730 research outputs found
Dynamics of quantum adiabatic evolution algorithm for Number Partitioning
We have developed a general technique to study the dynamics of the quantum
adiabatic evolution algorithm applied to random combinatorial optimization
problems in the asymptotic limit of large problem size . We use as an
example the NP-complete Number Partitioning problem and map the algorithm
dynamics to that of an auxilary quantum spin glass system with the slowly
varying Hamiltonian. We use a Green function method to obtain the adiabatic
eigenstates and the minimum excitation gap, ,
corresponding to the exponential complexity of the algorithm for Number
Partitioning. The key element of the analysis is the conditional energy
distribution computed for the set of all spin configurations generated from a
given (ancestor) configuration by simulteneous fipping of a fixed number of
spins. For the problem in question this distribution is shown to depend on the
ancestor spin configuration only via a certain parameter related to the energy
of the configuration. As the result, the algorithm dynamics can be described in
terms of one-dimenssional quantum diffusion in the energy space. This effect
provides a general limitation on the power of a quantum adiabatic computation
in random optimization problems. Analytical results are in agreement with the
numerical simulation of the algorithm.Comment: 32 pages, 5 figures, 3 Appendices; List of additions compare to v.3:
(i) numerical solution of the stationary Schroedinger equation for the
adiabatic eigenstates and eigenvalues; (ii) connection between the scaling
law of the minimum gap with the problem size and the shape of the
coarse-grained distribution of the adiabatic eigenvalues at the
avoided-crossing poin
Tree decompositions of real-world networks from simulated annealing
Decompositions of networks are useful not only for structural exploration.
They also have implications and use in analysis and computational solution of
processes (such as the Ising model, percolation, SIR model) running on a given
network. Tree and branch decompositions considered here directly represent
network structure as trees for recursive computation of network properties.
Unlike coarse-graining approximations in terms of community structure or
metapopulations, tree decompositions of sufficiently small width allow for
exact results on equilibrium processes. Here we use simulated annealing to find
tree decompositions of narrow width for a set of medium-size empirical
networks. Rather than optimizing tree decompositions directly, we employ a
search space constituted by so-called elimination orders being permutations on
the network's node set. For each in a database of empirical networks with up to
1000 edges, we find a tree decomposition of low width.Comment: 11 pages, 2 figures, 1 tabl
Equation-Free Multiscale Computational Analysis of Individual-Based Epidemic Dynamics on Networks
The surveillance, analysis and ultimately the efficient long-term prediction
and control of epidemic dynamics appear to be one of the major challenges
nowadays. Detailed atomistic mathematical models play an important role towards
this aim. In this work it is shown how one can exploit the Equation Free
approach and optimization methods such as Simulated Annealing to bridge
detailed individual-based epidemic simulation with coarse-grained,
systems-level, analysis. The methodology provides a systematic approach for
analyzing the parametric behavior of complex/ multi-scale epidemic simulators
much more efficiently than simply simulating forward in time. It is shown how
steady state and (if required) time-dependent computations, stability
computations, as well as continuation and numerical bifurcation analysis can be
performed in a straightforward manner. The approach is illustrated through a
simple individual-based epidemic model deploying on a random regular connected
graph. Using the individual-based microscopic simulator as a black box
coarse-grained timestepper and with the aid of Simulated Annealing I compute
the coarse-grained equilibrium bifurcation diagram and analyze the stability of
the stationary states sidestepping the necessity of obtaining explicit closures
at the macroscopic level under a pairwise representation perspective
Dynamics of Co-translational Membrane Protein Integration and Translocation via the Sec Translocon
An important aspect of cellular function is the correct targeting and delivery of newly synthesized proteins. Central to this task is the machinery of the Sec translocon, a transmembrane channel that is involved in both the translocation of nascent proteins across cell membranes and the integration of proteins into the membrane. Considerable experimental and computational effort has focused on the Sec translocon and its role in nascent protein biosynthesis, including the correct folding and expression of integral membrane proteins. However, the use of molecular simulation methods to explore Sec-facilitated protein biosynthesis is hindered by the large system sizes and long (i.e., minute) timescales involved. In this work, we describe the development and application of a coarse-grained simulation approach that addresses these challenges and allows for direct comparison with both in vivo and in vitro experiments. The method reproduces a wide range of experimental observations, providing new insights into the underlying molecular mechanisms, predictions for new experiments, and a strategy for the rational enhancement of membrane protein expression levels
Coarse-grained dynamics of an activity bump in a neural field model
We study a stochastic nonlocal PDE, arising in the context of modelling
spatially distributed neural activity, which is capable of sustaining
stationary and moving spatially-localized ``activity bumps''. This system is
known to undergo a pitchfork bifurcation in bump speed as a parameter (the
strength of adaptation) is changed; yet increasing the noise intensity
effectively slowed the motion of the bump. Here we revisit the system from the
point of view of describing the high-dimensional stochastic dynamics in terms
of the effective dynamics of a single scalar "coarse" variable. We show that
such a reduced description in the form of an effective Langevin equation
characterized by a double-well potential is quantitatively successful. The
effective potential can be extracted using short, appropriately-initialized
bursts of direct simulation. We demonstrate this approach in terms of (a) an
experience-based "intelligent" choice of the coarse observable and (b) an
observable obtained through data-mining direct simulation results, using a
diffusion map approach.Comment: Corrected aknowledgement
Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis
We show how the Equation-Free approach for multi-scale computations can be
exploited to systematically study the dynamics of neural interactions on a
random regular connected graph under a pairwise representation perspective.
Using an individual-based microscopic simulator as a black box coarse-grained
timestepper and with the aid of simulated annealing we compute the
coarse-grained equilibrium bifurcation diagram and analyze the stability of the
stationary states sidestepping the necessity of obtaining explicit closures at
the macroscopic level. We also exploit the scheme to perform a rare-events
analysis by estimating an effective Fokker-Planck describing the evolving
probability density function of the corresponding coarse-grained observables
Quantum Optimization of Fully-Connected Spin Glasses
The Sherrington-Kirkpatrick model with random couplings is programmed
on the D-Wave Two annealer featuring 509 qubits interacting on a Chimera-type
graph. The performance of the optimizer compares and correlates to simulated
annealing. When considering the effect of the static noise, which degrades the
performance of the annealer, one can estimate an improvement on the comparative
scaling of the two methods in favor of the D-Wave machine. The optimal choice
of parameters of the embedding on the Chimera graph is shown to be associated
to the emergence of the spin-glass critical temperature of the embedded
problem.Comment: includes supplemental materia
- …