R&D Outsourcing Contract with Information Leakage

This paper studies an R&D outsourcing contract between a firm and a contractor, considereing the possibility that in the interim stage, the contractor might sell the innovation to the rival firm. Our result points out that due to the competition in the interim stage, the reward needed to prevent leakage will be pushed up to the extent that a profitable leakage free contract does not exist. This result will also apply to cases considering revenue-sharing schemes and a disclosure punishment for commercial theft. Then, we demonstrate that in a competitive mechanism where the R&D firm hires two contractors together with a relative performance scheme, the disclosure punishment might help and there exists a perfect Bayesian Nash equilibrium where the probability of information leakage is lower and the equilibrium reward is also cheaper than hiring one contractor.R&D outsourcing, Contract, Information leakage, Collusion, Multiple agents

A Neural Network Subgrid Model of the Early Stages of Planet Formation

Planet formation is a multi-scale process in which the coagulation of $\mathrm{\mu m}$-sized dust grains in protoplanetary disks is strongly influenced by the hydrodynamic processes on scales of astronomical units ($\approx 1.5\times 10^8 \,\mathrm{km}$). Studies are therefore dependent on subgrid models to emulate the micro physics of dust coagulation on top of a large scale hydrodynamic simulation. Numerical simulations which include the relevant physical effects are complex and computationally expensive. Here, we present a fast and accurate learned effective model for dust coagulation, trained on data from high resolution numerical coagulation simulations. Our model captures details of the dust coagulation process that were so far not tractable with other dust coagulation prescriptions with similar computational efficiency.Comment: 6 pages, 4 figures, accepted at the Machine Learning and the Physical Sciences workshop, NeurIPS 202

MApping the Most Massive Overdensities Through Hydrogen (MAMMOTH) I: Methodology

Modern cosmology predicts that a galaxy overdensity is associated to a large reservoir of the intergalactic gas, which can be traced by the Ly$\alpha$ forest absorption. We have undertaken a systematic study of the relation between Coherently Strong intergalactic Ly$\alpha$ Absorption systems (CoSLAs), which have highest optical depth ($\tau$) in $\tau$ distribution, and mass overdensities on the scales of $\sim$ 10 - 20 $h^{-1}$ comoving Mpc. On such large scales, our cosmological simulations show a strong correlation between the effective optical depth ($\tau_{\rm{eff}}$) of the CoSLAs and the 3-D mass overdensities. In moderate signal-to-noise spectra, however, the profiles of CoSLAs can be confused with high column density absorbers. For $z>2.6$, where the corresponding Ly$\beta$ is redshifted to the optical, we have developed the technique to differentiate between these two alternatives. We have applied this technique to SDSS-III quasar survey at $z = 2.6$ - 3.3, and we present a sample of five CoSLA candidates with $\tau_{\rm{eff}}$ on 15 $h^{-1}$ Mpc greater than $4.5\times$ the mean optical depth. At lower redshifts of $z < 2.6$, where the background quasar density is higher, the overdensity can be traced by intergalactic absorption groups using multiple sight lines. Our overdensity searches fully utilize the current and next generation of Ly$\alpha$ forest surveys which cover a survey volume of $> (1\ h^{-1}$ Gpc)$^3$. In addition, systems traced by CoSLAs will build a uniform sample of the most massive overdensities at $z > 2$ to constrain the models of structure formation, and offer a unique laboratory to study the interactions between galaxy overdensities and the intergalactic medium.Comment: 24 pages, 30 figures, 8 tables, submitted to the Astrophysical Journa

Detection of Baryon Acoustic Oscillation Features in the Large-Scale 3-Point Correlation Function of SDSS BOSS DR12 CMASS Galaxies

We present the large-scale 3-point correlation function (3PCF) of the SDSS DR12 CMASS sample of $777,202$ Luminous Red Galaxies, the largest-ever sample used for a 3PCF or bispectrum measurement. We make the first high-significance ($4.5\sigma$) detection of Baryon Acoustic Oscillations (BAO) in the 3PCF. Using these acoustic features in the 3PCF as a standard ruler, we measure the distance to $z=0.57$ to $1.7\%$ precision (statistical plus systematic). We find $D_{\rm V}= 2024\pm29\;{\rm Mpc\;(stat)}\pm20\;{\rm Mpc\;(sys)}$ for our fiducial cosmology (consistent with Planck 2015) and bias model. This measurement extends the use of the BAO technique from the 2-point correlation function (2PCF) and power spectrum to the 3PCF and opens an avenue for deriving additional cosmological distance information from future large-scale structure redshift surveys such as DESI. Our measured distance scale from the 3PCF is fairly independent from that derived from the pre-reconstruction 2PCF and is equivalent to increasing the length of BOSS by roughly 10\%; reconstruction appears to lower the independence of the distance measurements. Fitting a model including tidal tensor bias yields a moderate significance ($2.6\sigma)$ detection of this bias with a value in agreement with the prediction from local Lagrangian biasing.Comment: 15 pages, 7 figures, submitted MNRA

Cluster Ellipticities as a Cosmological Probe

We investigate the dependence of ellipticities of clusters of galaxies on cosmological parameters using large-scale cosmological simulations. We determine cluster ellipticities out to redshift unity for LCDM models with different mean densities $\Omega_m$ and amplitudes of mass fluctuation $\sigma_{8,0}$. The mean ellipticity increases monotonically with redshift for all models. Larger values of $\sigma_{8,0}$, i.e., earlier cluster formation time, produce lower ellipticities. The dependence of ellipticity on $\Omega_m$ is relatively weak in the range $0.2 \leq \Omega_m \leq 0.5$ for high mass clusters. The mean ellipticity $\bar{e}(z)$ decreases linearly with the amplitude of fluctuations at the cluster redshift $z$, nearly independent of $\Omega_m$; on average, older clusters are more relaxed and are thus less elliptical. The distribution of ellipticities about the mean is approximated by a Gaussian, allowing a simple characterization of the evolution of ellipticity with redshift as a function of cosmological parameters. At $z=0$, the mean ellipticity of high mass clusters is approximated by $\bar{e}(z=0) = 0.248-0.069 \sigma_{8,0} + 0.013 \Omega_{m,0}$. This relation opens up the possibility that, when compared with future observations of large cluster samples, the mean cluster ellipticity and its evolution could be used as a new, independent tool to constrain cosmological parameters, especially the amplitude of mass fluctuations, $\sigma_{8,0}$.Comment: 16 pages, 4 figure