3,041 research outputs found

### Propagation of fluctuations in interaction networks governed by the law of mass action

Using an example of physical interactions between proteins, we study how
perturbations propagate in interconnected networks whose equilibrium state is
governed by the law of mass action. We introduce a comprehensive matrix
formalism which predicts the response of this equilibrium to small changes in
total concentrations of individual molecules, and explain it using a heuristic
analogy to a current flow in a network of resistors. Our main conclusion is
that on average changes in free concentrations exponentially decay with the
distance from the source of perturbation. We then study how this decay is
influenced by such factors as the topology of a network, binding strength, and
correlations between concentrations of neighboring nodes. An exact analytic
expression for the decay constant is obtained for the case of uniform
interactions on the Bethe lattice. Our general findings are illustrated using a
real biological network of protein-protein interactions in baker's yeast with
experimentally determined protein concentrations.Comment: 4 pages; 2 figure

### Promise and Pitfalls of Extending Google's PageRank Algorithm to Citation Networks

We review our recent work on applying the Google PageRank algorithm to find
scientific "gems" among all Physical Review publications, and its extension to
CiteRank, to find currently popular research directions. These metrics provide
a meaningful extension to traditionally-used importance measures, such as the
number of citations and journal impact factor. We also point out some pitfalls
of over-relying on quantitative metrics to evaluate scientific quality.Comment: 3 pages, 1 figure, invited comment for the Journal of Neuroscience.
The arxiv version is microscopically different from the published versio

### On the superfluidity of classical liquid in nanotubes

In 2001, the author proposed the ultra second quantization method. The ultra
second quantization of the Schr\"odinger equation, as well as its ordinary
second quantization, is a representation of the N-particle Schr\"odinger
equation, and this means that basically the ultra second quantization of the
equation is the same as the original N-particle equation: they coincide in
3N-dimensional space.
We consider a short action pairwise potential V(x_i -x_j). This means that as
the number of particles tends to infinity, $N\to\infty$, interaction is
possible for only a finite number of particles. Therefore, the potential
depends on N in the following way: $V_N=V((x_i-x_j)N^{1/3})$. If V(y) is finite
with support $\Omega_V$, then as $N\to\infty$ the support engulfs a finite
number of particles, and this number does not depend on N.
As a result, it turns out that the superfluidity occurs for velocities less
than $\min(\lambda_{\text{crit}}, \frac{h}{2mR})$, where
$\lambda_{\text{crit}}$ is the critical Landau velocity and R is the radius of
the nanotube.Comment: Latex, 20p. The text is presented for the International Workshop
"Idempotent and tropical mathematics and problems of mathematical physics",
Independent University of Moscow, Moscow, August 25--30, 2007 and to be
published in the Russian Journal of Mathematical Physics, 2007, vol. 15, #

### Expansion Around the Mean-Field Solution of the Bak-Sneppen Model

We study a recently proposed equation for the avalanche distribution in the
Bak-Sneppen model. We demonstrate that this equation indirectly relates
$\tau$,the exponent for the power law distribution of avalanche sizes, to $D$,
the fractal dimension of an avalanche cluster.We compute this relation
numerically and approximate it analytically up to the second order of expansion
around the mean field exponents. Our results are consistent with Monte Carlo
simulations of Bak-Sneppen model in one and two dimensions.Comment: 5 pages, 2 ps-figures iclude

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