Generalized methods and solvers for noise removal from piecewise constant signals. I. Background theory

Removing noise from piecewise constant (PWC) signals is a challenging signal processing problem arising in many practical contexts. For example, in exploration geosciences, noisy drill hole records need to be separated into stratigraphic zones, and in biophysics, jumps between molecular dwell states have to be extracted from noisy fluorescence microscopy signals. Many PWC denoising methods exist, including total variation regularization, mean shift clustering, stepwise jump placement, running medians, convex clustering shrinkage and bilateral filtering; conventional linear signal processing methods are fundamentally unsuited. This paper (part I, the first of two) shows that most of these methods are associated with a special case of a generalized functional, minimized to achieve PWC denoising. The minimizer can be obtained by diverse solver algorithms, including stepwise jump placement, convex programming, finite differences, iterated running medians, least angle regression, regularization path following and coordinate descent. In the second paper, part II, we introduce novel PWC denoising methods, and comparisons between these methods performed on synthetic and real signals, showing that the new understanding of the problem gained in part I leads to new methods that have a useful role to play

Large-scale data for multiple-view stereopsis

The seminal multiple-view stereo benchmark evaluations from Middlebury and by Strecha et al. have played a major role in propelling the development of multi-view stereopsis (MVS) methodology. The somewhat small size and variability of these data sets, however, limit their scope and the conclusions that can be derived from them. To facilitate further development within MVS, we here present a new and varied data set consisting of 80 scenes, seen from 49 or 64 accurate camera positions. This is accompanied by accurate structured light scans for reference and evaluation. In addition all images are taken under seven different lighting conditions. As a benchmark and to validate the use of our data set for obtaining reasonable and statistically significant findings about MVS, we have applied the three state-of-the-art MVS algorithms by Campbell et al., Furukawa et al., and Tola et al. to the data set. To do this we have extended the evaluation protocol from the Middlebury evaluation, necessitated by the more complex geometry of some of our scenes. The data set and accompanying evaluation framework are made freely available online. Based on this evaluation, we are able to observe several characteristics of state-of-the-art MVS, e.g. that there is a tradeoff between the quality of the reconstructed 3D points (accuracy) and how much of an object’s surface is captured (completeness). Also, several issues that we hypothesized would challenge MVS, such as specularities and changing lighting conditions did not pose serious problems. Our study finds that the two most pressing issues for MVS are lack of texture and meshing (forming 3D points into closed triangulated surfaces)

Towards Machine Wald

The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of sophisticated statistical models, these models are still designed \emph{by humans} because there is currently no known recipe or algorithm for dividing the design of a statistical model into a sequence of arithmetic operations. Indeed enabling computers to \emph{think} as \emph{humans} have the ability to do when faced with uncertainty is challenging in several major ways: (1) Finding optimal statistical models remains to be formulated as a well posed problem when information on the system of interest is incomplete and comes in the form of a complex combination of sample data, partial knowledge of constitutive relations and a limited description of the distribution of input random variables. (2) The space of admissible scenarios along with the space of relevant information, assumptions, and/or beliefs, tend to be infinite dimensional, whereas calculus on a computer is necessarily discrete and finite. With this purpose, this paper explores the foundations of a rigorous framework for the scientific computation of optimal statistical estimators/models and reviews their connections with Decision Theory, Machine Learning, Bayesian Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty Quantification and Information Based Complexity.Comment: 37 page

Efeitos de retardadores de crescimento na frutificação da videira 'Niagara Rosada'

