275,098 research outputs found
Taming a non-convex landscape with dynamical long-range order: memcomputing Ising benchmarks
Recent work on quantum annealing has emphasized the role of collective
behavior in solving optimization problems. By enabling transitions of clusters
of variables, such solvers are able to navigate their state space and locate
solutions more efficiently despite having only local connections between
elements. However, collective behavior is not exclusive to quantum annealers,
and classical solvers that display collective dynamics should also possess an
advantage in navigating a non-convex landscape. Here, we give evidence that a
benchmark derived from quantum annealing studies is solvable in polynomial time
using digital memcomputing machines, which utilize a collection of dynamical
components with memory to represent the structure of the underlying
optimization problem. To illustrate the role of memory and clarify the
structure of these solvers we propose a simple model of these machines that
demonstrates the emergence of long-range order. This model, when applied to
finding the ground state of the Ising frustrated-loop benchmarks, undergoes a
transient phase of avalanches which can span the entire lattice and
demonstrates a connection between long-range behavior and their probability of
success. These results establish the advantages of computational approaches
based on collective dynamics of continuous dynamical systems
Monte Carlo algorithms are very effective in finding the largest independent set in sparse random graphs
The effectiveness of stochastic algorithms based on Monte Carlo dynamics in
solving hard optimization problems is mostly unknown. Beyond the basic
statement that at a dynamical phase transition the ergodicity breaks and a
Monte Carlo dynamics cannot sample correctly the probability distribution in
times linear in the system size, there are almost no predictions nor intuitions
on the behavior of this class of stochastic dynamics. The situation is
particularly intricate because, when using a Monte Carlo based algorithm as an
optimization algorithm, one is usually interested in the out of equilibrium
behavior which is very hard to analyse. Here we focus on the use of Parallel
Tempering in the search for the largest independent set in a sparse random
graph, showing that it can find solutions well beyond the dynamical threshold.
Comparison with state-of-the-art message passing algorithms reveals that
parallel tempering is definitely the algorithm performing best, although a
theory explaining its behavior is still lacking.Comment: 14 pages, 12 figure
On the Properties of Energy Stable Flux Reconstruction Schemes for Implicit Large Eddy Simulation
We begin by investigating the stability, order of accuracy, and dispersion and dissipation characteristics of the extended range of energy stable flux reconstruction (E-ESFR) schemes in the context of implicit large eddy simulation (ILES). We proceed to demonstrate that subsets of the E-ESFR schemes are more stable than collocation nodal discontinuous Galerkin methods recovered with the flux reconstruction approach (FRDG) for marginally-resolved ILES simulations of the Taylor-Green vortex. These schemes are shown to have reduced dissipation and dispersion errors relative to FRDG schemes of the same polynomial degree and, simultaneously, have increased CourantFriedrichs-Lewy (CFL) limits. Finally, we simulate turbulent flow over an SD7003 aerofoil using two of the most stable E-ESFR schemes identified by the aforementioned Taylor-Green vortex experiments. Results demonstrate that subsets of E-ESFR schemes appear more stable than the commonly used FRDG method, have increased CFL limits, and are suitable for ILES of complex turbulent flows on unstructured grids
Modified Gravity Away from a CDM Background
Within the effective field theory approach to cosmic acceleration, the
background expansion can be specified separately from the gravitational
modifications. We explore the impact of modified gravity in a background
different from a cosmological constant plus cold dark matter (CDM) on
the stability and cosmological observables, including covariance between
gravity and expansion parameters. In No Slip Gravity the more general
background allows more gravitational freedom, including both positive and
negative Planck mass running. We examine the effects on cosmic structure
growth, as well as showing that a viable positive integrated Sachs-Wolfe effect
crosscorrelation easily arises from this modified gravity theory. Using current
data we constrain parameters with a Monte Carlo analysis, finding a maximum
running . We provide the modified {\tt hi\_class} code
publicly on GitHub, now enabling computation and inclusion of the redshift
space distortion observable as well as the No Slip Gravity
modifications.Comment: 14 pages, 13 figures. Matches published version in JCAP, LCDM
discussion adde
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Surface constraints on the depth of the Atlantic meridional overturning circulation: Southern Ocean versus North Atlantic
Paleoclimate proxy evidence suggests that the Atlantic meridional overturning circulation (AMOC) was about 1000 m shallower at the Last Glacial Maximum (LGM) compared to the present. Yet it remains unresolved what caused this glacial shoaling of the AMOC, and many climate models instead simulate a deeper AMOC under LGM forcing. While some studies suggest that Southern Ocean surface buoyancy forcing controls the AMOC depth, others have suggested alternatively that North Atlantic surface forcing or interior diabatic mixing plays the dominant role. To investigate the key processes that set the AMOC depth, here we carry out a number of MITgcm ocean-only simulations with surface forcing fields specified from the simulation results of three coupled climate models that span much of the range of glacial AMOC depth changes in phase 3 of the Paleoclimate Model Intercomparison Project (PMIP3). We find that the MITgcm simulations successfully reproduce the changes in AMOC depth between glacial and modern conditions simulated in these three PMIP3 models. By varying the restoring time scale in the surface forcing, we show that the AMOC depth is more strongly constrained by the surface density field than the surface buoyancy flux field. Based on these results, we propose a mechanism by which the surface density fields in the high latitudes of both hemispheres are connected to the AMOC depth. We illustrate the mechanism using MITgcm simulations with idealized surface forcing perturbations as well as an idealized conceptual geometric model. These results suggest that the AMOC depth is largely determined by the surface density fields in both the North Atlantic and the Southern Ocean
The People\u27s Republic of China\u27s Potential Growth Rate: The Long-Run Constraints
We estimate the People’s Republic of China’s (PRC’s) potential growth rate in 2012 at 8.7% and at 9.2% for the average of 2008–2012, about the same as the average actual growth rate for this period. This rate is the natural growth rate, that is, the rate consistent with a constant unemployment rate and stable inflation. The PRC’s natural growth rate displays a downward trend since 2006, when it peaked at 11.1%. Probably the Great Recession has been an important factor, although we argue that there are other factors. We show that the PRC’s potential growth rate is not demand constrained, in particular by the balance of payments. The PRC’s potential growth rate is determined by the supply side of the economy, in particular by: (i) changes in the structure of the economy, in particular in the share of industrial employment; (ii) the working-age population; (iii) the share of net exports in gross domestic product (GDP); (iv) export growth; (v) the share of foreign direct investment (FDI) in GDP; and (vi) human capital accumulation
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