About the Stabilization of a Nonlinear Perturbed Difference Equation

This paper investigates the local asymptotic stabilization of a very general class of instable autonomous nonlinear difference equations which are subject to perturbed dynamics which can have a different order than that of the nominal difference equation. In the general case, the controller consists of two combined parts, namely, the feedback nominal controller which stabilizes the nominal (i.e., perturbation-free) difference equation plus an incremental controller which completes the stabilization in the presence of perturbed or unmodeled dynamics in the uncontrolled difference equation. A stabilization variant consists of using a single controller to stabilize both the nominal difference equation and also the perturbed one under a small-type characterization of the perturbed dynamics. The study is based on Banach fixed point principle, and it is also valid with slight modification for the stabilization of unstable oscillatory solutions.

Fine mapping and functional analysis of the multiple sclerosis risk gene CD6

CD6 has recently been identified and validated as risk gene for multiple sclerosis (MS), based on the association of a single nucleotide polymorphism (SNP), rs17824933, located in intron 1. CD6 is a cell surface scavenger receptor involved in T-cell activation and proliferation, as well as in thymocyte differentiation. In this study, we performed a haptag SNP screen of the CD6 gene locus using a total of thirteen tagging SNPs, of which three were non-synonymous SNPs, and replicated the recently reported GWAS SNP rs650258 in a Spanish-Basque collection of 814 controls and 823 cases. Validation of the six most strongly associated SNPs was performed in an independent collection of 2265 MS patients and 2600 healthy controls. We identified association of haplotypes composed of two non-synonymous SNPs [rs11230563 (R225W) and rs2074225 (A257V)] in the 2nd SRCR domain with susceptibility to MS (Pmax(T) permutation=161024). The effect of these haplotypes on CD6 surface expression and cytokine secretion was also tested. The analysis showed significantly different CD6 expression patterns in the distinct cell subsets, i.e. – CD4+ naı¨ve cells, P = 0.0001; CD8+ naı¨ve cells, P,0.0001; CD4+ and CD8+ central memory cells, P = 0.01 and 0.05, respectively; and natural killer T (NKT) cells, P = 0.02; with the protective haplotype (RA) showing higher expression of CD6. However, no significant changes were observed in natural killer (NK) cells, effector memory and terminally differentiated effector memory T cells. Our findings reveal that this new MS-associated CD6 risk haplotype significantly modifies expression of CD6 on CD4+ and CD8+ T cells.

Advances in Nonlinear Complexity Analysis for Partial Differential Equations

1 p. -- [Editorial Material]

Subdiffusion of nonlinear waves in quasiperiodic potentials

19 p.

An observer-based vaccination control law for an SEIR epidemic model based on feedback linearization techniques for nonlinear systems

This paper presents a vaccination strategy for fighting against the propagation of epidemic diseases. The disease propagation is described by an SEIR (susceptible plus infected plus infectious plus removed populations) epidemic model. The model takes into account the total population amounts as a refrain for the illness transmission since its increase makes the contacts among susceptible and infected more difficult. The vaccination strategy is based on a continuous-time nonlinear control law synthesised via an exact feedback input-output linearization approach. An observer is incorporated into the control scheme to provide online estimates for the susceptible and infected populations in the case when their values are not available from online measurement but they are necessary to implement the control law. The vaccination control is generated based on the information provided by the observer. The control objective is to asymptotically eradicate the infection from the population so that the removed-by-immunity population asymptotically tracks the whole one without precise knowledge of the partial populations. The model positivity, the eradication of the infection under feedback vaccination laws and the stability properties as well as the asymptotic convergence of the estimation errors to zero as time tends to infinity are investigated.

Towards a Comprehensive Approach to Quantifying and Mapping Ecosystem Services Flows

25 p.

