Instabilities in multi-asset and multi-agent market impact games

We consider the general problem of a set of agents trading a portfolio of assets in the presence of transient price impact and additional quadratic transaction costs and we study, with analytical and numerical methods, the resulting Nash equilibria. Extending significantly the framework of Schied and Zhang (2019) and Luo and Schied (2020), who considered the single asset case, we prove the existence and uniqueness of the corresponding Nash equilibria for the related mean-variance optimization problem. We then focus our attention on the conditions on the model parameters making the trading profile of the agents at equilibrium, and as a consequence the price trajectory, wildly oscillating and the market unstable. While Schied and Zhang (2019) and Luo and Schied (2020) highlighted the importance of the value of transaction cost in determining the transition between a stable and an unstable phase, we show that also the scaling of market impact with the number of agents J and the number of assets M determines the asymptotic stability (in J and M) of markets

Extended main sequence turnoff as a common feature of Milky Way open clusters

We present photometric analysis of twelve Galactic open clusters and show that the same multiple-population phenomenon observed in Magellanic Clouds (MCs) is present in nearby open clusters. Nearly all the clusters younger than $\sim$2.5 Gyr of both MCs exhibit extended main-sequence turnoffs (eMSTOs) and all the cluster younger than $\sim$700 Myr show broadened/split main sequences (MSs). High-resolution spectroscopy has revealed that these clusters host stars with a large spread in the observed projected rotations. In addition to rotation, internal age variation is indicated as a possible responsible for the eMSTOs, making these systems the possible young counterparts of globular clusters with multiple populations. Recent work has shown that the eMSTO+broadened MSs are not a peculiarity of MCs clusters. Similar photometric features have been discovered in a few Galactic open clusters, challenging the idea that the color-magnitude diagrams (CMDs) of these systems are similar to single isochrones and opening new windows to explore the eMSTO phenomenon. We exploit photometry+proper motions from Gaia DR2 to investigate the CMDs of open clusters younger than $\sim$1.5 Gyr. Our analysis suggests that: (i) twelve open clusters show eMSTOs and/or broadened MSs, that cannot be due neither to field contamination, nor binaries; (ii) split/broadened MSs are observed in clusters younger than $\sim$700 Myr, while older objects display only an eMSTO, similarly to MCs clusters; (iii) the eMSTO, if interpreted as a pure age spread, increases with age, following the relation observed in MCs clusters and demonstrating that rotation is the responsible for this phenomenon.Comment: 17 pages, 42 figures, 1 table, accepted for publication in ApJ (31/10/2018

Four stellar populations and extreme helium variation in the massive outer-halo globular cluster NGC 2419

Recent work revealed that both the helium variation within globular clusters (GCs) and the relative numbers of first and second-generation stars (1G, 2G) depend on the mass of the host cluster. Precise determination of the internal helium variations and of the fraction of 1G stars are crucial constraints to the formation scenarios of multiple populations (MPs). We exploit multi-band Hubble Space Telescope photometry to investigate MPs in NGC 2419, which is one of the most-massive and distant GCs of the Galaxy, almost isolated from its tidal influence. We find that the 1G hosts the ~37% of the analyzed stars, and identified three populations of 2G stars, namely 2GA, 2GB, and 2GC, which comprise the ~20%, ~31% and ~12% of stars, respectively. We compare the observed colors of these four populations with the colors derived from appropriate synthetic spectra to infer the relative helium abundances. We find that 2GA, 2GB, and 2GC stars are enhanced in helium mass fraction by deltaY ~0.01, 0.06, and 0.19 with respectto 1G stars that have primordial helium (Y=0.246). The high He enrichment of 2GC stars is hardly reconcilable with most of the current scenarios for MPs. Furthermore, the relatively larger fraction of 1G stars (~37%) compared to other massive GCs is noticeable. By exploiting literature results, we find that the fractions of 1G stars of GCs with large perigalactic distance are typically higher than in the other GCs with similar masses. This suggests that NGC 2419, similarly to other distant GCs, lost a lower fraction of 1G stars.Comment: 10 pages, 8 figures, submitted to MNRAS January 22n

The Hubble Space Telescope UV Legacy Survey of Galactic Globular Clusters. XIX. A Chemical Tagging of the Multiple Stellar Populations Over the Chromosome Maps

