Multi-q Pattern Classification of Polarization Curves

Several experimental measurements are expressed in the form of one-dimensional profiles, for which there is a scarcity of methodologies able to classify the pertinence of a given result to a specific group. The polarization curves that evaluate the corrosion kinetics of electrodes in corrosive media are an application where the behavior is chiefly analyzed from profiles. Polarization curves are indeed a classic method to determine the global kinetics of metallic electrodes, but the strong nonlinearity from different metals and alloys can overlap and the discrimination becomes a challenging problem. Moreover, even finding a typical curve from replicated tests requires subjective judgement. In this paper we used the so-called multi-q approach based on the Tsallis statistics in a classification engine to separate multiple polarization curve profiles of two stainless steels. We collected 48 experimental polarization curves in aqueous chloride medium of two stainless steel types, with different resistance against localized corrosion. Multi-q pattern analysis was then carried out on a wide potential range, from cathodic up to anodic regions. An excellent classification rate was obtained, at a success rate of 90%, 80%, and 83% for low (cathodic), high (anodic), and both potential ranges, respectively, using only 2% of the original profile data. These results show the potential of the proposed approach towards efficient, robust, systematic and automatic classification of highly non-linear profile curves.Comment: 12 pages, 7 figure

Entropic Gravity, Phase-Space Noncommutativity and the Equivalence Principle

We generalize E. Verlinde's entropic gravity reasoning to a phase-space noncommutativity set-up. This allow us to impose a bound on the product of the noncommutative parameters based on the Equivalence Principle. The key feature of our analysis is an effective Planck's constant that naturally arises when accounting for the noncommutative features of the phase-space.Comment: 12 pages. Version to appear at the Classical and Quantum Gravit

An experience with Desmos in the study of the quadratic function

In this paper we present a didactic experience in the subject of Mathematics carried out in a distance learning context, on the topic Quadratic Function, using the digital and free platform Desmos. The use of this tool was determinant for the teaching and learning of quadratic function since its teaching took place in distance education, due to the pandemic situation. In a pandemic context, the use of tools to gauge student learning was a necessity, but practices such as the one described in this paper should be incorporated into a normal classroom environment, promoting discovery through graphical and algebraic manipulation.publishe

Non-commutative Quantum Mechanics in Three Dimensions and Rotational Symmetry

We generalize the formulation of non-commutative quantum mechanics to three dimensional non-commutative space. Particular attention is paid to the identification of the quantum Hilbert space in which the physical states of the system are to be represented, the construction of the representation of the rotation group on this space, the deformation of the Leibnitz rule accompanying this representation and the implied necessity of deforming the co-product to restore the rotation symmetry automorphism. This also implies the breaking of rotational invariance on the level of the Schroedinger action and equation as well as the Hamiltonian, even for rotational invariant potentials. For rotational invariant potentials the symmetry breaking results purely from the deformation in the sense that the commutator of the Hamiltonian and angular momentum is proportional to the deformation.Comment: 21 page

Noncommutative Black Holes

One considers phase-space noncommutativity in the context of a Kantowski-Sachs cosmological model to study the interior of a Schwarzschild black hole. It is shown that the potential function of the corresponding quantum cosmology problem has a local minimum. One deduces the thermodynamics and show that the Hawking temperature and entropy exhibit an explicit dependence on the momentum noncommutativity regime and it is shown that the wave function vanishes in this limit.Comment: Based on a talk presented by CB at 1st Mediterranean Conference on Classical and Quantum Gravity 2009, Kolymbari, Crete, 14th-18th September 2009, Greec

Sequence-based prediction for vaccine strain selection and identification of antigenic variability in foot-and-mouth disease virus

Identifying when past exposure to an infectious disease will protect against newly emerging strains is central to understanding the spread and the severity of epidemics, but the prediction of viral cross-protection remains an important unsolved problem. For foot-and-mouth disease virus (FMDV) research in particular, improved methods for predicting this cross-protection are critical for predicting the severity of outbreaks within endemic settings where multiple serotypes and subtypes commonly co-circulate, as well as for deciding whether appropriate vaccine(s) exist and how much they could mitigate the effects of any outbreak. To identify antigenic relationships and their predictors, we used linear mixed effects models to account for variation in pairwise cross-neutralization titres using only viral sequences and structural data. We identified those substitutions in surface-exposed structural proteins that are correlates of loss of cross-reactivity. These allowed prediction of both the best vaccine match for any single virus and the breadth of coverage of new vaccine candidates from their capsid sequences as effectively as or better than serology. Sub-sequences chosen by the model-building process all contained sites that are known epitopes on other serotypes. Furthermore, for the SAT1 serotype, for which epitopes have never previously been identified, we provide strong evidence - by controlling for phylogenetic structure - for the presence of three epitopes across a panel of viruses and quantify the relative significance of some individual residues in determining cross-neutralization. Identifying and quantifying the importance of sites that predict viral strain cross-reactivity not just for single viruses but across entire serotypes can help in the design of vaccines with better targeting and broader coverage. These techniques can be generalized to any infectious agents where cross-reactivity assays have been carried out. As the parameterization uses pre-existing datasets, this approach quickly and cheaply increases both our understanding of antigenic relationships and our power to control disease