On arithmetic intersection numbers on self-products of curves

We give a close formula for the N\'eron-Tate height of tautological integral cycles on Jacobians of curves over number fields as well as a new lower bound for the arithmetic self-intersection number $\hat{\omega}^2$ of the dualizing sheaf of a curve in terms of Zhang's invariant $\varphi$. As an application, we obtain an effective Bogomolov-type result for the tautological cycles. We deduce these results from a more general combinatorial computation of arithmetic intersection numbers of adelic line bundles on higher self-products of curves, which are linear combinations of pullbacks of line bundles on the curve and the diagonal bundle.Comment: 21 pages. Comments are welcome

Sparse canonical correlation analysis from a predictive point of view

Canonical correlation analysis (CCA) describes the associations between two sets of variables by maximizing the correlation between linear combinations of the variables in each data set. However, in high-dimensional settings where the number of variables exceeds the sample size or when the variables are highly correlated, traditional CCA is no longer appropriate. This paper proposes a method for sparse CCA. Sparse estimation produces linear combinations of only a subset of variables from each data set, thereby increasing the interpretability of the canonical variates. We consider the CCA problem from a predictive point of view and recast it into a regression framework. By combining an alternating regression approach together with a lasso penalty, we induce sparsity in the canonical vectors. We compare the performance with other sparse CCA techniques in different simulation settings and illustrate its usefulness on a genomic data set

Designing strategies to control grey mould in strawberry cultivation using decision support systems

Grey mould is one of the major diseases in strawberry cultivation. Fungicides to control Botrytis cinerea are applied frequently during flowering and sometimes at harvest. Reduction of pesticide use is one of the major aims of the Dutch government. Implementation of a Decision Support System (DSS) helps to achieve this goal. Pin point timing of fungicide application can possibly improve the efficacy of the treatment and reduce the number of spray applications. Predicted weather data to forecast infection risks are used by most DSS’s. However in strawberry cultivation irrigation is a daily practice. The effect of overhead irrigation on the Botrytis infection risk is unknown. This is one of the reasons that strawberry growers infrequently use DSS’s. Therefore adaptation of the model to agricultural management is necessary. Under low disease pressure DSS BoWaS controlled Botrytis fruit rot 62% better then routine applications of fungicides, with a 50% reduction of fungicide input. Adding an irrigation or a disease pressure sub-routine did not improve the model under low disease pressure. BoWaS based on disease pressure and weather resulted in better control of grey mould then the weather based BoWaS, under high disease pressure. Adding an irrigation rule did not improve the model further. Using the modified BoWaS reduced fungicide input with 36% compared to routine applications with the same efficacy

Reading out a spatiotemporal population code by imaging neighbouring parallel fibre axons in vivo.

The spatiotemporal pattern of synaptic inputs to the dendritic tree is crucial for synaptic integration and plasticity. However, it is not known if input patterns driven by sensory stimuli are structured or random. Here we investigate the spatial patterning of synaptic inputs by directly monitoring presynaptic activity in the intact mouse brain on the micron scale. Using in vivo calcium imaging of multiple neighbouring cerebellar parallel fibre axons, we find evidence for clustered patterns of axonal activity during sensory processing. The clustered parallel fibre input we observe is ideally suited for driving dendritic spikes, postsynaptic calcium signalling, and synaptic plasticity in downstream Purkinje cells, and is thus likely to be a major feature of cerebellar function during sensory processing

Robust Sparse Canonical Correlation Analysis

Canonical correlation analysis (CCA) is a multivariate statistical method which describes the associations between two sets of variables. The objective is to find linear combinations of the variables in each data set having maximal correlation. This paper discusses a method for Robust Sparse CCA. Sparse estimation produces canonical vectors with some of their elements estimated as exactly zero. As such, their interpretability is improved. We also robustify the method such that it can cope with outliers in the data. To estimate the canonical vectors, we convert the CCA problem into an alternating regression framework, and use the sparse Least Trimmed Squares estimator. We illustrate the good performance of the Robust Sparse CCA method in several simulation studies and two real data examples

Sparse cointegration

Cointegration analysis is used to estimate the long-run equilibrium relations between several time series. The coefficients of these long-run equilibrium relations are the cointegrating vectors. In this paper, we provide a sparse estimator of the cointegrating vectors. The estimation technique is sparse in the sense that some elements of the cointegrating vectors will be estimated as zero. For this purpose, we combine a penalized estimation procedure for vector autoregressive models with sparse reduced rank regression. The sparse cointegration procedure achieves a higher estimation accuracy than the traditional Johansen cointegration approach in settings where the true cointegrating vectors have a sparse structure, and/or when the sample size is low compared to the number of time series. We also discuss a criterion to determine the cointegration rank and we illustrate its good performance in several simulation settings. In a first empirical application we investigate whether the expectations hypothesis of the term structure of interest rates, implying sparse cointegrating vectors, holds in practice. In a second empirical application we show that forecast performance in high-dimensional systems can be improved by sparsely estimating the cointegration relations

Land use mapping and change detection using ERTS imagery in Montgomery County, Alabama

The feasibility of using remotely sensed data from ERTS-1 for mapping land use and detecting land use change was investigated. Land use information was gathered from 1964 air photo mosaics and from 1972 ERTS data. The 1964 data provided the basis for comparison with ERTS-1 imagery. From this comparison, urban sprawl was quite evident for the city of Montgomery. A significant trend from forestland to agricultural was also discovered. The development of main traffic arteries between 1964 and 1972 was a vital factor in the development of some of the urban centers. Even though certain problems in interpreting and correlating land use data from ERTS imagery were encountered, it has been demonstrated that remotely sensed data from ERTS is useful for inventorying land use and detecting land use change