Revolutionaries and spies: Spy-good and spy-bad graphs

We study a game on a graph $G$ played by $r$ {\it revolutionaries} and $s$ {\it spies}. Initially, revolutionaries and then spies occupy vertices. In each subsequent round, each revolutionary may move to a neighboring vertex or not move, and then each spy has the same option. The revolutionaries win if $m$ of them meet at some vertex having no spy (at the end of a round); the spies win if they can avoid this forever. Let $\sigma(G,m,r)$ denote the minimum number of spies needed to win. To avoid degenerate cases, assume |V(G)|\ge r-m+1\ge\floor{r/m}\ge 1. The easy bounds are then \floor{r/m}\le \sigma(G,m,r)\le r-m+1. We prove that the lower bound is sharp when $G$ has a rooted spanning tree $T$ such that every edge of $G$ not in $T$ joins two vertices having the same parent in $T$. As a consequence, \sigma(G,m,r)\le\gamma(G)\floor{r/m}, where $\gamma(G)$ is the domination number; this bound is nearly sharp when $\gamma(G)\le m$. For the random graph with constant edge-probability $p$, we obtain constants $c$ and $c'$ (depending on $m$ and $p$) such that $\sigma(G,m,r)$ is near the trivial upper bound when $r<c\ln n$ and at most $c'$ times the trivial lower bound when $r>c'\ln n$. For the hypercube $Q_d$ with $d\ge r$, we have $\sigma(G,m,r)=r-m+1$ when $m=2$, and for $m\ge 3$ at least $r-39m$ spies are needed. For complete $k$-partite graphs with partite sets of size at least $2r$, the leading term in $\sigma(G,m,r)$ is approximately $\frac{k}{k-1}\frac{r}{m}$ when $k\ge m$. For $k=2$, we have \sigma(G,2,r)=\bigl\lceil{\frac{\floor{7r/2}-3}5}\bigr\rceil and \sigma(G,3,r)=\floor{r/2}, and in general $\frac{3r}{2m}-3\le \sigma(G,m,r)\le\frac{(1+1/\sqrt3)r}{m}$.Comment: 34 pages, 2 figures. The most important changes in this revision are improvements of the results on hypercubes and random graphs. The proof of the previous hypercube result has been deleted, but the statement remains because it is stronger for m<52. In the random graph section we added a spy-strategy resul

A frame-bundle formulation of quantum reference frames: from superposition of perspectives to superposition of geometries

Recent experimental advances suggest we may soon be able to probe the gravitational field of a mass in a coherent superposition of position states---a system which is widely believed to lie outside the scope of classical and semiclassical gravity. The recent theoretical literature has applied the idea of quantum reference frames (QRFs), originally introduced for non-gravitational contexts, to such a scenario. Here, we provide a possible fully geometric formulation of the core idea of QRFs as it has been applied in the context of gravity, freeing its definition from unnecessary (though convenient) ingredients, such as coordinate systems. Our formulation is based on two main ideas. First, a QRF encodes uncertainty about what is the observer’s (and, hence, the measuring apparatus's) perception of time and space at each spacetime point (i.e., event). For this, an observer at an event $p$ is modeled, as usual, as a tetrad in the tangent space $T_p$. So a QRF at an event $p$ is a complex function on the tetrads at $p$. Second, we use the result that one can specify a metric on a given manifold by stipulating that a basis one assigns at each tangent space is to be a tetrad in the metric one wants to specify. Hence a spacetime, i.e. manifold plus metric, together with a choice of ``point of view'' on it, is represented by a section of the bundle of bases, understood as taking the basis assigned to each point to be a tetrad. Thus a superposition of spacetimes gets represented as, roughly speaking, an assignment of complex amplitudes to sections of this bundle. A QRF, defined here as the collection of complex amplitudes assigned to bases at events---i.e., a complex function defined on the bundle of bases of the manifold---can describe, in a local way (i.e., attributing the amplitudes to bases at events instead of to whole sections), these superpositions. We believe that this formulation sheds some light on some conceptual aspects and possible extensions of current ideas about QRFs. For instance, thinking in geometric terms makes it clear that the idea of QRFs applied to the gravitational scenarios treated in the literature (beyond linear approximation) lacks predictive power due to arbitrariness which, we argue, can only be resolved by some further input from physics

