812 research outputs found
Force Modulating Dynamic Disorder: Physical Theory of Catch-slip bond Transitions in Receptor-Ligand Forced Dissociation Experiments
Recently experiments showed that some adhesive receptor-ligand complexes
increase their lifetimes when they are stretched by mechanical force, while the
force increase beyond some thresholds their lifetimes decrease. Several
specific chemical kinetic models have been developed to explain the intriguing
transitions from the "catch-bonds" to the "slip-bonds". In this work we suggest
that the counterintuitive forced dissociation of the complexes is a typical
rate process with dynamic disorder. An uniform one-dimension force modulating
Agmon-Hopfield model is used to quantitatively describe the transitions
observed in the single bond P-selctin glycoprotein ligand
1(PSGL-1)P-selectin forced dissociation experiments, which were respectively
carried out on the constant force [Marshall, {\it et al.}, (2003) Nature {\bf
423}, 190-193] and the force steady- or jump-ramp [Evans {\it et al.}, (2004)
Proc. Natl. Acad. Sci. USA {\bf 98}, 11281-11286] modes. Our calculation shows
that the novel catch-slip bond transition arises from a competition of the two
components of external applied force along the dissociation reaction coordinate
and the complex conformational coordinate: the former accelerates the
dissociation by lowering the height of the energy barrier between the bound and
free states (slip), while the later stabilizes the complex by dragging the
system to the higher barrier height (catch).Comment: 8 pages, 3 figures, submitte
Work probability distribution and tossing a biased coin
We show that the rare events present in dissipated work that enters Jarzynski
equality, when mapped appropriately to the phenomenon of large deviations found
in a biased coin toss, are enough to yield a quantitative work probability
distribution for Jarzynski equality. This allows us to propose a recipe for
constructing work probability distribution independent of the details of any
relevant system. The underlying framework, developed herein, is expected to be
of use in modelling other physical phenomena where rare events play an
important role.Comment: 6 pages, 4 figures
Effect of Poisson ratio on cellular structure formation
Mechanically active cells in soft media act as force dipoles. The resulting
elastic interactions are long-ranged and favor the formation of strings. We
show analytically that due to screening, the effective interaction between
strings decays exponentially, with a decay length determined only by geometry.
Both for disordered and ordered arrangements of cells, we predict novel phase
transitions from paraelastic to ferroelastic and anti-ferroelastic phases as a
function of Poisson ratio.Comment: 4 pages, Revtex, 4 Postscript figures include
Spectral statistics for unitary transfer matrices of binary graphs
Quantum graphs have recently been introduced as model systems to study the
spectral statistics of linear wave problems with chaotic classical limits. It
is proposed here to generalise this approach by considering arbitrary, directed
graphs with unitary transfer matrices. An exponentially increasing contribution
to the form factor is identified when performing a diagonal summation over
periodic orbit degeneracy classes. A special class of graphs, so-called binary
graphs, is studied in more detail. For these, the conditions for periodic orbit
pairs to be correlated (including correlations due to the unitarity of the
transfer matrix) can be given explicitly. Using combinatorial techniques it is
possible to perform the summation over correlated periodic orbit pair
contributions to the form factor for some low--dimensional cases. Gradual
convergence towards random matrix results is observed when increasing the
number of vertices of the binary graphs.Comment: 18 pages, 8 figure
Relative Entropy: Free Energy Associated with Equilibrium Fluctuations and Nonequilibrium Deviations
Using a one-dimensional macromolecule in aqueous solution as an illustration,
we demonstrate that the relative entropy from information theory, , has a natural role in the energetics of equilibrium and
nonequilibrium conformational fluctuations of the single molecule. It is
identified as the free energy difference associated with a fluctuating density
in equilibrium, and is associated with the distribution deviate from the
equilibrium in nonequilibrium relaxation. This result can be generalized to any
other isothermal macromolecular systems using the mathematical theories of
large deviations and Markov processes, and at the same time provides the
well-known mathematical results with an interesting physical interpretations.Comment: 5 page
Asymptotics of the mean-field Heisenberg model
We consider the mean-field classical Heisenberg model and obtain detailed
information about the total spin of the system by studying the model on a
complete graph and sending the number of vertices to infinity. In particular,
we obtain Cramer- and Sanov-type large deviations principles for the total spin
and the empirical spin distribution and demonstrate a second-order phase
transition in the Gibbs measures. We also study the asymptotics of the total
spin throughout the phase transition using Stein's method, proving central
limit theorems in the sub- and supercritical phases and a nonnormal limit
theorem at the critical temperature.Comment: 44 page
Stochastic Budget Optimization in Internet Advertising
Internet advertising is a sophisticated game in which the many advertisers
"play" to optimize their return on investment. There are many "targets" for the
advertisements, and each "target" has a collection of games with a potentially
different set of players involved. In this paper, we study the problem of how
advertisers allocate their budget across these "targets". In particular, we
focus on formulating their best response strategy as an optimization problem.
Advertisers have a set of keywords ("targets") and some stochastic information
about the future, namely a probability distribution over scenarios of cost vs
click combinations. This summarizes the potential states of the world assuming
that the strategies of other players are fixed. Then, the best response can be
abstracted as stochastic budget optimization problems to figure out how to
spread a given budget across these keywords to maximize the expected number of
clicks.
We present the first known non-trivial poly-logarithmic approximation for
these problems as well as the first known hardness results of getting better
than logarithmic approximation ratios in the various parameters involved. We
also identify several special cases of these problems of practical interest,
such as with fixed number of scenarios or with polynomial-sized parameters
related to cost, which are solvable either in polynomial time or with improved
approximation ratios. Stochastic budget optimization with scenarios has
sophisticated technical structure. Our approximation and hardness results come
from relating these problems to a special type of (0/1, bipartite) quadratic
programs inherent in them. Our research answers some open problems raised by
the authors in (Stochastic Models for Budget Optimization in Search-Based
Advertising, Algorithmica, 58 (4), 1022-1044, 2010).Comment: FINAL versio
Dobrushin states in the \phi^4_1 model
We consider the van der Waals free energy functional in a bounded interval
with inhomogeneous Dirichlet boundary conditions imposing the two stable phases
at the endpoints. We compute the asymptotic free energy cost, as the length of
the interval diverges, of shifting the interface from the midpoint. We then
discuss the effect of thermal fluctuations by analyzing the \phi^4_1-measure
with Dobrushin boundary conditions. In particular, we obtain a nontrivial limit
in a suitable scaling in which the length of the interval diverges and the
temperature vanishes. The limiting state is not translation invariant and
describes a localized interface. This result can be seen as the probabilistic
counterpart of the variational convergence of the associated excess free
energy.Comment: 34 page
Discrete-time classical and quantum Markovian evolutions: Maximum entropy problems on path space
The theory of Schroedinger bridges for diffusion processes is extended to
classical and quantum discrete-time Markovian evolutions. The solution of the
path space maximum entropy problems is obtained from the a priori model in both
cases via a suitable multiplicative functional transformation. In the quantum
case, nonequilibrium time reversal of quantum channels is discussed and
space-time harmonic processes are introduced.Comment: 34 page
The cavity method for large deviations
A method is introduced for studying large deviations in the context of
statistical physics of disordered systems. The approach, based on an extension
of the cavity method to atypical realizations of the quenched disorder, allows
us to compute exponentially small probabilities (rate functions) over different
classes of random graphs. It is illustrated with two combinatorial optimization
problems, the vertex-cover and coloring problems, for which the presence of
replica symmetry breaking phases is taken into account. Applications include
the analysis of models on adaptive graph structures.Comment: 18 pages, 7 figure
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