A linear algebra approach to OLAP

Inspired by the relational algebra of data processing, this paper addresses the foundations of data analytical processing from a linear algebra perspective. The paper investigates, in particular, how aggregation operations such as cross tabulations and data cubes essential to quantitative analysis of data can be expressed solely in terms of matrix multiplication, transposition and the Khatri–Rao variant of the Kronecker product. The approach offers a basis for deriving an algebraic theory of data consolidation, handling the quantitative as well as qualitative sides of data science in a natural, elegant and typed way. It also shows potential for parallel analytical processing, as the parallelization theory of such matrix operations is well acknowledged.     

Factors of low individual degree polynomials

Kaltofen (Randomness in computation, vol 5, pp 375–412, 1989) proved the remarkable fact that multivariate polynomial factorization can be done efficiently, in randomized polynomial time. Still, more than twenty years after Kaltofen’s work, many questions remain unanswered regarding the complexity aspects of polynomial factorization, such as the question of whether factors of polynomials efficiently computed by arithmetic formulas also have small arithmetic formulas, asked in Kopparty et al. (2014), and the question of bounding the depth of the circuits computing the factors of a polynomial. We are able to answer these questions in the affirmative for the interesting class of polynomials of bounded individual degrees, which contains polynomials such as the determinant and the permanent. We show that if \({P(x_{1},\ldots,x_{n})}\) is a polynomial with individual degrees bounded by r that can be computed by a formula of size s and depth d, then any factor \({f(x_{1},\ldots, x_{n})}\) of \({P(x_{1},\ldots,x_{n})}\) can be computed by a formula of size \({\textsf{poly}((rn)^{r},s)}\) and depth d + 5. This partially answers the question above posed in Kopparty et al. (2014), who asked if this result holds without the dependence on r. Our work generalizes the main factorization theorem from Dvir et al. (SIAM J Comput 39(4):1279–1293, 2009), who proved it for the special case when the factors are of the form \({f(x_{1}, \ldots, x_{n}) \equiv x_{n} - g(x_{1}, \ldots, x_{n-1})}\). Along the way, we introduce several new technical ideas that could be of independent interest when studying arithmetic circuits (or formulas).     

Exploring the costs of technical debt management – a case study

Technical debt is a metaphor for delayed software maintenance tasks. Incurring technical debt may bring short-term benefits to a project, but such benefits are often achieved at the cost of extra work in future, analogous to paying interest on the debt. Currently technical debt is managed implicitly, if at all. However, on large systems, it is too easy to lose track of delayed tasks or to misunderstand their impact. Therefore, we have proposed a new approach to managing technical debt, which we believe to be helpful for software managers to make informed decisions. In this study we explored the costs of the new approach by tracking the technical debt management activities in an on-going software project. The results from the study provided insights into the impact of technical debt management on software projects. In particular, we found that there is a significant start-up cost when beginning to track and monitor technical debt, but the cost of ongoing management soon declines to very reasonable levels.     

A two‐step control approach for docking of autonomous underwater vehicles

This paper presents a novel integrated guidance and control strategy for docking of autonomous underwater vehicles. The approach to the base, and hence the control design, is divided in two steps: (i) in the first, at higher speed, the vehicle dynamics is assumed to be underactuated, and an appropriate control law is derived to steer the vehicle towards the final docking path, achieving convergence to zero of the appropriate error variables for almost all initial conditions; (ii) in the second stage, at low speed, the vehicle is assumed to be fully actuated, and a robust control law is designed that achieves convergence to zero of the appropriate error variables for all initial conditions, in the presence of parametric model uncertainty. Simulations are presented illustrating the performance of the proposed controllers, including model uncertainty and sensor noise. Copyright © 2014 John Wiley & Sons, Ltd.     

High‐Order Recursive Filtering of Non‐Uniformly Sampled Signals for Image and Video Processing

We present a discrete‐time mathematical formulation for applying recursive digital filters to non‐uniformly sampled signals. Our solution presents several desirable features: it preserves the stability of the original filters; is well‐conditioned for low‐pass, high‐pass, and band‐pass filters alike; its cost is linear in the number of samples and is not affected by the size of the filter support. Our method is general and works with any non‐uniformly sampled signal and any recursive digital filter defined by a difference equation. Since our formulation directly uses the filter coefficients, it works out‐of‐the‐box with existing methodologies for digital filter design. We demonstrate the effectiveness of our approach by filtering non‐uniformly sampled signals in various image and video processing tasks including edge‐preserving color filtering, noise reduction, stylization, and detail enhancement. Our formulation enables, for the first time, edge‐aware evaluation of any recursive infinite impulse response digital filter (not only low‐pass), producing high‐quality filtering results in real time.     

Fractal dimension applied to plant identification

This article discusses methods to identify plants by analysing leaf complexity based on estimating their fractal dimension. Leaves were analyzed according to the complexity of their internal and external shapes. A computational program was developed to process, analyze and extract the features of leaf images, thereby allowing for automatic plant identification. Results are presented from two experiments, the first to identify plant species from the Brazilian Atlantic forest and Brazilian Cerrado scrublands, using fifty leaf samples from ten different species, and the second to identify four different species from genus Passiflora, using twenty leaf samples for each class. A comparison is made of two methods to estimate fractal dimension (box-counting and multiscale Minkowski). The results are discussed to determine the best approach to analyze shape complexity based on the performance of the technique, when estimating fractal dimension and identifying plants.     

A multiscale directional operator and morphological tools for reconnecting broken ridges in fingerprint images

In this paper, we introduce a multiscale operator which, together with some morphological tools, can be used to reconnect broken components of fingerprint images. This operator, which can be applied to both binary and gray-scale pictures, extracts the orientation field of an image by taking into account information parameters of sets of pixels in a given neighborhood and located in different directions. It has proved to be very robust to noise and outperforms the gradient- and directional mask-based methods, generally used for orientation field definition. Although we illustrate its application in the fingerprint domain, the approach described here can be easily extended to images whose components exhibit well-defined directional information.     

Log-Burr XII regression models with censored data

In survival analysis applications, the failure rate function may frequently present a unimodal shape. In such case, the log-normal or log-logistic distributions are used. In this paper, we shall be concerned only with parametric forms, so a location-scale regression model based on the Burr XII distribution is proposed for modeling data with a unimodal failure rate function as an alternative to the log-logistic regression model. Assuming censored data, we consider a classic analysis, a Bayesian analysis and a jackknife estimator for the parameters of the proposed model. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the log-logistic and log-Burr XII regression models. Besides, we use sensitivity analysis to detect influential or outlying observations, and residual analysis is used to check the assumptions in the model. Finally, we analyze a real data set under log-Burr XII regression models.