BAMS: A Tool for Supervised Burned Area Mapping Using Landsat Data

A new supervised burned area mapping software named BAMS (Burned Area Mapping Software) is presented in this paper. The tool was built from standard ArcGIS (TM) libraries. It computes several of the spectral indexes most commonly used in burned area detection and implements a two-phase supervised strategy to map areas burned between two Landsat multitemporal images. The only input required from the user is the visual delimitation of a few burned areas, from which burned perimeters are extracted. After the discrimination of burned patches, the user can visually assess the results, and iteratively select additional sampling burned areas to improve the extent of the burned patches. The final result of the BAMS program is a polygon vector layer containing three categories: (a) burned perimeters, (b) unburned areas, and (c) non-observed areas. The latter refer to clouds or sensor observation errors. Outputs of the BAMS code meet the requirements of file formats and structure of standard validation protocols. This paper presents the tool's structure and technical basis. The program has been tested in six areas located in the United States, for various ecosystems and land covers, and then compared against the National Monitoring Trends in Burn Severity (MTBS) Burned Area Boundaries Dataset.

Nonlinear magnetic vortex dynamics in a circular nanodot excited by spin-polarized current

We investigate analytically and numerically nonlinear vortex spin torque oscillator dynamics in a circular magnetic nanodot induced by a spin-polarized current perpendicular to the dot plane. We use a generalized nonlinear Thiele equation including spin-torque term by Slonczewski for describing the nanosize vortex core transient and steady orbit motions and analyze nonlinear contributions to all forces in this equation. Blue shift of the nano-oscillator frequency increasing the current is explained by a combination of the exchange, magnetostatic, and Zeeman energy contributions to the frequency nonlinear coefficient. Applicability and limitations of the standard nonlinear nano-oscillator model are discussed.

Epitope mapping of antibodies to alpha-synuclein in LRRK2 mutation carriers, idiopathic Parkinson disease patients, and healthy controls

Alpha-synuclein (Snca) plays a major role in Parkinson disease (PD). Circulating anti-Snca antibodies has been described in PD patients and healthy controls, but they have been poorly characterized. This study was designed to assess the prevalence of anti-Snca reactivity in human subjects carrying the LRRK2 mutation, idiopathic PD (iPD) patients, and healthy controls and to map the epitopes of the anti-Snca antibodies. Antibodies to Snca were detected by ELISA and immunoblotting using purified recombinant Snca in plasma from individuals carrying LRRK2 mutations (104), iPD patients (59), and healthy controls (83). Epitopes of antibodies were mapped using recombinant protein constructs comprising different regions of Snca. Clear positive anti-Snca reactivity showed no correlation with age, sex, years of evolution, or the disability scores for PD patients and anti-Snca reactivity was not prevalent in human patients with other neurological or autoimmune diseases. Thirteen of the positive individuals were carriers of LRRK2 mutations either non-manifesting (8 out 49 screened) or manifesting (5 positive out 55), three positive (out of 59) were iPD patients, and five positive (out of 83) were healthy controls. Epitope mapping showed that antibodies against the N-terminal (a.a. 1-60) or C-terminal (a.a. 109-140) regions of Snca predominate in LRRK2 mutation carriers and iPD patients, being N122 a critical amino acid for recognition by the anti-C-terminal directed antibodies. Anti-Snca circulating antibodies seem to cluster within families carrying the LRRK2 mutation indicating possible genetic or common environmental factors in the generation of anti-Snca antibodies. These results suggest that case-controls' studies are insufficient and further studies in family cohorts of patients and healthy controls should be undertaken, to progress in the understanding of the possible relationship of anti-Snca antibodies and PD patholog

Density-potential mapping in the standard and quantum electrodynamical time-dependent density functional theory

131 p.

Approximate Solutions by Truncated Taylor Series Expansions of Nonlinear Differential Equations and Related Shadowing Property with Applications

This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial condition. The class of differential equations is assumed to be approximated by well-posed truncated Taylor series expansions up to a certain order obtained about certain, in general nonperiodic, sampling points t(i) is an element of [t(0), t(J)] for i = 0, 1, . . . , J of the solution. Two examples are provided.

Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability

This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.