Comparison data for Seasat altimetry in the western North Atlantic

The radar altimeter flown on Seasat in 1978 collected approximately 1,000 orbits of high quality data (5-8 precision). In the western North Atlantic these data were combined with a detailed gravimetric geoid in an attempt to produce profiles of dynamic topography. In order to provide a basis for evaluation of these profiles, available oceanographic observations in the Gulf Stream/Sargasso Sea region have been compiled into a series of biweekly maps. The data include XBT's, satellite infrared imagery, and selected trajectories of surface drifters and sub-surface SOFAR floats. The maps document the known locations of the Gulf Stream, cyclonic and anticyclonic rings, and mid-ocean eddies during the period July to October 1978

Nonparametric Markovian Learning of Triggering Kernels for Mutually Exciting and Mutually Inhibiting Multivariate Hawkes Processes

In this paper, we address the problem of fitting multivariate Hawkes processes to potentially large-scale data in a setting where series of events are not only mutually-exciting but can also exhibit inhibitive patterns. We focus on nonparametric learning and propose a novel algorithm called MEMIP (Markovian Estimation of Mutually Interacting Processes) that makes use of polynomial approximation theory and self-concordant analysis in order to learn both triggering kernels and base intensities of events. Moreover, considering that N historical observations are available, the algorithm performs log-likelihood maximization in $O(N)$ operations, while the complexity of non-Markovian methods is in $O(N^{2})$. Numerical experiments on simulated data, as well as real-world data, show that our method enjoys improved prediction performance when compared to state-of-the art methods like MMEL and exponential kernels

Case-control study to detect protective factors on pig farms with low Salmonella prevalence

The prevalence of Salmonella in UK pigs is amongst the highest in Europe, highlighting the risk to public health and the need to investigate on-farm controls. The objective of this study was to identify factors currently in operation on pig farms that had maintained a low Salmonella seroprevalence. For this purpose a case-control study was designed and pig farms with a low (\u3c10%) seroprevalence were compared against two randomly selected control farms, sharing the same geographical region and production type. A total of 11,452 samples, including pooled and individual floor faeces and environmental samples from pigs and their vicinity were tested and prevalence examined. In addition, detailed questionnaires were completed during the farm visits to collect descriptive data for risk factor analysis. It was shown that control farms had significantly higher prevalence compared to the case farms (19.4% and 4.3% for pooled and 6.7% and 0.1% for individual samples, respectively). The two risk factor analyses identified multiple variables associated with Salmonella prevalence including variables related to feed, effectiveness of cleaning and disinfection, biosecurity and batch production

Super-resolution, Extremal Functions and the Condition Number of Vandermonde Matrices

Super-resolution is a fundamental task in imaging, where the goal is to extract fine-grained structure from coarse-grained measurements. Here we are interested in a popular mathematical abstraction of this problem that has been widely studied in the statistics, signal processing and machine learning communities. We exactly resolve the threshold at which noisy super-resolution is possible. In particular, we establish a sharp phase transition for the relationship between the cutoff frequency ($m$) and the separation ($\Delta$). If $m > 1/\Delta + 1$, our estimator converges to the true values at an inverse polynomial rate in terms of the magnitude of the noise. And when $m < (1-\epsilon) /\Delta$ no estimator can distinguish between a particular pair of $\Delta$-separated signals even if the magnitude of the noise is exponentially small. Our results involve making novel connections between {\em extremal functions} and the spectral properties of Vandermonde matrices. We establish a sharp phase transition for their condition number which in turn allows us to give the first noise tolerance bounds for the matrix pencil method. Moreover we show that our methods can be interpreted as giving preconditioners for Vandermonde matrices, and we use this observation to design faster algorithms for super-resolution. We believe that these ideas may have other applications in designing faster algorithms for other basic tasks in signal processing.Comment: 19 page

