a b s t r a c tLet f be a univariate polynomial with real coefficients, f ∈ R[X ].Subdivision algorithms based on algebraic techniques (e.g., Sturm or Descartes methods) are widely used for isolating the real roots of f in a given interval. In this paper, we consider a simple subdivision algorithm whose primitives are purely numerical (e.g., function evaluation). The complexity of this algorithm is adaptive because the algorithm makes decisions based on local data. The complexity analysis of adaptive algorithms (and this algorithm in particular) is a new challenge for computer science. In this paper, we compute the size of the subdivision tree for the SqFreeEVAL algorithm.The SqFreeEVAL algorithm is an evaluation-based numerical algorithm which is well-known in several communities. The algorithm itself is simple, but prior attempts to compute its complexity have proven to be quite technical and have yielded sub-optimal results. Our main result is a simple O(d (L +ln d)) bound on the size of the subdivision tree for the SqFreeEVAL algorithm on the benchmark problem of isolating all real roots of an integer polynomial f of degree d and whose coefficients can be written with at most L bits. Our proof uses two amortization-based techniques: first, we use the algebraic amortization technique of the standard Mahler-Davenport root bounds to interpret the integral in terms of d and L. Second, we use a continuous amortization technique based on an integral to bound the size of the subdivision tree. This paper is the first to use the novel analysis technique of continuous amortization to derive state of the art complexity bounds.

We describe a simple system enabling accurate measurement of swimming marine mammals and other large vertebrates from low-altitude single-frame photogrammetry via inexpensive modifications to a "prosumer" unmanned aerial vehicle (UAV) equipped with gimballed micro4/3 camera and 25 mm lens. Image scale is established via an independently powered LIDAR/GPS data-logging system recording altitude and GPS location at 1 Hz. Photogrammetric calibration of the camera and lens allowed distortion parameters to be rigorously accounted for during image analysis, via a custom-programmed Graphical User Interface (GUI) running in MATLAB. The datalogger, camera calibration methods and measurement software are adaptable to a wide range of UAV platforms. Mean LIDAR accuracy, measured from 10 bridges 9-39 m above water, was 99.9%. We conducted 136 flights in New Zealand's subantarctic Auckland Islands to measure southern right whales. Mean lengths of 10 individual whales, each photographed between 7 and 15 times, had CVs (SD/mean) ranging from 0.5 to 1.8% (mean = 1.2%). Repeated measurements of a floating reference target showed a mean error of c.1%. Our system is relatively inexpensive, easily put together, produces accurate, repeatable measurements from single vertical images, and hence is applicable to a wide range of ecological questions in marine and terrestrial habitats.

Patterns in morphology, pigment concentration, and light saturation kinetics of Ecklonia radiata reveal great morphological and physiological variability among individuals from sites spanning strong gradients in topographic shading and wave exposure among the 14 fjords in southwestern New Zealand. Morphology of E. radiata varies from relatively narrow (85 6 4.7 mm) (mean 6 standard error), thick (3.2 6 0.30 mm) blades from the well-illuminated, wave-exposed outer coast sites to wide, undulate (460 6 36.8 mm,) and thin (0.46 6 0.059 mm) blades from quiescent, topographically shaded inner fjord sites. Chlorophyll a (Chl a) concentration of blades (0.084-1.34 mg g 21 of tissue) and the ratio of fucoxanthin to Chl a (0.33 to 0.56) also increased along this gradient, indicating photoacclimation within the inner fjord populations. In situ measurements of light saturation kinetics indicate maximum photosynthetic rates at lower irradiance (I max 5 43.7 vs. 257 mmol quanta m 22 s 21 ) for algae at inner fjord sites relative to well-lit outer fjord locations. Individuals exhibiting characteristically photoacclimated relative electron transfer rate curves had more deplete d 13 C (213.35% to 222.35%) than individuals with higher I max . There was no significant association between the kelp morphology or geographic location and the observed recombinant DNA diversity of ITS sequences that would indicate the presence of two Ecklonia species in the fjords. E. radiata occupies a wide range of habitats in Fiordland and displays variability in morphology and photo-physiological responses to low light that coincide with gradients in wave exposure and topographically shaded light conditions.

