7,935 research outputs found
Generating functional analysis of complex formation and dissociation in large protein interaction networks
We analyze large systems of interacting proteins, using techniques from the
non-equilibrium statistical mechanics of disordered many-particle systems.
Apart from protein production and removal, the most relevant microscopic
processes in the proteome are complex formation and dissociation, and the
microscopic degrees of freedom are the evolving concentrations of unbound
proteins (in multiple post-translational states) and of protein complexes. Here
we only include dimer-complexes, for mathematical simplicity, and we draw the
network that describes which proteins are reaction partners from an ensemble of
random graphs with an arbitrary degree distribution. We show how generating
functional analysis methods can be used successfully to derive closed equations
for dynamical order parameters, representing an exact macroscopic description
of the complex formation and dissociation dynamics in the infinite system
limit. We end this paper with a discussion of the possible routes towards
solving the nontrivial order parameter equations, either exactly (in specific
limits) or approximately.Comment: 14 pages, to be published in Proc of IW-SMI-2009 in Kyoto (Journal of
Phys Conference Series
On the degree conjecture for separability of multipartite quantum states
We settle the so-called degree conjecture for the separability of
multipartite quantum states, which are normalized graph Laplacians, first given
by Braunstein {\it et al.} [Phys. Rev. A \textbf{73}, 012320 (2006)]. The
conjecture states that a multipartite quantum state is separable if and only if
the degree matrix of the graph associated with the state is equal to the degree
matrix of the partial transpose of this graph. We call this statement to be the
strong form of the conjecture. In its weak version, the conjecture requires
only the necessity, that is, if the state is separable, the corresponding
degree matrices match. We prove the strong form of the conjecture for {\it
pure} multipartite quantum states, using the modified tensor product of graphs
defined in [J. Phys. A: Math. Theor. \textbf{40}, 10251 (2007)], as both
necessary and sufficient condition for separability. Based on this proof, we
give a polynomial-time algorithm for completely factorizing any pure
multipartite quantum state. By polynomial-time algorithm we mean that the
execution time of this algorithm increases as a polynomial in where is
the number of parts of the quantum system. We give a counter-example to show
that the conjecture fails, in general, even in its weak form, for multipartite
mixed states. Finally, we prove this conjecture, in its weak form, for a class
of multipartite mixed states, giving only a necessary condition for
separability.Comment: 17 pages, 3 figures. Comments are welcom
Rank one discrete valuations of power series fields
In this paper we study the rank one discrete valuations of the field
whose center in k\lcor\X\rcor is the maximal ideal. In
sections 2 to 6 we give a construction of a system of parametric equations
describing such valuations. This amounts to finding a parameter and a field of
coefficients. We devote section 2 to finding an element of value 1, that is, a
parameter. The field of coefficients is the residue field of the valuation, and
it is given in section 5.
The constructions given in these sections are not effective in the general
case, because we need either to use the Zorn's lemma or to know explicitly a
section of the natural homomorphism R_v\to\d between the ring and
the residue field of the valuation .
However, as a consequence of this construction, in section 7, we prove that
k((\X)) can be embedded into a field L((\Y)), where is an algebraic
extension of and the {\em ``extended valuation'' is as close as possible to
the usual order function}
Enskog Theory for Polydisperse Granular Mixtures II. Sonine Polynomial Approximation
The linear integral equations defining the Navier-Stokes (NS) transport
coefficients for polydisperse granular mixtures of smooth inelastic hard disks
or spheres are solved by using the leading terms in a Sonine polynomial
expansion. Explicit expressions for all the NS transport coefficients are given
in terms of the sizes, masses, compositions, density and restitution
coefficients. In addition, the cooling rate is also evaluated to first order in
the gradients. The results hold for arbitrary degree of inelasticity and are
not limited to specific values of the parameters of the mixture. Finally, a
detailed comparison between the derivation of the current theory and previous
theories for mixtures is made, with attention paid to the implication of the
various treatments employed to date.Comment: 26 pages, to be published in Phys. Rev.
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