A new equilibrium torus solution and GRMHD initial conditions

General relativistic magnetohydrodynamic (GRMHD) simulations are providing influential models for black hole spin measurements, gamma ray bursts, and supermassive black hole feedback. Many of these simulations use the same initial condition: a rotating torus of fluid in hydrostatic equilibrium. A persistent concern is that simulation results sometimes depend on arbitrary features of the initial torus. For example, the Bernoulli parameter (which is related to outflows), appears to be controlled by the Bernoulli parameter of the initial torus. In this paper, we give a new equilibrium torus solution and describe two applications for the future. First, it can be used as a more physical initial condition for GRMHD simulations than earlier torus solutions. Second, it can be used in conjunction with earlier torus solutions to isolate the simulation results that depend on initial conditions. We assume axisymmetry, an ideal gas equation of state, constant entropy, and ignore self-gravity. We fix an angular momentum distribution and solve the relativistic Euler equations in the Kerr metric. The Bernoulli parameter, rotation rate, and geometrical thickness of the torus can be adjusted independently. Our torus tends to be more bound and have a larger radial extent than earlier torus solutions. While this paper was in preparation, several GRMHD simulations appeared based on our equilibrium torus. We believe it will continue to provide a more realistic starting point for future simulations.Comment: 8 pages, 4 figures, A&A accepte

Why States Save: Using Evidence to Inform How Large Rainy Day Funds Should Grow

As revenue and spending pressures shift along with the booms and busts of the economy, states stand to benefit from the additional flexibility provided by robust rainy day funds to smooth over unexpected bumps in the road. But absent a clear purpose for saving, some states also find it extremely difficult to set a meaningful savings target, which can confound their efforts to manage the budgetary ups and downs of economic activity.This report examines how state policymakers should design their funds to help inform an optimal savings target. It analyzes existing guidelines -- set in statutory or constitutional language -- around the management of rainy day funds and offers key questions to consider while crafting such guidelines

Characterizing the Communication Requirements of GNN Accelerators: A Model-Based Approach

Relational data present in real world graph representations demands for tools capable to study it accurately. In this regard Graph Neural Network (GNN) is a powerful tool, wherein various models for it have also been developed over the past decade. Recently, there has been a significant push towards creating accelerators that speed up the inference and training process of GNNs. These accelerators, however, do not delve into the impact of their dataflows on the overall data movement and, hence, on the communication requirements. In this paper, we formulate analytical models that capture the amount of data movement in the most recent GNN accelerator frameworks. Specifically, the proposed models capture the dataflows and hardware setup of these accelerator designs and expose their scalability characteristics for a set of hardware, GNN model and input graph parameters. Additionally, the proposed approach provides means for the comparative analysis of the vastly different GNN accelerators.Comment: ISCAS 202

Contextual Search in the Presence of Irrational Agents

We study contextual search, a generalization of binary search in higher dimensions, which captures settings such as feature-based dynamic pricing. Standard game-theoretic formulations of this problem assume that agents act in accordance with a specific behavioral model. In practice, however, some agents may not prescribe to the dominant behavioral model or may act in ways that are seemingly arbitrarily irrational. Existing algorithms heavily depend on the behavioral model being (approximately) accurate for all agents and have poor performance in the presence of even a few such arbitrarily irrational agents. We initiate the study of contextual search when some of the agents can behave in ways inconsistent with the underlying behavioral model. In particular, we provide two algorithms, one built on robustifying multidimensional binary search methods and one on translating the setting to a proxy setting appropriate for gradient descent. Our techniques draw inspiration from learning theory, game theory, high-dimensional geometry, and convex analysis.Comment: Compared to the first version titled "Corrupted Multidimensional Binary Search: Learning in the Presence of Irrational Agents", this version provides a broader scope of behavioral models of irrationality, specifies how the results apply to different loss functions, and discusses the power and limitations of additional algorithmic approache

GRMHD simulations of magnetized advection-dominated accretion on a non-spinning black hole: role of outflows

We present results from two long-duration GRMHD simulations of advection-dominated accretion around a non-spinning black hole. The first simulation was designed to avoid significant accumulation of magnetic flux around the black hole. This simulation was run for a time of 200,000GM/c^3 and achieved inflow equilibrium out to a radius \sim90GM/c^2. Even at this relatively large radius, the mass outflow rate \dot{M}_{out} is found to be only 60% of the net mass inflow rate \dot{M}_{BH} into the black hole. The second simulation was designed to achieve substantial magnetic flux accumulation around the black hole in a magnetically arrested disc. This simulation was run for a shorter time of 100,000GM/c^3. Nevertheless, because the mean radial velocity was several times larger than in the first simulation, it reached inflow equilibrium out to a radius \sim170GM/c^2. Here, \dot{M}_{out} becomes equal to \dot{M}_{BH} at r\sim 160GM/c^2. Since the mass outflow rates in the two simulations do not show robust convergence with time, it is likely that the true outflow rates are lower than our estimates. The effect of black hole spin on mass outflow remains to be explored. Neither simulation shows strong evidence for convection, though a complete analysis including the effect of magnetic fields is left for the future.Astronom