Quantification of the effect of environmental changes on the brownification of Lake Kukkia in southern Finland

The browning of surface waters due to the increased terrestrial loading of dissolved organic carbon is observed across the northern hemisphere. Brownification is often explained by changes in large-scale anthropogenic pressures (including acidification, and climate and land-use changes). We quantified the effect of environmental changes on the brownification of an important lake for birds, Kukkia in southern Finland. We studied the past trends of organic carbon loading from catchments based on observations taken since the 1990s. We created hindcasting scenarios for deposition, climate and land-use change in order to simulate their quantitative effect on brownification by using process-based models. Changes in forest cuttings were shown to be the primary reason for the brownification. According to the simulations, a decrease in deposition has resulted in a slightly lower leaching of total organic carbon (TOC). In addition, runoff and TOC leaching from terrestrial areas to the lake was smaller than it would have been without the observed increasing trend in temperature by 2 & DEG;C in 25 years

Eroosiota ja sedimentin kulkeutumista kuvaavan INCA-SED mallin sovellus neljälle valuma-alueelle Suomessa

Suomessa. Valumavesien mukana maa-ainekseen kiinnittyneenä kulkeutuu myös ravinteitavastaanottaviin vesistöihin. Suomessa tärkeimmät eroosion mekanismit ovat sadepisaroiden iskutmaan pintaan, sekä erityisesti savimailla hiukkasten diffuusio kiinteästä maasta veteen. Lisäksimaahiukkasten kulkeutumiseen vaikuttavat uomassa tapahtuvat prosessit. Termillä 'sedimentinkulkeutuminen' kuvataan sekä maa-alueilla tapahtuvaa eroosiota että maahiukkasten kulkeutumistauomia pitkin valuma-alueen purkupisteeseen. Matemaattisen sedimentin kulkeutumista kuvaavanINCA-SED (Integrated Nutrients from CAtchment- Sediment) mallin sovellettavuutta jakäytettävyyttä ilmastonmuutoksen ja maankäytön muutosten vaikutusten arviointiin testattiin EU:nrahoittamassa Euro-limpacs projektissa. Mallista tehtiin sovellukset neljälle pienelle valuma-alueelle,joilla on erilaiset maalajit. Peltoprosentti tutkituilla valuma-alueilla vaihteli 12 ja 36 välillä. INCASEDmalli kykeni simuloimaan sekä joen kiintoainekonsentraation oikean tason että kausivaihtelunsekä savimailla että karkeammilla maalajeilla. Lisäksi mallinnettu sedimentin kulkeutuminen erimaankäyttöluokista vastasi Suomessa mitattuja arvoja. Esimerkiksi mallinnettu eroosiomaankäyttöluokassa 'viljakasvit savimaalla' oli 806 kg ha-1 a-1, kun mitattu arvo vaihteli välillä 760-1500 kg ha-1 a-1. Kiintoaineskonsentraation ja virtaaman välinen korrelaatio vaihteli selvästi eri joissa.Tämä ero selittyi INCA-SED mallissa valuma-alueiden maankäytöllä ja jokien erilaisellamorfologialla. Koska joen kiintoainekonsentraation kausivaihtelun oikea tavoittaminen onedellytyksenä ilmastomuutoksen vaikutusten luotettavalle mallintamiselle INCA-SED mallin voisanoa sopivan sekä maankäytön muutosten että ilmastonmuutoksen vaikutusten arviointiin Suomessa

Analysis of the potential of near-ground measurements of CO2 and CH4 in London, UK, for the monitoring of city-scale emissions using an atmospheric transport model

