491,573 research outputs found
: Random Walk Diffusion meets Hashing for Scalable Graph Embeddings
Learning node representations is a crucial task with a plethora of
interdisciplinary applications. Nevertheless, as the size of the networks
increases, most widely used models face computational challenges to scale to
large networks. While there is a recent effort towards designing algorithms
that solely deal with scalability issues, most of them behave poorly in terms
of accuracy on downstream tasks. In this paper, we aim at studying models that
balance the trade-off between efficiency and accuracy. In particular, we
propose , a scalable embedding model that
computes binary node representations.
exploits random walk diffusion probabilities via stable random projection
hashing, towards efficiently computing embeddings in the Hamming space. Our
extensive experimental evaluation on various graphs has demonstrated that the
proposed model achieves a good balance between accuracy and efficiency compared
to well-known baseline models on two downstream tasks
Clustering in the Phase Space of Dark Matter Haloes. II. Stable Clustering and Dark Matter Annihilation
We present a model for the structure of the particle phase space average
density () in galactic haloes, introduced recently as a novel measure
of the clustering of dark matter. Our model is based on the stable clustering
hypothesis in phase space, the spherical collapse model, and tidal disruption
of substructures, which is calibrated against the Aquarius simulations. Using
this model, we can predict the behaviour of in the numerically
unresolved regime, down to the decoupling mass limit of generic WIMP models.
This prediction can be used to estimate signals sensitive to the small scale
structure of dark matter. For example, the dark matter annihilation rate can be
estimated for arbitrary velocity-dependent cross sections in a convenient way
using a limit of to zero separation in physical space. We illustrate
our method by computing the global and local subhalo annihilation boost to that
of the smooth dark matter distribution in a Milky-Way-size halo. Two cases are
considered, one where the cross section is velocity independent and one that
approximates Sommerfeld-enhanced models. We find that the global boost is
, which is at the low end of current estimates (weakening
expectations of large extragalactic signals), while the boost at the solar
radius is below the percent level. We make our code to compute
publicly available, which can be used to estimate various observables that
probe the nanostructure of dark matter haloes.Comment: 12 pages, 7 figures, version published in MNRAS (minor corrections),
publicly available code in IDL at http://spaces.perimeterinstitute.ca/p2sad
An efficient and numerically stable method for computing bounds for the interval availability distribution
This paper is concerned with the computation of the interval availability (proportion of time in a time interval in which the system is up) distribution of a fault-tolerant system modeled by a finite (homogeneous) continuous-time Markov chain (CTMC). General-purpose methods for performing that computation tend to be very expensive when the CTMC and the time interval are large. Based on a previously available method
(regenerative transformation) for computing the interval availability complementary distribution, we develop a method called bounding regenerative transformation for the computation of bounds for that measure. Similar to regenerative transformation, bounding regenerative transformation requires the selection of a regenerative state. The method is targeted at a certain class of models, including both exact and bounding failure/repair models of fault-tolerant systems with increasing structure function, with exponential failure and repair time distributions and repair in every state with failed components having failure rates much smaller than repair rates (F/R models), with a “natural” selection for the regenerative state. The method is numerically stable and computes the bounds with well-controlled error. For models in the targeted class and the natural selection for the regenerative state, computational cost should be traded off with bounds tightness through a control parameter. For large models in the class, the version of the method that should have the smallest computational cost should have small computational cost relative to the model size if the value above which the interval availability
has to be guaranteed to be is close to 1. In addition, under additional conditions satisfied by F/R models, the bounds obtained with the natural selection for the regenerative state by the version that should have the smallest computational cost seem to be tight for all time intervals or not small time intervals, depending on whether the initial probability distribution of the CTMC is concentrated in the regenerative state or not.Postprint (published version
Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators
We present an estimator-based control design procedure for flow control,
using reduced-order models of the governing equations, linearized about a
possibly unstable steady state. The reduced models are obtained using an
approximate balanced truncation method that retains the most controllable and
observable modes of the system. The original method is valid only for stable
linear systems, and we present an extension to unstable linear systems. The
dynamics on the unstable subspace are represented by projecting the original
equations onto the global unstable eigenmodes, assumed to be small in number. A
snapshot-based algorithm is developed, using approximate balanced truncation,
for obtaining a reduced-order model of the dynamics on the stable subspace. The
proposed algorithm is used to study feedback control of 2-D flow over a flat
plate at a low Reynolds number and at large angles of attack, where the natural
flow is vortex shedding, though there also exists an unstable steady state. For
control design, we derive reduced-order models valid in the neighborhood of
this unstable steady state. The actuation is modeled as a localized body force
near the leading edge of the flat plate, and the sensors are two velocity
measurements in the near-wake of the plate. A reduced-order Kalman filter is
developed based on these models and is shown to accurately reconstruct the flow
field from the sensor measurements, and the resulting estimator-based control
is shown to stabilize the unstable steady state. For small perturbations of the
steady state, the model accurately predicts the response of the full
simulation. Furthermore, the resulting controller is even able to suppress the
stable periodic vortex shedding, where the nonlinear effects are strong, thus
implying a large domain of attraction of the stabilized steady state.Comment: 36 pages, 17 figure
Numerical simulation of individual wells in a field simulation model
Conventional numerical simulation of hydrocarbon reservoirs is inadequate for the prediction of bottom-hole pressures at production wells. This problem can be overcome by using a special mathematical model which combines individual well simulation with reservoir simulation. Severe computational instability is commonly encountered in the radial models due to the relatively small grid-blocks and high fluid velocities in the vicinity of the well bore. This instability is found to be more pronounced during depletion of the reservoir when the pressure near the well bore is below bubble-point pressure. A new technique is introduced here for saturation calculations in the critical region near the well. This technique is found to be stable for computing saturations in the small inner elements of the radial grid. Stability is maintained even for the simulation of reservoir behavior within a few inches of the producing sand face.
The mathematical model developed in this study was used to predict performance of a hypothetical oil field, and these predictions were com- , pared to the performance predicted by an areal model. It is suggested that this type of model be used for reservoirs where pressure drawdown at producing wells is large, and bottom-hole pressure is less than bubble-point pressure --Abstract, pages ii-iii
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