Linear-Quadratic Mean Field Games Bensoussan, A.; Sung, K. C. J.; Yam, S. C. P. ...
Journal of optimization theory and applications,
05/2016, Letnik:
169, Številka:
2
Journal Article
Recenzirano
We provide a comprehensive study of a general class of linear-quadratic mean field games. We adopt the adjoint equation approach to investigate the unique existence of their equilibrium strategies. ...Due to the linearity of the adjoint equations, the optimal mean field term satisfies a forward–backward ordinary differential equation. For the one-dimensional case, we establish the unique existence of the equilibrium strategy. For a dimension greater than one, by applying the Banach fixed point theorem under a suitable norm, a sufficient condition for the unique existence of the equilibrium strategy is provided, which is independent of the coefficients of controls in the underlying dynamics and is always satisfied whenever the coefficients of the mean field term are vanished, and hence, our theories include the classical linear-quadratic stochastic control problems as special cases. As a by-product, we also establish a neat and instructive sufficient condition, which is apparently absent in the literature and only depends on coefficients, for the unique existence of the solution for a class of nonsymmetric Riccati equations. Numerical examples of nonexistence of the equilibrium strategy will also be illustrated. Finally, a similar approach has been adopted to study the linear-quadratic mean field type stochastic control problems and their comparisons with mean field games.
The final fate of massive stars, and the nature of the compact remnants they leave behind (black holes and neutron stars), are open questions in astrophysics. Many massive stars are stripped of their ...outer hydrogen envelopes as they evolve. Such Wolf-Rayet stars
emit strong and rapidly expanding winds with speeds greater than 1,000 kilometres per second. A fraction of this population is also helium-depleted, with spectra dominated by highly ionized emission lines of carbon and oxygen (types WC/WO). Evidence indicates that the most commonly observed supernova explosions that lack hydrogen and helium (types Ib/Ic) cannot result from massive WC/WO stars
, leading some to suggest that most such stars collapse directly into black holes without a visible supernova explosion
. Here we report observations of SN 2019hgp, beginning about a day after the explosion. Its short rise time and rapid decline place it among an emerging population of rapidly evolving transients
. Spectroscopy reveals a rich set of emission lines indicating that the explosion occurred within a nebula composed of carbon, oxygen and neon. Narrow absorption features show that this material is expanding at high velocities (greater than 1,500 kilometres per second), requiring a compact progenitor. Our observations are consistent with an explosion of a massive WC/WO star, and suggest that massive Wolf-Rayet stars may be the progenitors of some rapidly evolving transients.
Based on high-resolution spectra obtained during gravitational microlensing events we present a detailed elemental abundance analysis of 32 dwarf and subgiant stars in the Galactic bulge. Combined ...with the sample of 26 stars from the previous papers in this series, we now have 58 microlensed bulge dwarfs and subgiants that have been homogeneously analysed. The results from the microlensed bulge dwarf stars in combination with other findings in the literature, in particular the evidence that the bulge has cylindrical rotation, indicate that the Milky Way could be an almost pure disk galaxy. The bulge would then just be a conglomerate of the other Galactic stellar populations, residing together in the central parts of the Galaxy, influenced by the Galactic bar.
The natural course of high-axial myopia is variable and the development of pathologic myopia is not fully understood. Advancements in optical coherence tomography (OCT) technology have revealed ...peculiar intraocular structures in highly myopic eyes and unprecedented pathologies that cause visual impairment. New OCT findings include posterior precortical vitreous pocket and precursor stages of posterior vitreous detachment; peripapillary intrachoroidal cavitation; morphological patterns of scleral inner curvature and dome-shaped macula. Swept source OCT is capable of imaging deeper layers in the posterior pole for investigation of optic nerve pits, stretched and thinned lamina cribrosa, elongated dural attachment at posterior scleral canal, and enlargement of retrobulbar subarachnoid spaces. This has therefore enabled further evaluation of various visual field defects in high myopia and the pathogenesis of glaucomatous optic neuropathy. OCT has many potential clinical uses in managing visual impairing conditions in pathologic myopia. Understanding how retinal nerve fibers are redistributed in axial elongation will allow the development of auto-segmentation software for diagnosis and monitoring progression of glaucoma. OCT is indispensable in the diagnosis of various conditions associated with myopic traction maculopathy and monitoring of post-surgical outcomes. In addition, OCT is commonly used in the multimodal imaging assessment of myopic choroidal neovascularization. Biometry and topography of the retinal layers and choroid will soon be validated for the classification of myopic maculopathy for utilization in epidemiological studies as well as clinical trials.
