Frequency locking of modulated waves

We consider the behavior of a modulated wave solution to an $\mathbb{S}^1$-equivariant autonomous system of differential equations under an external forcing of modulated wave type. The modulation frequency of the forcing is assumed to be close to the modulation frequency of the modulated wave solution, while the wave frequency of the forcing is supposed to be far from that of the modulated wave solution. We describe the domain in the three-dimensional control parameter space (of frequencies and amplitude of the forcing) where stable locking of the modulation frequencies of the forcing and the modulated wave solution occurs. Our system is a simplest case scenario for the behavior of self-pulsating lasers under the influence of external periodically modulated optical signals

Existence and stability of solutions with periodically moving weak internal layers

We consider the periodic parabolic differential equation $ep^2 Big( fracpartial^2 upartial x^2 -fracpartial upartial t Big)=f(u,x,t,ep)$ under the assumption that $ve$ is a small positive parameter and that the degenerate equation $f(u,x,t,0) =0$ has two intersecting solutions. We derive conditions such that there exists an asymptotically stable solution $u_p(x,t,ep)$ which is $T$-periodic in $t$, satisfies no-flux boundary conditions and tends to the stable composed root of the degenerate equation as $eprightarrow 0$

Асимптотика, устойчивость и область притяжения периодического решения сингулярно возмущённой параболической задачи с двукратным корнем вырожденного уравнения

For a singularly perturbed parabolic problem with Dirichlet conditions we prove the existence of a solution periodic in time and with boundary layers at both ends of the space interval in the case that the degenerate equation has a double root. We construct the corresponding asymptotic expansion in a small parameter. It turns out that the algorithm of the construction of the boundary layer functions and the behavior of the solution in the boundary layers essentially differ from that ones in case of a simple root. We also investigate the stability of this solution and the corresponding region of attraction.Для сингулярно возмущённой параболической задачи с краевыми условиями Дирихле построено и обосновано асимптотическое разложение периодического по времени решения с пограничными слоями вблизи концов отрезка в случае, когда вырожденное уравнение имеет двукратный корень. Поведение решения в пограничных слоях и сам алгоритм построения асимптотики существенно отличаются от случая однократного корня вырожденного уравнения. Исследован также вопрос об устойчивости периодического решения и области его притяжения

Risk for cancer development in familial Mediterranean fever and associated predisposing factors: an ambidirectional cohort study from the international AIDA Network registries

Objective: Inflammation has been associated with an increased risk for cancer development, while innate immune system activation could counteract the risk for malignancies. Familial Mediterranean fever (FMF) is a severe systemic inflammatory condition and also represents the archetype of innate immunity deregulation. Therefore, the aim of this study is to investigate the risk for cancer development in FMF. Methods: The risk ratio (RR) for malignancies was separately compared between FMF patients and fibromyalgia subjects, Still’s disease patients and Behçet’s disease patients. Clinical variables associated with cancer development in FMF patients were searched through binary logistic regression. Results: 580 FMF patients and 102 fibromyalgia subjects, 1012 Behçet’s disease patients and 497 Still’s disease patients were enrolled. The RR for the occurrence of malignant neoplasms was 0.26 (95% Confidence Interval [CI.] 0.10-0.73, p=0.006) in patients with FMF compared to fibromyalgia subjects; the RR for the occurrence of malignant cancer was 0.51 (95% CI. 0.23-1.16, p=0.10) in FMF compared to Still’s disease and 0.60 (95% CI. 0.29-1.28, p=0.18) in FMF compared to Behçet’s disease. At logistic regression, the risk of occurrence of malignant neoplasms in FMF patients was associated with the age at disease onset (β1 = 0.039, 95% CI. 0.001-0.071, p=0.02), the age at the diagnosis (β1 = 0.048, 95% CI. 0.039-0.085, p=0.006), the age at the enrolment (β1 = 0.05, 95% CI. 0.007-0.068, p=0.01), the number of attacks per year (β1 = 0.011, 95% CI. 0.001- 0.019, p=0.008), the use of biotechnological agents (β1 = 1.77, 95% CI. 0.43-3.19, p=0.009), the use of anti-IL-1 agents (β1 = 2.089, 95% CI. 0.7-3.5, p=0.002). Conclusions: The risk for cancer is reduced in Caucasic FMF patients; however, when malignant neoplasms occur, this is more frequent in FMF cases suffering from a severe disease phenotype and presenting a colchicine-resistant disease

Prevalence of pemphigus and pemphigoid autoantibodies in the general population

Background: Mucocutaneous blistering is characteristic of autoimmune bullous dermatoses (AIBD). Blisters are caused by autoantibodies directed against structural components of the skin. Hence, detection of specific autoantibodies has become a hallmark for AIBD diagnosis. Studies on prevalence of AIBD autoantibodies in healthy individuals yielded contradictory results. Methods: To clarify this, samples from 7063 blood donors were tested for presence of anti-BP180-NC16A, anti-BP230 and anti-Dsg1/3 IgG by indirect immunofluorescence (IF) microscopy using a biochip. Results: Cumulative prevalence of these autoantibodies was 0.9 % (CI: 0.7-1.1 %), with anti-BP180-NC16A IgG being most prevalent. Validation of IF findings using ELISA confirmed presence of autoantibodies in 7/15 (anti-Dsg1), 6/7 (anti-Dsg3), 35/37 (anti-BP180-NC16A) and 2/3 (anti-BP230) cases. Moreover, in 16 samples, anti-BP180-NC16A autoantibody concentrations exceeded the cut-off for the diagnosis of bullous pemphigoid. Interestingly, these anti-BP180-NC16A autoantibodies from healthy individuals formed immune complexes with recombinant antigen and dose-dependently activated neutrophils in vitro. However, fine-epitope mapping within NC16A showed a different binding pattern of anti-BP180-NC16A autoantibodies from healthy individuals compared to bullous pemphigoid patients, while IgG subclasses were identical. Conclusions: Collectively, we here report a low prevalence of AIBD autoantibodies in a large cohort of healthy individuals. Furthermore, functional analysis shows differences between autoantibodies from healthy donors and AIBD patients

Crandall-Rabinowitz type bifurcation for non-differentiable perturbations of smooth mappings

We consider abstract equations of the type ..., where lambda is a bifurcation parameter and tau is a perturbation parameter. We suppose that ... for all lambda and tau, F is smooth and the unperturbed equation ... describes a Crandall-Rabinowitz bifurcation in lambda=0, that is, two half-branches of nontrivial solutions bifurcate from the trivial solution in lambda=0. Concerning G, we suppose only a certain Lipschitz condition; in particular, G is allowed to be non-differentiable. We show that for fixed small ... there exist also two half-branches of nontrivial solutions to the perturbed equation, but they bifurcate from the trivial solution in two bifurcation points, which are different, in general. Moreover, we determine the bifurcation directions of those two half-branches, and we describe, asymptotically as ..., how the bifurcation points depend on tau. Finally, we present applications to boundary value problems for quasilinear elliptic equations and..