Heterogeneous Air Defense Battery Location: A Game Theoretic Approach

The Unites States and its allies confront a persistent and evolving threat from missile attacks as nations around the world continue to invest and advance their current capabilities. Within the air defense context of a missile-and-interceptor engagement, a challenge for the defender is that surface to air interceptor missile batteries often must be located to protect high-value targets dispersed over a vast area, subject to an attacker observing the disposition of batteries prior to developing and implementing an attack plan. To model this scenario, we formulate a two-player, three-stage, perfect information, sequential move, zero-sum game that accounts for, respectively, a defender\u27s location of batteries, an attacker\u27s launch of missiles against targets, and a defender\u27s assignment of interceptors to incoming missiles. The resulting trilevel math programming formulation cannot be solved via direct optimization and it is not suitable to solve via full enumeration for realistically-sized instances. We instead utilize the game tree search technique Double Oracle, within which we embed alternative heuristics to solve an important subproblem for the attacker. We test and compare these solution methods to solve a designed set of 26 instances of parametric variation, from which we derive insights regarding the nature of the underlying problem. Whereas full enumeration required up to 8.6 hours to solve the largest instance considered, our superlative implementation of Double Oracle terminates in a maximum of 3.39 seconds over the set of instances, with an average termination time of less than one second. Double Oracle also properly identifies the optimal SPNE strategies in 75% of our test instances and, regarding those instances for which Double Oracle failed, we note that the relative deviation is less than 2.5% from optimal, on average, yielding promise as a solution method to solve realistically-sized instances

Deployment Policies to Reliably Maintain and Maximize Expected Coverage in a Wireless Sensor Network

The long-term operation of a wireless sensor network (WSN) requires the deployment of new sensors over time to restore any loss in network coverage and communication ability resulting from sensor failures. Over the course of several deployment actions it is important to consider the cost of maintaining the WSN in addition to any desired performance measures such as coverage, connectivity, or reliability. The resulting problem formulation is approached first through a time-based deployment model in which the network is restored to a fixed size at periodic time intervals. The network destruction spectrum (D-spectrum) has been introduced to estimate reliability and is more commonly applied to a static network, rather than a dynamic network where new sensors are deployed over time. We discuss how the D-spectrum can be incorporated to estimate reliability of a time-based deployment policy and the features that allow a wide range of deployment policies to be evaluated in an efficient manner. We next focus on a myopic condition-based deployment model where the network is observed at periodic time intervals and a fixed budget is available to deploy new sensors with each observation. With a limited budget available the model must address the complexity present in a dynamic network size in addition to a dynamic network topology, and the dependence of network reliability on the deployment action. We discuss how the D-spectrum can be applied to the myopic condition-based deployment problem, illustrating the value of the D-spectrum in a variety of maintenance settings beyond the traditional static network reliability problem. From the insight of the time-based and myopic condition-based deployment models, we present a Markov decision process (MDP) model for the condition-based deployment problem that captures the benefit of an action beyond the current time period. Methodology related to approximate dynamic programming (ADP) and approximate value iteration algorithms is presented to search for high quality deployment policies. In addition to the time-based and myopic condition-based deployment models, the MDP model is one of the few addressing the repeated deployment of new sensors as well as an emphasis on network reliability. For each model we discuss the relevant problem formulation, methodology to estimate network reliability, and demonstrate the performance in a range of test instances, comparing to alternative policies or models as appropriate. We conclude with a stochastic optimization model focused on a slightly different objective to maximize expected coverage with uncertainty in where a sensor lands in the network. We discuss a heuristic solution method that seeks to determine an optimal deployment of sensors, present results for a wide range of network sizes and explore the impact of sensor failures on both the model formulation and resulting deployment policy

The dark and luminous structure of early-type galaxies : observational dynamics and stellar populations

Lenticular and elliptical galaxies, collectively referred to as "early-type galaxies" (ETGs), are commonly thought to represent the end-points of galaxy evolution. Lying in the red sequence of galaxies, these objects are defined by their mostly old stellar populations and by their "red and dead" appearance in optical observations. Much progress in understanding these objects has been made with integral-field spectroscopy in recent years, with results repeatedly pointing to a link between early-type galaxies and high-redshift spiral galaxies. However, the exact nature of this link remains unclear, with a wide variety of evolution scenarios likely required to fully explain the range of observed early-type galaxy properties. In my study, I analysed observations of twelve early-type galaxies taken with the Mitchell Integral-Field Spectrograph at McDonald Observatory, Texas. These galaxies have previously been found to contain detectable quantities of neutral hydrogen gas, with ten out of the twelve displaying large-scale hydrogen disks. I extracted line-of-sight kinematics of the stellar and ionised gas components of these galaxies, and I used various modelling approaches to constrain their stellar population parameters as well as their three-dimensional mass structure in terms of both dark and visible components. An important feature of this study is the wide field of view of the spectroscopic observations, which reach beyond two half-light radii for almost all of the sample; this remains rare for integral-field unit (IFU) studies of ETGs, and so sets this study apart from most earlier works. The gas-rich nature of the sample is likewise novel. I find all aspects of my analysis to yield a consistent view of these galaxies’ evolution, in which one or more gaseous interaction events served to shape them into their observed forms. I find these galaxies to contain low dark matter fractions on average within the inner half-light radius, and I also find mass modelling to favour near-isothermal total density profiles over much of the sample