Highlights • White adipose tissue (WAT), plasma leptin and leptin mRNA in WAT are lastingly reduced after chronic early-life stress (ES). • Brown adipose tissue mass and browning of WAT is increased ...after ES exposure. • Leptin receptor expression is upregulated in the choroid plexus and unaffected in the hippocampus in adulthood after ES. • ES-induced cognitive impairments correlate with reduced adiposity in male mice only. • Exposure to moderate western-style diet results in higher body fat accumulations in offspring with a history of ES.
Massive stars end their short lives in spectacular explosions--supernovae--that synthesize new elements and drive galaxy evolution. Historically, supernovae were discovered mainly through their ...'delayed' optical light (some days after the burst of neutrinos that marks the actual event), preventing observations in the first moments following the explosion. As a result, the progenitors of some supernovae and the events leading up to their violent demise remain intensely debated. Here we report the serendipitous discovery of a supernova at the time of the explosion, marked by an extremely luminous X-ray outburst. We attribute the outburst to the 'break-out' of the supernova shock wave from the progenitor star, and show that the inferred rate of such events agrees with that of all core-collapse supernovae. We predict that future wide-field X-ray surveys will catch each year hundreds of supernovae in the act of exploding.
Because of the development of large-format, wide-field cameras, microlensing surveys are now able to monitor millions of stars with sufficient cadence to detect planets. These new discoveries will ...span the full range of significance levels including planetary signals too small to be distinguished from the noise. At present, we do not understand where the threshold is for detecting planets. MOA-2011-BLG-293Lb is the first planet to be published from the new surveys, and it also has substantial follow-up observations. This planet is robustly detected in survey+follow-up data ( Delta chi super(2) ~ 5400). The planet/host mass ratio is q = (5.3 + or - 0.2) x 10 super(-3). The best-fit projected separation is s = 0.548 + or - 0.005 Einstein radii. However, due to the s left right arrow s super(-1) degeneracy, projected separations of s super(-1) are only marginally disfavored at Delta chi super(2) = 3. A Bayesian estimate of the host mass gives ML = 0.43 super(+0.27) sub(-0.17) M sub(middot in circle), with a sharp upper limit of ML < 1.2 M sub(middot in circle) from upper limits on the lens flux. Hence, the planet mass is mp = 2.4 super(+1.5) sub(-0.9) M sub(Jup), and the physical projected separation is either r sub(perpendicular) Asymptotically = to 1.0 AU or r sub(perpendicular) Asymptotically = to 3.4 AU. We show that survey data alone predict this solution and are able to characterize the planet, but the Delta chi super(2) is much smaller ( Delta chi super(2) ~ 500) than with the follow-up data. The Delta chi super(2) for the survey data alone is smaller than for any other securely detected planet. This event suggests a means to probe the detection threshold, by analyzing a large sample of events like MOA-2011-BLG-293, which have both follow-up data and high-cadence survey data, to provide a guide for the interpretation of pure survey microlensing data.
