Multiscale change-point segmentation: beyond step functions.

Modern multiscale type segmentation methods are known to detect multiple change-points with high statistical accuracy, while allowing for fast computation. Underpinning (minimax) estimation theory has been developed mainly for models that assume the signal as a piecewise constant function. In this paper, for a large collection of multiscale segmentation methods (including various existing procedures), such theory will be extended to certain function classes beyond step functions in a nonparametric regression setting. This extends the interpretation of such methods on the one hand and on the other hand reveals these methods as robust to deviation from piecewise constant functions. Our main finding is the adaptation over nonlinear approximation classes for a universal thresholding, which includes bounded variation functions, and (piecewise) Holder functions of smoothness order 0 < alpha <= 1 as special cases. From this we derive statistical guarantees on feature detection in terms of jumps and modes. Another key finding is that these multiscale segmentation methods perform nearly (up to a log-factor) as well as the oracle piecewise constant segmentation estimator (with known jump locations), and the best piecewise constant approximants of the (unknown) true signal. Theoretical findings are examined by various numerical simulations

Simultaneous epidemic development of scald and net blotch on single leaf layers of a spring barley crop

Background and objectives Two pathogens growing on the same leaf compete for the same resources, i.e. space and plant nutrients. This may lead to density dependent disease development. The pathogens may also influence each other directly such that the influence of one on the other is more complex than a simple function of the area of the other pathogen. Different interaction types are, for example, competition, mutualism and exploitation. The importance of such interactions for epidemics of simultaneously occurring pathogens has received little attention. The objective of this study is to investigate the simultaneous epidemic development of Rhynchosporium secalis (causing scald) and Drechslera teres (causing net blotch) on spring barley under field conditions. Materials and methods The field trial was performed with artificial inoculation of R. secalis and D. teres on three spring barley varieties differing in their susceptibility towards the pathogens. The pathogens were inoculated in three combinations: only one was inoculated, they were inoculated together, the second pathogen was inoculated 26 days after the first. A non-inoculated treatment was included. The trial had three replications. Nine plants were harvested from each plot five times during the season. Leaves were dried and disease severity and senescence observed. Only leaves with < 50 % senescence were included in the analysis. Whole-plant disease severity over time was calculated as average of disease severity on leaves weighted by leaf area. Disease development per leaf layer was evaluated by fitting an exponential model to severity data over time for each leaf layer per variety, treatment and replicate. Association between scald and net blotch severity on individual leaves was analysed using Kendall’s tau. Results and discussion Net blotch developed on all leaf layers and reached whole-plant disease severities up to 15%. Scald did not develop on upper leaf layers and whole-plant severity was less than 2%. Disease severity curves at whole-plant level showed no effect of inoculating the other pathogen. The analysis of the growth rate of each disease per leaf layer showed a significant effect of variety and leaf layer within variety but no effect of treatment. However, we observed significant negative associations between the diseases on individual leaves for several combinations of leaf layer and variety. These results show that the individual leaf approach can provide new information and underline the importance of considering interactions between pathogens in the field. Acknowledgement This work was funded by the DARCOF II project BAR-O

Net blotch severity is best assessed at early grain filling with respect to its effect on grain weight of spring barley