Carbon dioxide (CO2) and methane (CH4) mole fractions were measured at four near-ground sites located in and around London during the summer of 2012 with a view to investigating the potential of assimilating such measurements in an atmospheric inversion system for the monitoring of the CO2 and CH4 emissions in the London area. These data were analysed and compared with simulations using a modelling framework suited to building an inversion system: a 2 km horizontal resolution south of England configuration of the transport model CHIMERE driven by European Centre for Medium-Range Weather Forecasts (ECMWF) meteorological forcing, coupled to a 1 km horizontal resolution emission inventory (the UK National Atmospheric Emission Inventory). First comparisons reveal that local sources, which cannot be represented in the model at a 2 km resolution, have a large impact on measurements. We evaluate methods to filter out the impact of some of the other critical sources of discrepancies between the measurements and the model simulation except that of the errors in the emission inventory, which we attempt to isolate. Such a separation of the impact of errors in the emission inventory should make it easier to identify the corrections that should be applied to the inventory. Analysis is supported by observations from meteorological sites around the city and a 3-week period of atmospheric mixing layer height estimations from lidar measurements. The difficulties of modelling the mixing layer depth and thus CO2 and CH4 concentrations during the night, morning and late afternoon lead to focusing on the afternoon period for all further analyses. The discrepancies between observations and model simulations are high for both CO2 and CH4 (i.e. their root mean square (RMS) is between 8 and 12 parts per million (ppm) for CO2 and between 30 and 55 parts per billion (ppb) for CH4 at a given site). By analysing the gradients between the urban sites and a suburban or rural reference site, we are able to decrease the impact of uncertainties in the fluxes and transport outside the London area and in the model domain boundary conditions. We are thus able to better focus attention on the signature of London urban CO2 and CH4 emissions in the atmospheric CO2 and CH4 concentrations. This considerably improves the statistical agreement between the model and observations for CO2 (with model–data RMS discrepancies that are between 3 and 7 ppm) and to a lesser degree for CH4 (with model–data RMS discrepancies that are between 29 and 38 ppb). Between one of the urban sites and either the rural or suburban reference site, selecting the gradients during periods wherein the reference site is upwind of the urban site further decreases the statistics of the discrepancies in general, though not systematically. In a further attempt to focus on the signature of the city anthropogenic emission in the mole fraction measurements, we use a theoretical ratio of gradients of carbon monoxide (CO) to gradients of CO2 from fossil fuel emissions in the London area to diagnose observation-based fossil fuel CO2 gradients, and compare them with the fossil fuel CO2 gradients simulated with CHIMERE. This estimate increases the consistency between the model and the measurements when considering only one of the two urban sites, even though the two sites are relatively close to each other within the city. While this study evaluates and highlights the merit of different approaches for increasing the consistency between the mesoscale model and the near-ground data, and while it manages to decrease the random component of the analysed model–data discrepancies to an extent that should not be prohibitive to extracting the signal from the London urban emissions, large biases, the sign of which depends on the measurement sites, remain in the final model–data discrepancies. Such biases are likely related to local emissions to which the urban near-ground sites are highly sensitive. This questions our current ability to exploit urban near-ground data for the atmospheric inversion of city emissions based on models at spatial resolution coarser than 2 km. Several measurement and modelling concepts are discussed to overcome this challenge

Controls on inorganic nitrogen leaching from Finnish catchments assessed using a sensitivity and uncertainty analysis of the INCA -N model

The semi-distributed, dynamic INCA-N model was used to simulate the behaviour of dissolved inorganic nitrogen (DIN) in two Finnish research catchments. Parameter sensitivity and model structural uncertainty were analysed using generalized sensitivity analysis. The Mustajoki catchment is a forested upstream catchment, while the Savijoki catchment represents intensively cultivated lowlands. In general, there were more influential parameters in Savijoki than Mustajoki. Model results were sensitive to N-transformation rates, vegetation dynamics, and soil and river hydrology. Values of the sensitive parameters were based on long-term measurements covering both warm and cold years. The highest measured DIN concentrations fell between minimum and maximum values estimated during the uncertainty analysis. The lowest measured concentrations fell outside these bounds, suggesting that some retention processes may be missing from the current model structure. The lowest concentrations occurred mainly during low flow periods; so effects on total loads were small

A new multibranch model for metals in river systems: Impacts and control of tannery wastes in Bangladesh