Based on high-resolution (R approximate to 42 000 to 48 000) and high signal-to-noise (S/N approximate to 50 to 150) spectra obtained with UVES/VLT, we present detailed elemental abundances (O, Na, ...Mg, Al, Si, Ca, Ti, Cr, Fe, Ni, Zn, Y, and Ba) and stellar ages for 12 new microlensed dwarf and subgiant stars in the Galactic bulge. Including previous microlensing events, the sample of homogeneously analysed bulge dwarfs has now grown to 26. The analysis is based on equivalent width measurements and standard 1-D LTE MARCS model stellar atmospheres. We also present NLTE Li abundances based on line synthesis of the Li-7 line at 670.8 nm. The results from the 26 microlensed dwarf and subgiant stars show that the bulge metallicity distribution (MDF) is double-peaked; one peak at Fe/H approximate to -0.6 and one at Fe/H approximate to +0.3, and with a dearth of stars around solar metallicity. This is in contrast to the MDF derived from red giants in Baade's window, which peaks at this exact value. A simple significance test shows that it is extremely unlikely to have such a gap in the microlensed dwarf star MDF if the dwarf stars are drawn from the giant star MDF. To resolve this issue we discuss several possibilities, but we can not settle on a conclusive solution for the observed differences. We further find that the metal-poor bulge dwarf stars are predominantly old with ages greater than 10 Gyr, while the metal-rich bulge dwarf stars show a wide range of ages. The metal-poor bulge sample is very similar to the Galactic thick disk in terms of average metallicity, elemental abundance trends, and stellar ages. Speculatively, the metal-rich bulge population might be the manifestation of the inner thin disk. If so, the two bulge populations could support the recent findings, based on kinematics, that there are no signatures of a classical bulge and that the Milky Way is a pure-disk galaxy. Also, recent claims of a flat IMF in the bulge based on the MDF of giant stars may have to be revised based on the MDF and abundance trends probed by our microlensed dwarf stars.
We analyze the mean rest-frame ultraviolet (UV) spectrum of Type Ia Supernovae (SNe) and its dispersion using high signal-to-noise ratio Keck-I/LRIS-B spectroscopy for a sample of 36 events at ...intermediate redshift (z=0.5) discovered by the Canada-France-Hawaii Telescope Supernova Legacy Survey (SNLS). We introduce a new method for removing host galaxy contamination in our spectra, exploiting the comprehensive photometric coverage of the SNLS SNe and their host galaxies, thereby providing the first quantitative view of the UV spectral properties of a large sample of distant SNe Ia. Although the mean SN Ia spectrum has not evolved significantly over the past 40% of cosmic history, precise evolutionary constraints are limited by the absence of a comparable sample of high-quality local spectra. The mean UV spectrum of our z~=0.5 SNe Ia and its dispersion is tabulated for use in future applications. Within the high-redshift sample, we discover significant UV spectral variations and exclude dust extinction as the primary cause by examining trends with the optical SN color. Although progenitor metallicity may drive some of these trends, the variations we see are much larger than predicted in recent models and do not follow expected patterns. An interesting new result is a variation seen in the wavelength of selected UV features with phase. We also demonstrate systematic differences in the SN Ia spectral features with SN light curve width in both the UV and the optical. We show that these intrinsic variations could represent a statistical limitation in the future use of high-redshift SNe Ia for precision cosmology. We conclude that further detailed studies are needed, both locally and at moderate redshift where the rest-frame UV can be studied precisely, in order that future missions can confidently be planned to fully exploit SNe Ia as cosmological probes.
Long-duration gamma-ray bursts (GRBs) are widely believed to be highly collimated explosions (bipolar conical outflows with half-opening angle theta{approx} 1{sup 0}-10{sup 0}). As a result of this ...beaming factor, the true energy release from a GRB is usually several orders of magnitude smaller than the observed isotropic value. Measuring this opening angle, typically inferred from an achromatic steepening in the afterglow light curve (a 'jet' break), has proven exceedingly difficult in the Swift era. Here, we undertake a study of five of the brightest (in terms of the isotropic prompt gamma-ray energy release, E{sub g}amma{sub ,iso}) GRBs in the Swift era to search for jet breaks and hence constrain the collimation-corrected energy release. We present multi-wavelength (radio through X-ray) observations of GRBs 050820A, 060418, and 080319B, and construct afterglow models to extract the opening angle and beaming-corrected energy release for all three events. Together with results from previous analyses of GRBs 050904 and 070125, we find evidence for an achromatic jet break in all five events, strongly supporting the canonical picture of GRBs as collimated explosions. The most natural explanation for the lack of observed jet breaks from most Swift GRBs is therefore selection effects. However, the opening angles for the events in our sample are larger than would be expected if all GRBs had a canonical energy release of {approx}10{sup 51} erg. The total energy release we measure for the 'hyper-energetic' (E{sub tot} {approx}> 10{sup 52} erg) events in our sample is large enough to start challenging models with a magnetar as the compact central remnant.
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