Anytime Point-Based Approximations for Large POMDPs

The Partially Observable Markov Decision Process has long been recognized as a rich framework for real-world planning and control problems, especially in robotics. However exact solutions in this framework are typically computationally intractable for all but the smallest problems. A well-known technique for speeding up POMDP solving involves performing value backups at specific belief points, rather than over the entire belief simplex. The efficiency of this approach, however, depends greatly on the selection of points. This paper presents a set of novel techniques for selecting informative belief points which work well in practice. The point selection procedure is combined with point-based value backups to form an effective anytime POMDP algorithm called Point-Based Value Iteration (PBVI). The first aim of this paper is to introduce this algorithm and present a theoretical analysis justifying the choice of belief selection technique. The second aim of this paper is to provide a thorough empirical comparison between PBVI and other state-of-the-art POMDP methods, in particular the Perseus algorithm, in an effort to highlight their similarities and differences. Evaluation is performed using both standard POMDP domains and realistic robotic tasks

Equilibrium Predictions in Wholesale Electricity Markets

We review supply function equilibrium models and their predictions on market outcomes in the wholesale electricity auctions. We discuss how observable market characteristics such as capacity constraints, number of power suppliers, load distribution and auction format affect the behavior of suppliers and performance of the market. We specifically focus on the possible market power exerted by pivotal suppliers and the comparison between discriminatory and uniform-price auctions. We also describe capacity investment behavior of electricity producers in the restructured industry.Electricity markets; Supply function equilibrium; Markov perfect equilibrium; electricity auctions; pivotal suppliers; capacity investment.

Electricity Trade Patterns in a Network: Evidence from the Ontario Market

We investigate whether trade has any effect on the price formation process in a specific electricity market, and identify interconnected markets that have higher impacts on prices in that market. In particular, we study Ontario wholesale electricity market and its trade with 12 interconnected markets including New York, Michigan, and Minnesota markets. We find that imports are unambiguously related to prices, while exports are not. Furthermore, imports have a positive and significant relationship with prices. We argue that the results are associated with auction design, production constraints, and technological differences. Out of the 12 studied interties, only three have a significant impact on price, two of which are the largest ones.electricity trade; simultaneous trade; transmission network; electricity prices; nonlinear Granger causality; Ontario, New York, Michigan, Manitoba, Quebec wholesale electricity markets.

Molecule survival in magnetized protostellar disk winds. II. Predicted H2O line profiles versus Herschel/HIFI observations

We investigate whether the broad wings of H2O emission identified with Herschel towards low-mass Class 0 and Class 1 protostars may be consistent with an origin in a dusty MHD disk wind, and the constraints it would set on the underlying disk properties. We present synthetic H2O line profiles predictions for a typical MHD disk wind solution with various values of disk accretion rate, stellar mass, extension of the launching area, and view angle. We compare them in terms of line shapes and intensities with the HIFI profiles observed by the WISH Key Program. We find that a dusty MHD disk wind launched from 0.2--0.6 AU AU to 3--25 AU can reproduce to a remarkable degree the observed shapes and intensities of the broad H2O component, both in the fundamental 557 GHz line and in more excited lines. Such a model also readily reproduces the observed correlation of 557 GHz line luminosity with envelope density, if the infall rate at 1000 AU is 1--3 times the disk accretion rate in the wind ejection region. It is also compatible with the typical disk size and bolometric luminosity in the observed targets. However, the narrower line profiles in Class 1 sources suggest that MHD disk winds in these sources, if present, would have to be slower and/or less water rich than in Class 0 sources. In conclusion, MHD disk winds appear as a valid (though not unique) option to consider for the origin of the broad H2O component in low-mass protostars. ALMA appears ideally suited to further test this model by searching for resolved signatures of the warm and slow wide-angle molecular wind that would be predicted.Comment: accepted for publication in A&

Temporal evolution of magnetic molecular shocks I. Moving grid simulations

We present time-dependent 1D simulations of multifluid magnetic shocks with chemistry resolved down to the mean free path. They are obtained with an adaptive moving grid implemented with an implicit scheme. We examine a broad range of parameters relevant to conditions in dense molecular clouds, with preshock densities between 10^3 and 10^5 cm-3, velocities between 10 and 40 km/s, and three different scalings for the transverse magnetic field: B=0,0.1,1 \mu G \sqrt{n.cm3}. We first use this study to validate the results of Chi\`eze, Pineau des For\^ets & Flower (1998), in particular the long delays necessary to obtain steady C-type shocks, and we provide evolutionary time-scales for a much greater range of parameters. We also present the first time-dependent models of dissociative shocks with a magnetic precursor, including the first models of stationary CJ shocks in molecular conditions. We find that the maximum speed for steady C-type shocks is reached before the occurrence of a sonic point in the neutral fluid, unlike previously thought. As a result, the maximum speed for C-shocks is lower than previously believed. Finally, we find a large amplitude bouncing instability in J-type fronts near the H2 dissociation limit (u ~ 25-30 km/s), driven by H2 dissociation/reformation. At higher speeds, we find an oscillatory behaviour of short period and small amplitude linked to collisional ionisation of H. Both instabilities are suppressed after some time when a magnetic field is present. In a companion paper, we use the present simulations to validate a new semi-analytical construction method for young low-velocity magnetic shocks based on truncated steady-state models.Comment: A&A in pres

