The branching structure of diffusion-limited aggregates

I analyze the topological structures generated by diffusion-limited aggregation (DLA), using the recently developed "branched growth model". The computed bifurcation number B for DLA in two dimensions is B ~ 4.9, in good agreement with the numerically obtained result of B ~ 5.2. In high dimensions, B -> 3.12; the bifurcation ratio is thus a decreasing function of dimensionality. This analysis also determines the scaling properties of the ramification matrix, which describes the hierarchy of branches.Comment: 6 pages, 1 figure, Euro-LaTeX styl

Information Gathering in Ad-Hoc Radio Networks with Tree Topology

We study the problem of information gathering in ad-hoc radio networks without collision detection, focussing on the case when the network forms a tree, with edges directed towards the root. Initially, each node has a piece of information that we refer to as a rumor. Our goal is to design protocols that deliver all rumors to the root of the tree as quickly as possible. The protocol must complete this task within its allotted time even though the actual tree topology is unknown when the computation starts. In the deterministic case, assuming that the nodes are labeled with small integers, we give an O(n)-time protocol that uses unbounded messages, and an O(n log n)-time protocol using bounded messages, where any message can include only one rumor. We also consider fire-and-forward protocols, in which a node can only transmit its own rumor or the rumor received in the previous step. We give a deterministic fire-and- forward protocol with running time O(n^1.5), and we show that it is asymptotically optimal. We then study randomized algorithms where the nodes are not labelled. In this model, we give an O(n log n)-time protocol and we prove that this bound is asymptotically optimal

Unified View of Scaling Laws for River Networks

Scaling laws that describe the structure of river networks are shown to follow from three simple assumptions. These assumptions are: (1) river networks are structurally self-similar, (2) single channels are self-affine, and (3) overland flow into channels occurs over a characteristic distance (drainage density is uniform). We obtain a complete set of scaling relations connecting the exponents of these scaling laws and find that only two of these exponents are independent. We further demonstrate that the two predominant descriptions of network structure (Tokunaga's law and Horton's laws) are equivalent in the case of landscapes with uniform drainage density. The results are tested with data from both real landscapes and a special class of random networks.Comment: 14 pages, 9 figures, 4 tables (converted to Revtex4, PRE ref added

Geometry of River Networks II: Distributions of Component Size and Number

The structure of a river network may be seen as a discrete set of nested sub-networks built out of individual stream segments. These network components are assigned an integral stream order via a hierarchical and discrete ordering method. Exponential relationships, known as Horton's laws, between stream order and ensemble-averaged quantities pertaining to network components are observed. We extend these observations to incorporate fluctuations and all higher moments by developing functional relationships between distributions. The relationships determined are drawn from a combination of theoretical analysis, analysis of real river networks including the Mississippi, Amazon and Nile, and numerical simulations on a model of directed, random networks. Underlying distributions of stream segment lengths are identified as exponential. Combinations of these distributions form single-humped distributions with exponential tails, the sums of which are in turn shown to give power law distributions of stream lengths. Distributions of basin area and stream segment frequency are also addressed. The calculations identify a single length-scale as a measure of size fluctuations in network components. This article is the second in a series of three addressing the geometry of river networks.Comment: 16 pages, 13 figures, 4 tables, Revtex4, submitted to PR

Geometry of River Networks I: Scaling, Fluctuations, and Deviations

This article is the first in a series of three papers investigating the detailed geometry of river networks. Large-scale river networks mark an important class of two-dimensional branching networks, being not only of intrinsic interest but also a pervasive natural phenomenon. In the description of river network structure, scaling laws are uniformly observed. Reported values of scaling exponents vary suggesting that no unique set of scaling exponents exists. To improve this current understanding of scaling in river networks and to provide a fuller description of branching network structure, we report here a theoretical and empirical study of fluctuations about and deviations from scaling. We examine data for continent-scale river networks such as the Mississippi and the Amazon and draw inspiration from a simple model of directed, random networks. We center our investigations on the scaling of the length of sub-basin's dominant stream with its area, a characterization of basin shape known as Hack's law. We generalize this relationship to a joint probability density and show that fluctuations about scaling are substantial. We find strong deviations from scaling at small scales which can be explained by the existence of linear network structure. At intermediate scales, we find slow drifts in exponent values indicating that scaling is only approximately obeyed and that universality remains indeterminate. At large scales, we observe a breakdown in scaling due to decreasing sample space and correlations with overall basin shape. The extent of approximate scaling is significantly restricted by these deviations and will not be improved by increases in network resolution.Comment: 16 pages, 13 figures, Revtex4, submitted to PR