A new multibranch Integrated Catchment (INCA) model INCA-Metals has been developed to simulate the impact of tannery discharges on river systems. The model accounts for the key chemical reaction kinetic processes operating as well as sedimentation, resuspension, dilution, mixing and redistribution of pollutants in rivers downstream of tannery discharge points and for mine discharges or acid rock drainage sites. The model is dynamic and simulates the daily behaviour of hydrology and eight metals, including cadmium, mercury, copper, zinc, lead, arsenic, manganese and chromium, as well as cyanide and ammonia. The model is semi-distributed and can simulate catchments, tributaries and instream river behaviour. The model can also account for diffuse pollution from rural runoff as well as point sources from effluent and trade discharges. The model has been applied to the new Savar tannery complex on the Dhaleshwari River system in Bangladesh to assess the impacts on pollution levels in the river system and to evaluate a set of treatment scenarios for pollution control, particularly in the dry season. It is shown that the new effluent treatment plant at Savar needs to significantly improve its operation and treatment capability in order to alleviate metal pollution in the downstream Dhaleshwari River System and also protect the Meghna River System that falls in the Bay of Bengal

The role of charge in the toxicity of polymer-coated cerium oxide nanomaterials to Caenorhabditis elegans

This study examined the impact of surface functionalization and charge on ceria nanomaterial toxicity to Caenorhabditis elegans. The examined endpoints included mortality, reproduction, protein expression, and protein oxidation profiles. Caenorhabditis elegans were exposed to identical 2–5 nm ceria nanomaterial cores which were coated with cationic (diethylaminoethyl dextran; DEAE), anionic (carboxymethyl dextran; CM), and non-ionic (dextran; DEX) polymers. Mortality and reproductive toxicity of DEAE-CeO2 was approximately two orders of magnitude higher than for CM-CeO2 or DEX-CeO2. Two-dimensional gel electrophoresis with orbitrap mass spectrometry identification revealed changes in the expression profiles of several mitochondrial-related proteins and proteins that are expressed in the C. elegans intestine. However, each type of CeO2 material exhibited a distinct protein expression profile. Increases in protein carbonyls and protein-bound 3-nitrotyrosine were also observed for some proteins, indicating oxidative and nitrosative damage. Taken together the results indicate that the magnitude of toxicity and toxicity pathways vary greatly due to surface functionalization of CeO2 nanomaterials

Learning modular policies for robotics

A promising idea for scaling robot learning to more complex tasks is to use elemental behaviors as building blocks to compose more complex behavior. Ideally, such building blocks are used in combination with a learning algorithm that is able to learn to select, adapt, sequence and co-activate the building blocks. While there has been a lot of work on approaches that support one of these requirements, no learning algorithm exists that unifies all these properties in one framework. In this paper we present our work on a unified approach for learning such a modular control architecture. We introduce new policy search algorithms that are based on information-theoretic principles and are able to learn to select, adapt and sequence the building blocks. Furthermore, we developed a new representation for the individual building block that supports co-activation and principled ways for adapting the movement. Finally, we summarize our experiments for learning modular control architectures in simulation and with real robots

CMZoom IV. Incipient High-Mass Star Formation Throughout the Central Molecular Zone

In this work, we constrain the star-forming properties of all possible sites of incipient high-mass star formation in the Milky Way's Galactic Center. We identify dense structures using the CMZoom 1.3mm dust continuum catalog of objects with typical radii of $\sim$0.1pc, and measure their association with tracers of high-mass star formation. We incorporate compact emission at 8, 21, 24, 25, and 70um from MSX, Spitzer, Herschel, and SOFIA, catalogued young stellar objects, and water and methanol masers to characterize each source. We find an incipient star formation rate (SFR) for the CMZ of ~0.08 Msun yr^{-1} over the next few 10^5 yr. We calculate upper and lower limits on the CMZ's incipient SFR of ~0.45 Msun yr^{-1} and ~0.05 Msun yr^{-1} respectively, spanning between roughly equal to and several times greater than other estimates of CMZ's recent SFR. Despite substantial uncertainties, our results suggest the incipient SFR in the CMZ may be higher than previously estimated. We find that the prevalence of star formation tracers does not correlate with source volume density, but instead ~75% of high-mass star formation is found in regions above a column density ratio (N_{SMA}/N_{Herschel}) of ~1.5. Finally, we highlight the detection of ``atoll sources'', a reoccurring morphology of cold dust encircling evolved infrared sources, possibly representing HII regions in the process of destroying their envelopes.Comment: Accepted for publication in Ap