No abstract

A 58 m long azimuthally oriented ice core has been collected from the floating lateral sinistral shear margin of the lower Priestley Glacier, Terra Nova Bay, Antarctica. The crystallographic preferred orientations (CPO) and microstructures are described in order to correlate the geometry of anisotropy with constrained large-scale kinematics. Cryogenic Electron Backscatter Diffraction analysis shows a very strong fabric (c-axis primary eigenvalue ∼0.9) with c-axes aligned horizontally sub-perpendicular to flow, rotating nearly 40° clockwise (looking down) to the pole to shear throughout the core. The c-axis maximum is sub-perpendicular to vertical layers, with the pole to layering always clockwise of the c-axes. Priestley ice microstructures are defined by largely sub-polygonal grains and constant mean grain sizes with depth. Grain long axis shape preferred orientations (SPO) are almost always 1–20° clockwise of the c-axis maximum. A minor proportion of “oddly” oriented grains that are distinct from the main c-axis maximum, are present in some samples. These have horizontal c-axes rotated clockwise from the primary c-axis maximum and may define a weaker secondary maximum up to 30° clockwise of the primary maximum. Intragranular misorientations are measured along the core, and although the statistics are weak, this could suggest recrystallization by subgrain rotation to occur. These microstructures suggest subgrain rotation (SGR) and recrystallization by grain boundary migration recrystallization (GBM) are active in the Priestley Glacier shear margin. Vorticity analysis based on intragranular distortion indicates a vertical axis of rotation in the shear margin. The variability in c-axis maximum orientation with depth indicates the structural heterogeneity of the Priestley Glacier shear margin occurs at the meter to tens of meters scale. We suggest that CPO rotations could relate to rigid rotation of blocks of ice within the glacial shear margin. Rotation either post-dates CPO and SPO development or is occurring faster than CPO evolution can respond to a change in kinematics.

Field surveys and laboratory experiments were used to investigate the influence of the physical environment on variability in δ13C and δ15N signatures of Ulva pertusa, an abundant macroalgae inhabiting the low salinity layer (LSL) of Doubtful Sound, a New Zealand fjord. Field surveys revealed significant spatial variability in δ13C (‐18% to ‐12%) and δ15N (0% to 6%). δ13C was enriched at high irradiance sites and depleted at the fjord’s wave‐exposed entrance. δ15N signatures increased from 0% at the fjord head where freshwater influence is greatest to an oceanic signature of 6% at the fjord entrance. δ15N also increased by up to 4% between 2‐m depth and the LSL‐seawater interface (4‐m depth); this pattern was less pronounced near the ocean. During laboratory experiments, δ13C of U. pertusa became significantly enriched under high levels of irradiance (>50 mmol quanta m−2 s−1). When exposed to high irradiance, increases in water motion rapidly depleted δ13C signatures by as much as 5%. Variability in δ13C of U. pertusa in Doubtful Sound is largely a function of the light regime, which influences rates of photosynthesis and in turn the algae’s dependence on HCO3−, an enriched source of carbon. However, increased water motion at the fjord entrance counteracts the influence of irradiance, leading to enhanced flux of CO2 and depleted δ13C signatures. Variation in δ15N of U. pertusa is less dependent on the physical environment and instead is driven by the source pool signature, which in turn varies between freshwater and marine sources of nitrogen.

Abstract. The elastic and anelastic properties of ice are of interest in the study of the dynamics of sea ice, glaciers, and ice sheets. Resonant ultrasound spectroscopy allows quantitative estimates of these properties and aids calibration of active and passive seismic data gathered in the field. The elastic properties and anelastic quality factor Q in laboratorymanufactured polycrystalline isotropic ice cores decrease (reversibly) with increasing temperature, but compressionalwave speed and attenuation prove most sensitive to temperature, indicative of pre-melting of the ice. This method of resonant ultrasound spectroscopy can be deployed in the field, for those situations where shipping samples is difficult (e.g. remote locations), or where the properties of ice change rapidly after extraction (e.g. in the case of sea ice).

Volcanic particles are commonly characterized using 2D morphometric analysis. Results of analysis are used to compare particles from different events or phases, and to infer clast-generating mechanisms, eruptive styles and the aerodynamic behavior of particles. Such particle-shape analyses can be made from images of particle silhouettes or cross-sectional slices. A number of different morphometric systems have been used to date, with each using its own nomenclature and mathematical definitions of shape-describing parameters. Some of the parameters can only be obtained using specific commercial software.With the PARTIcle Shape ANalyzer PARTISAN we present a freeware tool which parameterizes 2D shapes and provides a suite of shape parameters, following the different standards of the five most commonly used 2D morphometric systems. PARTISAN enables the user to study and archive the results of particle-shape analysis in a format compatible with various published routines, thus increasing the potential for linking new work with results of work previously published by other groups. It will also allow cross-comparison of results obtained by different morphological routines. We see PARTISAN as a "Rosetta Stone" for volcanological particle morphometry, and it opens the way for development of widely agreed treatment of particle shapes in 2D.