Equilibrium distributions of discrete non-autonomous graphs

We introduce the notions of equilibrium distribution and time of convergence in discrete non-autonomous graphs. Under some conditions we give an estimate to the convergence time to the equilibrium distribution using the second largest eigenvalue of some matrices associated with the system.

Introduction to fractional linear systems. Part 2: discrete-time case

IEE Proceedings - Vision, Image, and Signal Processing, Vol. 147, nº 1

Rhapsody in fractional

This paper studies several topics related with the concept of “fractional” that are not directly related with Fractional Calculus, but can help the reader in pursuit new research directions. We introduce the concept of non-integer positional number systems, fractional sums, fractional powers of a square matrix, tolerant computing and FracSets, negative probabilities, fractional delay discrete-time linear systems, and fractional Fourier transform.

IMMUNOGENICITY OF LOW-DOSE INTRAMUSCULAR AND INTRADERMAL VACCINATION WITH RECOMBINANT HEPATITIS B VACCINE

The study is a randomized trial using recombinant DNA vaccine to determine whether an intramuscular 10 µg dose or intradermal 2 µg induces satisfactory anti-HBs levels compared to the standard dose of intramuscular 20 µg. participants were 359 healthy medical and nurse students randomly allocated to one of the three groups: Group I - IM 20 µg; Group II - IM 10 µg; Group III - ID 2 µg at 0, 1 and 6 months. Anti-HBs titres were measured after complete vaccine schedule by ELISA/Pasteur. Baseline variables were similar among groups and side effects were mild after any dose. Vaccinees in the IM-10 µg group had seroconversion rate and geometric mean titre (GMT 2344 IU L-1), not significant different from the IM-20 µg group (GMT 4570 IU L-1). On the contrary, 21.4% of the ID - 2 µg recipients mount antibody concentration below 10 IU L1 and GMT of 91 IU L-1, a statiscally significant difference compared with the standard schedule IM-20 µg (p < 0.001). A three dose regimen of half dosse IM could be considered an appropriate schedule to prevent hepatitis B in young health adults which is of relevance to the expansion of hepatitis B vaccine programme

Arc exchange systems and renormalization

We exhibit the construction of stable arc exchange systems from the stable laminations of hyperbolic diffeomorphisms. We prove a one-to-one correspondence between (i) Lipshitz conjugacy classes of C(1+H) stable arc exchange systems that are C(1+H) fixed points of renormalization and (ii) Lipshitz conjugacy classes of C(1+H) diffeomorphisms f with hyperbolic basic sets Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. Let HD(s)(Lambda) and HD(u)(Lambda) be, respectively, the Hausdorff dimension of the stable and unstable leaves intersected with the hyperbolic basic set L. If HD(u)(Lambda) = 1, then the Lipschitz conjugacy is, in fact, a C(1+H) conjugacy in (i) and (ii). We prove that if the stable arc exchange system is a C(1+HDs+alpha) fixed point of renormalization with bounded geometry, then the stable arc exchange system is smooth conjugate to an affine stable arc exchange system.

Two new power indices based on winning coalitions

Deegan and Packel (1979) and Holler (1982) proposed two power indices for simple games: the Deegan–Packel index and the Public Good Index. In the definition of these indices, only minimal winning coalitions are taken into account. Using similar arguments, we define two new power indices. These new indices are defined taking into account only those winning coalitions that do not contain null players. The results obtained with the different power indices are compared by means of two real-world examples taken from the political field.

Rhapsody in Fractional

This paper studies several topics related with the concept of “fractional” that are not directly related with Fractional Calculus, but can help the reader in pursuit new research directions. We introduce the concept of non-integer positional number systems, fractional sums, fractional powers of a square matrix, tolerant computing and FracSets, negative probabilities, fractional delay discrete-time linear systems, and fractional Fourier transform.

Variational inequalities in Hilbert spaces with measures and optimal stopping problems

We study the existence theory for parabolic variational inequalities in weighted L2 spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L2 setting allows us to cover some singular cases, such as optimal stopping for stochastic equations with degenerate diffusion coeficient. As an application of the theory, we consider the pricing of American-style contingent claims. Among others, we treat the cases of assets with stochastic volatility and with path-dependent payoffs.

Apparent competition through facilitation between Melanoides tuberculata and Biomphalaria glabrata and the control of schistosomiasis

Interactions between two species that result in reduced growth rates for both and extinction of one of the species are generally considered cases of asymmetric interspecific competition. Exploitative or interference competition is the usual mechanism invoked. Here we describe another mechanism producing the same result, named apparent competition through facilitation (ACF), observed between Melanoides tuberculata and Biomphalaria glabrata populations. The superior competitor actually gives some benefit to the other species, whose population becomes unstable with progressively increasing oscillations, leading to extinction. A model of ACF using difference equations suggests initial dynamics distinct from traditional interspecific competition. The dynamics of two freshwater snails in the field and in laboratory experiments suggest ACF, and these relations should be considered in studies of schistosomiasis control. ACF could occur in natural populations, but might have gone undetected because the final result is similar to traditional interspecific competition.

