Spectral and weak polynomial completeness for the product of nonsingular matrices

Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F, satisfying the following property: for every monic polynomial f (x) = x(n) + a(n-1)x(n-1) +... + a(1)x + a(0) over F, with a root in F and a(0) = (-1)(n) det(AB), there are nonsingular matrices X, Y is an element of F-nxn such that XAX(-1)Y BY-1 has characteristic polynomial f (x).

Spectral invariants of periodic nonautonomous discrete dynamical systems

For an interval map, the poles of the Artin-Mazur zeta function provide topological invariants which are closely connected to topological entropy. It is known that for a time-periodic nonautonomous dynamical system F with period p, the p-th power [zeta(F) (z)](p) of its zeta function is meromorphic in the unit disk. Unlike in the autonomous case, where the zeta function zeta(f)(z) only has poles in the unit disk, in the p-periodic nonautonomous case [zeta(F)(z)](p) may have zeros. In this paper we introduce the concept of spectral invariants of p-periodic nonautonomous discrete dynamical systems and study the role played by the zeros of [zeta(F)(z)](p) in this context. As we will see, these zeros play an important role in the spectral classification of these systems.

Molecular fingerprint of human gastric cell line infected by Helicobacter pylori

Helicobacter pylori infection represents a serious health problem, given its association with serious gastric diseases as gastric ulcers, cancer and MALT lymphoma. Currently no vaccine exists and antibiotic-based eradication therapy is already failing in more than 20% of cases. To increase the knowledge on the infection process diverse gastric cell lines, e.g. the adenocarcinona gastric (AGS) cell line, are routinely used has in vitro models of gastric epithelia. In the present work the molecular fingerprint of infected and non-infected AGS cell lines, by diverse H. pylori strains, was acquired using vibrational infrared spectroscopy. These molecular fingerprints enabled to discriminate infected from non-infected AGS cells, and infection due to different strains, by performing Principal Component Analysis. It was also possible to estimate, from the AGS cells molecular fingerprint, the effect of the infection on diverse biochemical and metabolic cellular status. In resume infra-red spectroscopy enabled the acquisition of infected AGS cells molecular fingerprint with minimal sample preparation, in a rapid, high-throughput, economic process yielding highly sensitive and informative data, most useful for promoting critical knowledge on the H. pylori infection process. © 2015 IEEE.

Comparative analysis of near and mid-infrared spectroscopy to monitor recombinant cyprosin production

Infrared spectroscopy, either in the near and mid (NIR/MIR) region of the spectra, has gained great acceptance in the industry for bioprocess monitoring according to Process Analytical Technology, due to its rapid, economic, high sensitivity mode of application and versatility. Due to the relevance of cyprosin (mostly for dairy industry), and as NIR and MIR spectroscopy presents specific characteristics that ultimately may complement each other, in the present work these techniques were compared to monitor and characterize by in situ and by at-line high-throughput analysis, respectively, recombinant cyprosin production by Saccharomyces cerevisiae. Partial least-square regression models, relating NIR and MIR-spectral features with biomass, cyprosin activity, specific activity, glucose, galactose, ethanol and acetate concentration were developed, all presenting, in general, high regression coefficients and low prediction errors. In the case of biomass and glucose slight better models were achieved by in situ NIR spectroscopic analysis, while for cyprosin activity and specific activity slight better models were achieved by at-line MIR spectroscopic analysis. Therefore both techniques enabled to monitor the highly dynamic cyprosin production bioprocess, promoting by this way more efficient platforms for the bioprocess optimization and control.

Estimation of 3D shapes using active surface models

This paper addresses the estimation of surfaces from a set of 3D points using the unified framework described in [1]. This framework proposes the use of competitive learning for curve estimation, i.e., a set of points is defined on a deformable curve and they all compete to represent the available data. This paper extends the use of the unified framework to surface estimation. It o shown that competitive learning performes better than snakes, improving the model performance in the presence of concavities and allowing to desciminate close surfaces. The proposed model is evaluated in this paper using syntheticdata and medical images (MRI and ultrasound images).

Spectral and dynamical invariants in a complete clustered network

The main result of this work is a new criterion for the formation of good clusters in a graph. This criterion uses a new dynamical invariant, the performance of a clustering, that characterizes the quality of the formation of clusters. We prove that the growth of the dynamical invariant, the network topological entropy, has the effect of worsening the quality of a clustering, in a process of cluster formation by the successive removal of edges. Several examples of clustering on the same network are presented to compare the behavior of other parameters such as network topological entropy, conductance, coefficient of clustering and performance of a clustering with the number of edges in a process of clustering by successive removal.