The HST UV Survey of Globular Clusters (GCs) has investigated GCs and their stellar populations. In previous papers of this series we have introduced a pseudo two-color diagram, "chromosome map" (ChM), that maximises the separation between the multiple populations. We have identified two main classes of GCs: Type I (~83% of the objects) and Type II, both hosting two main groups of stars, referred to in this series as first (1G) and second generation (2G). Type II clusters exhibit two or more parallel sequences of 1G and 2G stars in their ChMs. We exploit elemental abundances from literature to assign the chemical composition to the distinct populations as identified on the ChMs of 29 GCs. We find that stars in different regions of the ChM have different composition: 1G stars share the same light-element content as field stars, while 2G stars are enhanced in N, Na and depleted in O. Stars enhanced in Al and depleted in Mg populate the extreme regions of the ChM. We investigate the color spread among 1G stars observed in many GCs, and find no evidence for variations in light elements, whereas either a 0.1 dex Fe spread or a variation in He remain to be verified. In the attempt of analysing the global properties of the multiple populations, we have constructed a universal ChM, which highlights that, though variegate, the phenomenon has some common pattern. The universal ChM reveals a tight connection with Na, for which we have provided an empirical relation. The additional ChM sequences typical of Type II GCs are enhanced in metallicity and, often, in s elements. Omega Cen can be classified as an extreme Type II GC, with a ChM displaying three main streams, each with its own variations in chemical abundances. One of the most noticeable differences is between the lower and upper streams, with the latter (associated with higher He) having higher Fe and lower Li. We publicly release ChMs.Comment: 35 pages, 28 figures, 3 tables. Submitted to MNRA

Mass loss of different stellar populations in Globular Clusters: the case of M4

In a Globular Cluster (GC), the mass loss during the red-giant branch (RGB) phase and the helium content are fundamental ingredients to constrain the horizontal branch (HB) morphology. While many papers have been dedicated to the helium abundance in the different stellar populations, small efforts have been done to disentangle the effects of mass loss and helium content. We exploit the nearby GC NGC6121 (M4), which hosts two well-studied main stellar populations, to infer both helium and RGB mass loss. We combine multi-band Hubble Space Telescope photometry of RGB and main sequence (MS) stars of M4 with synthetic spectra to constrain the relative helium content of its stellar populations. We find that the second generation stars in M4 is enhanced in helium mass fraction by $\rm \Delta Y = 0.013 \pm 0.002$ with respect to the remaining stars that have pristine helium content. We then infer the mass of the HB stars by searching for the best match between the observations and HB populations modelled assuming the helium abundance of each population estimated from the MS. By comparing the masses of stars along the HB, we constrain the mass loss of first- and second-generation stars in M4. We find that the mass lost by the helium enriched population is $\sim 13$% larger than the mass lost by the first generation stars ($\rm \Delta \mu = 0.027 \pm 0.006 \ M_\odot$). We discuss the possibility that this mass loss difference depends on helium abundance, the different formation environment of the two generations, or a combination of both.Comment: 10 pages, 4 figures, 1 table. Accepted for publication in Ap

The Generalized Stochastic Microdosimetric Model: the main formulation

The present work introduces a rigorous stochastic model, named Generalized Stochastic Microdosimetric Model (GSM2), to describe biological damage induced by ionizing radiation. Starting from microdosimetric spectra of energy deposition in tissue, we derive a master equation describing the time evolution of the probability density function of lethal and potentially lethal DNA damage induced by radiation in a cell nucleus. The resulting probability distribution is not required to satisfy any a priori assumption. Furthermore, we generalized the master equation to consider damage induced by a continuous dose delivery. In addition, spatial features and damage movement inside the nucleus have been taken into account. In doing so, we provide a general mathematical setting to fully describe the spatiotemporal damage formation and evolution in a cell nucleus. Finally, we provide numerical solutions of the master equation exploiting Monte Carlo simulations to validate the accuracy of GSM2. Development of GSM2 can lead to improved modeling of radiation damage to both tumor and normal tissues, and thereby impact treatment regimens for better tumor control and reduced normal tissue toxicities

On the role of dust and mass loss in the extended main sequence turnoff of star clusters: the case of NGC 1783

The Color Magnitude Diagram (CMD) morphology of the "extended" main sequence turnoff (eMSTO) and upper main sequence (MS) of the intermediate age ($\lesssim 2$ Gyr) Large Magellanic Cloud Cluster NGC 1783 shows the presence of a small group of UV-dim stars, that, in the ultraviolet Hubble Space Telescope filters, are located at colors on the red side of the typical "fan" shape displayed by the eMSTO. We model the UV-dim stars by assuming that some of the stars which would intrinsically be located on the left side of the eMSTO are obscured by a ring of dust due to grain condensation at the periphery of the excretion disc expelled when they spin at the high rotation rates typical of stars in the Be stage. A reasonably low optical depth at 10$\mu$ is necessary to model the UV-dim group. Introduction of dust in the interpretation of the eMSTO may require a substantial re-evaluation of previous conclusions concerning the role of age and/or rotation spreads in the MC clusters: the entire eMSTO can be populated by dusty stars, and the reddest UV-dim stars simply represents the tail of the distribution with both maximum obscuration and the dust ring seen along the line of sight. The model stars having higher rotational projected velocity ($v \sin$ i) are predicted to be preferentially redder than the slowly-rotating stars. The mass loss responsible for the dust may also cause the non-monotonic distribution of stars in the upper main sequence, with two peaks and gaps showing up in the UV CMD.Comment: 11 pages, 13 figures. This is a pre-copyedited, author-produced PDF of an article (stad851) accepted for publication in MNRAS following peer revie