Remotely sensed albedo allows the identification of two ecosystem states along aridity gradients in Africa

Empirical verification of multiple states in drylands is scarce, impeding the design of indicators to anticipate the onset of desertification. Remote sensing‐derived indicators of ecosystem states are gaining new ground due to the possibilities they bring to be applied inexpensively over large areas. Remotely sensed albedo has been often used to monitor drylands due to its close relationship with ecosystem status and climate. Here, we used a space‐for‐time‐substitution approach to evaluate whether albedo (averaged from 2000 to 2016) can identify multiple ecosystem states in African drylands spanning from the Saharan desert to tropical Africa. By using latent class analysis, we found that albedo showed two states (low and high; the cut‐off level was 0.22 at the shortwave band). Potential analysis revealed that albedo exhibited an abrupt and discontinuous increase with increased aridity (1 − [precipitation/potential evapotranspiration]). The two albedo states co‐occurred along aridity values ranging from 0.72 to 0.78, during which vegetation cover exhibited a rapid, continuous decrease from ~90% to ~50%. At aridity values of 0.75, the low albedo state started to exhibit less attraction than the high albedo state. Low albedo areas beyond this aridity value were considered as vulnerable regions where abrupt shifts in albedo may occur if aridity increases, as forecasted by current climate change models. Our findings indicate that remotely sensed albedo can identify two ecosystem states in African drylands. They support the suitability of albedo indices to inform us about discontinuous responses to aridity experienced by drylands, which can be linked to the onset of land degradation.This work was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant XDA19030500), the National Key Research and Development Program of China (Grant 2016YFC0503302), the European Research Council (BIODESERT project, ERC Grant Agreement 647038), the Joint PhD, Training Program of the University of Chinese Academy of Sciences, and the Research Foundation of Henan University of Technology (Grant 31401178)

A Multimetric Assessment of Stream Condition in the Northern Lakes and Forests Ecoregion Using Spatially Explicit Statistical Modeling and Regional Normalization

We sampled fish communities, water temperature, water chemistry, physical habitat, and catchment characteristics for 94 stream sites selected randomly throughout the Northern Lakes and Forests ecoregion and used those data to explicitly model reference conditions and assess ecological stream condition at each site via a regional normalization framework. The streams we sampled were first order through fourth order, and the catchments ranged from 0.9 to 458 km2. We developed multiple linear regression (MLR) models that predicted fish community metrics, water chemistry characteristics, and local physical habitat from catchment characteristics; we used these models to compare existing conditions with the conditions that would be expected based on the regression models. Our results indicated that the fish communities were relatively unimpaired because the catchment variables associated with human‐induced land use change were important in only 1 of the 10 fish metric models. Agricultural land use was a significant variable in the MLR equation for species of Lepomis (sunfish). Agricultural land use and urban land use were both significant variables in all of the MLR models predicting water chemistry variables; urban land use was a significant variable in the MLR model predicting the percent coverage of all instream cover types. Regional normalization indicated that none of the sites were impaired based on fish community attributes. However, our analysis based on water chemistry metrics indicated that 22– 35% of the sites were impaired and that, based on physical habitat, 6–14% of the sites were impaired. A comparison with other published studies of the ecoregion suggested that the regional normalization process correctly characterized stream condition.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141590/1/tafs0697.pd

Determining neutrino oscillation parameters from atmospheric muon neutrino disappearance with three years of IceCube DeepCore data

