Graf-type theorem for Laguerre and Legendre functions

In this paper, we discuss Graf-type series for Laguerre and Legendre functions. Within this context, we indicate the existence of two-variable, one-index generalized functions and discuss their properties. This class of special functions represents a useful tool for dealing with a large number of physical problems, from that relevant to multilevel system dynamics to the study of incommensurate structures.     

Identification of active compounds in vegetal extracts based on correlation between activity and HPLC–MS data

We propose a method identifying candidates for active compounds in vegetal extracts. From a collection of samples, the method requires, for each sample, a HPLC–MS analysis and a measurement of the activity. By applying a correlation analysis between the activity and the chromatographic area for each interval of elution time and m/z ratio, the peaks corresponding to candidates for active compounds can be identified. Additionally, when peaks are identified, a model can be estimated to predict the activity in new samples. Both methods are evaluated in one experiment involving the phenolic extract (PE) from 22 samples of extra virgin olive oil (EVOO) where the activity is a cytotoxicity index against JIMT-1 breast cancer cells. In this experiment, the samples were separated into two disjunct partitions: one was used for training (identification of candidates and estimation of prediction model), while the other was used for validation (by comparing the predicted and the measured activities). Three compounds were identified as candidates to be responsible for the cytotoxicity of the EVOO-PE against JIMT-1 cells. The prediction model provided an accurate estimation of the activity.     

Native carotenoids composition of some tropical fruits

Many tropical fruits can be considered a reservoir of bioactive substances with a special interest due to their possible health-promoting properties. The interest in carotenoids from a nutritional standpoint has recently greatly increased, because of their important health benefits. Here we report the native carotenoids composition in six tropical fruits from Panama, which is considered a region of great biodiversity. The native carotenoid composition was directly investigated by an HPLC-DAD-APCI-MS methodology, for the first time. In Corozo 32 different carotenoids were detected, including a high content of β-carotene and lycopene. Sastra showed the highest content of zeaxanthin among the fruit investigated. In Sapote 22 different carotenoids were detected, including β-carotene and 10 different zeaxanthin-di-esters. Frutita showed a very high content of the apo-carotenoid β-citraurin, and of a number of its esters. In Maracuyà chino 14 carotenoids were detected, including a high amounts of mono-esterified lauric acid with β-cryptoxanthin and with cryptocapsin. Mamey rojo was characterised by ketocarotenoids with κ rings, both hydroxylated and not hydroxylated.     

On edge detection

Edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them. A critical, intermediate goal of edge detection is the detection and characterization of significant intensity changes. This paper discusses this part of the edge detection problem. To characterize the types of intensity changes derivatives of different types, and possibly different scales, are needed. Thus, we consider this part of edge detection as a problem in numerical differentiation. We show that numerical differentiation of images is an ill-posed problem in the sense of Hadamard. Differentiation needs to be regularized by a regularizing filtering operation before differentiation. This shows that this part of edge detection consists of two steps, a filtering step and a differentiation step. Following this perspective, the paper discusses in detail the following theoretical aspects of edge detection. 1) The properties of different types of filters-with minimal uncertainty, with a bandpass spectrum, and with limited support-are derived. Minimal uncertainty filters optimize a tradeoff between computational efficiency and regularizing properties. 2) Relationships among several 2-D differential operators are established. In particular, we characterize the relation between the Laplacian and the second directional derivative along the gradient. Zero crossings of the Laplacian are not the only features computed in early vision. 3) Geometrical and topological properties of the zero crossings of differential operators are studied in terms of transversality and Morse theory.     

Exemplar driven development of software product lines

The benefits of following a product line approach to develop similar software systems are well documented. Nevertheless, some case studies have revealed significant barriers to adopt such approach. In order to minimize the paradigm shift between conventional software engineering and software product line engineering, this paper presents a new development process where the products of a domain are made by analogy to an existing product. Furthermore, this paper discusses the capabilities and limitations of different techniques to implement the analogy relation and proposes a new language to overcome such limitations.     

A dynamic logic for privacy compliance

Knowledge based privacy policies are more declarative than traditional action based ones, because they specify only what is permitted or forbidden to know, and leave the derivation of the permitted actions to a security monitor. This inference problem is already non trivial with a static privacy policy, and becomes challenging when privacy policies can change over time. We therefore introduce a dynamic modal logic that permits not only to reason about permitted and forbidden knowledge to derive the permitted actions, but also to represent explicitly the declarative privacy policies together with their dynamics. The logic can be used to check both regulatory and behavioral compliance, respectively by checking that the permissions and obligations set up by the security monitor of an organization are not in conflict with the privacy policies, and by checking that these obligations are indeed enforced.     

Image-based Shaving

Many categories of objects, such as human faces, can be naturally viewed as a composition of several different layers. For example, a bearded face with glasses can be decomposed into three layers: a layer for glasses, a layer for the beard and a layer for other permanent facial features. While modeling such a face with a linear subspace model could be very difficult, layer separation allows for easy modeling and modification of some certain structures while leaving others unchanged. In this paper, we present a method for automatic layer extraction and its applications to face synthesis and editing. Layers are automatically extracted by utilizing the differences between subspaces and modeled separately. We show that our method can be used for tasks such beard removal (virtual shaving), beard synthesis, and beard transfer, among others.     

Motion synthesis through 1D affine matching

We present the study of a data-driven motion synthesis approach based on a 1D affine image-matching equation. We start by deriving the relevant properties of the exact matching operator, such as the existence of a singular point. Next, we approximate such operator by the Green’s function of a second-order differential equation, finding that it leads to a more compelling motion impression, due to the incorporation of blur. We then proceed to show that, by judicious choice of the matching parameters, the 1D affine Green’s filter allows the simulation of a broad class of effects, such as zoom-in and zoom-out, and of complex nonrigid motions such as that of a pulsating heart.

Poisson's and Laplace's equations in inhomogeneous magnetic media

Poisson's equation in inhomogeneous static magnetic media is derived for the magnetic vector potential and for the magnetic scalar potential. A modified three-dimensional seven-point finite-difference operator to be used in numerical solutions is presented. The special case of discrete inhomogeneity as discussed.     

Rietveld Quantitative Analysis of Buen Retiro Porcelains

Porcelains represent the foundation of the ceramic discipline. The variable-phase assembly within porcelains makes these materials very complex ceramics. Fine porcelains from Buen Retiro were produced between 1760 and 1808 by Spanish court ceramists. The factory and its records were totally destroyed in 1812 during the Peninsular War. Recently, some pieces of porcelain and remains of whiteware belonging to the ancient factory were discovered during an excavation. In the present work, some of the secret formulas that enabled the Spanish ceramists to produce porcelains have been investigated by quantitative full-phase analysis (including amorphous content) using the Rietveld method. Three porcelains belonging to the Sureda period (1803–1808) and another from an earlier time of the factory (1760–1783) have been analyzed. The phase results are discussed and conclusions are derived by using appropriate phase equilibrium diagrams. It has also been found that the Rietveld quantitative amorphous content analysis is effective in determining the glassy content in porcelains.