Mapping the dark matter halo of early-type galaxy NGC 2974 through orbit-based models with combined stellar and cold gas kinematics

We present an orbit-based method of combining stellar and cold gas kinematics to constrain the dark matter profile of early-type galaxies. We apply this method to early-type galaxy NGC 2974, using Pan-STARRS imaging and SAURON stellar kinematics to model the stellar orbits, and introducing H I kinematics from VLA observation as a tracer of the gravitational potential. The introduction of the cold gas kinematics shows a significant effect on the confidence limits of especially the dark halo properties: we exclude more than 95 per cent of models within the 1σ confidence level of Schwarzschild modelling with only stellar kinematics, and reduce the relative uncertainty of the dark matter fraction significantly to 10 per cent within 5Re. Adopting a generalized Navarro-Frenk-White (NFW) dark matter profile, we measure a shallow cuspy inner slope of 0.6^{+0.2}_{-0.3} when including the cold gas kinematics in our model. We cannot constrain the inner slope with the stellar kinematics alone.PostprintPeer reviewe

Observational constraints on the origin of the elements. VI. Origin and evolution of neutron-capture elements as probed by the Gaia-ESO survey

Most heavy elements beyond the iron peak are synthesized via neutron capture processes. The nature of the astrophysical sites of neutron capture processes is still very unclear. In this work we explore the observational constraints of the chemical abundances of s-process and r-process elements on the sites of neutron-capture processes by applying Galactic chemical evolution (GCE) models to the data from Gaia-ESO large spectroscopic stellar survey. For the r-process, the [Eu/Fe]-[Fe/H] distribution suggests a short delay time of the site that produces Eu. Other independent observations (e.g., NS-NS binaries), however, suggest a significant fraction of long delayed ($>1$Gyr) neutron star mergers (NSM). When assuming NSM as the only r-process sites, these two observational constraints are inconsistent at above 1$\sigma$ level. Including short delayed r-process sites like magneto-rotational supernova can resolve this inconsistency. For the s-process, we find a weak metallicity dependence of the [Ba/Y] ratio, which traces the s-process efficiency. Our GCE model with up-to-date yields of AGB stars qualitatively reproduces this metallicity dependence, but the model predicts a much higher [Ba/Y] ratio compared to the data. This mismatch suggests that the s-process efficiency of low mass AGB stars in the current AGB nucleosynthesis models could be overestimated.Comment: 14 pages, 11 figures, accepted by MNRA

Chemical evolution of local post-starburst galaxies: Implications for the mass-metallicity relation

We use the stellar fossil record to constrain the stellar metallicity evolution and star-formation histories of the post-starburst regions within 45 local post-starburst galaxies from the MaNGA survey. The direct measurement of the regions' stellar metallicity evolution is achieved by a new two-step metallicity model that allows for stellar metallicity to change at the peak of the starburst. We also employ a Gaussian process noise model that accounts for correlated errors introduced by the observational data reduction or inaccuracies in the models. We find that a majority of post-starburst regions (69% at $>1\sigma$ significance) increased in stellar metallicity during the recent starburst, with an average increase of 0.8 dex and a standard deviation of 0.4 dex. A much smaller fraction of PSBs are found to have remained constant (22%) or declined in metallicity (9%, average decrease 0.4 dex, standard deviation 0.3 dex). The pre-burst metallicities of the post-starburst galaxies are in good agreement with the mass-metallicity relation of local star-forming galaxies. These results are consistent with hydrodynamic simulations, which suggest that mergers between gas-rich galaxies are the primary formation mechanism of local PSBs, and rapid metal recycling during the starburst outweighs the impact of dilution by any gas inflows. The final mass-weighted metallicities of the post-starburst galaxies are consistent with the mass-metallicity relation of local passive galaxies. Our results suggest that rapid quenching following a merger-driven starburst is entirely consistent with the observed gap between the stellar mass-metallicity relations of local star-forming and passive galaxies.Comment: 18+4 pages, 8+2 figures, submitted to MNRA

SDSS-IV MaNGA: Radial Gradients in Stellar Population Properties of Early-Type and Late-Type Galaxies

