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.     

Signage Versus Environmental Affordances: Is the Explicit Information Strong Enough to Guide Human Behavior During a Wayfinding Task?

This study aims to explore how people behave when they have to find a location within a complex building and are confronted with situations where directional signage (i.e., explicit information) is in opposition to environmental affordances that naturally direct users towards a specific path, creating a situation with conflicting information (e.g., a brighter corridor vs. a darker corridor but with a directional sign indicating to follow the darker one). A virtual reality–based methodology was used and a between‐subject design was considered. Thus, participants were given the tasks of finding three publicly accessible central points in a virtual hotel and confronted with a two forced‐choice task of local scenes in which environmental variables (i.e., corridor width and brightness) and signage varied systematically, in two experimental conditions (i.e., neutral and signage). For the signage condition, signs were inserted to explicitly point in the opposite direction than that implicitly suggested by the environmental affordances, creating situations with conflicting information. Results indicate that environmental variables were able to direct people indoors acting as environmental affordances. Users preferred to follow the wider and brighter paths. However, when directional signage pointed in the opposite direction of the paths preferred by the participants, most of them complied with signage.     

A high-shear, low Reynolds number microfluidic rheometer

We present a microfluidic rheometer that uses in situ pressure sensors to measure the viscosity of liquids at low Reynolds number. Viscosity is measured in a long, straight channel using a PDMS-based microfluidic device that consists of a channel layer and a sensing membrane integrated with an array of piezoresistive pressure sensors via plasma surface treatment. The micro-pressure sensor is fabricated using conductive particles/PDMS composites. The sensing membrane maps pressure differences at various locations within the channel in order to measure the fluid shear stress in situ at a prescribed shear rate to estimate the fluid viscosity. We find that the device is capable to measure the viscosity of both Newtonian and non-Newtonian fluids for shear rates up to 10⁴ s^?1 while keeping the Reynolds number well below 1.     

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.