Hyers-Ulam-Rassias Stability of Functional Differential Systems with Point and Distributed Delays

This paper investigates stability and asymptotic properties of the error with respect to its nominal version of a nonlinear time-varying perturbed functional differential system subject to point, finite-distributed, and Volterra-type distributed delays associated with linear dynamics together with a class of nonlinear delayed dynamics. The boundedness of the error and its asymptotic convergence to zero are investigated with the results being obtained based on the Hyers-Ulam-Rassias analysis.

On Nonnegative Solutions of Fractional q-Linear Time-Varying Dynamic Systems with Delayed Dynamics

This paper is devoted to the investigation of nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic linear time-varying systems involving delayed dynamics with delays. The dynamic systems are described based on q-calculus and Caputo fractional derivatives on any order.

Patterns of genetic variation in the endangered European mink (Mustela lutreola L., 1761)

Background: The European mink (Mustela lutreola, L. 1761) is a critically endangered mustelid, which inhabits several main river drainages in Europe. Here, we assess the genetic variation of existing populations of this species, including new sampling sites and additional molecular markers (newly developed microsatellite loci specific to European mink) as compared to previous studies. Probabilistic analyses were used to examine genetic structure within and between existing populations, and to infer phylogeographic processes and past demography. Results: According to both mitochondrial and nuclear microsatellite markers, Northeastern (Russia, Estonia and Belarus) and Southeastern (Romania) European populations showed the highest intraspecific diversity. In contrast, Western European (France and Spain) populations were the least polymorphic, featuring a unique mitochondrial DNA haplotype. The high differentiation values detected between Eastern and Western European populations could be the result of genetic drift in the latter due to population isolation and reduction. Genetic differences among populations were further supported by Bayesian clustering and two main groups were confirmed (Eastern vs. Western Europe) along with two contained subgroups at a more local scale (Northeastern vs. Southeastern Europe; France vs. Spain). Conclusions: Genetic data and performed analyses support a historical scenario of stable European mink populations, not affected by Quaternary climate oscillations in the Late Pleistocene, and posterior expansion events following river connections in both North-and Southeastern European populations. This suggests an eastern refuge during glacial maxima (as already proposed for boreal and continental species). In contrast, Western Europe was colonised more recently following either natural expansions or putative human introductions. Low levels of genetic diversity observed within each studied population suggest recent bottleneck events and stress the urgent need for conservation measures to counteract the demographic decline experienced by the European mink.

Muscle wasting in myotonic dystrophies: a model of premature aging

Myotonic dystrophy type 1 (DM1 or Steinert's disease) and type 2 (DM2) are multisystem disorders of genetic origin. Progressive muscular weakness, atrophy and myotonia are the most prominent neuromuscular features of these diseases, while other clinical manifestations such as cardiomyopathy, insulin resistance and cataracts are also common. From a clinical perspective, most DM symptoms are interpreted as a result of an accelerated aging (cataracts, muscular weakness and atrophy, cognitive decline, metabolic dysfunction, etc.), including an increased risk of developing tumors. From this point of view, DM1 could be described as a progeroid syndrome since a notable age dependent dysfunction of all systems occurs. The underlying molecular disorder in DM1 consists of the existence of a pathological (CTG) triplet expansion in the 3' untranslated region (UTR) of the Dystrophia ll/Iyotonica Protein Kinase (DMPK) gene, whereas (CCTG)n repeats in the first intron of the Cellular Nucleic acid Binding Protein/Zinc Finger Protein 9 (CNBP/ZNF9) gene cause DM2. The expansions are transcribed into (CUG)n and (CCUG)n-containing RNA, respectively, which form secondary structures and sequester RNA binding proteins, such as the splicing factor muscleblind-like protein (MBNL), forming nuclear aggregates known as foci. Other splicing factors, such as CUGBP, are also disrupted, leading to a spliceopathy of a large number of downstream genes linked to the clinical features of these diseases. Skeletal muscle regeneration relies on muscle progenitor cells, known as satellite cells, which are activated after muscle damage, and which proliferate and differentiate to muscle cells, thus regenerating the damaged tissue. Satellite cell dysfunction seems to be a common feature of both age-dependent muscle degeneration (sarcopenia) and muscle wasting in DM and other muscle degenerative diseases. This review aims to describe the cellular, molecular and macrostructural processes involved in the muscular degeneration seen in DM patients, highlighting the similarities found with muscle aging.

Stability analysis and observer design for discrete-time SEIR epidemic models

This paper applies Micken's discretization method to obtain a discrete-time SEIR epidemic model. The positivity of the model along with the existence and stability of equilibrium points is discussed for the discrete-time case. Afterwards, the design of a state observer for this discrete-time SEIR epidemic model is tackled. The analysis of the model along with the observer design is faced in an implicit way instead of obtaining first an explicit formulation of the system which is the novelty of the presented approach. Moreover, some sufficient conditions to ensure the asymptotic stability of the observer are provided in terms of a matrix inequality that can be cast in the form of a LMI. The feasibility of the matrix inequality is proved, while some simulation examples show the operation and usefulness of the observer.