Shocks in dense clouds. IV. Effects of grain-grain processing on molecular line emission

Grain-grain processing has been shown to be an indispensable ingredient of shock modelling in high density environments. For densities higher than \sim10^5 cm-3, shattering becomes a self-enhanced process that imposes severe chemical and dynamical consequences on the shock characteristics. Shattering is accompanied by the vaporization of grains, which can directly release SiO to the gas phase. Given that SiO rotational line radiation is used as a major tracer of shocks in dense clouds, it is crucial to understand the influence of vaporization on SiO line emission. We have developed a recipe for implementing the effects of shattering and vaporization into a 2-fluid shock model, resulting in a reduction of computation time by a factor \sim100 compared to a multi-fluid modelling approach. This implementation was combined with an LVG-based modelling of molecular line radiation transport. Using this model we calculated grids of shock models to explore the consequences of different dust-processing scenarios. Grain-grain processing is shown to have a strong influence on C-type shocks for a broad range of magnetic fields: they become hotter and thinner. The reduction in column density of shocked gas lowers the intensity of molecular lines, at the same time as higher peak temperatures increase the intensity of highly excited transitions compared to shocks without grain-grain processing. For OH the net effect is an increase in line intensities, while for CO and H2O it is the contrary. The intensity of H2 emission is decreased in low transitions and increased for highly excited lines. For all molecules, the highly excited lines become sensitive to the value of the magnetic field. Although vaporization increases the intensity of SiO rotational lines, this effect is weakened by the reduced shock width. The release of SiO early in the hot shock changes the excitation characteristics of SiO radiation.Comment: Published in Astronomy and Astrophysics (2013). 26 pages, 16 figures, 14 table

Strategic storage use in a hydro-thermal power system with carbon constraints

Several interconnected power systems worldwide have largely thermal and hydro production along with CO_{2} cap-and-trade (C&T) systems and variable renewable energy sources (VRES). C&T policies increase VRES generation, and socially optimal storage deployment could integrate VRES output. However, hydro reservoirs may be used strategically due to market power. We investigate these distortions and assess measures for their mitigation via a bottom-up equilibrium model of New York and Québec. In particular, we find evidence that hydro producers shift water between seasons to manipulate electricity prices even under a net-hydro production constraint. Alternative regulation covering net imports as well as net-hydro production limits such temporal arbitrage but enables firms with both thermal generation and pumped-hydro storage to exercise spatial arbitrage. We demonstrate that these distortions will be exacerbated under more stringent C&T policies because price-taking thermal producers are less able to respond to price signals

Dense molecular globulettes and the dust arc towards the runaway O star AE Aur (HD 34078)

Some runaway stars are known to display IR arc-like structures around them, resulting from their interaction with surrounding interstellar material. The properties of these features as well as the processes involved in their formation are still poorly understood. We aim at understanding the physical mechanisms that shapes the dust arc observed near the runaway O star AEAur (HD34078). We obtained and analyzed a high spatial resolution map of the CO(1-0) emission that is centered on HD34078, and that combines data from both the IRAM interferometer and 30m single-dish antenna. The line of sight towards HD34078 intersects the outer part of one of the detected globulettes, which accounts for both the properties of diffuse UV light observed in the field and the numerous molecular absorption lines detected in HD34078's spectra, including those from highly excited H2 . Their modeled distance from the star is compatible with the fact that they lie on the 3D paraboloid which fits the arc detected in the 24 {\mu}m Spitzer image. Four other compact CO globulettes are detected in the mapped area. These globulettes have a high density and linewidth, and are strongly pressure-confined or transient. The good spatial correlation between the CO globulettes and the IR arc suggests that they result from the interaction of the radiation and wind emitted by HD 34078 with the ambient gas. However, the details of this interaction remain unclear. A wind mass loss rate significantly larger than the value inferred from UV lines is favored by the large IR arc size, but does not easily explain the low velocity of the CO globulettes. The effect of radiation pressure on dust grains also meets several issues in explaining the observations. Further observational and theoretical work is needed to fully elucidate the processes shaping the gas and dust in bow shocks around runaway O stars. (Abridged)Comment: Accepted for publication in Astronomy & Astrophysic