Revisiting the Problem of Searching on a Line

We revisit the problem of searching for a target at an unknown location on a line when given upper and lower bounds on the distance D that separates the initial position of the searcher from the target. Prior to this work, only asymptotic bounds were known for the optimal competitive ratio achievable by any search strategy in the worst case. We present the first tight bounds on the exact optimal competitive ratio achievable, parameterized in terms of the given bounds on D, along with an optimal search strategy that achieves this competitive ratio. We prove that this optimal strategy is unique. We characterize the conditions under which an optimal strategy can be computed exactly and, when it cannot, we explain how numerical methods can be used efficiently. In addition, we answer several related open questions, including the maximal reach problem, and we discuss how to generalize these results to m rays, for any m >= 2

Diffusion and Home Range Parameters for Rodents: Peromyscus maniculatus in New Mexico

We analyze data from a long term field project in New Mexico, consisting of repeated sessions of mark-recaptures of Peromyscus maniculatus (Rodentia: Muridae), the host and reservoir of Sin Nombre Virus (Bunyaviridae: Hantavirus). The displacements of the recaptured animals provide a means to study their movement from a statistical point of view. We extract two parameters from the data with the help of a simple model: the diffusion constant of the rodents, and the size of their home range. The short time behavior shows the motion to be approximately diffusive and the diffusion constant to be 470+/-50m^2/day. The long time behavior provides an estimation of the diameter of the rodent home ranges, with an average value of 100+/-25m. As in previous investigations directed at Zygodontomys brevicauda observations in Panama, we use a box model for home range estimation. We also use a harmonic model in the present investigation to study the sensitivity of the conclusions to the model used and find that both models lead to similar estimates.Comment: The published paper in Ecol. Complexity has an old version of Figure 6. Here we have put the correct version of Figure

The Fueling and Evolution of AGN: Internal and External Triggers

In this chapter, I review the fueling and evolution of active galactic nuclei (AGN) under the influence of internal and external triggers, namely intrinsic properties of host galaxies (morphological or Hubble type, color, presence of bars and other non-axisymmetric features, etc) and external factors such as environment and interactions. The most daunting challenge in fueling AGN is arguably the angular momentum problem as even matter located at a radius of a few hundred pc must lose more than 99.99 % of its specific angular momentum before it is fit for consumption by a BH. I review mass accretion rates, angular momentum requirements, the effectiveness of different fueling mechanisms, and the growth and mass density of black BHs at different epochs. I discuss connections between the nuclear and larger-scale properties of AGN, both locally and at intermediate redshifts, outlining some recent results from the GEMS and GOODS HST surveys.Comment: Invited Review Chapter to appear in LNP Volume on "AGN Physics on All Scales", Chapter 6, in press. 40 pages, 12 figures. Typo in Eq 5 correcte

Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics

International audienceWe provide a complete and rigorous description of phase transitions for kinetic models of self-propelled particles interacting through alignment. These models exhibit a competition between alignment and noise. Both the alignment frequency and noise intensity depend on a measure of the local alignment. We show that, in the spatially homogeneous case, the phase transition features (number and nature of equilibria, stability, convergence rate, phase diagram, hysteresis) are totally encoded in how the ratio between the alignment and noise intensities depend on the local alignment. In the spatially inhomogeneous case, we derive the macroscopic models associated to the stable equilibria and classify their hyperbolicity according to the same function

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Characterisation of riverine dissolved organic matter using a complementary suite of chromatographic and mass spectrometric methods

Dissolved organic matter (DOM) plays a fundamental role in nutrient cycling dynamics in riverine systems. Recent research has confirmed that the concentration of riverine DOM is not the only factor regulating its functional significance; the need to define the chemical composition of DOM is a priority. Past studies of riverine DOM rested on bulk quantification, however technological advancements have meant there has been a shift towards analytical methods which allow the characterisation of DOM either at compound class or more recently molecular level. However, it is important to consider that all analytical methods only consider a defined analytical window. Thus, herein, we explore the use of a hierarchy of methods which can be used in combination for the investigation of a wide range of DOM chemistries. By using these methods to investigate the DOM composition of a range of streams draining catchments of contrasting environmental character, a wide range of compounds were identified across a range of polarities and molecular weight, thereby extending the analytical window. Through the elucidation of the DOM character in stream samples, information can be collected about likely the sources of DOM. The identification of individual key compounds within the DOM pool is a key step in the design of robust and informative bioassay experiments, used to understand in-stream ecosystem responses. This is critical if we are to assess the role of DOM as a bioavailable nutrient resource and/or ecotoxicological factor in freshwater

Microbial use of low molecular weight DOM in filtered and unfiltered freshwater:Role of ultra-small microorganisms and implications for water quality monitoring

Dissolved organic matter (DOM) plays a central role in regulating productivity and nutrient cycling in freshwaters. It is therefore vital that we can representatively sample and preserve DOM in freshwaters for subsequent analysis. Here we investigated the effect of filtration, temperature (5 and 25 °C) and acidification (HCl) on the persistence of low molecular weight (MW) dissolved organic carbon (DOC), nitrogen (DON) and orthophosphate in oligotrophic and eutrophic freshwater environments. Our results showed the rapid loss of isotopically-labelled glucose and amino acids from both filtered (0.22 and 0.45 μm) and unfiltered waters. We ascribe this substrate depletion in filtered samples to the activity of ultra-small (< 0.45 μm) microorganisms (bacteria and archaea) present in the water. As expected, the rate of C, N and P loss was much greater at higher temperatures and was repressed by the addition of HCl. Based on our results and an evaluation of the protocols used in recently published studies, we conclude that current techniques used to sample water for low MW DOM characterisation are frequently inadequate and lack proper validation. In contrast to the high degree of analytical precision and rigorous statistical analysis of most studies, we argue that insufficient consideration is still given to the presence of ultra-small microorganisms and potential changes that can occur in the low MW fraction of DOM prior to analysis

Determining patterns in the composition of dissolved organic matter in fresh waters according to land use and management

In fresh waters, the origins of dissolved organic matter (DOM) have been found to exert a fundamental control on its reactivity, and ultimately, its ecosystem functional role. A detailed understanding of landscape scale factors that control the export of DOM to aquatic ecosystems is, therefore, pivotal if the effects of DOM flux to fresh waters are to be fully understood. In this study we present data from a national sampling campaign across the United Kingdom in which we explore the variability in DOM composition in three broad landscape types defined by similar precipitation, geology, land use and management, hydrology, and nutrient enrichment status. We characterised samples from fifty-one sites, grouping them into one of three major underlying classifications: circumneutral streams underlain by clay and mudstone (referred to as ‘clay’), alkaline streams underlain by Cretaceous Chalk or by Carboniferous or Jurassic Limestone (‘limestone’), and acidic streams in peatland catchments underlain by a range of low permeability lithologies (‘peat’). DOM composition was assessed through organic matter stoichiometry (organic carbon: organic nitrogen; organic carbon: organic phosphorus; C/N(P)DOM) and metrics derived from ultra-violet (UV)/visible spectroscopic analysis of DOM such as specific UV absorption (a254 nm; SUVA254). We found similar SUVA254, C/NDOM and DOM/a254 relationships within classifications, demonstrating that despite a large degree of heterogeneity within environments, catchments with shared environmental character and anthropogenic disturbance export DOM with a similar composition and character. Improving our understanding of DOM characterisation is important to help predict shifts in stream ecosystem function, and ecological responses to enrichment or mitigation efforts and how these may result in species composition shifts and biodiversity loss in freshwater ecosystems