Studies were carried out to establish the effects of exogenous growth regulators on Vitis (labrusca x vinifera) 'Niagara Rosada' fruiting. The investigations were done in the Jundiaí Research Station, Agronomic Institute State of São Paulo, always using disease-free vineyards of good productivity. The morphological transformations of clusters were studied under the following aspects: weight, length and width of cluster; weight, length average and width average of berries: length average/width average ratio of berries; length and diameter of rachis; width of cluster minus berries; length and diameter of secondary rachis. The yield for the first half of the period from flowering to maturation was first determined. The same characteristics were determined at the time of maturity plus the number of berries, number of seeds, total sugars, total acid, Maturity Index and reducing sugars in samples of all treatments. The experiment was conducted in order to determine the doses that resulted in the most beneficial effects, always using applications by immersion of the inflorescence. In the experiment was realized applications of (2-chloroethyl) trimethylammonium chloride (CCC) and succinic aeid-2, 2-dimethylhydrazide (SADH) at concentrations of 50, 100, 250, 500, 1000 and 2000 ppm; CCC 500 ppm plus SADH 500 ppm and nontreated, 5 days before flowering, in 1971. The concentrations of CCC applied before flowering did not affect favorably cluster morphology under the conditions of the experiment. Application of SADH at 250 ppm before flowering increased the cluster weight and length, berries number and weight, and seed number. In the first yield treatment of 1000 ppm of SADH increased the cluster weight and lenght, berry weight and rachis lenght.Estudou-se a influência da aplicação por imersão, de retardadores de crescimento (CCC e SADH), 5 dias antes do florescimento, nas características morfológicas da panícuia da videira Vitis (labrusca x vinifera) 'Niagara Rosada'. Neste ensaio verificou-se que as concentrações de CCC aplicadas em pré-florescimento, não afetaram favoravelmente a morfologia das panículas da cultivar estudada, nas condições do ensaio. SADH na dosagem de 1000 ppm provocou, na primeira colheita, aumento no peso e comprimento da panícula, no peso das bagas, e no comprimento da ráquis, proporcionando a formação desejada de uma panícula mais alongada, nas condições estudadas. Aplicação de SADH na concentração de 250 ppm em pré-florescimento, promoveu aumento no peso e comprimento da panícula, número e peso das bagas, além do inconveniente de elevar o número de sementes

Stability of gene contributions and identification of outliers in multivariate analysis of microarray data

BACKGROUND: Multivariate ordination methods are powerful tools for the exploration of complex data structures present in microarray data. These methods have several advantages compared to common gene-by-gene approaches. However, due to their exploratory nature, multivariate ordination methods do not allow direct statistical testing of the stability of genes. RESULTS: In this study, we developed a computationally efficient algorithm for: i) the assessment of the significance of gene contributions and ii) the identification of sample outliers in multivariate analysis of microarray data. The approach is based on the use of resampling methods including bootstrapping and jackknifing. A statistical package of R functions was developed. This package includes tools for both inferring the statistical significance of gene contributions and identifying outliers among samples. CONCLUSION: The methodology was successfully applied to three published data sets with varying levels of signal intensities. Its relevance was compared with alternative methods. Overall, it proved to be particularly effective for the evaluation of the stability of microarray data

Big-Data Science in Porous Materials: Materials Genomics and Machine Learning

By combining metal nodes with organic linkers we can potentially synthesize millions of possible metal organic frameworks (MOFs). At present, we have libraries of over ten thousand synthesized materials and millions of in-silico predicted materials. The fact that we have so many materials opens many exciting avenues to tailor make a material that is optimal for a given application. However, from an experimental and computational point of view we simply have too many materials to screen using brute-force techniques. In this review, we show that having so many materials allows us to use big-data methods as a powerful technique to study these materials and to discover complex correlations. The first part of the review gives an introduction to the principles of big-data science. We emphasize the importance of data collection, methods to augment small data sets, how to select appropriate training sets. An important part of this review are the different approaches that are used to represent these materials in feature space. The review also includes a general overview of the different ML techniques, but as most applications in porous materials use supervised ML our review is focused on the different approaches for supervised ML. In particular, we review the different method to optimize the ML process and how to quantify the performance of the different methods. In the second part, we review how the different approaches of ML have been applied to porous materials. In particular, we discuss applications in the field of gas storage and separation, the stability of these materials, their electronic properties, and their synthesis. The range of topics illustrates the large variety of topics that can be studied with big-data science. Given the increasing interest of the scientific community in ML, we expect this list to rapidly expand in the coming years.Comment: Editorial changes (typos fixed, minor adjustments to figures