Formalization of Ring Theory in PVS

This paper presents a PVS development of relevant results of the theory of rings. The PVS theory includes complete proofs of the three classical isomorphism theorems for rings, and characterizations of principal, prime and maximal ideals. Algebraic concepts and properties are specified and formalized as generally as possible allowing in this manner their application to other algebraic structures. The development provides the required elements to formalize important algebraic theorems. In particular, the paper presents the formalization of the general algebraic-theoretical version of the Chinese remainder theorem (CRT) for the theory of rings, as given in abstract algebra textbooks, proved as a consequence of the first isomorphism theorem. Also, the PVS theory includes a formalization of the number-theoretical version of CRT for the structure of integers, which is the version of CRT found in formalizations. CRT for integers is obtained as a consequence of the general version of CRT for the theory of rings.

     

The effects of polarization mode dispersion on 2D wavelength-hopping time spreading code routed networks

In this study, we investigate the effects of multiple access interference (MAI) and polarization mode dispersion (PMD) in 2D wavelength-hopping time spreading optical code paths. The main results show the MAI effects and PMD constraint at the outage probability. The contribution of these sources of interference is analysed to choose the better design of code parameters in order to increase the performance of networks based on optical code paths. These results could be applied to determine the parameters design in code/wavelength routed networks.     

A Formalization of the Knuth–Bendix(–Huet) Critical Pair Theorem

A mechanical proof of the Knuth–Bendix Critical Pair Theorem in the higher-order language of the theorem prover PVS is described. This well-known theorem states that a Term Rewriting System is locally confluent if and only if all its critical pairs are joinable. The formalization of this theorem follows Huet’s well-known structure of proof in which the restriction on strong normalization or Noetherian was dropped and the result presented as a lemma. In order to formalize the Knuth–Bendix Critical Pair Theorem we rely on previously developed PVS theories for abstract reduction systems, named ars, and term rewriting systems, named trs, which were built upon the PVS libraries for finite sequences and sets. On the one hand, the theory trs is composed of subtheories for dealing with the structure of terms, for replacements of subterms and substitutions and jointly with the theory ars it allows for adequate specifications of elaborate notions of term rewriting systems such as the one of critical pairs. On the other hand, ars specifies basic definitions and notions of abstract reduction systems such as reduction, termination, normal forms, and confluence as well as non basic concepts such as strong normalization.     

Evolution of hybrid WDM/OCDM technology in OBS networks with optical code and wavelength conversion

The performance of a hybrid WDM/OCDM technology is investigated under impairments of Multiple Access Interference. We employed analytical models of Optical Orthogonal Codes to evaluate the switching network resources, such as the number of optical codes carried on each wavelength. Moreover, we propose and analyze a few optical code and wavelength conversion switching architectures, in order to scale the number of codes and wavelength converters and obtain a minimum burst blocking probability. The results demonstrate that architectures comprising Sparse-Partial Optical Code Converters with Sparse-Partial Wavelength Converters provide better performance. The network resources utilization are improved with number of converters, hence reaching a better cost benefit.     

Simple and robust analytically derived variable step-size least mean squares algorithm for channel estimation

A new variable step-size least mean squares (VSS-LMS) algorithm for the estimation of frequency selective communications channels is herein presented. In contrast to previous works, in which the step-size adaptation is based on the instantaneous samples of the error signal, this algorithm is derived on the basis of analytical minimisation of the ensemble-averaged mean-square weight error. A very simple rule for step-size adaptation is obtained, using a small number of communication system parameters. This is another significant difference from other proposals, in which a large number of control parameters should be tuned for proper use. The algorithm here proposed is shown to be applicable to both time-varying and time-invariant scenarios. While the lack of a termination rule for step-size adaptation is a common characteristic of other schemes, the algorithm here presented adopts a criterion for stopping the step-size adaptation that assures optimal steadystate performance and leads to large computational savings. A simulation-based performance comparison with other VSS-LMS schemes is provided, including their application to maximum likelihood sequence estimation receivers using per survivor processing (MLSE/PSP). The results show that the algorithm proposed in this work has good performance characteristics and a very low computational cost, specially in the application to MLSE/ PSP receivers. Besides, this algorithm is shown to be robust to changes in the signal-to-noise ratio (SNR).     

