491,573 research outputs found

    NodeSig{\rm N{\small ode}S{\small ig}}: Random Walk Diffusion meets Hashing for Scalable Graph Embeddings

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    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 NodeSig{\rm N{\small ode}S{\small ig}}, a scalable embedding model that computes binary node representations. NodeSig{\rm N{\small ode}S{\small ig}} 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

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    We present a model for the structure of the particle phase space average density (P2SADP^2SAD) 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 P2SADP^2SAD 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 P2SADP^2SAD 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 1030\sim10-30, 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 P2SADP^2SAD 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

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    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

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    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

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    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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