Parameterized expectations approach; Some practical issues

We discuss some practical issues related to the use of the Parameterized Expectations Approach (PEA) for solving non-linear stochastic dynamic models with rational expectations. This approach has been applied in models of macroeconomics, financial economics, economic growth, contracttheory, etc. It turns out to be a convenient algorithm, especially when there is a large number of state variables and stochastic shocks in the conditional expectations. We discuss some practical issues having to do with the application of the algorithm, and we discuss a Fortran program for implementing the algorithm that is available through the internet.We discuss these issues in a battery of six examples.

Dynamical properties of nonmarkovian stochastic differential equations

We study nonstationary non-Markovian processes defined by Langevin-type stochastic differential equations with an OrnsteinUhlenbeck driving force. We concentrate on the long time limit of the dynamical evolution. We derive an approximate equation for the correlation function of a nonlinear nonstationary non-Markovian process, and we discuss its consequences. Non-Markovicity can introduce a dependence on noise parameters in the dynamics of the correlation function in cases in which it becomes independent of these parameters in the Markovian limit. Several examples are discussed in which the relaxation time increases with respect to the Markovian limit. For a Brownian harmonic oscillator with fluctuating frequency, the non-Markovicity of the process decreases the domain of stability of the system, and it can change an infradamped evolution into an overdamped one.

Vestibulo-ocular reflex characteristics in patients with unilateral Ménière's disease.

OBJECTIVE: The pathophysiologic concept of Ménière's disease assumes that endolymphatic hydrops is the cause of the symptoms via increased pressure in the endolymphatic space and/or ionic disorder due to ruptured membrane. The goal of this study was to assess whether the vestibulo-ocular reflex (VOR) properties in patients with Ménière's disease were consistent with the classical theory. MATERIAL AND METHODS: We studied 34 patients (19 women, 15 men) presenting with unilateral Ménière's disease divided into 2 groups according to the duration of the disease: 18 were in the early stage (< 12 mo), and 16 were in the late stage (> or = 12 mo). Nineteen patients were examined during an attack. Eight of them and the 15 other patients were tested during the interval between attacks. Their characteristics were compared with those of a group of 22 normal subjects. The VOR function was evaluated via standard caloric and impulse rotatory tests (velocity step). A mathematic model of vestibular function was used to characterize the VOR response to rotational stimulation. Dynamic VOR parameters (sensitivity coefficient, time constant, gain, and asymmetries between the 2 directions of rotation) were statistically compared between the 2 groups of patients during and between attacks and between the patients and controls. RESULTS: All dynamic VOR parameters showed no statistically significant difference both with normal controls and among the patients during and between attacks (p > 0.05) except for gain asymmetry (p < or = 0.008). During attacks, patients with early Ménière's disease displayed a higher gain in rotation toward the affected ear, the opposite being observed in patients with late disease. Caloric test revealed a moderate canal paresis on the affected side during the crisis and a slight asymmetry between attacks. CONCLUSION: During attacks in patients with early Ménière's disease, the VOR gain toward the affected side is higher than that toward the intact side, supporting the fact that that the sensitivity of the cupuloendolymphatic system on the affected ear is increased. This observation is in agreement with a mechanical pressure effect of hydrops on the vestibular organs.

Rational periodic sequences for the Lyness recurrence

Consider the celebrated Lyness recurrence $x_{n+2}=(a+x_{n+1})/x_{n}$ with $a\in\Q$. First we prove that there exist initial conditions and values of $a$ for which it generates periodic sequences of rational numbers with prime periods $1,2,3,5,6,7,8,9,10$ or $12$ and that these are the only periods that rational sequences $\{x_n\}_n$ can have. It is known that if we restrict our attention to positive rational values of $a$ and positive rational initial conditions the only possible periods are $1,5$ and $9$. Moreover 1-periodic and 5-periodic sequences are easily obtained. We prove that for infinitely many positive values of $a,$ positive 9-period rational sequences occur. This last result is our main contribution and answers an open question left in previous works of Bastien \& Rogalski and Zeeman. We also prove that the level sets of the invariant associated to the Lyness map is a two-parameter family of elliptic curves that is a universal family of the elliptic curves with a point of order $n, n\ge5,$ including $n$ infinity. This fact implies that the Lyness map is a universal normal form for most birrational maps on elliptic curves.

Integrability and non-integrability of periodic non-autonomous Lyness recurrences

This paper studies non-autonomous Lyness type recurrences of the form x_{n+2}=(a_n+x_n)/x_{n+1}, where a_n is a k-periodic sequence of positive numbers with prime period k. We show that for the cases k in {1,2,3,6} the behavior of the sequence x_n is simple(integrable) while for the remaining cases satisfying k not a multiple of 5 this behavior can be much more complicated(chaotic). The cases k multiple of 5 are studied separately.

Integrability and non-integrability of periodic non-autonomous Lyness recurrences (revised and enlarged version)

This paper studies non-autonomous Lyness type recurrences of the form xn+2 = (an+xn+1)=xn, where fang is a k-periodic sequence of positive numbers with primitive period k. We show that for the cases k 2 f1; 2; 3; 6g the behavior of the sequence fxng is simple (integrable) while for the remaining cases satisfying this behavior can be much more complicated (chaotic). We also show that the cases where k is a multiple of 5 present some di erent features.