Myosin-X functions in polarized epithelial cells

Myosin-X, an unconventional myosin that has been studied primarily in fibroblast-like cells, has been shown to have important functions in polarized epithelial cell junction formation, regulation of paracellular permeability, and epithelial morphogenesis.Myosin-X (Myo10) is an unconventional myosin that localizes to the tips of filopodia and has critical functions in filopodia. Although Myo10 has been studied primarily in nonpolarized, fibroblast-like cells, Myo10 is expressed in vivo in many epithelia-rich tissues, such as kidney. In this study, we investigate the localization and functions of Myo10 in polarized epithelial cells, using Madin-Darby canine kidney II cells as a model system. Calcium-switch experiments demonstrate that, during junction assembly, green fluorescent protein–Myo10 localizes to lateral membrane cell–cell contacts and to filopodia-like structures imaged by total internal reflection fluorescence on the basal surface. Knockdown of Myo10 leads to delayed recruitment of E-cadherin and ZO-1 to junctions, as well as a delay in tight junction barrier formation, as indicated by a delay in the development of peak transepithelial electrical resistance (TER). Although Myo10 knockdown cells eventually mature into monolayers with normal TER, these monolayers do exhibit increased paracellular permeability to fluorescent dextrans. Importantly, knockdown of Myo10 leads to mitotic spindle misorientation, and in three-dimensional culture, Myo10 knockdown cysts exhibit defects in lumen formation. Together these results reveal that Myo10 functions in polarized epithelial cells in junction formation, regulation of paracellular permeability, and epithelial morphogenesis

A dependent nominal type theory

Nominal abstract syntax is an approach to representing names and binding pioneered by Gabbay and Pitts. So far nominal techniques have mostly been studied using classical logic or model theory, not type theory. Nominal extensions to simple, dependent and ML-like polymorphic languages have been studied, but decidability and normalization results have only been established for simple nominal type theories. We present a LF-style dependent type theory extended with name-abstraction types, prove soundness and decidability of beta-eta-equivalence checking, discuss adequacy and canonical forms via an example, and discuss extensions such as dependently-typed recursion and induction principles

Improving the condition number of estimated covariance matrices

High dimensional error covariance matrices and their inverses are used to weight the contribution of observation and background information in data assimilation procedures. As observation error covariance matrices are often obtained by sampling methods, estimates are often degenerate or ill-conditioned, making it impossible to invert an observation error covariance matrix without the use of techniques to reduce its condition number. In this paper we present new theory for two existing methods that can be used to ‘recondition’ any covariance matrix: ridge regression, and the minimum eigenvalue method. We compare these methods with multiplicative variance inflation, which cannot alter the condition number of a matrix, but is often used to account for neglected correlation information. We investigate the impact of reconditioning on variances and correlations of a general covariance matrix in both a theoretical and practical setting. Improved theoretical understanding provides guidance to users regarding method selection, and choice of target condition number. The new theory shows that, for the same target condition number, both methods increase variances compared to the original matrix, with larger increases for ridge regression than the minimum eigenvalue method. We prove that the ridge regression method strictly decreases the absolute value of off-diagonal correlations. Theoretical comparison of the impact of reconditioning and multiplicative variance inflation on the data assimilation objective function shows that variance inflation alters information across all scales uniformly, whereas reconditioning has a larger effect on scales corresponding to smaller eigenvalues. We then consider two examples: a general correlation function, and an observation error covariance matrix arising from interchannel correlations. The minimum eigenvalue method results in smaller overall changes to the correlation matrix than ridge regression, but can increase off-diagonal correlations. Data assimilation experiments reveal that reconditioning corrects spurious noise in the analysis but underestimates the true signal compared to multiplicative variance inflation

Positive approximations of the inverse of fractional powers of SPD M-matrices

This study is motivated by the recent development in the fractional calculus and its applications. During last few years, several different techniques are proposed to localize the nonlocal fractional diffusion operator. They are based on transformation of the original problem to a local elliptic or pseudoparabolic problem, or to an integral representation of the solution, thus increasing the dimension of the computational domain. More recently, an alternative approach aimed at reducing the computational complexity was developed. The linear algebraic system $\cal A^\alpha \bf u=\bf f$, $0< \alpha <1$ is considered, where $\cal A$ is a properly normalized (scalded) symmetric and positive definite matrix obtained from finite element or finite difference approximation of second order elliptic problems in $\Omega\subset\mathbb{R}^d$, $d=1,2,3$. The method is based on best uniform rational approximations (BURA) of the function $t^{\beta-\alpha}$ for $0 < t \le 1$ and natural $\beta$. The maximum principles are among the major qualitative properties of linear elliptic operators/PDEs. In many studies and applications, it is important that such properties are preserved by the selected numerical solution method. In this paper we present and analyze the properties of positive approximations of $\cal A^{-\alpha}$ obtained by the BURA technique. Sufficient conditions for positiveness are proven, complemented by sharp error estimates. The theoretical results are supported by representative numerical tests