We derive ages, metallicities, and individual element abundances of early- and late-type galaxies (ETGs and LTGs) out to 1.5 R$_e$. We study a large sample of 1900 galaxies spanning $8.6 - 11.3 \log M/M_{\odot}$ in stellar mass, through key absorption features in stacked spectra from the SDSS-IV/MaNGA survey. We use mock galaxy spectra with extended star formation histories to validate our method for LTGs and use corrections to convert the derived ages into luminosity- and mass-weighted quantities. We find flat age and negative metallicity gradients for ETGs and negative age and negative metallicity gradients for LTGs. Age gradients in LTGs steepen with increasing galaxy mass, from $-0.05\pm0.11~\log$ Gyr/R$_e$ for the lowest mass galaxies to $-0.82\pm0.08~\log$ Gyr/R$_e$ for the highest mass ones. This strong gradient-mass relation has a slope of $-0.70\pm0.18$. Comparing local age and metallicity gradients with the velocity dispersion $\sigma$ within galaxies against the global relation with $\sigma$ shows that internal processes regulate metallicity in ETGs but not age, and vice versa for LTGs. We further find that metallicity gradients with respect to local $\sigma$ show a much stronger dependence on galaxy mass than radial metallicity gradients. Both galaxy types display flat [C/Fe] and [Mg/Fe], and negative [Na/Fe] gradients, whereas only LTGs display gradients in [Ca/Fe] and [Ti/Fe]. ETGs have increasingly steep [Na/Fe] gradients with local $\sigma$ reaching $6.50\pm0.78$ dex/$\log$ km/s for the highest masses. [Na/Fe] ratios are correlated with metallicity for both galaxy types across the entire mass range in our sample, providing support for metallicity dependent supernova yields.Comment: 21 pages, 21 figures, 4 tables + Appendi

Chemical evolution of local post-starburst galaxies : implications for the mass-metallicity relation

We use the stellar fossil record to constrain the stellar metallicity evolution and star-formation histories of the post-starburst (PSB) regions within 45 local PSB galaxies from the MaNGA survey. The direct measurement of the regions’ stellar metallicity evolution is achieved by a new two-step metallicity model that allows for stellar metallicity to change at the peak of the starburst. We also employ a Gaussian process noise model that accounts for correlated errors introduced by the observational data reduction or inaccuracies in the models. We find that a majority of PSB regions (69 per cent at >1σ significance) increased in stellar metallicity during the recent starburst, with an average increase of 0.8 dex and a standard deviation of 0.4 dex. A much smaller fraction of PSBs are found to have remained constant (22 per cent) or declined in metallicity (9 per cent, average decrease 0.4 dex, standard deviation 0.3 dex). The pre-burst metallicities of the PSB galaxies are in good agreement with the mass–metallicity (MZ) relation of local star-forming galaxies. These results are consistent with hydrodynamic simulations, which suggest that mergers between gas-rich galaxies are the primary formation mechanism of local PSBs, and rapid metal recycling during the starburst outweighs the impact of dilution by any gas inflows. The final mass-weighted metallicities of the PSB galaxies are consistent with the MZ relation of local passive galaxies. Our results suggest that rapid quenching following a merger-driven starburst is entirely consistent with the observed gap between the stellar mass–metallicity relations of local star-forming and passive galaxies.Peer reviewe

Capturing One of the Human Gut Microbiome's Most Wanted:Reconstructing the Genome of a Novel Butyrate-Producing, Clostridia! Scavenger from Metagenomic Sequence Data

The role of the microbiome in health and disease is attracting great attention, yet we still know little about some of the most prevalent microorganisms inside our bodies. Several years ago, Human Microbiome Project (HMP) researchers generated a list of “most wanted” taxa: bacteria both prevalent among healthy volunteers and distantly related to any sequenced organisms. Unfortunately, the challenge of assembling high-quality genomes from a tangle of metagenomic reads has slowed progress in learning about these uncultured bacteria. Here, we describe how recent advances in sequencing and analysis allowed us to assemble “most wanted” genomes from metagenomic data collected from four stool samples. Using a combination of both de novo and guided assembly methods, we assembled and binned over 100 genomes from an initial data set of over 1,300 Gbp. One of these genome bins, which met HMP’s criteria for a “most wanted” taxa, contained three essentially complete genomes belonging to a previously uncultivated species. This species is most closely related to Eubacterium desmolans and the clostridial cluster IV/Clostridium leptum subgroup species Butyricicoccus pullicaecorum (71–76% average nucleotide identity). Gene function analysis indicates that the species is an obligate anaerobe, forms spores, and produces the anti-inflammatory short-chain fatty acids acetate and butyrate. It also appears to take up metabolically costly molecules such as cobalamin, methionine, and branch-chained amino acids from the environment, and to lack virulence genes. Thus, the evidence is consistent with a secondary degrader that occupies a host-dependent, nutrient-scavenging niche within the gut; its ability to produce butyrate, which is thought to play an anti-inflammatory role, makes it intriguing for the study of diseases such as colon cancer and inflammatory bowel disease. In conclusion, we have assembled essentially complete genomes from stool metagenomic data, yielding valuable information about uncultured organisms’ metabolic and ecologic niches, factors that may be required to successfully culture these bacteria, and their role in maintaining health and causing disease