Appropriate disease assessment methods and parameters reflecting whole-season disease severity levels in field plots remain important issues in studies related to plant disease epidemiology, disease resistance of crop cultivars, and disease-induced yield losses. Such methods and parameters should be yield-related to ensure relevance. Net blotch severity was determined over time in inoculated and non-inoculated field plots of three spring barley varieties by whole plot assessments and by assessments of individual leaves of single main tillers. Disease severity measures such as the area-under-disease-progress-curve, mean and maximum severity as well as severity levels at specific growth stages (GS) were derived from the data. Their relation to thousand grain weight (TGW) and their inter-correlations were examined by means of general linear model (GLM) and factor analyses (FA), respectively. All parameters of net blotch severity were significantly negatively correlated with TGW. Disease parameters derived from whole-plot assessments gave a slightly better explanation of TGW than parameters derived by assessing single main tillers. Net blotch severity at GS 70 (beginning of grain filling) of whole plot assessments yielded the highest adjusted R-squared (0.43) while the adjusted R-squared values resulting from using the same parameter of assessments of the upper three, four or all leaves of single tillers were between 0.34 and 0.35. Also, the residuals of TGW of GLM’s using disease covariates from whole-plot assessments and variety effects as independent variables exhibited less pattern related to other sources of variation than residuals of the corresponding models that used single-tiller-based disease covariates. FA revealed that all disease parameters were highly inter-correlated and co-varied along the 1 principal component axis. The results indicate that disease assessments at GS 70 are appropriate to reflect whole-season severity levels of net blotch. In this respect, the time consuming single-tiller method is in this respect not superior to the simpler whole-plot method. However, assessing individual leaf layers of single tillers allows to observe the epidemic development and thus to examine the dynamics of epidemics in much greater detail than assessing whole-plots. This showed, for example, how much each leaf layer contributed at any given time to the total disease and revealed that a substantial fraction of the total disease is being removed during the course of an epidemic by senescence of diseased lower leaves. This level of detail in examining the dynamics of epidemics cannot be achieved by the whole-plot method

A critical wind speed for air-sea boundary processes

Most processes at the air-sea boundary are modified by the existing wind pattern. In general the rate of these processes varies gradually with wind speed. An exception seems to occur at a wind speed of about 7 m/sec; at that speed a number of apparently unrelated processes have been observed to undergo such abrupt changes that, in some instances, one is led to suspect the existance of discontinuities. Not only the rate, but the very nature of these processes seems to be altered at this critical wind speed...

Testing for lack of fit in inverse regression - with applications to photonic imaging.

Regression; Problems; Lack-of-fit; Applications;

High frequency spectrum of ocean waves

The subject Motion in the Ocean, assigned to me by President Bronk, includes fish, Aqua-lung divers and density flows. For a very good reason I must confine myself to motion of the water itself. Further, I will limit myself by considering only that part of the motion of ocean water that can be associated with surface waves. It is nearly, but not quite, the irrotational component of the motion...

FDR-control in multiscale change-point segmentation.

Fast multiple change-point segmentation methods, which additionally provide faithful statistical statements on the number, locations and sizes of the segments, have recently received great attention. In this paper, we propose a multiscale segmentation method, FDRSeg, which controls the false discovery rate (FDR) in the sense that the number of false jumps is bounded linearly by the number of true jumps. In this way, it adapts the detection power to the number of true jumps. We prove a non-asymptotic upper bound for its FDR in a Gaussian setting, which allows to calibrate the only parameter of FDRSeg properly. Moreover, we show that FDRSeg estimates change-point locations, as well as the signal, in a uniform sense at optimal minimax convergence rates up to a log-factor. The latter is w.r.t. Lp-risk, p≥1, over classes of step functions with bounded jump sizes and either bounded, or even increasing, number of change-points. FDRSeg can be efficiently computed by an accelerated dynamic program; its computational complexity is shown to be linear in the number of observations when there are many change-points. The performance of the proposed method is examined by comparisons with some state of the art methods on both simulated and real datasets. An R-package is available online

Vekselvirkning mellem plantesygdomme påvirker sygdomsudviklingen

Sygdomme i planter kan være forårsaget af mange forskellige mikroorganismer, og ofte vil der i en enkelt afgrøde og på én plante være flere arter tilstede samtidigt. På trods af denne erfaring har der været tradition for at forske i sygdomme enkeltvis, og betydningen på det totale sygdomsniveau af vekselvirkninger mellem de enkelte patogener er kun blevet studeret i begrænset omfang. Her beskrives vekselvirkningen mellem sygdommene bladplet og skoldplet på byg i markforsøg

Absorption of nutrients by aquatic plants

Formulae are derived for the rate of nutrient absorption by aquatic plants approximating the shapes of spheres, discs, cylinders, and plates. Other parameters are the size and specific gravity of the plant, the nutrient concentration of the medium, and the physical properties affecting the transfer of nutrients toward the plant surface. The formulae allow for convection, i. e., the movement of water relative to the plant. Hence absorption is aided by a current in the case of attached plants and by a rapid sinking rate in the case of plankton. The results are not materially modified by turbulence...