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In this paper, the feasibility of using spectral profiles for modeling water activity a w in white quinoa grains (Chenopodium quinoa Willd.) is studied. For this purpose, five hundred samples of five white varieties were stabilized at different a w values using the isopiestic method. Next, hyperspectral images (HSIs) of ten grains for each combination (variety, a w value), covering the range of 400–1000 nm were acquired, and mean spectral for each grain extracted. Then, due to a linear relationship that the spectral profiles are shown, the modeling was performed with a w values over 0.741 using partial least square regression (PLSR). From total spectra, three hundred spectrum were selected and randomly divided into training and validation sets. The results shown coefficient of determination from 0.59 to 0.834 concluding than for a w over 0.741, HSI + PLSR show potential for a w prediction in white quinoa grains.

The evaluation of cheese texture during the ripening phase usually involves invasive and destructive methods, as well as specialized equipment, which are non-advantageous characteristics for routine tests. Therefore, new noninvasive technologies for measuring texture properties are being studied. In this paper, forty Swiss-type cheese samples were prepared and carried to the ripening stage. During this process, hyperspectral images (HSI) were obtained in reflectance mode, in a range of 400–1000 nm. The hardness of Swiss-type cheese was measured using the technique of texture profile analysis. The relationship between spectral profiles and hardness values was modeled using two types of regression models, i.e., partial least squares regression (PLSR) and artificial neural networks (ANN). For both PLSR and ANN, two models were created, the first one uses all the wavelengths and the second makes a selection of the relevant wavelengths. The ANN models showed slightly better performance than the PLSR models. As result, it is possible to use the proposed technique (HSI + ANN) to predict the texture properties of Swiss-type cheeses throughout the ripening period.

Consumption of bread and the demands concerning its quality features, being one of them its appearance, have been experiencing rapid growth. Thus, the standardization of its production aiming to keep its quality, applying new methods. The objective of this research was to develop a method to optimize the bread-making processes based on the acceptability of its crust color. For this effect, bread was experimentally produced using a Box-Behnken experimental design with three factors (sugar-flour relation, Baking temperature and Baking time) and three answer variables (L*, a*, b* = parameters of CIELab color space); determination of color, by means of the acquisition, pre-processing, and analysis of images of bread samples until getting the color expressed in CIELab coordinates; an analysis of sensorial acceptance was made determining the L*, a*, and b* with the highest acceptance by consumers; finally, the optimization of the production process was made based on the L*, a*, and b* parameters, getting the optimal production parameters. The results show that by using the proposed method, it is possible to correlate the parameters of CIELab color space and the acceptance of the final consumer aiming to optimize bread making processes, it means getting bread with crust color of maximum acceptability.

Partial Least Square Regression (PLSR) is considered useful for constructing prediction equations when there are many explanatory variables and comparatively few training samples; mainly because of the method is it possible to combine the advantages from Principal Component Analysis and the multiple regression analysis. Most of the initial applications of PLSR have been in analytical chemistry, particularly food chemistry. Additionally, the use of a shortened number of key-variables reduces the needs of computational resources in the model’s calibration, and, hence, the time for analysis, which allows for the construction of online systems for quality evaluation. The analysis of different compounds of interest in foods has utilized univariate inferential methods, such as spectroscopy, refractometry, and others, reading one variable or characteristic at a time and, based on this, predicting properties of interest.

Covering arrays are combinatorial structures which have applications in fields like software testing and hardware Trojan detection. In this paper we proposed a two-stage simulated annealing algorithm to construct covering arrays. The proposed algorithm is instanced in this paper through the construction of ternary covering arrays of strength three. We were able to get 579 new upper bounds. In order to show the generality of our proposal, we defined a new benchmark composed of 25 instances of MCAs taken from the literature, all instances were improved.

Software test suites based on the concept of interaction testing are very useful for testing software components in an economical way. Test suites of this kind may be created using mathematical objects called covering arrays. A covering array, denoted by CA(N; t, k, v), is an N × k array over [Formula: see text] with the property that every N × t sub-array covers all t-tuples of [Formula: see text] at least once. Covering arrays can be used to test systems in which failures occur as a result of interactions among components or subsystems. They are often used in areas such as hardware Trojan detection, software testing, and network design. Because system testing is expensive, it is critical to reduce the amount of testing required. This paper addresses the Optimal Shortening of Covering ARrays (OSCAR) problem, an optimization problem whose objective is to construct, from an existing covering array matrix of uniform level, an array with dimensions of (N - δ) × (k - Δ) such that the number of missing t-tuples is minimized. Two applications of the OSCAR problem are (a) to produce smaller covering arrays from larger ones and (b) to obtain quasi-covering arrays (covering arrays in which the number of missing t-tuples is small) to be used as input to a meta-heuristic algorithm that produces covering arrays. In addition, it is proven that the OSCAR problem is NP-complete, and twelve different algorithms are proposed to solve it. An experiment was performed on 62 problem instances, and the results demonstrate the effectiveness of solving the OSCAR problem to facilitate the construction of new covering arrays.

