductions are indicated.Comment: 8 page
Democratization in a passive dendritic tree : an analytical investigation
One way to achieve amplification of distal synaptic inputs on a dendritic tree is to scale the amplitude and/or duration of the synaptic conductance with its distance from the soma. This is an example of what is often referred to as “dendritic democracy”. Although well studied experimentally, to date this phenomenon has not been thoroughly explored from a mathematical perspective. In this paper we adopt a passive model of a dendritic tree with distributed excitatory synaptic conductances and analyze a number of key measures of democracy. In particular, via moment methods we derive laws for the transport, from synapse to soma, of strength, characteristic time, and dispersion. These laws lead immediately to synaptic scalings that overcome attenuation with distance. We follow this with a Neumann approximation of Green’s representation that readily produces the synaptic scaling that democratizes the peak somatic voltage response. Results are obtained for both idealized geometries and for the more realistic geometry of a rat CA1 pyramidal cell. For each measure of democratization we produce and contrast the synaptic scaling associated with treating the synapse as either a conductance change or a current injection. We find that our respective scalings agree up to a critical distance from the soma and we reveal how this critical distance decreases with decreasing branch radius
Universal Statistical Behavior of Neural Spike Trains
We construct a model that predicts the statistical properties of spike trains
generated by a sensory neuron. The model describes the combined effects of the
neuron's intrinsic properties, the noise in the surrounding, and the external
driving stimulus. We show that the spike trains exhibit universal statistical
behavior over short times, modulated by a strongly stimulus-dependent behavior
over long times. These predictions are confirmed in experiments on H1, a
motion-sensitive neuron in the fly visual system.Comment: 7 pages, 4 figure
Anomalous diffusion and the first passage time problem
We study the distribution of first passage time (FPT) in Levy type of
anomalous diffusion. Using recently formulated fractional Fokker-Planck
equation we obtain three results. (1) We derive an explicit expression for the
FPT distribution in terms of Fox or H-functions when the diffusion has zero
drift. (2) For the nonzero drift case we obtain an analytical expression for
the Laplace transform of the FPT distribution. (3) We express the FPT
distribution in terms of a power series for the case of two absorbing barriers.
The known results for ordinary diffusion (Brownian motion) are obtained as
special cases of our more general results.Comment: 25 pages, 4 figure
Noise and Periodic Modulations in Neural Excitable Media
We have analyzed the interplay between noise and periodic modulations in a
mean field model of a neural excitable medium. To this purpose, we have
considered two types of modulations; namely, variations of the resistance and
oscillations of the threshold. In both cases, stochastic resonance is present,
irrespective of if the system is monostable or bistable.Comment: 13 pages, RevTex, 5 PostScript figure
Inhibition of rhythmic neural spiking by noise: the occurrence of a minimum in activity with increasing noise
The effects of noise on neuronal dynamical systems are of much current interest. Here, we investigate noise-induced changes in the rhythmic firing activity of single Hodgkin–Huxley neurons. With additive input current, there is, in the absence of noise, a critical mean value µ = µc above which sustained periodic firing occurs. With initial conditions as resting values, for a range of values of the mean µ near the critical value, we have found that the firing rate is greatly reduced by noise, even of quite small amplitudes. Furthermore, the firing rate may undergo a pronounced minimum as the noise increases. This behavior has the opposite character to stochastic resonance and coherence resonance. We found that these phenomena occurred even when the initial conditions were chosen randomly or when the noise was switched on at a random time, indicating the robustness of the results. We also examined the effects of conductance-based noise on Hodgkin–Huxley neurons and obtained similar results, leading to the conclusion that the phenomena occur across a wide range of neuronal dynamical systems. Further, these phenomena will occur in diverse applications where a stable limit cycle coexists with a stable focus
Local variation of hashtag spike trains and popularity in Twitter
We draw a parallel between hashtag time series and neuron spike trains. In
each case, the process presents complex dynamic patterns including temporal
correlations, burstiness, and all other types of nonstationarity. We propose
the adoption of the so-called local variation in order to uncover salient
dynamics, while properly detrending for the time-dependent features of a
signal. The methodology is tested on both real and randomized hashtag spike
trains, and identifies that popular hashtags present regular and so less bursty
behavior, suggesting its potential use for predicting online popularity in
social media.Comment: 7 pages, 7 figure
Beyond the Fokker-Planck equation: Pathwise control of noisy bistable systems
We introduce a new method, allowing to describe slowly time-dependent
Langevin equations through the behaviour of individual paths. This approach
yields considerably more information than the computation of the probability
density. The main idea is to show that for sufficiently small noise intensity
and slow time dependence, the vast majority of paths remain in small space-time
sets, typically in the neighbourhood of potential wells. The size of these sets
often has a power-law dependence on the small parameters, with universal
exponents. The overall probability of exceptional paths is exponentially small,
with an exponent also showing power-law behaviour. The results cover time spans
up to the maximal Kramers time of the system. We apply our method to three
phenomena characteristic for bistable systems: stochastic resonance, dynamical
hysteresis and bifurcation delay, where it yields precise bounds on transition
probabilities, and the distribution of hysteresis areas and first-exit times.
We also discuss the effect of coloured noise.Comment: 37 pages, 11 figure
Dimensions and Global Twist of Single-Layer DNA Origami Measured by Small-Angle X-ray Scattering
The
rational design of complementary DNA sequences can be used
to create nanostructures that self-assemble with nanometer precision.
DNA nanostructures have been imaged by atomic force microscopy and
electron microscopy. Small-angle X-ray scattering (SAXS) provides
complementary structural information on the ensemble-averaged state
of DNA nanostructures in solution. Here we demonstrate that SAXS can
distinguish between different single-layer DNA origami tiles that
look identical when immobilized on a mica surface and imaged with
atomic force microscopy. We use SAXS to quantify the magnitude of
global twist of DNA origami tiles with different crossover periodicities:
these measurements highlight the extreme structural sensitivity of
single-layer origami to the location of strand crossovers. We also
use SAXS to quantify the distance between pairs of gold nanoparticles
tethered to specific locations on a DNA origami tile and use this
method to measure the overall dimensions and geometry of the DNA nanostructure
in solution. Finally, we use indirect Fourier methods, which have
long been used for the interpretation of SAXS data from biomolecules,
to measure the distance between DNA helix pairs in a DNA origami nanotube.
Together, these results provide important methodological advances
in the use of SAXS to analyze DNA nanostructures in solution and insights
into the structures of single-layer DNA origami
- …