Using denoising at the receiver front-end for frequency-selective channels

This article proposes the use of denoising techniques at the receiver front-end in order to combat the effects of additive noise in digital transmission over frequency-selective channels. The proposed technique does not require knowledge of the channel impulse response, and is, therefore, potentially suitable for application in several receiver structures, including those with blind equalizers and adaptive receivers for mobile communications.     

Gram‐Negative Bacteria Targeting Mediated by Carbohydrate–Carbohydrate Interactions Induced by Surface‐Modified Nanoparticles

Antibiotic resistant pathogens are a modern threat to the human health. As a worldwide spreading problem, there is an urgency for new strategies to minimize antibiotic resistance, particularly the super‐resistant strains. Here, the efficient design of carbohydrate‐coated silica nanoparticles is reported which specifically target Gram‐negative bacteria cells. The system is functionalized with gluconamide moieties and demonstrates increased binding ability to the bacterial membrane, enabling controlled drug delivery onto the pathogen wall. In addition, the high stability of the nanoparticles in biological media and the lack of non‐specific protein adhesion are engendered by such functionalization, which also demonstrates low cytotoxicity and hemolytic activity prevention. Local interaction between nanoparticles and the bacterium membrane is experimentally accessed at the biomolecular level unveiling a short‐range chemical connection. Atomistic molecular dynamics simulations depict the rapid penetration of gluconamide in the lipopolysaccharide region of the bacterial outer membrane, corroborating the experimental findings. Thus, this novel outer membrane‐targeting platform provides a new strategy to reduce drug intake and, hence, minimize bacterial resistance.     

Analytical performance of the LMS algorithm on the estimation of wide sense stationary channels

The performance of the least mean square (LMS) algorithm on the estimation of time-varying channels is analytically evaluated, using the estimation error correlation matrix, the mean-square weight error (MSWE) and the mean-square estimation error (MSE) as parameters. Expressions for those parameters are obtained from a set of hypotheses usually adopted in the communication systems context. The channel is modeled as a wide sense stationary (WSS) discrete time stochastic field with known autocorrelation. The expressions for the steady-state MSWE and MSE are particularized for the class of WSS channel models, and an original analysis of the optimum LMS step-size parameter for usual channel models is addressed. For the sake of comparison with other works, the analytical step-size optimization for random-walk models is also considered. Several estimates of MSWE curves obtained by computer simulation are compared with analytical results for validation purposes. A very good agreement between simulated and analytical results for both the MSWE expressions and the optimum value of the LMS step-size parameter is shown.     

Natural rubber latex LbL films: Characterization and growth of fibroblasts

The recent biomedical applications of natural rubber (NR) latex, mostly in dry membranes, have motivated research into novel, more noble uses of this low-cost biomaterial. In this article, we provide the first report on the fabrication of layer-by-layer (LbL) films of NR alternated with the polyelectrolytes polyethylenimine (PEI) and polyallylamine hydrochloride (PAH). Stable (PAH/NR)_n and (PEI/NR)_n LbL films displayed similar physicochemical properties, but differed in terms of film morphology according to atomic force microscopy (AFM) and scanning electron microscopy (SEM) data. Most significantly, (PEI/NR)₅ LbL films were made of smaller and flattened particles, which were not efficient for the growth and proliferation of normal human fibroblasts (NHF). In contrast, efficient NHF proliferation could be obtained with (PAH/NR)_n LbL films, with the fibroblasts exhibiting the expected elongated morphology. Furthermore, cell growth did not occur for cast films of NR, thus demonstrating the suitability of the LbL method for this biologically related application. The differences between the two polyelectrolytes illustrate the importance of the film architecture and morphology, which open the way for exploiting the molecular control inherent in the LbL technique for further applications of NR-containing films. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012