The objective of this research was to develop a methodology for optimizing multilayer-per - ceptron-type neural networks by evaluating the effects of three neural architecture parame- ters, namely, number of hidden layers (HL), neurons per hidden layer (NHL), and activation function type (AF), on the sum of squares error (SSE). The data for the study were obtained from quality parameters (physicochemical and microbiological) of milk samples. Architec- tures or combinations were organized in groups (G1, G2, and G3) generated upon inter- spersing one, two, and three layers. Within each group, the networks had three neurons in the input layer, six neurons in the output layer, three to twenty-seven NHL, and three AF (tan-sig, log-sig, and linear) types. The number of architectures was determined using three factorial-type experimental designs, which reached 63, 2 187, and 50 049 combinations for G1, G2 and G3, respectively. Using MATLAB 2015a, a logical sequence was designed and implemented for constructing, training, and evaluating multilayer-perceptro n-type neural networks using parallel computing techniques. The results show that HL and NHL have a statistically relevant effect on SSE, and from two hidden layers, AF also has a significant effect; thus, both AF and NHL can be evaluated to determine the optimal combination per group. Moreover, in the three study groups, it is observed that there is an inverse relation- ship between the number of processors and the total optimization time.

A branch of mathematics commonly used in cryptography is Galois Fields GF(pn). Two basic operations performed in GF(pn) are the addition and the multiplication. While the addition is generally easy to compute, the multiplication requires a special treatment. A well-known method to compute the multiplication is based on logarithm and antilogarithm tables. A primitive element of a GF(pn) is a key part in the construction of such tables, but it is generally hard to find a primitive element for arbitrary values of p and n. This article presents a naive algorithm that can simultaneously find a primitive element of GF(pn) and construct its corresponding logarithm and antilogarithm tables. The proposed algorithm was tested in GF(pn) for several values of p and n; the results show a good performance, having an average time of 0.46 seconds to find the first primitive element of a given GF(pn) for values of n = {2, 3, 4, 5, 8, 12} and prime values p between 2 and 97.

Covering arrays are used in testing deterministic systems where failures occur as a result of interactions among subsystems. The goal is to reveal if any interaction induces a failure in the system. Application areas include software and hardware testing. A binary covering array CA(N;t,k,2) is an \(N \times k\) array over the alphabet \(\{0,1\}\) with the property that each set of t columns contains all the \(2^t\) possible t-tuples of 0’s and 1’s at least once. In this paper we propose a direct method to construct binary covering arrays using an specific interpretation of binomial coefficients: a binomial coefficient with parameters k and r will be interpreted as the set of all the k-tuples from \(\{0,1\}\) having r ones and \(k-r\) zeroes. For given values of k and t, the direct method uses an explicit formula in terms of both k and t to provide a covering array CA(N;t,k,2) expressed as the juxtaposition of a set of binomial coefficients; this covering array will be of the minimum size that can be obtained by any juxtaposition of binomial coefficients. In order to derive the formula, a Branch & Bound (BB the BB however, the major achievement is that nine upper bounds were significantly improved by our direct method, plus the fact that the method is able to set an infinite number of new upper bounds for \(t \ge 7\) given that little work has been done to compute binary covering arrays for general values of k and t.

Of particular interest in this chapter are the combinatorial objects called Orthogonal Arrays (OAs). These objects have been studied given of their wide range of applications in the industry, Gopalakrishnan & Stinson (2008) present their applications in computer science; among them are in the generation of error correcting codes presented by (Hedayat et al., 1999; Stinson, 2004), or in the design of experiments for software testing as shown by Taguchi (1994).

A covering array (CA) is a combinatorial structure specified as a matrix of N rows and k columns over an alphabet on v symbols such that for each set of t columns every t-tuple of symbols is covered at least once. Given the values of t, k, and v, the optimal covering array construction problem (CAC) consists in constructing a CA (N; t, k, v) with the minimum possible value of N. There are several reported methods to attend the CAC problem, among them are direct methods, recursive methods, greedy methods, and metaheuristics methods. In this paper, There are three parallel approaches for simulated annealing: the independent, semi-independent, and cooperative searches are applied to the CAC problem. The empirical evidence supported by statistical analysis indicates that cooperative approach offers the best execution times and the same bounds as the independent and semi-independent approaches. Extensive experimentation was carried out, using 182 well-known benchmark instances of ternary covering arrays, for assessing its performance with respect to the best-known bounds reported previously. The results show that cooperative approach attains 134 new bounds and equals the solutions for other 29 instances. © 2012 Himer Avila-George et al., The authors thankfully acknowledge the computer resources and assistance provided by Spanish Supercomputing Network (TIRANT-UV). This research work was partially funded by the following projects: CONACyT 58554; Calculo de Covering Arrays; 51623-Fondo Mixto CONACyT; Gobierno del Estado de Tamaulipas.

This paper presents a simulated annealing (SA) algorithm for the construction of ternary covering arrays (CAs) using a trinomial coefficient representation. A ternary CA, denoted by CA(t, k, 3), is an N × k array where each N × t subarray contains each of the 3t combinations of symbols at least once. The construction of optimal CAs is, in general, an NP-complete problem. Many reported SA implementations use an N × k matrix representation for the CA construction. Instead of this, we represent ternary CAs using trinomial coefficients in order to reduce the search space for the SA algorithm.