We present a measurement of neutrino oscillations via atmospheric muon neutrino disappearance with three years of data of the completed IceCube neutrino detector. DeepCore, a region of denser instrumentation, enables the detection and reconstruction of atmospheric muon neutrinos between 10 GeV and 100 GeV, where a strong disappearance signal is expected. The detector volume surrounding DeepCore is used as a veto region to suppress the atmospheric muon background. Neutrino events are selected where the detected Cherenkov photons of the secondary particles minimally scatter, and the neutrino energy and arrival direction are reconstructed. Both variables are used to obtain the neutrino oscillation parameters from the data, with the best fit given by $\Delta m^2_{32}=2.72^{+0.19}_{-0.20}\times 10^{-3}\,\mathrm{eV}^2$ and $\sin^2\theta_{23} = 0.53^{+0.09}_{-0.12}$ (normal mass hierarchy assumed). The results are compatible and comparable in precision to those of dedicated oscillation experiments.Comment: 10 pages, 7 figure

Search for non-relativistic Magnetic Monopoles with IceCube

The IceCube Neutrino Observatory is a large Cherenkov detector instrumenting $1\,\mathrm{km}^3$ of Antarctic ice. The detector can be used to search for signatures of particle physics beyond the Standard Model. Here, we describe the search for non-relativistic, magnetic monopoles as remnants of the GUT (Grand Unified Theory) era shortly after the Big Bang. These monopoles may catalyze the decay of nucleons via the Rubakov-Callan effect with a cross section suggested to be in the range of $10^{-27}\,\mathrm{cm^2}$ to $10^{-21}\,\mathrm{cm^2}$. In IceCube, the Cherenkov light from nucleon decays along the monopole trajectory would produce a characteristic hit pattern. This paper presents the results of an analysis of first data taken from May 2011 until May 2012 with a dedicated slow-particle trigger for DeepCore, a subdetector of IceCube. A second analysis provides better sensitivity for the brightest non-relativistic monopoles using data taken from May 2009 until May 2010. In both analyses no monopole signal was observed. For catalysis cross sections of $10^{-22}\,(10^{-24})\,\mathrm{cm^2}$ the flux of non-relativistic GUT monopoles is constrained up to a level of $\Phi_{90} \le 10^{-18}\,(10^{-17})\,\mathrm{cm^{-2}s^{-1}sr^{-1}}$ at a 90% confidence level, which is three orders of magnitude below the Parker bound. The limits assume a dominant decay of the proton into a positron and a neutral pion. These results improve the current best experimental limits by one to two orders of magnitude, for a wide range of assumed speeds and catalysis cross sections.Comment: 20 pages, 20 figure

A combined maximum-likelihood analysis of the high-energy astrophysical neutrino flux measured with IceCube

Evidence for an extraterrestrial flux of high-energy neutrinos has now been found in multiple searches with the IceCube detector. The first solid evidence was provided by a search for neutrino events with deposited energies $\gtrsim30$ TeV and interaction vertices inside the instrumented volume. Recent analyses suggest that the extraterrestrial flux extends to lower energies and is also visible with throughgoing, $\nu_\mu$-induced tracks from the Northern hemisphere. Here, we combine the results from six different IceCube searches for astrophysical neutrinos in a maximum-likelihood analysis. The combined event sample features high-statistics samples of shower-like and track-like events. The data are fit in up to three observables: energy, zenith angle and event topology. Assuming the astrophysical neutrino flux to be isotropic and to consist of equal flavors at Earth, the all-flavor spectrum with neutrino energies between 25 TeV and 2.8 PeV is well described by an unbroken power law with best-fit spectral index $-2.50\pm0.09$ and a flux at 100 TeV of $\left(6.7_{-1.2}^{+1.1}\right)\cdot10^{-18}\,\mathrm{GeV}^{-1}\mathrm{s}^{-1}\mathrm{sr}^{-1}\mathrm{cm}^{-2}$. Under the same assumptions, an unbroken power law with index $-2$ is disfavored with a significance of 3.8 $\sigma$ ($p=0.0066\%$) with respect to the best fit. This significance is reduced to 2.1 $\sigma$ ($p=1.7\%$) if instead we compare the best fit to a spectrum with index $-2$ that has an exponential cut-off at high energies. Allowing the electron neutrino flux to deviate from the other two flavors, we find a $\nu_e$ fraction of $0.18\pm0.11$ at Earth. The sole production of electron neutrinos, which would be characteristic of neutron-decay dominated sources, is rejected with a significance of 3.6 $\sigma$ ($p=0.014\%$).Comment: 16 pages, 10 figures; accepted for publication in The Astrophysical Journal; updated one referenc